diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..42cb5b8193ac208e4569737efa9709604d677c53 Binary files /dev/null and b/.DS_Store differ diff --git a/.gitattributes b/.gitattributes index a6344aac8c09253b3b630fb776ae94478aa0275b..07b1811a31baa0dddb4ff5073fc800b3ff7a4528 100644 --- a/.gitattributes +++ b/.gitattributes @@ -1,5 +1,6 @@ *.7z filter=lfs diff=lfs merge=lfs -text *.arrow filter=lfs diff=lfs merge=lfs -text +*.avro filter=lfs diff=lfs merge=lfs -text *.bin filter=lfs diff=lfs merge=lfs -text *.bz2 filter=lfs diff=lfs merge=lfs -text *.ckpt filter=lfs diff=lfs merge=lfs -text @@ -8,6 +9,8 @@ *.h5 filter=lfs diff=lfs merge=lfs -text *.joblib filter=lfs diff=lfs merge=lfs -text *.lfs.* filter=lfs diff=lfs merge=lfs -text +*.lz4 filter=lfs diff=lfs merge=lfs -text +*.mds filter=lfs diff=lfs merge=lfs -text *.mlmodel filter=lfs diff=lfs merge=lfs -text *.model filter=lfs diff=lfs merge=lfs -text *.msgpack filter=lfs diff=lfs merge=lfs -text @@ -33,3 +36,27 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text *.zip filter=lfs diff=lfs merge=lfs -text *.zst filter=lfs diff=lfs merge=lfs -text *tfevents* filter=lfs diff=lfs merge=lfs -text +# Audio files - uncompressed +*.pcm filter=lfs diff=lfs merge=lfs -text +*.sam filter=lfs diff=lfs merge=lfs -text +*.raw filter=lfs diff=lfs merge=lfs -text +# Audio files - compressed +*.aac filter=lfs diff=lfs merge=lfs -text +*.flac filter=lfs diff=lfs merge=lfs -text +*.mp3 filter=lfs diff=lfs merge=lfs -text +*.ogg filter=lfs diff=lfs merge=lfs -text +*.wav filter=lfs diff=lfs merge=lfs -text +# Image files - uncompressed +*.bmp filter=lfs diff=lfs merge=lfs -text +*.gif filter=lfs diff=lfs merge=lfs -text +*.png filter=lfs diff=lfs merge=lfs -text +*.tiff filter=lfs diff=lfs merge=lfs -text +# Image files - compressed +*.jpg filter=lfs diff=lfs merge=lfs -text +*.jpeg filter=lfs diff=lfs merge=lfs -text +*.webp filter=lfs diff=lfs merge=lfs -text +# Video files - compressed +*.mp4 filter=lfs diff=lfs merge=lfs -text +*.webm filter=lfs diff=lfs merge=lfs -text +*.csv filter=lfs diff=lfs merge=lfs -text +Data/Math_Standards1.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/Code/LICENSE b/Code/LICENSE new file mode 100644 index 0000000000000000000000000000000000000000..ac0d51a15ba6361a25fb5dc06c055ee0ee7d5e45 --- /dev/null +++ b/Code/LICENSE @@ -0,0 +1,40 @@ +Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0) + +Copyright (c) 2024 FoundationalED Authors + +You are free to: + + Share — copy and redistribute the material in any medium or format + + Adapt — remix, transform, and build upon the material + +Under the following terms: + + Attribution — You must give appropriate credit, provide a link to the license, + and indicate if changes were made. You may do so in any reasonable manner, but + not in any way that suggests the licensor endorses you or your use. + + NonCommercial — You may not use the material for commercial purposes. + + No additional restrictions — You may not apply legal terms or technological + measures that legally restrict others from doing anything the license permits. + +Notices: + + You do not have to comply with the license for elements of the material in + the public domain or where your use is permitted by an applicable exception + or limitation. + + No warranties are given. The license may not give you all of the permissions + necessary for your intended use. For example, other rights such as publicity, + privacy, or moral rights may limit how you use the material. + +Full license text: https://creativecommons.org/licenses/by-nc/4.0/legalcode + +================================================================================ + +ADDITIONAL TERMS FOR FOUNDATIONALED DATASET + +By accessing or using the FoundationalED dataset, you additionally agree to the +Data Usage Agreement specified in the README.md file, which includes restrictions +on re-identification, ethical use requirements, and compliance obligations. diff --git a/Code/__pycache__/clean_utils.cpython-312.pyc b/Code/__pycache__/clean_utils.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..eff7defb3013cf491bb3ddb9055480a2a5076380 Binary files /dev/null and b/Code/__pycache__/clean_utils.cpython-312.pyc differ diff --git a/Code/__pycache__/process_to_single_file.cpython-312.pyc b/Code/__pycache__/process_to_single_file.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..7db181d9101f5c27b77cb1a86efdd1f9c352e50d Binary files /dev/null and b/Code/__pycache__/process_to_single_file.cpython-312.pyc differ diff --git a/Code/build_skill_set.py b/Code/build_skill_set.py new file mode 100644 index 0000000000000000000000000000000000000000..ed234994366fd34843527de28fadb39b153521ed --- /dev/null +++ b/Code/build_skill_set.py @@ -0,0 +1,157 @@ +#!/usr/bin/env python3 +"""Build Skill_List.csv from Skills.csv and CASE Common Core standards JSON. + +Output columns: +- index (1-based) +- skill_code +- full_description + +The output contains only skill codes that appear in both: +1) Skills.csv (column: node_code) +2) CASE JSON CFItems (field: humanCodingScheme) + +Rows are sorted by skill_code. +""" + +from __future__ import annotations + +import argparse +import csv +import html +import json +import re +from pathlib import Path +from typing import Dict, Set + +_TAG_RE = re.compile(r"<[^>]+>") +_WS_RE = re.compile(r"\s+") +_DOT_BEFORE_SUFFIX_RE = re.compile(r"(?<=\d)\.(?=[A-Za-z]$)") + + +def _clean_text(text: str) -> str: + """Normalize whitespace and strip simple HTML tags from a description.""" + text = html.unescape(text or "") + text = _TAG_RE.sub("", text) + text = _WS_RE.sub(" ", text).strip() + return text + + +def _normalize_skill_code(code: str) -> str: + """Normalize equivalent skill code formats to a common representation. + + Example: + - 3.MD.C.7a -> 3.MD.C.7a + - 3.MD.C.7.a -> 3.MD.C.7a + """ + normalized = (code or "").strip() + normalized = _DOT_BEFORE_SUFFIX_RE.sub("", normalized) + return normalized + + +def load_skill_codes(skills_csv_path: Path) -> Set[str]: + """Read unique skill codes from Skills.csv node_code column.""" + codes: Set[str] = set() + with skills_csv_path.open("r", encoding="utf-8", newline="") as f: + reader = csv.DictReader(f) + if "node_code" not in (reader.fieldnames or []): + raise ValueError( + f"Missing required column 'node_code' in {skills_csv_path}" + ) + for row in reader: + code = (row.get("node_code") or "").strip() + if code: + codes.add(code) + return codes + + +def load_case_mapping(case_json_path: Path) -> Dict[str, str]: + """Map skill code -> full standard statement from CASE JSON CFItems.""" + with case_json_path.open("r", encoding="utf-8") as f: + payload = json.load(f) + + mapping: Dict[str, str] = {} + for item in payload.get("CFItems", []): + raw_code = (item.get("humanCodingScheme") or "").strip() + code = _normalize_skill_code(raw_code) + if not code: + continue + + # Keep both Standards and Components. + # In CASE, codes like 3.MD.C.7.a are often CFItemType=Component. + if item.get("CFItemType") not in {"Standard", "Component"}: + continue + + statement = _clean_text(item.get("fullStatement") or "") + if not statement: + continue + + # Keep first non-empty definition if duplicates appear. + if code not in mapping: + mapping[code] = statement + + return mapping + + +def write_output(output_csv_path: Path, rows: list[tuple[str, str]]) -> None: + """Write final CSV with a 1-based index.""" + output_csv_path.parent.mkdir(parents=True, exist_ok=True) + with output_csv_path.open("w", encoding="utf-8", newline="") as f: + writer = csv.writer(f) + writer.writerow(["index", "skill_code", "full_description"]) + for idx, (code, desc) in enumerate(rows, start=1): + writer.writerow([idx, code, desc]) + + +def main() -> None: + parser = argparse.ArgumentParser( + description="Create Skill_List.csv from Skills.csv and CASE standards JSON." + ) + parser.add_argument( + "--skills-csv", + type=Path, + default=Path("../Data/Skills.csv"), + help="Path to Skills.csv", + ) + parser.add_argument( + "--case-json", + type=Path, + default=Path("../Data/CASE-Common Core State Standards for Math.json"), + help="Path to CASE JSON", + ) + parser.add_argument( + "--output-csv", + type=Path, + default=Path("../Data/Skill_Set.csv"), + help="Output path for Skill_Set.csv", + ) + + args = parser.parse_args() + + skills_csv = args.skills_csv.resolve() + case_json = args.case_json.resolve() + output_csv = args.output_csv.resolve() + + skill_codes = load_skill_codes(skills_csv) + case_map = load_case_mapping(case_json) + + matched_codes = sorted( + code for code in skill_codes if _normalize_skill_code(code) in case_map + ) + rows = [(code, case_map[_normalize_skill_code(code)]) for code in matched_codes] + + write_output(output_csv, rows) + + missing = sorted( + code for code in skill_codes if _normalize_skill_code(code) not in case_map + ) + print(f"Wrote {len(rows)} skills to {output_csv}") + print(f"Unique skill codes in Skills.csv: {len(skill_codes)}") + print(f"Missing codes not found in CASE: {len(missing)}") + if missing: + preview = ", ".join(missing[:20]) + suffix = " ..." if len(missing) > 20 else "" + print(f"Missing preview: {preview}{suffix}") + + +if __name__ == "__main__": + main() diff --git a/Code/clean_utils.py b/Code/clean_utils.py new file mode 100644 index 0000000000000000000000000000000000000000..48cd150b87444e8e452094f8a1307872cba19383 --- /dev/null +++ b/Code/clean_utils.py @@ -0,0 +1,148 @@ +""" +HTML cleaning utilities for problem text. + +Provides functions to clean HTML content while preserving: +- Inline MathML (fractions, superscripts, subscripts) +- Wiris math images (extracted from data-mathml attribute) +- Table structure (formatted with | separators) +- Image placeholders +""" + +import html +import pandas as pd +from bs4 import BeautifulSoup, NavigableString + + +def parse_mathml_element(elem): + """Recursively parse a MathML element to text.""" + if elem.name is None: + return str(elem).strip() + + if elem.name == "mfrac": + children = [c for c in elem.children if c.name] + if len(children) >= 2: + num = parse_mathml_element(children[0]) + denom = parse_mathml_element(children[1]) + return f"({num}/{denom})" + return elem.get_text(strip=True) + + elif elem.name == "msup": + children = [c for c in elem.children if c.name] + if len(children) >= 2: + base = parse_mathml_element(children[0]) + exp = parse_mathml_element(children[1]) + return f"{base}^{exp}" + return elem.get_text(strip=True) + + elif elem.name == "msub": + children = [c for c in elem.children if c.name] + if len(children) >= 2: + base = parse_mathml_element(children[0]) + sub = parse_mathml_element(children[1]) + return f"{base}_{sub}" + return elem.get_text(strip=True) + + elif elem.name == "msqrt": + content = parse_mathml_element_children(elem) + return f"√({content})" + + elif elem.name == "mo": + op = elem.get_text(strip=True) + if op in ["÷", "×", "·", "+", "-", "=", "<", ">", "≤", "≥", "≠"]: + return f" {op} " + return op + + elif elem.name in ["mn", "mi", "mtext"]: + return elem.get_text(strip=True) + + elif elem.name in ["mrow", "math", "mpadded", "mstyle"]: + return parse_mathml_element_children(elem) + + else: + return elem.get_text(strip=True) + + +def parse_mathml_element_children(elem): + """Parse all children of a MathML element.""" + parts = [] + for child in elem.children: + if isinstance(child, NavigableString): + text = str(child).strip() + if text: + parts.append(text) + elif child.name: + parts.append(parse_mathml_element(child)) + return "".join(parts) + + +def clean_problem_body(text): + """ + Clean HTML problem body with full MathML handling. + + Handles: + - Inline MathML (, , , etc.) → (4/3), x^2 + - Wiris math images (data-mathml attribute) → [15÷12] + - Tables → [Table: Col1 | Col2 ...] + - Regular images → [image] + - HTML entities → decoded properly + """ + if pd.isna(text) or text == "": + return "" + soup = BeautifulSoup(str(text), "html.parser") + + # 1. Handle inline MathML + for math in soup.find_all("math"): + parsed = parse_mathml_element(math) + math.replace_with(f" {parsed} ") + + # 2. Handle Wiris images + for img in soup.find_all("img"): + alt = img.get("alt", "") + src = img.get("src", "") + data_mathml = img.get("data-mathml", "") + + if "wiris" in src.lower() or "pluginwiris" in src: + if alt and alt.strip() and alt not in ["NO ALT", "NONE"]: + img.replace_with(f" [{alt.strip()}] ") + elif data_mathml: + math_str = ( + data_mathml.replace("«", "<").replace("»", ">").replace("¨", '"') + ) + msoup = BeautifulSoup(math_str, "html.parser") + math_elem = msoup.find("math") + if math_elem: + mtext = parse_mathml_element(math_elem) + else: + mtext = msoup.get_text(separator="") + mtext = mtext.replace("§#247;", "÷").replace("§#215;", "×") + mtext = ( + mtext.replace("§#8722;", "-") + .replace("§#160;", " ") + .replace("§#183;", "·") + ) + mtext = mtext.replace("§#", "&#") + mtext = html.unescape(mtext).strip() + img.replace_with(f" [{mtext}] " if mtext else " [math] ") + else: + img.replace_with(" [math] ") + elif alt and alt.strip(): + img.replace_with(f" [Image: {alt.strip()[:100]}] ") + else: + img.replace_with(" [image] ") + + # 3. Handle tables + for table in soup.find_all("table"): + rows = [] + for tr in table.find_all("tr"): + cells = [td.get_text(strip=True) for td in tr.find_all(["td", "th"])] + if any(cells): + rows.append(" | ".join(cells)) + if rows: + table.replace_with(f"\n[Table:\n{chr(10).join(rows)}]\n") + else: + table.decompose() + + text = soup.get_text(separator=" ") + text = html.unescape(text) + text = " ".join(text.split()) + return text.strip() diff --git a/Code/cleantext.py b/Code/cleantext.py new file mode 100644 index 0000000000000000000000000000000000000000..bc0f979e8b5ad70d6148af1a7123d3ccadba6fdd --- /dev/null +++ b/Code/cleantext.py @@ -0,0 +1,102 @@ +import pandas as pd + +def add_pi_if_missing(input_string): + # Check if "se 3.14 for" is in the input string + if "se 3.14 for" in input_string: + # Check if "pi" is not already present after "se 3.14 for" + if "pi" not in input_string[input_string.index("se 3.14 for") + len("se 3.14 for"):]: + return input_string[:input_string.index("se 3.14 for") + len("se 3.14 for")] + " pi" + input_string[input_string.index("se 3.14 for") + len("se 3.14 for"):] + return input_string + +def convert_mathml_to_fraction(mathml_content): + mathml_content = mathml_content.replace('', "___") + mathml_content = mathml_content.replace('', '(') + mathml_content = mathml_content.replace('', ')') + mathml_content = mathml_content.replace('', '/') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('', '') + mathml_content = mathml_content.replace('§#960;', '') + mathml_content = mathml_content.replace(' ', ' ') + mathml_content = mathml_content.replace('§#160;', ' ') + mathml_content = mathml_content.replace('>', '>') + mathml_content = mathml_content.replace('<', '<') + mathml_content = mathml_content.replace('&', '&') + + mathml_content = mathml_content.replace('«/math', '') + + mathml_content = mathml_content.rstrip('/') + + return mathml_content + + +from bs4 import BeautifulSoup +def alt_text(html: str) -> str: + soup = BeautifulSoup(html, 'html.parser') + + # Replace each with its alt text if it exists + for img in soup.find_all('img'): + alt = img.get('alt') + if alt: + img.replace_with(alt) + + return str(soup) + +def mathml_to_text(html): + soup = BeautifulSoup(html, 'html.parser') + + # Convert MathML fractions + for math in soup.find_all('math'): + frac = math.find('mfrac') + if frac: + nums = frac.find_all('mn') + if len(nums) == 2: + numerator = nums[0].text + denominator = nums[1].text + frac_text = f"{numerator}/{denominator}" + math.replace_with(frac_text) + else: + math.replace_with(math.get_text()) # Fallback if not a valid mfrac + else: + math.replace_with(math.get_text()) # Handle non-fraction math + + # Return clean text + return soup.get_text(separator=" ", strip=True) + + +def clean_text(input_text): + if pd.isna(input_text) or input_text.strip() == "": + return "" + + # Replace   and decode HTML entities + input_text = input_text.replace(' ', ' ') + + # Replace tags with their alt text + input_text = mathml_to_text(input_text) + input_text = alt_text(input_text) + + # Convert MathML if it exists + soup = BeautifulSoup(input_text, 'html.parser') + for img in soup.find_all('img', class_='Wirisformula'): + mathml_formula = img.get('data-mathml') + if mathml_formula: + # Extract inner MathML content + start_index = mathml_formula.find('') + len('') + end_index = mathml_formula.find('') + mathml_formula_content = mathml_formula[start_index:end_index] + mathml_formula_content_cleaned = mathml_formula_content.replace( + 'xmlns=¨http://www.w3.org/1998/Math/MathML¨»', '') + fraction = convert_mathml_to_fraction(mathml_formula_content_cleaned) + img.replace_with(fraction) + + text = soup.get_text(separator=' ', strip=True) + text = convert_mathml_to_fraction(text) + text = add_pi_if_missing(text) + return text \ No newline at end of file diff --git a/Code/detect_similar_node_codes.py b/Code/detect_similar_node_codes.py new file mode 100644 index 0000000000000000000000000000000000000000..858fe565a9612771b7058739f386e8c6bd6ce236 --- /dev/null +++ b/Code/detect_similar_node_codes.py @@ -0,0 +1,285 @@ +#!/usr/bin/env python3 +"""Detect skills that have similar node_code values but different skill_id values. + +By default, the script detects conflicts after normalizing node_code values +(uppercasing and removing punctuation differences). It can also perform optional +fuzzy matching on normalized compact node codes. +""" + +from __future__ import annotations + +import argparse +import re +from difflib import SequenceMatcher +from itertools import combinations +from pathlib import Path + +import pandas as pd + + +DEFAULT_SKILLS_PATH = Path(__file__).resolve().parent.parent / "Data" / "Skills.csv" +DEFAULT_OUTPUT_PATH = ( + Path(__file__).resolve().parent.parent + / "Results" + / "similar_node_code_conflicts.csv" +) + + +def parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser( + description=( + "Detect skills whose node_code values are similar but map to " + "different skill_id values." + ) + ) + parser.add_argument( + "--skills-path", + type=Path, + default=DEFAULT_SKILLS_PATH, + help="Path to Skills.csv.", + ) + parser.add_argument( + "--output-path", + type=Path, + default=DEFAULT_OUTPUT_PATH, + help="Path to save the detected conflicts as CSV.", + ) + parser.add_argument( + "--include-fuzzy", + action="store_true", + help="Also run fuzzy matching across compact node_code values.", + ) + parser.add_argument( + "--similarity-threshold", + type=float, + default=0.9, + help="Minimum SequenceMatcher ratio for fuzzy matches (0.0 to 1.0).", + ) + parser.add_argument( + "--max-fuzzy-pairs", + type=int, + default=200, + help="Maximum number of fuzzy match pairs to keep after sorting.", + ) + parser.add_argument( + "--print-limit", + type=int, + default=20, + help="Maximum number of rows to print for each conflict section.", + ) + return parser.parse_args() + + +def normalize_node_code(node_code: str) -> str: + canonical = re.sub(r"[^A-Za-z0-9]+", ".", node_code.upper().strip()) + canonical = re.sub(r"\.+", ".", canonical).strip(".") + return canonical + + +def compact_node_code(canonical_node_code: str) -> str: + return canonical_node_code.replace(".", "") + + +def unique_sorted_strings(series: pd.Series) -> list[str]: + values: set[str] = set() + for value in series.dropna(): + text = str(value).strip() + if text: + values.add(text) + return sorted(values) + + +def unique_sorted_ints(series: pd.Series) -> list[int]: + values: set[int] = set() + for value in series.dropna(): + values.add(int(value)) + return sorted(values) + + +def join_pipe(values: list[str]) -> str: + return " | ".join(values) + + +def join_csv_ints(values: list[int]) -> str: + return ",".join(str(v) for v in values) + + +def load_skills(skills_path: Path) -> pd.DataFrame: + required_columns = ["problem_id", "skill_id", "node_code", "node_name"] + df = pd.read_csv(skills_path, usecols=required_columns, low_memory=False) + + df["problem_id"] = pd.to_numeric(df["problem_id"], errors="coerce") + df["skill_id"] = pd.to_numeric(df["skill_id"], errors="coerce") + + df = df.dropna(subset=["problem_id", "skill_id", "node_code"]).copy() + df["problem_id"] = df["problem_id"].astype(int) + df["skill_id"] = df["skill_id"].astype(int) + + df["node_code"] = df["node_code"].astype(str).str.strip() + df["node_name"] = df["node_name"].fillna("").astype(str).str.strip() + df = df[df["node_code"] != ""].copy() + + df["node_code_canonical"] = df["node_code"].apply(normalize_node_code) + df["node_code_compact"] = df["node_code_canonical"].apply(compact_node_code) + return df + + +def summarize_compact_codes(df: pd.DataFrame) -> pd.DataFrame: + summary = ( + df.groupby("node_code_compact", sort=True) + .agg( + canonical_node_codes=("node_code_canonical", unique_sorted_strings), + raw_node_codes=("node_code", unique_sorted_strings), + skill_ids=("skill_id", unique_sorted_ints), + node_names=("node_name", unique_sorted_strings), + problem_count=("problem_id", "nunique"), + mapping_count=("skill_id", "size"), + ) + .reset_index() + .rename(columns={"node_code_compact": "compact_node_code"}) + ) + + summary["n_skill_ids"] = summary["skill_ids"].apply(len) + return summary + + +def build_normalized_conflicts(summary: pd.DataFrame) -> pd.DataFrame: + conflicts = summary[summary["n_skill_ids"] > 1].copy() + if conflicts.empty: + return conflicts + + conflicts.insert(0, "conflict_type", "normalized_match") + conflicts["skill_ids"] = conflicts["skill_ids"].apply(join_csv_ints) + conflicts["canonical_node_codes"] = conflicts["canonical_node_codes"].apply( + join_pipe + ) + conflicts["raw_node_codes"] = conflicts["raw_node_codes"].apply(join_pipe) + conflicts["node_names"] = conflicts["node_names"].apply(join_pipe) + + return conflicts.sort_values( + ["n_skill_ids", "compact_node_code"], ascending=[False, True] + ) + + +def build_fuzzy_conflicts( + summary: pd.DataFrame, + threshold: float, + max_pairs: int, +) -> pd.DataFrame: + rows: list[dict[str, object]] = [] + + records = summary.to_dict(orient="records") + for left, right in combinations(records, 2): + left_code = str(left["compact_node_code"]) + right_code = str(right["compact_node_code"]) + + if left_code == right_code: + continue + + similarity = SequenceMatcher(None, left_code, right_code).ratio() + if similarity < threshold: + continue + + left_skills = set(left["skill_ids"]) + right_skills = set(right["skill_ids"]) + if left_skills == right_skills: + continue + + rows.append( + { + "conflict_type": "fuzzy_match", + "similarity": round(similarity, 4), + "left_compact_node_code": left_code, + "right_compact_node_code": right_code, + "left_canonical_node_codes": join_pipe(left["canonical_node_codes"]), + "right_canonical_node_codes": join_pipe(right["canonical_node_codes"]), + "left_skill_ids": join_csv_ints(left["skill_ids"]), + "right_skill_ids": join_csv_ints(right["skill_ids"]), + "overlap_skill_ids": join_csv_ints( + sorted(left_skills.intersection(right_skills)) + ), + } + ) + + fuzzy = pd.DataFrame(rows) + if fuzzy.empty: + return fuzzy + + fuzzy = fuzzy.sort_values( + ["similarity", "left_compact_node_code", "right_compact_node_code"], + ascending=[False, True, True], + ) + if max_pairs > 0: + fuzzy = fuzzy.head(max_pairs).copy() + return fuzzy + + +def print_section(title: str, df: pd.DataFrame, print_limit: int) -> None: + print(f"\n{title}") + if df.empty: + print(" None") + return + + to_show = df.head(print_limit) + print(to_show.to_string(index=False)) + if len(df) > len(to_show): + print(f" ... ({len(df) - len(to_show)} more rows)") + + +def main() -> int: + args = parse_args() + + if args.similarity_threshold < 0.0 or args.similarity_threshold > 1.0: + raise ValueError("--similarity-threshold must be in [0.0, 1.0].") + + if not args.skills_path.exists(): + raise FileNotFoundError(f"Skills file not found: {args.skills_path}") + + skills_df = load_skills(args.skills_path) + summary_df = summarize_compact_codes(skills_df) + + normalized_conflicts = build_normalized_conflicts(summary_df) + fuzzy_conflicts = pd.DataFrame() + if args.include_fuzzy: + fuzzy_conflicts = build_fuzzy_conflicts( + summary_df, + threshold=args.similarity_threshold, + max_pairs=args.max_fuzzy_pairs, + ) + + frames = [normalized_conflicts] + if args.include_fuzzy: + frames.append(fuzzy_conflicts) + combined_output = pd.concat(frames, ignore_index=True, sort=False) + + args.output_path.parent.mkdir(parents=True, exist_ok=True) + combined_output.to_csv(args.output_path, index=False) + + print("Loaded rows:", len(skills_df)) + print("Unique compact node codes:", len(summary_df)) + print("Normalized conflicts:", len(normalized_conflicts)) + if args.include_fuzzy: + print( + "Fuzzy conflicts (threshold " f"{args.similarity_threshold:.2f}):", + len(fuzzy_conflicts), + ) + + print_section( + "Normalized node_code conflicts (same compact code, different skill_id):", + normalized_conflicts, + args.print_limit, + ) + + if args.include_fuzzy: + print_section( + "Fuzzy node_code conflicts (near compact codes, different skill_id):", + fuzzy_conflicts, + args.print_limit, + ) + + print(f"\nSaved conflicts to: {args.output_path}") + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/Code/evaluate_kt.py b/Code/evaluate_kt.py new file mode 100644 index 0000000000000000000000000000000000000000..de9ad12db4b0008bad1fe4c4531741454bdf52e7 --- /dev/null +++ b/Code/evaluate_kt.py @@ -0,0 +1,205 @@ +#!/usr/bin/env python3 +""" +Evaluate LLM knowledge tracing predictions against FKT benchmark tasks. + +Tasks evaluated: + - Task 1 (FKT): Foundational Knowledge Tracing - predict if student answers correctly (question-level) + - Task 1 Variant 2: Cognitive Student Modeling - predict the actual student response + +Usage: + python evaluate_kt.py results.jsonl +""" + +import argparse +import json +import math +from sklearn.metrics import roc_auc_score + + +def normalize_mcq_answer(answer_str: str) -> str: + """ + Normalize MCQ answer format for consistent comparison. + + Handles variations like: + - 'C, A' -> 'A, C' (order normalization) + - 'A,C' -> 'A, C' (spacing normalization) + - 'a, c' -> 'A, C' (case normalization) + + Args: + answer_str: Answer string to normalize + + Returns: + Normalized answer string, or original if not MCQ format + """ + # Split by comma, strip whitespace, uppercase, sort, rejoin + parts = [p.strip().upper() for p in answer_str.split(',')] + # Filter out empty parts + parts = [p for p in parts if p] + # Only normalize if all parts are single letters (MCQ format) + if parts and all(len(p) == 1 and p.isalpha() for p in parts): + return ', '.join(sorted(set(parts))) + return answer_str + + +def numerical_match(answer1: str, answer2: str, atol: float = 0.01, rtol: float = 0.01) -> bool: + """ + Check if two answers are numerically close within tolerance. + + Uses math.isclose for robust comparison that handles both absolute + and relative tolerance. + + Args: + answer1: First answer string + answer2: Second answer string + atol: Absolute tolerance (default: 0.01) + rtol: Relative tolerance (default: 0.01) + + Returns: + True if answers are numerically close, False otherwise + """ + try: + a = float(answer1.strip()) + b = float(answer2.strip()) + return math.isclose(a, b, abs_tol=atol, rel_tol=rtol) + except (ValueError, AttributeError): + return False + + +def answers_match(pred, actual): + """Check if predicted answer matches actual answer.""" + if pred is None or actual is None: + return False + + pred_str = str(pred).strip() + actual_str = str(actual).strip() + + # Exact string match + if pred_str == actual_str: + return True + + # Normalize MCQ answers (handles case, order, spacing) + pred_normalized = normalize_mcq_answer(pred_str) + actual_normalized = normalize_mcq_answer(actual_str) + if pred_normalized == actual_normalized: + return True + + # Numeric match with tolerance + return numerical_match(pred_str, actual_str) + + +def load_results(jsonl_path): + """Load results from JSONL file.""" + results = [] + with open(jsonl_path, 'r') as f: + for line in f: + if line.strip(): + results.append(json.loads(line)) + return results + + +def evaluate(results): + """Compute evaluation metrics aligned with FKT benchmark tasks.""" + total = len(results) + + if total == 0: + print("No results to evaluate.") + return + + # Compute class distribution + n_correct = sum(1 for r in results if r.get('actual_score') == 1) + n_incorrect = total - n_correct + + # Task 1: FKT - Question-level accuracy + valid_q = [(r.get('actual_score'), r.get('predicted_question_level')) + for r in results + if r.get('actual_score') is not None and r.get('predicted_question_level') is not None] + + if valid_q: + y_true, y_pred = zip(*valid_q) + question_correct = sum(1 for t, p in valid_q if t == p) + question_acc = question_correct / len(valid_q) + # AUC-ROC (note: with binary predictions, this is limited) + try: + auc_roc = roc_auc_score(y_true, y_pred) + except ValueError: + auc_roc = None # Only one class present + else: + question_correct = 0 + question_acc = 0.0 + auc_roc = None + + # Task 1 Variant 2: Cognitive Modeling - Answer prediction accuracy + answer_correct = sum( + 1 for r in results + if answers_match(r.get('predicted_student_answer'), r.get('actual_answer')) + ) + + # Baselines + prior_baseline = 0.615 # True correctness rate from Interactions.csv + majority_baseline = max(n_correct, n_incorrect) / total + + # Print results + print(f"{'='*60}") + print(f"Evaluation Results ({total} predictions)") + print(f"{'='*60}") + print() + print(f"Class distribution: {n_correct} correct, {n_incorrect} incorrect") + print() + + # Task 1: Foundational Knowledge Tracing (FKT) - question-level prediction + print("Task 1: Foundational Knowledge Tracing (FKT) - Question-Level") + print(f" Accuracy: {question_correct}/{len(valid_q)} = {question_acc:.3f}") + if auc_roc is not None: + print(f" AUC-ROC: {auc_roc:.3f}") + else: + print(f" AUC-ROC: N/A (single class)") + print(f" Baselines: Prior={prior_baseline:.3f}, Majority={majority_baseline:.3f}") + print() + + # Task 1 Variant 2: Cognitive Student Modeling + print("Task 1 Variant 2: Cognitive Student Modeling") + print(f" Overall Accuracy: {answer_correct}/{total} = {answer_correct/total:.3f}") + + # Breakdown by problem type + problem_types = ['Multiple Choice (select 1)', 'Multiple Choice (select all)', 'Fill-in-the-blank(s)'] + has_problem_type = any(r.get('problem_type') for r in results) + if has_problem_type: + print(" By problem type:") + for ptype in problem_types: + subset = [r for r in results if r.get('problem_type') == ptype] + if subset: + n = len(subset) + a_acc = sum(1 for r in subset if answers_match(r.get('predicted_student_answer'), r.get('actual_answer'))) / n + label = ptype.replace('Multiple Choice ', 'MC ') + print(f" {label:20s}: n={n:4d}, acc={a_acc:.3f}") + # Breakdown by ground truth within problem type + for gt in ['correct', 'incorrect']: + gt_subset = [r for r in subset if r.get('prediction_type') == gt] + if gt_subset: + gt_n = len(gt_subset) + gt_acc = sum(1 for r in gt_subset if answers_match(r.get('predicted_student_answer'), r.get('actual_answer'))) / gt_n + print(f" {gt:18s}: n={gt_n:4d}, acc={gt_acc:.3f}") + print() + + # Breakdown by prediction type (correct/incorrect ground truth) + print("By ground truth (prediction_type):") + for ptype in ['correct', 'incorrect']: + subset = [r for r in results if r.get('prediction_type') == ptype] + if subset: + n = len(subset) + q_acc = sum(1 for r in subset if r.get('predicted_question_level') == r.get('actual_score')) / n + a_acc = sum(1 for r in subset if answers_match(r.get('predicted_student_answer'), r.get('actual_answer'))) / n + print(f" {ptype:10s}: n={n:4d}, FKT_acc={q_acc:.3f}, cognitive_acc={a_acc:.3f}") + + +def main(): + parser = argparse.ArgumentParser(description="Evaluate LLM knowledge tracing predictions") + parser.add_argument("jsonl_file", help="Path to JSONL results file") + args = parser.parse_args() + + results = load_results(args.jsonl_file) + evaluate(results) + + +if __name__ == "__main__": + main() diff --git a/Code/evaluate_kt_by_context.py b/Code/evaluate_kt_by_context.py new file mode 100644 index 0000000000000000000000000000000000000000..785a7f4c4e6ae4f6c9651f0ca65c29dc4c7781c9 --- /dev/null +++ b/Code/evaluate_kt_by_context.py @@ -0,0 +1,339 @@ +#!/usr/bin/env python3 +""" +Evaluate KT performance by context length (history size). + +Analyzes how KT accuracy changes as student history grows from 50 to 400 interactions. +Plots all models in a single figure for comparison. + +Usage: + python evaluate_kt_by_context.py +""" + +import argparse +import json +import math +import os +from glob import glob +from collections import defaultdict + +import matplotlib.pyplot as plt +import numpy as np +from sklearn.metrics import roc_auc_score + +# Set publication-quality font sizes +plt.rcParams.update({ + 'font.size': 14, + 'axes.titlesize': 16, + 'axes.labelsize': 14, + 'xtick.labelsize': 12, + 'ytick.labelsize': 12, + 'legend.fontsize': 12, +}) + +# Model name mapping for display +MODEL_NAMES = { + 'gptoss120b': 'GPT-OSS-120B', + 'llama33_70b_instruct': 'Llama-3.3-70B-Instruct', + 'qwen3next80binstruct': 'Qwen3-80B-Instruct', + 'qwen3next80bthinking': 'Qwen3-80B-Thinking', +} + +# Colors for each model +MODEL_COLORS = { + 'gptoss120b': '#1f77b4', # blue + 'llama33_70b_instruct': '#ff7f0e', # orange + 'qwen3next80binstruct': '#2ca02c', # green + 'qwen3next80bthinking': '#d62728', # red +} + + +def normalize_mcq_answer(answer_str: str) -> str: + """Normalize MCQ answer format for consistent comparison.""" + parts = [p.strip().upper() for p in answer_str.split(',')] + parts = [p for p in parts if p] + if parts and all(len(p) == 1 and p.isalpha() for p in parts): + return ', '.join(sorted(set(parts))) + return answer_str + + +def numerical_match(answer1: str, answer2: str, atol: float = 0.01, rtol: float = 0.01) -> bool: + """Check if two answers are numerically close within tolerance.""" + try: + a = float(answer1.strip()) + b = float(answer2.strip()) + return math.isclose(a, b, abs_tol=atol, rel_tol=rtol) + except (ValueError, AttributeError): + return False + + +def answers_match(pred, actual): + """Check if predicted answer matches actual answer.""" + if pred is None or actual is None: + return False + + pred_str = str(pred).strip() + actual_str = str(actual).strip() + + if pred_str == actual_str: + return True + + pred_normalized = normalize_mcq_answer(pred_str) + actual_normalized = normalize_mcq_answer(actual_str) + if pred_normalized == actual_normalized: + return True + + return numerical_match(pred_str, actual_str) + + +def parse_args(): + parser = argparse.ArgumentParser(description="Evaluate KT by context length") + parser.add_argument( + "--results-dir", "-r", + type=str, + default="inference_data_kt_results", + help="Directory containing JSONL results files" + ) + parser.add_argument( + "--output-dir", "-o", + type=str, + default="dataset_analysis/plots", + help="Directory to save output plots" + ) + parser.add_argument( + "--no-plots", + action="store_true", + help="Skip generating plots" + ) + return parser.parse_args() + + +def extract_model_name(filename): + """Extract model identifier from filename.""" + basename = os.path.basename(filename) + # Pattern: modelname_n500_bin10_hist50.jsonl + for model_key in MODEL_NAMES.keys(): + if basename.startswith(model_key): + return model_key + return basename.replace('.jsonl', '') + + +def load_results(jsonl_path): + """Load results from JSONL file.""" + results = [] + with open(jsonl_path, 'r') as f: + for line in f: + if line.strip(): + results.append(json.loads(line)) + return results + + +def compute_metrics_by_bin(results): + """Compute metrics grouped by history_size.""" + bins = defaultdict(list) + + for r in results: + history_size = r.get('history_size', 50) + bins[history_size].append(r) + + metrics = {} + for history_size in sorted(bins.keys()): + bin_results = bins[history_size] + n = len(bin_results) + + # FKT: Collect valid predictions for AUC-ROC + y_true = [] + y_pred = [] + for r in bin_results: + actual = r.get('actual_score') + pred = r.get('predicted_question_level') + if actual is not None and pred is not None: + y_true.append(int(actual)) + y_pred.append(int(pred)) + + # Compute AUC-ROC (requires both classes present) + fkt_auc = None + if len(set(y_true)) == 2 and len(y_true) > 0: + try: + fkt_auc = roc_auc_score(y_true, y_pred) + except ValueError: + pass + + # FKT accuracy (for reference) + fkt_correct = sum(1 for t, p in zip(y_true, y_pred) if t == p) + fkt_acc = fkt_correct / len(y_true) if y_true else 0.0 + + # Cognitive accuracy (answer match) + cognitive_correct = sum( + 1 for r in bin_results + if answers_match(r.get('predicted_student_answer'), r.get('actual_answer')) + ) + + metrics[history_size] = { + 'n': n, + 'fkt_auc': fkt_auc, + 'fkt_acc': fkt_acc, + 'fkt_valid': len(y_true), + 'cognitive_acc': cognitive_correct / n if n > 0 else 0.0, + } + + return metrics + + +def print_table(all_metrics): + """Print metrics table to console.""" + # Get all history sizes across all models + all_history_sizes = sorted(set( + hs for model_metrics in all_metrics.values() + for hs in model_metrics.keys() + )) + + # Header + print("\n" + "=" * 100) + print("KT Performance by Context Length (History Size)") + print("=" * 100) + + # Print FKT AUC-ROC table + print("\nFKT AUC-ROC (Question-Level):") + print("-" * 80) + header = f"{'History':>8}" + for model_key in all_metrics.keys(): + header += f" {MODEL_NAMES.get(model_key, model_key)[:20]:>20}" + print(header) + print("-" * 80) + + for hs in all_history_sizes: + row = f"{hs:>8}" + for model_key in all_metrics.keys(): + if hs in all_metrics[model_key]: + auc = all_metrics[model_key][hs]['fkt_auc'] + if auc is not None: + row += f" {auc:>20.3f}" + else: + row += f" {'N/A':>20}" + else: + row += f" {'N/A':>20}" + print(row) + + # Print Cognitive accuracy table + print("\nCognitive Accuracy (Answer Prediction):") + print("-" * 80) + print(header) + print("-" * 80) + + for hs in all_history_sizes: + row = f"{hs:>8}" + for model_key in all_metrics.keys(): + if hs in all_metrics[model_key]: + acc = all_metrics[model_key][hs]['cognitive_acc'] + row += f" {acc:>20.3f}" + else: + row += f" {'N/A':>20}" + print(row) + + +def plot_results(all_metrics, output_dir): + """Generate plot with all models.""" + os.makedirs(output_dir, exist_ok=True) + + fig, axes = plt.subplots(1, 2, figsize=(14, 5)) + + # Plot 1: FKT AUC-ROC + for model_key, metrics in all_metrics.items(): + history_sizes = sorted(metrics.keys()) + # Filter out None values + valid_hs = [hs for hs in history_sizes if metrics[hs]['fkt_auc'] is not None] + fkt_aucs = [metrics[hs]['fkt_auc'] for hs in valid_hs] + + if valid_hs: + axes[0].plot( + valid_hs, fkt_aucs, + marker='o', markersize=4, + color=MODEL_COLORS.get(model_key, 'gray'), + label=MODEL_NAMES.get(model_key, model_key), + linewidth=2 + ) + + axes[0].set_xlabel('History Size (# prior interactions)') + axes[0].set_ylabel('AUC-ROC') + axes[0].set_title('FKT AUC-ROC vs Context Length') + axes[0].legend(loc='best') + axes[0].grid(True, alpha=0.3) + axes[0].set_xlim(40, 410) + axes[0].axhline(y=0.5, color='gray', linestyle='--', alpha=0.5, label='Random') + + # Plot 2: Cognitive Accuracy + for model_key, metrics in all_metrics.items(): + history_sizes = sorted(metrics.keys()) + cognitive_accs = [metrics[hs]['cognitive_acc'] for hs in history_sizes] + + axes[1].plot( + history_sizes, cognitive_accs, + marker='o', markersize=4, + color=MODEL_COLORS.get(model_key, 'gray'), + label=MODEL_NAMES.get(model_key, model_key), + linewidth=2 + ) + + axes[1].set_xlabel('History Size (# prior interactions)') + axes[1].set_ylabel('Accuracy') + axes[1].set_title('Cognitive Modeling Accuracy vs Context Length') + axes[1].legend(loc='best') + axes[1].grid(True, alpha=0.3) + axes[1].set_xlim(40, 410) + + plt.tight_layout() + + plot_path = os.path.join(output_dir, 'kt_context_scaling.png') + plt.savefig(plot_path, dpi=150) + plt.close() + + print(f"\nSaved: {plot_path}") + + +def main(): + args = parse_args() + + # Find all JSONL files + jsonl_files = glob(os.path.join(args.results_dir, '*.jsonl')) + + if not jsonl_files: + print(f"No JSONL files found in {args.results_dir}") + return + + print(f"Found {len(jsonl_files)} result files:") + for f in jsonl_files: + print(f" - {os.path.basename(f)}") + + # Load and analyze each model + all_metrics = {} + + for jsonl_path in sorted(jsonl_files): + model_key = extract_model_name(jsonl_path) + print(f"\nProcessing {MODEL_NAMES.get(model_key, model_key)}...") + + results = load_results(jsonl_path) + print(f" Loaded {len(results):,} predictions") + + metrics = compute_metrics_by_bin(results) + all_metrics[model_key] = metrics + + # Print quick summary + history_sizes = sorted(metrics.keys()) + valid_aucs = [metrics[hs]['fkt_auc'] for hs in history_sizes if metrics[hs]['fkt_auc'] is not None] + avg_auc = np.mean(valid_aucs) if valid_aucs else 0.0 + avg_cognitive = np.mean([metrics[hs]['cognitive_acc'] for hs in history_sizes]) + print(f" Avg FKT AUC-ROC: {avg_auc:.3f}") + print(f" Avg Cognitive accuracy: {avg_cognitive:.3f}") + + # Print detailed table + print_table(all_metrics) + + # Generate plot + if not args.no_plots: + plot_results(all_metrics, args.output_dir) + + print("\nDone!") + + +if __name__ == "__main__": + main() diff --git a/Code/find_duplicate_problem_body.py b/Code/find_duplicate_problem_body.py new file mode 100644 index 0000000000000000000000000000000000000000..ace336e54447560cccc6fabca8cb55c1b39dfbca --- /dev/null +++ b/Code/find_duplicate_problem_body.py @@ -0,0 +1,152 @@ +#!/usr/bin/env python3 +"""Export rows that share the same Problem Body but have different problem_id. + +Default input: +- ../Data/Problems.csv + +Default output: +- ../Data/Problems_same_body_different_problem_id.csv + +The output includes all original columns plus: +- duplicate_group_id +- distinct_problem_id_count +- distinct_problem_ids +""" + +from __future__ import annotations + +import argparse +import csv +import html +import re +from collections import defaultdict +from pathlib import Path +from typing import Dict, List, Set + +_TAG_RE = re.compile(r"<[^>]+>") +_WS_RE = re.compile(r"\s+") + + +def normalize_body(text: str, strip_html: bool, collapse_whitespace: bool) -> str: + """Normalize Problem Body text for grouping.""" + value = html.unescape(text or "") + if strip_html: + value = _TAG_RE.sub("", value) + if collapse_whitespace: + value = _WS_RE.sub(" ", value).strip() + return value + + +def main() -> None: + parser = argparse.ArgumentParser( + description=( + "Find rows in Problems.csv where the same Problem Body is mapped " + "to different problem_id values." + ) + ) + parser.add_argument( + "--input-csv", + type=Path, + default=Path("../Data/Problems.csv"), + help="Path to Problems.csv", + ) + parser.add_argument( + "--output-csv", + type=Path, + default=Path("../Results/Problems_same_body_different_problem_id.csv"), + help="Output CSV path", + ) + parser.add_argument( + "--body-column", + type=str, + default="Problem Body", + help="Column name for problem statement text", + ) + parser.add_argument( + "--id-column", + type=str, + default="problem_id", + help="Column name for problem identifier", + ) + parser.add_argument( + "--strip-html", + action="store_true", + help="Strip HTML tags before grouping", + ) + parser.add_argument( + "--collapse-whitespace", + action="store_true", + help="Collapse runs of whitespace before grouping", + ) + + args = parser.parse_args() + + input_csv = args.input_csv.resolve() + output_csv = args.output_csv.resolve() + + with input_csv.open("r", encoding="utf-8", newline="") as f: + reader = csv.DictReader(f) + fieldnames = reader.fieldnames or [] + + if args.body_column not in fieldnames: + raise ValueError(f"Missing body column '{args.body_column}' in {input_csv}") + if args.id_column not in fieldnames: + raise ValueError(f"Missing id column '{args.id_column}' in {input_csv}") + + rows: List[dict] = list(reader) + + groups: Dict[str, List[int]] = defaultdict(list) + group_ids: Dict[str, Set[str]] = defaultdict(set) + + for idx, row in enumerate(rows): + body_raw = row.get(args.body_column, "") + body_key = normalize_body( + body_raw, + strip_html=args.strip_html, + collapse_whitespace=args.collapse_whitespace, + ) + if not body_key: + continue + + problem_id = str(row.get(args.id_column, "")).strip() + groups[body_key].append(idx) + if problem_id: + group_ids[body_key].add(problem_id) + + duplicate_keys = [k for k, ids in group_ids.items() if len(ids) > 1] + + # Preserve first-seen order of duplicate groups. + duplicate_keys.sort(key=lambda k: groups[k][0]) + + output_rows: List[dict] = [] + for group_num, key in enumerate(duplicate_keys, start=1): + ids_sorted = sorted(group_ids[key]) + ids_joined = ";".join(ids_sorted) + + for row_idx in groups[key]: + out_row = dict(rows[row_idx]) + out_row["duplicate_group_id"] = str(group_num) + out_row["distinct_problem_id_count"] = str(len(ids_sorted)) + out_row["distinct_problem_ids"] = ids_joined + output_rows.append(out_row) + + output_csv.parent.mkdir(parents=True, exist_ok=True) + output_fieldnames = fieldnames + [ + "duplicate_group_id", + "distinct_problem_id_count", + "distinct_problem_ids", + ] + + with output_csv.open("w", encoding="utf-8", newline="") as f: + writer = csv.DictWriter(f, fieldnames=output_fieldnames) + writer.writeheader() + writer.writerows(output_rows) + + print(f"Input rows: {len(rows)}") + print(f"Duplicate body groups (different problem_id): {len(duplicate_keys)}") + print(f"Output rows: {len(output_rows)}") + print(f"Wrote: {output_csv}") + + +if __name__ == "__main__": + main() diff --git a/Code/find_duplicate_problem_id.py b/Code/find_duplicate_problem_id.py new file mode 100644 index 0000000000000000000000000000000000000000..1fbd6d9ae3bce82cefd3b9af412b90d4ae05f0fa --- /dev/null +++ b/Code/find_duplicate_problem_id.py @@ -0,0 +1,148 @@ +#!/usr/bin/env python3 +"""Export rows that have duplicated problem_id values. + +Default input: +- ../Data/Problems.csv + +Default output: +- ../Results/Problems_duplicated_problem_id.csv + +The output includes all original columns plus: +- duplicate_group_id +- duplicate_problem_id_count +- distinct_problem_body_count +""" + +from __future__ import annotations + +import argparse +import csv +import html +import re +from collections import defaultdict +from pathlib import Path +from typing import Dict, List, Set + +_TAG_RE = re.compile(r"<[^>]+>") +_WS_RE = re.compile(r"\s+") + + +def normalize_body(text: str, strip_html: bool, collapse_whitespace: bool) -> str: + """Normalize Problem Body text for distinct-body counting.""" + value = html.unescape(text or "") + if strip_html: + value = _TAG_RE.sub("", value) + if collapse_whitespace: + value = _WS_RE.sub(" ", value).strip() + return value + + +def main() -> None: + parser = argparse.ArgumentParser( + description="Find rows in Problems.csv where problem_id is duplicated." + ) + parser.add_argument( + "--input-csv", + type=Path, + default=Path("../Data/Problems.csv"), + help="Path to Problems.csv", + ) + parser.add_argument( + "--output-csv", + type=Path, + default=Path("../Results/Problems_duplicated_problem_id.csv"), + help="Output CSV path", + ) + parser.add_argument( + "--id-column", + type=str, + default="problem_id", + help="Column name for problem identifier", + ) + parser.add_argument( + "--body-column", + type=str, + default="Problem Body", + help="Column name for problem statement text", + ) + parser.add_argument( + "--strip-html", + action="store_true", + help="Strip HTML tags before counting distinct problem bodies", + ) + parser.add_argument( + "--collapse-whitespace", + action="store_true", + help="Collapse runs of whitespace before counting distinct problem bodies", + ) + + args = parser.parse_args() + + input_csv = args.input_csv.resolve() + output_csv = args.output_csv.resolve() + + with input_csv.open("r", encoding="utf-8", newline="") as f: + reader = csv.DictReader(f) + fieldnames = reader.fieldnames or [] + + if args.id_column not in fieldnames: + raise ValueError(f"Missing id column '{args.id_column}' in {input_csv}") + if args.body_column not in fieldnames: + raise ValueError(f"Missing body column '{args.body_column}' in {input_csv}") + + rows: List[dict] = list(reader) + + groups: Dict[str, List[int]] = defaultdict(list) + for idx, row in enumerate(rows): + problem_id = str(row.get(args.id_column, "")).strip() + if not problem_id: + continue + groups[problem_id].append(idx) + + duplicate_ids = [pid for pid, row_idxs in groups.items() if len(row_idxs) > 1] + + # Preserve first-seen order of duplicate groups. + duplicate_ids.sort(key=lambda pid: groups[pid][0]) + + output_rows: List[dict] = [] + for group_num, pid in enumerate(duplicate_ids, start=1): + row_idxs = groups[pid] + + distinct_bodies: Set[str] = set() + for row_idx in row_idxs: + body_raw = rows[row_idx].get(args.body_column, "") + distinct_bodies.add( + normalize_body( + body_raw, + strip_html=args.strip_html, + collapse_whitespace=args.collapse_whitespace, + ) + ) + + for row_idx in row_idxs: + out_row = dict(rows[row_idx]) + out_row["duplicate_group_id"] = str(group_num) + out_row["duplicate_problem_id_count"] = str(len(row_idxs)) + out_row["distinct_problem_body_count"] = str(len(distinct_bodies)) + output_rows.append(out_row) + + output_csv.parent.mkdir(parents=True, exist_ok=True) + output_fieldnames = fieldnames + [ + "duplicate_group_id", + "duplicate_problem_id_count", + "distinct_problem_body_count", + ] + + with output_csv.open("w", encoding="utf-8", newline="") as f: + writer = csv.DictWriter(f, fieldnames=output_fieldnames) + writer.writeheader() + writer.writerows(output_rows) + + print(f"Input rows: {len(rows)}") + print(f"Duplicated {args.id_column} groups: {len(duplicate_ids)}") + print(f"Output rows: {len(output_rows)}") + print(f"Wrote: {output_csv}") + + +if __name__ == "__main__": + main() diff --git a/Code/gptoss120bvllmmcq.py b/Code/gptoss120bvllmmcq.py new file mode 100644 index 0000000000000000000000000000000000000000..b8040fb21905dba6ddad20aacdf4ee62633baf33 --- /dev/null +++ b/Code/gptoss120bvllmmcq.py @@ -0,0 +1,31 @@ +""" +Knowledge Tracing inference with GPT-OSS-120B model. + +Usage: + CUDA_VISIBLE_DEVICES=0,1,2,3 python gptoss120bvllmmcq.py \ + --data-dir foundationalktdataset/ \ + --num-gpus 4 \ + --batch-size 10 \ + --cache-dir /data1/ \ + --num-students 500 \ + --bin-size 50 \ + --min-history 50 +""" + +from kt_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "openai/gpt-oss-120b", + "gen_configs": { + "temperature": 0.7, + "top_p": 0.95, + "top_k": 20, + "max_tokens": 32768, + "repetition_penalty": 1.0, + }, + "output_prefix": "gptoss120b", + "system_prompt_prefix": "Reasoning: medium\n\n", +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Code/kt_inference_base.py b/Code/kt_inference_base.py new file mode 100644 index 0000000000000000000000000000000000000000..314e53575892f5443909411675ba539e52fdced5 --- /dev/null +++ b/Code/kt_inference_base.py @@ -0,0 +1,849 @@ +""" +Base module for Knowledge Tracing LLM inference. + +This module contains all shared logic for running KT inference with different models. +Each model script imports this and provides model-specific configuration. + +Usage in model scripts: + from kt_inference_base import run_inference + + MODEL_CONFIG = { + "model_id": "model/name", + "gen_configs": {...}, + "output_prefix": "prefix", + "system_prompt_prefix": "", # e.g., "Reasoning: medium\n\n" + } + + if __name__ == "__main__": + run_inference(MODEL_CONFIG) +""" + +import argparse +import contextlib +import os +from vllm import LLM, SamplingParams +import pandas as pd +import gc +import torch +from vllm.distributed.parallel_state import ( + destroy_model_parallel, + destroy_distributed_environment, +) +import json +import re +import numpy as np +from tqdm import tqdm +from multiprocessing import Pool, cpu_count +from clean_utils import clean_problem_body +from cleantext import clean_text as clean_text_legacy + + +class NumpyEncoder(json.JSONEncoder): + """Custom JSON encoder that handles numpy types.""" + def default(self, obj): + if isinstance(obj, np.integer): + return int(obj) + if isinstance(obj, np.floating): + return float(obj) + if isinstance(obj, np.ndarray): + return obj.tolist() + return super().default(obj) + + +# Batch processing config defaults +DEFAULT_BATCH_SIZE = 10000 +DEFAULT_NUM_STUDENTS = 500 +DEFAULT_BIN_SIZE = 50 +DEFAULT_MIN_HISTORY = 50 + +# Input file names +STUDENT_FILE = "Interactions.csv" +PROBLEMS_FILE = "Problems.csv" +SKILL_FILE = "Skills.csv" + +# Base system prompt (without any prefix like "Reasoning: medium") +BASE_SYSTEM_PROMPT = """You are a reasoning model trained to simulate a student's evolving knowledge and response behavior in mathematics. + +Your goal is to infer, from past problem–answer pairs, how this same student is likely to perform on a new problem — at multiple levels of granularity. + +You must reason about the student's learning progression, skill mastery, and recurring misconceptions, then produce structured predictions for the new item. + +--- + +Your Task: + +Generate three coordinated predictions for this student: + +1) **Skill-level knowledge tracing (0 or 1):** Whether the student has mastered the underlying skill involved in the new problem. +2) **Question-level knowledge tracing (0 or 1):** Whether the student will answer this specific problem correctly. +3) **Cognitive-level prediction (string):** The exact answer text or option the student would most likely produce, written in their own response style. + +--- + +Reasoning Guidelines: + +- Use the student's historical data (problems, answers, hints, timestamps) to infer learning and forgetting patterns. +- Consider recency and exposure: later timestamps often indicate updated knowledge. +- Treat `UsedHint=True` or `SawAnswer=True` as evidence that the student's recorded answer may not reflect true mastery — they might have seen or been helped toward the solution. +- Attend to how the student's accuracy, style, and misconceptions evolve over time. +- You may think step-by-step internally, but your final output must follow the format below. +--- + +Output Format: + +When you are done reasoning, **finish your response with** the JSON object in this exact structure: + +For Multiple Choice (select 1) problems: +{ +"skill_level": 0 or 1, +"question_level": 0 or 1, +"student_answer": "A" (single letter only) +} + +For Multiple Choice (select all) problems: +{ +"skill_level": 0 or 1, +"question_level": 0 or 1, +"student_answer": "A, C" (comma-separated letters if multiple selections) +} + +For Fill-in problems: +{ +"skill_level": 0 or 1, +"question_level": 0 or 1, +"student_answer": "" +} + +Predictions must be consistent. If you predict question_level to be 1, then student_answer must match the correct answer. If you predict question_level to be 0, student_answer must not match the correct answer.""" + + +def parse_args(default_output_jsonl): + """Parse command line arguments.""" + parser = argparse.ArgumentParser(description="Knowledge Tracing with LLM") + parser.add_argument( + "--batch-size", "-b", + type=int, + default=DEFAULT_BATCH_SIZE, + help=f"Batch size for LLM inference (default: {DEFAULT_BATCH_SIZE})" + ) + parser.add_argument( + "--output", "-o", + type=str, + default=None, + help="Output JSONL file path (overrides auto-generated name)" + ) + parser.add_argument( + "--output-dir", + type=str, + default=".", + help="Output directory for results (default: current directory)" + ) + parser.add_argument( + "--data-dir", "-d", + type=str, + default=".", + help="Directory containing input CSV files (default: current directory)" + ) + parser.add_argument( + "--cache-dir", "-c", + type=str, + default=None, + help="Directory for vLLM model cache (default: vLLM default)" + ) + parser.add_argument( + "--num-students", "-n", + type=int, + default=DEFAULT_NUM_STUDENTS, + help=f"Number of students to sample (default: {DEFAULT_NUM_STUDENTS}, use 0 or -1 for all students)" + ) + parser.add_argument( + "--bin-size", + type=int, + default=DEFAULT_BIN_SIZE, + help=f"Size of each prediction bin (default: {DEFAULT_BIN_SIZE})" + ) + parser.add_argument( + "--min-history", + type=int, + default=DEFAULT_MIN_HISTORY, + help=f"Minimum history size before making predictions (default: {DEFAULT_MIN_HISTORY})" + ) + parser.add_argument( + "--num-gpus", + type=int, + default=1, + help="Number of GPUs for tensor parallelism (default: 1)" + ) + parser.add_argument( + "--max-num-seqs", + type=int, + default=None, + help="Maximum number of sequences to process in a batch (vLLM, default: 256)" + ) + parser.add_argument( + "--reasoning-level", + type=str, + choices=["none", "low", "medium", "high"], + default=None, + help="Reasoning level for GPT-OSS models only. Default: uses model config (medium for GPT-OSS, none for Qwen)" + ) + parser.add_argument( + "--max-model-len", + type=int, + default=None, + help="Maximum sequence length in tokens (vLLM, default: model's context length)" + ) + parser.add_argument( + "--gpu-memory-utilization", + type=float, + default=0.9, + help="Fraction of GPU memory to use (vLLM, default: 0.9, range: 0.0-1.0)" + ) + parser.add_argument( + "--legacy-clean", + action="store_true", + default=False, + help="Use legacy text cleaner (cleantext.py) instead of clean_utils.py" + ) + return parser.parse_args() + + +def label_answer_options(answer_string): + """ + Convert pipe-delimited answers to lettered format. + Input: "Han is correct || Elena is correct || Both are correct" + Output: {"A": "Han is correct", "B": "Elena is correct", "C": "Both are correct"} + """ + if pd.isna(answer_string) or answer_string == '': + return None + + options = [opt.strip() for opt in answer_string.split('||')] + letters = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'] + return {letters[i]: opt for i, opt in enumerate(options) if i < len(letters)} + + +def clean_html_and_normalize(text): + """ + Remove HTML tags and normalize text for comparison. + """ + if pd.isna(text): + return "" + # Remove HTML tags + text = re.sub(r'<[^>]+>', '', str(text)) + # Normalize whitespace + text = ' '.join(text.split()) + # Remove extra spaces around colons + text = re.sub(r'\s*:\s*', ':', text) + return text.strip() + + +def match_student_answer_to_letters(student_answer_text, answer_options_dict): + """ + Match student's comma-delineated answers to letter options. + + Args: + student_answer_text: String like "Answer A text , Answer C text , Answer B text" + answer_options_dict: Dict like {"A": "Answer A text", "B": "Answer B text", ...} + + Returns: + String like "A, B, C" or original text if no match + """ + if pd.isna(student_answer_text) or not answer_options_dict: + return student_answer_text + + # Split by " , " (comma with spaces, which is the delimiter used in the actual_answer) + student_answers = [ans.strip() for ans in str(student_answer_text).split(' , ')] + + # Clean and normalize all options for comparison + normalized_options = { + letter: clean_html_and_normalize(text) + for letter, text in answer_options_dict.items() + } + + matched_letters = [] + for student_ans in student_answers: + normalized_student = clean_html_and_normalize(student_ans) + + # Try to find exact match first + for letter, normalized_option in normalized_options.items(): + if normalized_student == normalized_option: + matched_letters.append(letter) + break + else: + # If no exact match, try substring match (student answer contained in option or vice versa) + for letter, normalized_option in normalized_options.items(): + if (normalized_student in normalized_option or + normalized_option in normalized_student): + matched_letters.append(letter) + break + + # Return comma-separated letters if we found matches, otherwise return original + if matched_letters: + return ', '.join(sorted(set(matched_letters))) # Remove duplicates and sort + return student_answer_text + + +def get_correct_option_letters(answer_options, correct_answers): + """ + Determine which letter(s) correspond to correct answer(s). + + Args: + answer_options: Dict like {"A": "Han is correct", "B": "Elena is correct", ...} + correct_answers: String like "Both are correct" or "Han is correct || Elena is correct" + + Returns: + String like "C" or "A, B" depending on how many correct options + """ + if not answer_options or pd.isna(correct_answers): + return correct_answers + + # Split correct answers if multiple + correct_list = [ans.strip() for ans in correct_answers.split('||')] + + # Find matching letters + correct_letters = [] + for letter, text in answer_options.items(): + if text in correct_list: + correct_letters.append(letter) + + return ', '.join(sorted(correct_letters)) if correct_letters else correct_answers + + +def format_answer_options_for_prompt(answer_options): + """ + Format answer options dictionary for display in prompt. + Input: {"A": "Han is correct", "B": "Elena is correct", ...} + Output: "A) Han is correct\nB) Elena is correct\n..." + """ + if not answer_options: + return None + + return '\n'.join([f"{letter}) {text}" for letter, text in answer_options.items()]) + + +def create_user_prompt(student_history, new_problem, problem_df): + """ + Creates a user prompt with student history and new problem. + + Args: + student_history: List of dicts with keys: problem_id, timestamp, problem_text, + correct_answer, student_answer, used_hint, saw_answer + new_problem: Dict with keys: problem_text, correct_answer, used_hint, saw_answer, + answer_options (optional) + """ + prompt = "Task Description:\n\n" + prompt += "Your task is to model a single student's learning process and predict how they will respond to a new mathematics problem based on their prior work.\n\n" + + prompt += """You will produce three coordinated predictions: + + 1) **Skill-level knowledge tracing (0 or 1):** Predict whether this student has mastered the underlying skill involved in the new problem. + 2) **Question-level knowledge tracing (0 or 1):** Predict whether this student will answer this specific problem correctly. + 3) **Cognitive-level prediction (string):** Generate the exact answer the student would most likely produce. + - For Multiple Choice (select 1): Predict a single letter (e.g., "A" or "B") + - For Multiple Choice (select all): Predict comma-separated letters (e.g., "A, C" or "B, D") + - For Fill-in problems: Predict the exact text the student would write + """ + + prompt += """--- + + Provided Data: + + You will receive: + - ProblemID: + - Timestamp: + - Problem: + - Problem Type: Multiple Choice (select 1) / Multiple Choice (select all) / Fill-in Problem + - Options: Answer choices in format "A) ...\nB) ...\nC) ..." + - Correct Answer(s): The letter(s) or text of correct answer(s) + - Student's First Answer: Letter(s) or fill-in text + - UsedHint: + - SawAnswer: + - Skill: + - A new problem (with optional answer choices), skill metadata, and context flags (`UsedHint`, `SawAnswer`). + + # About the context flags: + - **UsedHint = True** → The student viewed or used a hint while solving this problem. + - **SawAnswer = True** → The student saw the correct answer before or during the attempt. + When either of these flags is True, treat the corresponding response as *less reliable evidence of mastery* — it indicates that the student has not fully learned the concept and required help solving the problem. +""" + + prompt += "**Student's Previous Problems:**\n\n" + for item in student_history: + prompt += f"Timestamp: {item['timestamp']}\n" + prompt += f"Problem: {item['problem_text']}\n" + prompt += f"Problem Type: {item['problem_type']}\n" + if item.get('answer_options_formatted'): + prompt += f"Options:\n{item['answer_options_formatted']}\n" + prompt += f"Correct Answer: {item['correct_answer']}\n" + prompt += f"Student's First Answer: {item['student_answer']}\n" + prompt += f"UsedHint: {item['used_hint']}\n" + prompt += f"SawAnswer: {item['saw_answer']}\n" + if item.get('node_name'): + prompt += f"Skill: {item['node_name']}\n" + else: + prompt += f"Skill: Undefined\n" + prompt += "---\n\n" + + prompt += "**New Problem to Predict:**\n\n" + prompt += f"Timestamp: {new_problem['timestamp']}\n" + prompt += f"Problem: {new_problem['problem_text']}\n" + prompt += f"Problem Type: {new_problem['problem_type']}\n" + if new_problem.get('answer_options_formatted'): + prompt += f"Answer Options:\n{new_problem['answer_options_formatted']}\n" + prompt += f"Correct Answer: {new_problem['correct_answer']}\n" + if new_problem.get('node_name'): + prompt += f"Skill: {new_problem['node_name']}\n" + else: + prompt += f"Skill: Undefined\n" + + return prompt + + +def extract_json_prediction(response_text): + """Extract the final JSON prediction from the model's response.""" + # Find all JSON objects in the response + json_matches = re.findall(r'\{[\s\S]*?\}', response_text) + + if json_matches: + # Take the last JSON object + json_str = json_matches[-1] + try: + # Decode escape sequences (like \n) before parsing + json_str = json_str.encode().decode('unicode_escape') + json_str = json_str.strip() + return json.loads(json_str) + except json.JSONDecodeError as e: + print(f"JSON decode error: {e}") + print(f"Attempted to parse:\n{json_str}") + except Exception as e: + print(f"Error processing JSON: {e}") + return None + + +def get_prediction_id(meta): + """Generate unique ID for a prediction""" + return f"{meta['user_id']}_{meta['bin_number']}_{meta['prediction_type']}" + + +def load_completed_predictions(output_jsonl): + """Load already-completed prediction IDs from JSONL file""" + completed = set() + if os.path.exists(output_jsonl): + with open(output_jsonl, 'r') as f: + for line in f: + if line.strip(): + result = json.loads(line) + completed.add(result['prediction_id']) + print(f"Loaded {len(completed)} completed predictions from {output_jsonl}") + return completed + + +def make_process_single_user(system_prompt): + """Create a process_single_user function with the given system prompt.""" + def process_single_user(args): + """Process a single user's data and return prompts and metadata.""" + user_id, user_records, min_history, bin_size = args + + prompts = [] + metadata = [] + + # Check if user has at least min_history + 1 rows + if len(user_records) < min_history + 1: + return prompts, metadata + + num_bins = (len(user_records) - min_history) // bin_size + + # Build initial history + student_history = [] + for hist_idx in range(min_history): + row = user_records[hist_idx] + student_history.append({ + 'problem_id': row['problem_id'], + 'timestamp': row['end_time'], + 'problem_text': row['cleaned body'], + 'correct_answer': row['Fill-in Answers'], + 'answer_options': row['answer_options'] if pd.notna(row['answer_options']) else None, + 'answer_options_formatted': row['answer_options_formatted'] if pd.notna(row.get('answer_options_formatted')) else None, + 'student_answer': row['answer_text'], + 'used_hint': row['hint_count'] > 0, + 'saw_answer': row['saw_answer'], + 'problem_type': row['Problem Type'], + 'node_name': row.get('node_name') + }) + + for bin_idx in range(num_bins): + # Extend history with previous bin's items + if bin_idx > 0: + prev_bin_start = min_history + ((bin_idx - 1) * bin_size) + prev_bin_end = min_history + (bin_idx * bin_size) + for hist_idx in range(prev_bin_start, prev_bin_end): + row = user_records[hist_idx] + student_history.append({ + 'problem_id': row['problem_id'], + 'timestamp': row['end_time'], + 'problem_text': row['cleaned body'], + 'correct_answer': row['Fill-in Answers'], + 'answer_options': row['answer_options'] if pd.notna(row['answer_options']) else None, + 'answer_options_formatted': row['answer_options_formatted'] if pd.notna(row.get('answer_options_formatted')) else None, + 'student_answer': row['answer_text'], + 'used_hint': row['hint_count'] > 0, + 'saw_answer': row['saw_answer'], + 'problem_type': row['Problem Type'], + 'node_name': row.get('node_name') + }) + + history_end = min_history + (bin_idx * bin_size) + bin_start = history_end + bin_end = bin_start + bin_size + current_bin = user_records[bin_start:bin_end] + + # Find first correct and first incorrect in this bin + first_correct_idx = None + first_incorrect_idx = None + + for idx, row in enumerate(current_bin): + actual_idx = bin_start + idx + score = row['discrete_score'] + + if score == 1 and first_correct_idx is None: + first_correct_idx = actual_idx + if score == 0 and first_incorrect_idx is None: + first_incorrect_idx = actual_idx + + if first_correct_idx is not None and first_incorrect_idx is not None: + break + + # Create predictions for found cases + for target_idx, prediction_type in [ + (first_correct_idx, 'correct'), + (first_incorrect_idx, 'incorrect') + ]: + if target_idx is None: + continue + + target_row = user_records[target_idx] + new_problem = { + 'problem_text': target_row['cleaned body'], + 'correct_answer': target_row['Fill-in Answers'], + 'answer_options': target_row['answer_options'] if pd.notna(target_row['answer_options']) else None, + 'answer_options_formatted': target_row['answer_options_formatted'] if pd.notna(target_row.get('answer_options_formatted')) else None, + 'problem_type': target_row['Problem Type'], + 'timestamp': target_row['end_time'], + 'node_name': target_row.get('node_name') + } + + user_prompt = create_user_prompt(student_history, new_problem, None) + full_prompt = system_prompt + "\n\n" + user_prompt + + prompts.append(full_prompt) + metadata.append({ + 'prediction_id': f"{user_id}_{bin_idx}_{prediction_type}", + 'row_index': target_idx, + 'user_id': user_id, + 'history_size': len(student_history), + 'bin_number': bin_idx, + 'prediction_type': prediction_type, + 'id': target_row.get('id_x', None), + 'problem_id': target_row.get('problem_id', None), + 'problem_type': target_row['Problem Type'], + 'actual_answer': target_row['answer_text'], + 'correct_answer': target_row['Fill-in Answers'], + 'actual_score': target_row['discrete_score'], + 'prompt': full_prompt + }) + + return prompts, metadata + + return process_single_user + + +def append_results_jsonl(results, output_jsonl): + """Append batch results to JSONL file""" + with open(output_jsonl, 'a') as f: + for result in results: + f.write(json.dumps(result, cls=NumpyEncoder) + '\n') + + +def process_batch(batch_metadata, batch_response_texts): + """Process a batch of responses and return results.""" + batch_results = [] + + for metadata, response_text in zip(batch_metadata, batch_response_texts): + # Extract prediction + prediction = extract_json_prediction(response_text) + + if prediction: + batch_results.append({ + **metadata, + 'predicted_skill_level': prediction.get('skill_level'), + 'predicted_question_level': prediction.get('question_level'), + 'predicted_student_answer': prediction.get('student_answer'), + 'full_response': response_text + }) + else: + batch_results.append({ + **metadata, + 'predicted_skill_level': None, + 'predicted_question_level': None, + 'predicted_student_answer': None, + 'full_response': response_text + }) + + return batch_results + + +# Global variable to hold process_single_user function for multiprocessing +_process_single_user_func = None + + +def _process_single_user_wrapper(args): + """Wrapper for multiprocessing that uses the global function.""" + return _process_single_user_func(args) + + +def run_inference(config): + """ + Main inference function that runs KT prediction with the given model config. + + Args: + config: Dict with keys: + - model_id: HuggingFace model ID + - gen_configs: Dict of generation parameters + - output_prefix: Prefix for output filename + - system_prompt_prefix: Optional prefix for system prompt (e.g., "Reasoning: medium\n\n") + """ + global _process_single_user_func + + model_id = config["model_id"] + gen_configs = config["gen_configs"] + output_prefix = config["output_prefix"] + + # Parse arguments first (needed for reasoning level) + default_output_jsonl = f"{output_prefix}.jsonl" + args = parse_args(default_output_jsonl) + + # Determine system prompt prefix + # CLI --reasoning-level overrides model config if provided + if args.reasoning_level is not None: + if args.reasoning_level == "none": + system_prompt_prefix = "" + else: + system_prompt_prefix = f"Reasoning: {args.reasoning_level}\n\n" + else: + system_prompt_prefix = config.get("system_prompt_prefix", "") + + # Build full system prompt + system_prompt = system_prompt_prefix + BASE_SYSTEM_PROMPT + + # Create the process_single_user function with this system prompt + _process_single_user_func = make_process_single_user(system_prompt) + + batch_size = args.batch_size + data_dir = args.data_dir + cache_dir = args.cache_dir + num_students = args.num_students + bin_size = args.bin_size + min_history = args.min_history + + # Generate output filename with params + n_str = "all" if num_students <= 0 else str(num_students) + params_suffix = f"_n{n_str}_bin{bin_size}_hist{min_history}" + + if args.output: + # Use explicit output path + output_jsonl = args.output + else: + # Auto-generate filename in output directory + filename = f"{output_prefix}{params_suffix}.jsonl" + output_jsonl = os.path.join(args.output_dir, filename) + + # Build input file paths + student_csv = os.path.join(data_dir, STUDENT_FILE) + problems_csv = os.path.join(data_dir, PROBLEMS_FILE) + skill_csv = os.path.join(data_dir, SKILL_FILE) + + print(f"Model: {model_id}") + print(f"Data directory: {data_dir}") + print(f"Batch size: {batch_size}") + print(f"Output JSONL: {output_jsonl}") + print(f"Num students: {num_students if num_students > 0 else 'all'}") + print(f"Bin size: {bin_size}") + print(f"Min history: {min_history}") + if cache_dir: + print(f"Model cache: {cache_dir}") + print(f"Text cleaner: {'legacy (cleantext.py)' if args.legacy_clean else 'default (clean_utils.py)'}") + + # Load the data + print("\nLoading data...") + student_df = pd.read_csv(student_csv) + student_df = student_df.sort_values(['user_id', 'id']).reset_index(drop=True) + problems_df = pd.read_csv(problems_csv) + clean_func = clean_text_legacy if args.legacy_clean else clean_problem_body + problems_df['cleaned body'] = problems_df['Problem Body'].apply(clean_func) + + # Label answer options for multiple-choice items + problems_df['answer_options'] = problems_df['Multiple Choice Options'].apply(label_answer_options) + + # Get correct answer letters for multiple-choice, keep original for fill-in + problems_df['correct_answers'] = problems_df.apply( + lambda row: get_correct_option_letters(row['answer_options'], row['Multiple Choice Answers']) + if row['Problem Type'] in ['Multiple Choice (select 1)', 'Multiple Choice (select all)'] + else row['Fill-in Answers'], + axis=1 + ) + + skill_df = pd.read_csv(skill_csv) + problems_df = pd.merge(problems_df, skill_df, on='problem_id', how='left') + + # Pre-compute formatted answer options once per problem + problems_df['answer_options_formatted'] = problems_df['answer_options'].apply( + lambda x: format_answer_options_for_prompt(x) if pd.notna(x) else None + ) + + # Sort student data by id (chronological order) + student_df = student_df.sort_values('id').reset_index(drop=True) + + # Merge with problems data + merged_df = student_df.merge(problems_df, on='problem_id', how='inner') + + # Convert student answers to letter format for multiple-choice problems + merged_df['answer_text'] = merged_df.apply( + lambda row: match_student_answer_to_letters(row['answer_text'], row['answer_options']) + if row['Problem Type'] in ['Multiple Choice (select 1)', 'Multiple Choice (select all)'] and pd.notna(row['answer_options']) + else row['answer_text'], + axis=1 + ) + + # Select users (all or random sample) + all_users = merged_df['user_id'].unique() + if num_students <= 0: + # Use all students + selected_users = all_users + print(f"\nUsing all {len(all_users)} users") + else: + # Random sample + np.random.seed(42) # For reproducibility + selected_users = np.random.choice(all_users, size=min(num_students, len(all_users)), replace=False) + merged_df = merged_df[merged_df['user_id'].isin(selected_users)] + print(f"\nSelected {len(selected_users)} random users from {len(all_users)} total users") + print(f"Filtered data: {len(merged_df)} rows") + + # Prepare data for batch processing + print("\nPreparing prompts in parallel...") + + # Prepare user groups for parallel processing + print("Grouping user data...") + user_groups = [ + (user_id, user_df.to_dict('records'), min_history, bin_size) + for user_id, user_df in merged_df.groupby('user_id') + ] + print(f"Processing {len(user_groups)} users with {cpu_count()} CPU cores...") + + # Process users in parallel + all_prompts = [] + all_metadata = [] + + with Pool(processes=cpu_count()) as pool: + results = list(tqdm( + pool.imap(_process_single_user_wrapper, user_groups), + total=len(user_groups), + desc="Preparing prompts" + )) + + # Merge results + for prompts, metadata in results: + all_prompts.extend(prompts) + all_metadata.extend(metadata) + + print(f"\nTotal predictions to make: {len(all_prompts)}") + + # Filter out already-completed predictions (resume support) + completed_ids = load_completed_predictions(output_jsonl) + remaining = [(p, m) for p, m in zip(all_prompts, all_metadata) + if m['prediction_id'] not in completed_ids] + + if not remaining: + print("All predictions already completed!") + return + + all_prompts, all_metadata = zip(*remaining) + all_prompts = list(all_prompts) + all_metadata = list(all_metadata) + + print(f"Already completed: {len(completed_ids)}") + print(f"Remaining to process: {len(all_prompts)}") + print(f"Processing in batches of {batch_size}") + + # Initialize vLLM engine + print("\nInitializing vLLM engine...") + sampling_params = SamplingParams(**gen_configs) + llm_kwargs = { + "model": model_id, + "tensor_parallel_size": args.num_gpus, + "trust_remote_code": True, + "gpu_memory_utilization": args.gpu_memory_utilization, + "enable_prefix_caching": True, + } + if args.max_num_seqs is not None: + llm_kwargs["max_num_seqs"] = args.max_num_seqs + if args.max_model_len is not None: + llm_kwargs["max_model_len"] = args.max_model_len + if cache_dir: + llm_kwargs["download_dir"] = cache_dir + llm = LLM(**llm_kwargs) + + # Process in batches + results = [] + num_batches = (len(all_prompts) + batch_size - 1) // batch_size + + for batch_idx in range(num_batches): + batch_start = batch_idx * batch_size + batch_end = min(batch_start + batch_size, len(all_prompts)) + + batch_prompts = all_prompts[batch_start:batch_end] + batch_metadata = all_metadata[batch_start:batch_end] + + print(f"\n{'='*80}") + print(f"Processing batch {batch_idx + 1}/{num_batches}") + print(f"Items: {batch_start} to {batch_end} ({len(batch_prompts)} prompts)") + print(f"{'='*80}") + + # Generate predictions for this batch + try: + outputs = llm.generate(batch_prompts, sampling_params) + response_texts = [o.outputs[0].text.strip() for o in outputs] + + # Process results for this batch + batch_results = process_batch(batch_metadata, response_texts) + results.extend(batch_results) + + print(f"Successfully processed batch {batch_idx + 1}") + print(f"Total results so far: {len(results)}") + + # Append results immediately after each batch + append_results_jsonl(batch_results, output_jsonl) + print(f"Saved {len(batch_results)} results to {output_jsonl}") + + except Exception as e: + print(f"\nERROR processing batch {batch_idx + 1}: {str(e)}") + print(f"Progress saved in {output_jsonl} - restart to resume") + raise + + print(f"\n{'='*80}") + print("All batches processed successfully!") + print(f"{'='*80}") + print(f"\nAll results saved to {output_jsonl}") + print(f"Total predictions processed: {len(results)}") + + # Cleanup + print("\nCleaning up...") + destroy_model_parallel() + destroy_distributed_environment() + del llm + with contextlib.suppress(AssertionError): + torch.distributed.destroy_process_group() + gc.collect() + torch.cuda.empty_cache() + + print("\nDone!") + exit(0) diff --git a/Code/llama33_70b_instruct_vllm.py b/Code/llama33_70b_instruct_vllm.py new file mode 100644 index 0000000000000000000000000000000000000000..d836df08da3c90b1cd9e553e65821001b3797d0b --- /dev/null +++ b/Code/llama33_70b_instruct_vllm.py @@ -0,0 +1,30 @@ +""" +Knowledge Tracing inference with Llama-3.3-70B-Instruct model. + +Usage: + CUDA_VISIBLE_DEVICES=0,1,2,3 python llama33_70b_instruct_vllm.py \ + --data-dir foundationalktdataset/ \ + --num-gpus 4 \ + --batch-size 10 \ + --cache-dir /data1/ \ + --num-students 500 \ + --bin-size 50 \ + --min-history 50 +""" + +from kt_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "meta-llama/Llama-3.3-70B-Instruct", + "gen_configs": { + "temperature": 0.7, + "top_p": 0.9, + "max_tokens": 32768, + "repetition_penalty": 1.0, + }, + "output_prefix": "llama33_70b_instruct", + "system_prompt_prefix": "", # No prefix - standard instruct model +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Code/plot_student_attempt_distribution.py b/Code/plot_student_attempt_distribution.py new file mode 100644 index 0000000000000000000000000000000000000000..6c86374ea8f851f859845b404ca888d6c6b87b09 --- /dev/null +++ b/Code/plot_student_attempt_distribution.py @@ -0,0 +1,357 @@ +#!/usr/bin/env python3 +"""Plot distribution of student attempts over elapsed time. + +This script reads FoundationalASSIST `Interactions.csv`, computes elapsed time +for each attempt from the student's first attempt, groups attempts into fixed +time bins, and plots the resulting column distribution. +""" + +from __future__ import annotations + +import argparse +import math +from pathlib import Path + +import matplotlib.pyplot as plt +import pandas as pd +from matplotlib.ticker import FuncFormatter, MaxNLocator + + +DEFAULT_INTERACTIONS_PATH = ( + Path(__file__).resolve().parent.parent / "Data" / "Interactions.csv" +) +DEFAULT_OUTPUT_PLOT = ( + Path(__file__).resolve().parent.parent + / "Results" + / "student_attempt_distribution.png" +) +DEFAULT_OUTPUT_COUNTS = ( + Path(__file__).resolve().parent.parent + / "Results" + / "student_attempt_distribution_counts.csv" +) + + +def parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser( + description=( + "Compute distribution of attempts over elapsed time from " + "Interactions.csv and plot binned columns." + ) + ) + parser.add_argument( + "--interactions-path", + type=Path, + default=DEFAULT_INTERACTIONS_PATH, + help="Path to Interactions.csv.", + ) + parser.add_argument( + "--output-plot", + type=Path, + default=DEFAULT_OUTPUT_PLOT, + help="Path to save the output figure.", + ) + parser.add_argument( + "--output-counts", + type=Path, + default=DEFAULT_OUTPUT_COUNTS, + help="Path to save binned attempt counts as CSV.", + ) + parser.add_argument( + "--max-rows", + type=int, + default=None, + help="Optional cap on rows after sorting (for quick debugging).", + ) + parser.add_argument( + "--bin-time", + type=float, + default=10.0, + help=( + "Fixed bin width in minutes. " + "For example, --bin-time 10 creates bins [0,10), [10,20), ..." + ), + ) + parser.add_argument( + "--plot-upper-limit-minutes", + type=float, + default=None, + help=( + "Optional upper limit for x-axis in minutes. " + "If omitted, uses the full range implied by bins." + ), + ) + parser.add_argument( + "--student-idx", + type=int, + default=None, + help=( + "Optional 0-based index of student to plot. Index is based on " + "sorted unique user_id values in the loaded interactions." + ), + ) + parser.add_argument( + "--log-y", + action="store_true", + help="Use log scale on y-axis.", + ) + return parser.parse_args() + + +def load_interactions(path: Path, max_rows: int | None = None) -> pd.DataFrame: + """Load fields required for student attempt timing analysis.""" + usecols = ["id", "user_id", "end_time"] + df = pd.read_csv(path, usecols=usecols, low_memory=False) + + df["id"] = pd.to_numeric(df["id"], errors="coerce") + df["id"] = df["id"].fillna(-1).astype(int) + df["user_id"] = df["user_id"].astype("string") + df["end_time"] = pd.to_datetime(df["end_time"], errors="coerce", utc=True) + + df = df.dropna(subset=["user_id", "end_time"]).copy() + df = df.sort_values(["user_id", "end_time", "id"], kind="mergesort") + + if max_rows is not None: + if max_rows <= 0: + raise ValueError("--max-rows must be a positive integer.") + df = df.head(max_rows).copy() + + return df + + +def select_student_by_index( + df: pd.DataFrame, + student_idx: int, +) -> tuple[pd.DataFrame, str, int]: + """Select one student's interactions by 0-based index over unique IDs.""" + student_ids = df["user_id"].drop_duplicates().tolist() + total_students = len(student_ids) + + if total_students == 0: + raise ValueError("No students found in loaded interactions.") + if student_idx < 0 or student_idx >= total_students: + raise ValueError( + f"--student-idx must be in [0, {total_students - 1}], got {student_idx}." + ) + + selected_student_id = str(student_ids[student_idx]) + selected_df = df[df["user_id"] == selected_student_id].copy() + return selected_df, selected_student_id, total_students + + +def append_student_id_to_output_path(path: Path, student_id: str) -> Path: + """Append a safe student-id suffix to output filename.""" + safe_id = "".join( + ch if ch.isalnum() or ch in ("-", "_") else "_" for ch in student_id + ) + return path.with_name(f"{path.stem}_{safe_id}{path.suffix}") + + +def compute_attempt_elapsed_minutes(df: pd.DataFrame) -> pd.Series: + """Compute elapsed minutes of each attempt from student's first attempt.""" + first_times = df.groupby("user_id", sort=False)["end_time"].transform("min") + elapsed_minutes = (df["end_time"] - first_times).dt.total_seconds() / 60.0 + elapsed_minutes.name = "elapsed_minutes" + return elapsed_minutes + + +def build_fixed_width_bin_edges_minutes( + valid_elapsed_minutes: pd.Series, + bin_time_minutes: float, +) -> list[float]: + """Build fixed-width bin edges from min/max elapsed minutes.""" + min_elapsed = float(valid_elapsed_minutes.min()) + max_elapsed = float(valid_elapsed_minutes.max()) + + start = bin_time_minutes * math.floor(min_elapsed / bin_time_minutes) + end = bin_time_minutes * math.ceil(max_elapsed / bin_time_minutes) + + if math.isclose(start, 0.0, abs_tol=1e-12): + start = 0.0 + if math.isclose(end, start, abs_tol=1e-12): + end = start + bin_time_minutes + + n_bins = int(round((end - start) / bin_time_minutes)) + edges = [start + i * bin_time_minutes for i in range(n_bins + 1)] + if edges[-1] <= max_elapsed: + edges.append(edges[-1] + bin_time_minutes) + + return edges + + +def format_minutes_tick(value: float, _pos: float) -> str: + if value < 60: + return f"{value:.0f}m" + if value < 1440: + return f"{value / 60:.0f}h" + return f"{value / 1440:.0f}d" + + +def summarize_attempt_distribution( + elapsed_minutes: pd.Series, + bin_time_minutes: float, +) -> pd.DataFrame: + valid = elapsed_minutes.dropna().copy() + if valid.empty: + raise ValueError("No valid elapsed attempt times found.") + + edges = build_fixed_width_bin_edges_minutes(valid, bin_time_minutes) + binned = pd.cut(valid, bins=edges, right=False, include_lowest=True) + counts = binned.value_counts(sort=False) + total_attempts = int(counts.sum()) + probabilities = (counts / total_attempts).astype(float) + + bin_left = pd.Series(edges[:-1], dtype=float) + bin_right = pd.Series(edges[1:], dtype=float) + bin_width = bin_right - bin_left + + summary = pd.DataFrame( + { + "bin_left_min": bin_left.to_numpy(), + "bin_right_min": bin_right.to_numpy(), + "bin_width_min": bin_width.to_numpy(), + "attempt_count": counts.to_numpy(), + "probability": probabilities.to_numpy(dtype=float), + "percentage": probabilities.to_numpy(dtype=float) * 100.0, + } + ) + return summary + + +def plot_distribution( + summary_df: pd.DataFrame, + output_path: Path, + log_y: bool = False, + plot_upper_limit_minutes: float | None = None, + student_idx: int | None = None, +) -> None: + """Create and save student-attempt distribution columns.""" + output_path.parent.mkdir(parents=True, exist_ok=True) + + plt.style.use("seaborn-v0_8-whitegrid") + if student_idx is not None: + fig, ax = plt.subplots(figsize=(10, 5)) + else: + fig, ax = plt.subplots(figsize=(20, 5)) + + left = summary_df["bin_left_min"].to_numpy(dtype=float) + width = summary_df["bin_width_min"].to_numpy(dtype=float) + counts = summary_df["attempt_count"].to_numpy(dtype=float) + + bars = ax.bar( + left, + counts, + width=width, + align="edge", + color="#4C78A8", + # edgecolor="white", + # linewidth=1.0, + ) + + title = "Distribution of Student Attempts Over Elapsed Time" + if student_idx is not None: + title = f"{title} (student_idx={student_idx})" + ax.set_title(title) + ax.set_xlabel("Elapsed Time Since Student's First Attempt") + ax.set_ylabel("Number of Attempts") + + x_min = float(left.min()) + x_max = float((left + width).max()) + if plot_upper_limit_minutes is not None: + x_max = min(x_max, float(plot_upper_limit_minutes)) + ax.set_xlim(x_min, x_max) + + ax.xaxis.set_major_locator(MaxNLocator(nbins=9)) + ax.xaxis.set_major_formatter(FuncFormatter(format_minutes_tick)) + ax.grid(axis="y", alpha=0.25, linewidth=0.8) + ax.spines["top"].set_visible(False) + ax.spines["right"].set_visible(False) + + if log_y: + ax.set_yscale("log") + + annotate_bars = len(summary_df) <= 40 + if annotate_bars: + for bar, pct in zip(bars, summary_df["percentage"]): + if pct < 1.0: + continue + h = bar.get_height() + if h <= 0: + continue + ax.annotate( + f"{pct:.1f}%", + xy=(bar.get_x() + bar.get_width() / 2.0, h), + xytext=(0, 3), + textcoords="offset points", + ha="center", + va="bottom", + fontsize=8, + ) + + plt.tight_layout() + fig.savefig(output_path, dpi=400, bbox_inches="tight") + plt.close(fig) + + +def main() -> None: + args = parse_args() + + if not args.interactions_path.exists(): + raise FileNotFoundError( + f"Interactions file not found: {args.interactions_path}" + ) + if args.bin_time <= 0: + raise ValueError("--bin-time must be a positive number.") + if args.plot_upper_limit_minutes is not None and args.plot_upper_limit_minutes <= 0: + raise ValueError("--plot-upper-limit-minutes must be a positive number.") + + df = load_interactions(args.interactions_path, max_rows=args.max_rows) + + selected_student_id: str | None = None + total_students = int(df["user_id"].nunique()) + if args.student_idx is not None: + df, selected_student_id, total_students = select_student_by_index( + df, + args.student_idx, + ) + + output_plot_path = args.output_plot + output_counts_path = args.output_counts + if selected_student_id is not None: + output_plot_path = append_student_id_to_output_path( + output_plot_path, + selected_student_id, + ) + output_counts_path = append_student_id_to_output_path( + output_counts_path, + selected_student_id, + ) + + elapsed_minutes = compute_attempt_elapsed_minutes(df) + summary = summarize_attempt_distribution(elapsed_minutes, args.bin_time) + output_counts_path.parent.mkdir(parents=True, exist_ok=True) + summary.to_csv(output_counts_path, index=False) + + plot_distribution( + summary, + output_plot_path, + log_y=args.log_y, + plot_upper_limit_minutes=args.plot_upper_limit_minutes, + student_idx=args.student_idx, + ) + + total_attempts = int(summary["attempt_count"].sum()) + print("Done.") + print(f"Interactions loaded: {len(df):,}") + print(f"Students in loaded data: {total_students:,}") + if selected_student_id is not None: + print(f"Selected student idx: {args.student_idx}") + print(f"Selected student id: {selected_student_id}") + print(f"Attempts used: {total_attempts:,}") + print(f"Bin width (min): {args.bin_time}") + print(f"Saved plot: {output_plot_path}") + print(f"Saved bin counts: {output_counts_path}") + + +if __name__ == "__main__": + main() diff --git a/Code/plot_timegap_distribution.py b/Code/plot_timegap_distribution.py new file mode 100644 index 0000000000000000000000000000000000000000..a116d21a0df920ad1c1c6aab53129fdf980bd224 --- /dev/null +++ b/Code/plot_timegap_distribution.py @@ -0,0 +1,484 @@ +#!/usr/bin/env python3 +"""Plot the distribution of time gaps between consecutive student attempts. + +This script reads FoundationalASSIST `Interactions.csv`, groups interactions by +student (`user_id`), computes the time difference between each pair of +consecutive attempts (`end_time`), discretizes these differences into bins, and +plots the resulting distribution. +""" + +from __future__ import annotations + +import argparse +import math +from pathlib import Path + +import matplotlib.pyplot as plt +import pandas as pd +from matplotlib.ticker import FuncFormatter, MaxNLocator + + +DEFAULT_INTERACTIONS_PATH = ( + Path(__file__).resolve().parent.parent / "Data" / "Interactions.csv" +) +DEFAULT_OUTPUT_PLOT = ( + Path(__file__).resolve().parent.parent / "Results" / "time_gap_distribution.png" +) +DEFAULT_OUTPUT_COUNTS = ( + Path(__file__).resolve().parent.parent + / "Results" + / "time_gap_distribution_counts.csv" +) +CDF_MARKER_MINUTES = 60.0 + + +def parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser( + description=( + "Compute per-student consecutive-attempt time gaps from " + "Interactions.csv and plot their binned distribution." + ) + ) + parser.add_argument( + "--interactions-path", + type=Path, + default=DEFAULT_INTERACTIONS_PATH, + help="Path to Interactions.csv.", + ) + parser.add_argument( + "--output-plot", + type=Path, + default=DEFAULT_OUTPUT_PLOT, + help="Path to save the output figure.", + ) + parser.add_argument( + "--output-counts", + type=Path, + default=DEFAULT_OUTPUT_COUNTS, + help="Path to save bin counts as CSV.", + ) + parser.add_argument( + "--max-rows", + type=int, + default=None, + help="Optional cap on rows after sorting (for quick debugging).", + ) + parser.add_argument( + "--keep-nonpositive-gaps", + action="store_true", + help=( + "Keep zero/negative gaps. By default, only strictly positive " + "gaps are used." + ), + ) + parser.add_argument( + "--log-y", + action="store_true", + help="Use log scale on y-axis.", + ) + parser.add_argument( + "--plot-upper-limit-minutes", + type=float, + default=None, + help=( + "Optional upper limit for x-axis in minutes. " + "If omitted, uses the full range implied by bins." + ), + ) + parser.add_argument( + "--bin-time", + type=float, + default=None, + help=( + "Optional fixed bin width in minutes. " + "For example, --bin-time 10 creates bins [0,10), [10,20), ..." + ), + ) + parser.add_argument( + "--student-idx", + type=int, + default=None, + help=( + "Optional 0-based index of student to plot. Index is based on " + "sorted unique user_id values in the loaded interactions." + ), + ) + return parser.parse_args() + + +def load_interactions(path: Path, max_rows: int | None = None) -> pd.DataFrame: + """Load the minimum columns required for time-gap analysis.""" + usecols = ["id", "user_id", "end_time"] + df = pd.read_csv(path, usecols=usecols, low_memory=False) + + df["id"] = pd.to_numeric(df["id"], errors="coerce") + df["id"] = df["id"].fillna(-1).astype(int) + df["user_id"] = df["user_id"].astype("string") + df["end_time"] = pd.to_datetime(df["end_time"], errors="coerce", utc=True) + + df = df.dropna(subset=["user_id", "end_time"]).copy() + df = df.sort_values(["user_id", "end_time", "id"], kind="mergesort") + + if max_rows is not None: + if max_rows <= 0: + raise ValueError("--max-rows must be a positive integer.") + df = df.head(max_rows).copy() + + return df + + +def compute_time_gaps_minutes(df: pd.DataFrame) -> pd.Series: + """Compute consecutive attempt gaps per student in minutes.""" + gaps_seconds = ( + df.groupby("user_id", sort=False)["end_time"].diff().dt.total_seconds() + ) + return gaps_seconds / 60.0 + + +def default_bin_edges_minutes() -> list[float]: + """Base minute-scale edges (final open tail may be added from data max).""" + return [ + 0.0, + 1.0, + 5.0, + 10.0, + 30.0, + 60.0, + 180.0, + 720.0, + 1440.0, + 4320.0, + 10080.0, + ] + + +def build_bin_edges_minutes(valid: pd.Series) -> list[float]: + """Build finite plotting edges so bar widths are proportional on x-axis.""" + edges = default_bin_edges_minutes() + base_tail_start = edges[-1] + max_gap = float(valid.max()) + + if max_gap > base_tail_start: + # Add a finite terminal edge that fully contains the data tail. + tail_edge = max(base_tail_start + 60.0, max_gap * 1.05) + edges.append(tail_edge) + + return edges + + +def build_fixed_width_bin_edges_minutes( + valid: pd.Series, bin_time_minutes: float +) -> list[float]: + """Build fixed-width edges from min/max observed gaps.""" + min_gap = float(valid.min()) + max_gap = float(valid.max()) + + start = bin_time_minutes * math.floor(min_gap / bin_time_minutes) + end = bin_time_minutes * math.ceil(max_gap / bin_time_minutes) + + if math.isclose(start, 0.0, abs_tol=1e-12): + start = 0.0 + if math.isclose(end, start, abs_tol=1e-12): + end = start + bin_time_minutes + + n_bins = int(round((end - start) / bin_time_minutes)) + edges = [start + i * bin_time_minutes for i in range(n_bins + 1)] + if edges[-1] <= max_gap: + edges.append(edges[-1] + bin_time_minutes) + + return edges + + +def format_bin_bound(minutes: float) -> str: + if math.isclose(minutes, round(minutes), abs_tol=1e-9): + return str(int(round(minutes))) + return f"{minutes:.2f}".rstrip("0").rstrip(".") + + +def make_bin_labels( + edges: list[float], open_tail_from: float | None = None +) -> list[str]: + labels: list[str] = [] + last_idx = len(edges) - 2 + for idx, (left, right) in enumerate(zip(edges[:-1], edges[1:])): + if open_tail_from is not None and idx == last_idx and left >= open_tail_from: + labels.append(f">= {format_bin_bound(left)} min") + else: + labels.append(f"[{format_bin_bound(left)}, {format_bin_bound(right)}) min") + return labels + + +def format_minutes_tick(value: float, _pos: float) -> str: + if value < 60: + return f"{int(round(value))}m" + + if value < 1440: + hours = value / 60.0 + if math.isclose(hours, round(hours), abs_tol=1e-9): + return f"{int(round(hours))}h" + return f"{hours:.1f}h" + + days = value / 1440.0 + if math.isclose(days, round(days), abs_tol=1e-9): + return f"{int(round(days))}d" + return f"{days:.1f}d" + + +def summarize_binned_distribution( + gaps_minutes: pd.Series, + keep_nonpositive: bool, + bin_time_minutes: float | None = None, +) -> pd.DataFrame: + valid = filter_valid_gaps(gaps_minutes, keep_nonpositive) + + if valid.empty: + raise ValueError("No valid time gaps found after filtering.") + + if bin_time_minutes is not None: + edges = build_fixed_width_bin_edges_minutes(valid, bin_time_minutes) + open_tail_from = None + else: + base_edges = default_bin_edges_minutes() + edges = build_bin_edges_minutes(valid) + open_tail_from = base_edges[-1] if len(edges) > len(base_edges) else None + + labels = make_bin_labels(edges, open_tail_from=open_tail_from) + binned = pd.cut(valid, bins=edges, labels=labels, right=False, include_lowest=True) + + counts = binned.value_counts(sort=False) + probabilities = (counts / counts.sum()).astype(float) + + bin_left = pd.Series(edges[:-1], dtype=float) + bin_right = pd.Series(edges[1:], dtype=float) + bin_width = bin_right - bin_left + probabilities_np = probabilities.to_numpy(dtype=float) + density_per_min = probabilities_np / bin_width.to_numpy(dtype=float) + + summary = pd.DataFrame( + { + "bin": counts.index.astype(str), + "bin_left_min": bin_left.to_numpy(), + "bin_right_min": bin_right.to_numpy(), + "bin_width_min": bin_width.to_numpy(), + "count": counts.values, + "probability": probabilities_np, + "percentage": probabilities_np * 100.0, + "density_per_min": density_per_min, + } + ) + return summary + + +def filter_valid_gaps(gaps_minutes: pd.Series, keep_nonpositive: bool) -> pd.Series: + valid = gaps_minutes.dropna().copy() + if not keep_nonpositive: + valid = valid[valid > 0] + return valid + + +def cumulative_probability_at_minutes( + gaps_minutes: pd.Series, + threshold_minutes: float, + keep_nonpositive: bool, +) -> float: + valid = filter_valid_gaps(gaps_minutes, keep_nonpositive) + if valid.empty: + raise ValueError("No valid time gaps found after filtering.") + return float((valid <= threshold_minutes).mean()) + + +def select_student_by_index( + df: pd.DataFrame, + student_idx: int, +) -> tuple[pd.DataFrame, str, int]: + """Select one student's interactions by 0-based index over unique IDs.""" + student_ids = df["user_id"].drop_duplicates().tolist() + total_students = len(student_ids) + + if total_students == 0: + raise ValueError("No students found in loaded interactions.") + if student_idx < 0 or student_idx >= total_students: + raise ValueError( + f"--student-idx must be in [0, {total_students - 1}], got {student_idx}." + ) + + selected_student_id = str(student_ids[student_idx]) + selected_df = df[df["user_id"] == selected_student_id].copy() + return selected_df, selected_student_id, total_students + + +def append_student_id_to_output_path(path: Path, student_id: str) -> Path: + """Append a safe student-id suffix to output filename.""" + safe_id = "".join( + ch if ch.isalnum() or ch in ("-", "_") else "_" for ch in student_id + ) + return path.with_name(f"{path.stem}_{safe_id}{path.suffix}") + + +def plot_distribution( + summary_df: pd.DataFrame, + output_path: Path, + log_y: bool = False, + plot_upper_limit_minutes: float | None = None, + cdf_marker_minutes: float = CDF_MARKER_MINUTES, + cdf_at_marker: float | None = None, + student_idx: int | None = None, +) -> None: + """Create and save a publication-ready distribution histogram.""" + output_path.parent.mkdir(parents=True, exist_ok=True) + + plt.style.use("seaborn-v0_8-whitegrid") + + if student_idx is not None: + fig, ax = plt.subplots(figsize=(10, 5)) + else: + fig, ax = plt.subplots(figsize=(20, 5)) + + left = summary_df["bin_left_min"].to_numpy(dtype=float) + width = summary_df["bin_width_min"].to_numpy(dtype=float) + height = summary_df["density_per_min"].to_numpy(dtype=float) + + bars = ax.bar( + left, + height, + width=width, + align="edge", + color="#4C78A8", + # edgecolor="white", + # linewidth=1.0, + ) + + title = "Distribution of Time Gaps Between Consecutive Attempts" + if student_idx is not None: + title = f"{title} (student_idx={student_idx})" + ax.set_title(title) + ax.set_xlabel("Time Gap") + ax.set_ylabel("Probability Density (1/min)") + x_min = float(left.min()) + x_max = float((left + width).max()) + if plot_upper_limit_minutes is not None: + x_max = min(x_max, float(plot_upper_limit_minutes)) + ax.set_xlim(x_min, x_max) + ax.xaxis.set_major_locator(MaxNLocator(nbins=9)) + ax.xaxis.set_major_formatter(FuncFormatter(format_minutes_tick)) + ax.grid(axis="y", alpha=0.25, linewidth=0.8) + ax.spines["top"].set_visible(False) + ax.spines["right"].set_visible(False) + + if log_y: + ax.set_yscale("log") + + marker_label = f"CDF <= {int(cdf_marker_minutes)} min" + if cdf_at_marker is not None: + marker_label = f"{marker_label}: {cdf_at_marker * 100:.1f}%" + ax.axvline( + cdf_marker_minutes, + color="#E45756", + linestyle="--", + linewidth=1.6, + label=marker_label, + ) + ax.legend(loc="upper right", frameon=False, fontsize=9) + + # Label non-trivial bins for readability in papers. + for bar, pct in zip(bars, summary_df["percentage"]): + if pct < 1.0: + continue + height = bar.get_height() + if height <= 0: + continue + ax.annotate( + f"{pct:.1f}%", + xy=(bar.get_x() + bar.get_width() / 2.0, height), + xytext=(0, 3), + textcoords="offset points", + ha="center", + va="bottom", + fontsize=8, + ) + + plt.tight_layout() + fig.savefig(output_path, dpi=400, bbox_inches="tight") + plt.close(fig) + + +def main() -> None: + args = parse_args() + + if not args.interactions_path.exists(): + raise FileNotFoundError( + f"Interactions file not found: {args.interactions_path}" + ) + + df = load_interactions(args.interactions_path, max_rows=args.max_rows) + selected_student_id: str | None = None + total_students = int(df["user_id"].nunique()) + if args.student_idx is not None: + df, selected_student_id, total_students = select_student_by_index( + df, + args.student_idx, + ) + + output_plot_path = args.output_plot + output_counts_path = args.output_counts + if selected_student_id is not None: + output_plot_path = append_student_id_to_output_path( + output_plot_path, + selected_student_id, + ) + output_counts_path = append_student_id_to_output_path( + output_counts_path, + selected_student_id, + ) + + gaps_minutes = compute_time_gaps_minutes(df) + + if args.plot_upper_limit_minutes is not None and args.plot_upper_limit_minutes <= 0: + raise ValueError("--plot-upper-limit-minutes must be a positive number.") + if args.bin_time is not None and args.bin_time <= 0: + raise ValueError("--bin-time must be a positive number.") + + summary = summarize_binned_distribution( + gaps_minutes, + keep_nonpositive=args.keep_nonpositive_gaps, + bin_time_minutes=args.bin_time, + ) + output_counts_path.parent.mkdir(parents=True, exist_ok=True) + summary.to_csv(output_counts_path, index=False) + + cdf_at_marker = cumulative_probability_at_minutes( + gaps_minutes=gaps_minutes, + threshold_minutes=CDF_MARKER_MINUTES, + keep_nonpositive=args.keep_nonpositive_gaps, + ) + + plot_distribution( + summary, + output_plot_path, + log_y=args.log_y, + plot_upper_limit_minutes=args.plot_upper_limit_minutes, + cdf_marker_minutes=CDF_MARKER_MINUTES, + cdf_at_marker=cdf_at_marker, + student_idx=args.student_idx, + ) + + total_pairs = int(summary["count"].sum()) + print("Done.") + print(f"Interactions loaded: {len(df):,}") + print(f"Students in loaded data: {total_students:,}") + if selected_student_id is not None: + print(f"Selected student idx: {args.student_idx}") + print(f"Selected student id: {selected_student_id}") + print(f"Consecutive attempt pairs used: {total_pairs:,}") + if args.bin_time is not None: + print(f"Bin width (min): {args.bin_time}") + print( + f"Cumulative P(gap <= {int(CDF_MARKER_MINUTES)} min): " + f"{cdf_at_marker * 100:.2f}%" + ) + print(f"Saved plot: {output_plot_path}") + print(f"Saved bin counts: {output_counts_path}") + + +if __name__ == "__main__": + main() diff --git a/Code/plot_totaltime_distribution.py b/Code/plot_totaltime_distribution.py new file mode 100644 index 0000000000000000000000000000000000000000..f2de0f0e7c37ca4c50a1bd180925887844f968e2 --- /dev/null +++ b/Code/plot_totaltime_distribution.py @@ -0,0 +1,433 @@ +#!/usr/bin/env python3 +"""Plot distribution of per-student total time from first to last attempt. + +This script reads FoundationalASSIST `Interactions.csv`, groups interactions by +student (`user_id`), computes each student's total time span from first to last +recorded attempt (`end_time`), discretizes these totals into bins, and plots +the resulting distribution. +""" + +from __future__ import annotations + +import argparse +import math +from pathlib import Path + +import matplotlib.pyplot as plt +import pandas as pd +from matplotlib.ticker import FuncFormatter, MaxNLocator + + +DEFAULT_INTERACTIONS_PATH = ( + Path(__file__).resolve().parent.parent / "Data" / "Interactions.csv" +) +DEFAULT_OUTPUT_PLOT = ( + Path(__file__).resolve().parent.parent / "Results" / "total_time_distribution.png" +) +DEFAULT_OUTPUT_COUNTS = ( + Path(__file__).resolve().parent.parent + / "Results" + / "total_time_distribution_counts.csv" +) +DEFAULT_CDF_MARKER_MINUTES = 1051200.0 + + +def parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser( + description=( + "Compute per-student total time (first to last attempt) from " + "Interactions.csv and plot the binned distribution." + ) + ) + parser.add_argument( + "--interactions-path", + type=Path, + default=DEFAULT_INTERACTIONS_PATH, + help="Path to Interactions.csv.", + ) + parser.add_argument( + "--output-plot", + type=Path, + default=DEFAULT_OUTPUT_PLOT, + help="Path to save the output figure.", + ) + parser.add_argument( + "--output-counts", + type=Path, + default=DEFAULT_OUTPUT_COUNTS, + help="Path to save bin counts as CSV.", + ) + parser.add_argument( + "--max-rows", + type=int, + default=None, + help="Optional cap on rows after sorting (for quick debugging).", + ) + parser.add_argument( + "--keep-nonpositive-total-times", + action="store_true", + help=( + "Keep zero/negative total times. By default, only strictly " + "positive total times are used." + ), + ) + parser.add_argument( + "--log-y", + action="store_true", + help="Use log scale on y-axis.", + ) + parser.add_argument( + "--plot-upper-limit-minutes", + type=float, + default=None, + help=( + "Optional upper limit for x-axis in minutes. " + "If omitted, uses the full range implied by bins." + ), + ) + parser.add_argument( + "--bin-time", + type=float, + default=None, + help=( + "Optional fixed bin width in minutes. " + "For example, --bin-time 60 creates hourly bins." + ), + ) + parser.add_argument( + "--cdf-marker-minutes", + type=float, + default=DEFAULT_CDF_MARKER_MINUTES, + help="Threshold (in minutes) for plotting cumulative probability marker.", + ) + return parser.parse_args() + + +def load_interactions(path: Path, max_rows: int | None = None) -> pd.DataFrame: + """Load minimum interaction fields required for timing analysis.""" + usecols = ["id", "user_id", "end_time"] + df = pd.read_csv(path, usecols=usecols, low_memory=False) + + df["id"] = pd.to_numeric(df["id"], errors="coerce") + df["id"] = df["id"].fillna(-1).astype(int) + df["user_id"] = df["user_id"].astype("string") + df["end_time"] = pd.to_datetime(df["end_time"], errors="coerce", utc=True) + + df = df.dropna(subset=["user_id", "end_time"]).copy() + df = df.sort_values(["user_id", "end_time", "id"], kind="mergesort") + + if max_rows is not None: + if max_rows <= 0: + raise ValueError("--max-rows must be a positive integer.") + df = df.head(max_rows).copy() + + return df + + +def compute_student_total_times_minutes(df: pd.DataFrame) -> pd.Series: + """Compute per-student total time span from first to last attempt.""" + grouped = df.groupby("user_id", sort=False)["end_time"] + first_times = grouped.min() + last_times = grouped.max() + total_minutes = (last_times - first_times).dt.total_seconds() / 60.0 + total_minutes.name = "total_time_minutes" + return total_minutes + + +def default_bin_edges_minutes() -> list[float]: + """Base edges for total-time distribution in minutes.""" + return [ + 0.0, + 10.0, + 30.0, + 60.0, + 180.0, + 360.0, + 720.0, + 1440.0, + 2880.0, + 4320.0, + 10080.0, + 20160.0, + 43200.0, + 100800.0, + ] + + +def build_bin_edges_minutes(valid: pd.Series) -> list[float]: + """Build finite plotting edges for proportional-width histogram bars.""" + edges = default_bin_edges_minutes() + base_tail_start = edges[-1] + max_total = float(valid.max()) + + if max_total > base_tail_start: + tail_edge = max(base_tail_start + 60.0, max_total * 1.05) + edges.append(tail_edge) + + return edges + + +def build_fixed_width_bin_edges_minutes( + valid: pd.Series, bin_time_minutes: float +) -> list[float]: + """Build fixed-width edges from min/max observed total times.""" + min_total = float(valid.min()) + max_total = float(valid.max()) + + start = bin_time_minutes * math.floor(min_total / bin_time_minutes) + end = bin_time_minutes * math.ceil(max_total / bin_time_minutes) + + if math.isclose(start, 0.0, abs_tol=1e-12): + start = 0.0 + if math.isclose(end, start, abs_tol=1e-12): + end = start + bin_time_minutes + + n_bins = int(round((end - start) / bin_time_minutes)) + edges = [start + i * bin_time_minutes for i in range(n_bins + 1)] + if edges[-1] <= max_total: + edges.append(edges[-1] + bin_time_minutes) + + return edges + + +def format_bin_bound(minutes: float) -> str: + if math.isclose(minutes, round(minutes), abs_tol=1e-9): + return str(int(round(minutes))) + return f"{minutes:.2f}".rstrip("0").rstrip(".") + + +def make_bin_labels( + edges: list[float], open_tail_from: float | None = None +) -> list[str]: + labels: list[str] = [] + last_idx = len(edges) - 2 + for idx, (left, right) in enumerate(zip(edges[:-1], edges[1:])): + if open_tail_from is not None and idx == last_idx and left >= open_tail_from: + labels.append(f">= {format_bin_bound(left)} min") + else: + labels.append(f"[{format_bin_bound(left)}, {format_bin_bound(right)}) min") + return labels + + +def format_minutes_tick(value: float, _pos: float) -> str: + if value < 60: + return f"{value:.0f}m" + if value < 1440: + return f"{value / 60:.0f}h" + return f"{value / 1440:.0f}d" + + +def filter_valid_total_times( + total_times_minutes: pd.Series, keep_nonpositive: bool +) -> pd.Series: + valid = total_times_minutes.dropna().copy() + if not keep_nonpositive: + valid = valid[valid > 0] + return valid + + +def summarize_binned_distribution( + total_times_minutes: pd.Series, + keep_nonpositive: bool, + bin_time_minutes: float | None = None, +) -> pd.DataFrame: + valid = filter_valid_total_times(total_times_minutes, keep_nonpositive) + + if valid.empty: + raise ValueError("No valid total times found after filtering.") + + if bin_time_minutes is not None: + edges = build_fixed_width_bin_edges_minutes(valid, bin_time_minutes) + open_tail_from = None + else: + base_edges = default_bin_edges_minutes() + edges = build_bin_edges_minutes(valid) + open_tail_from = base_edges[-1] if len(edges) > len(base_edges) else None + + labels = make_bin_labels(edges, open_tail_from=open_tail_from) + binned = pd.cut(valid, bins=edges, labels=labels, right=False, include_lowest=True) + + counts = binned.value_counts(sort=False) + probabilities = (counts / counts.sum()).astype(float) + + bin_left = pd.Series(edges[:-1], dtype=float) + bin_right = pd.Series(edges[1:], dtype=float) + bin_width = bin_right - bin_left + probabilities_np = probabilities.to_numpy(dtype=float) + density_per_min = probabilities_np / bin_width.to_numpy(dtype=float) + + summary = pd.DataFrame( + { + "bin": counts.index.astype(str), + "bin_left_min": bin_left.to_numpy(), + "bin_right_min": bin_right.to_numpy(), + "bin_width_min": bin_width.to_numpy(), + "count": counts.values, + "probability": probabilities_np, + "percentage": probabilities_np * 100.0, + "density_per_min": density_per_min, + } + ) + return summary + + +def cumulative_probability_at_minutes( + total_times_minutes: pd.Series, + threshold_minutes: float, + keep_nonpositive: bool, +) -> float: + valid = filter_valid_total_times(total_times_minutes, keep_nonpositive) + if valid.empty: + raise ValueError("No valid total times found after filtering.") + return float((valid <= threshold_minutes).mean()) + + +def plot_distribution( + summary_df: pd.DataFrame, + output_path: Path, + log_y: bool = False, + plot_upper_limit_minutes: float | None = None, + cdf_marker_minutes: float = DEFAULT_CDF_MARKER_MINUTES, + cdf_at_marker: float | None = None, +) -> None: + """Create and save a publication-ready total-time distribution histogram.""" + output_path.parent.mkdir(parents=True, exist_ok=True) + + plt.style.use("seaborn-v0_8-whitegrid") + + fig, ax = plt.subplots(figsize=(20, 5)) + + left = summary_df["bin_left_min"].to_numpy(dtype=float) + width = summary_df["bin_width_min"].to_numpy(dtype=float) + height = summary_df["density_per_min"].to_numpy(dtype=float) + + bars = ax.bar( + left, + height, + width=width, + align="edge", + color="#4C78A8", + # edgecolor="white", + # linewidth=1.0, + ) + + ax.set_title("Distribution of Student Total Time (First to Last Attempt)") + ax.set_xlabel("Total Time Per Student") + ax.set_ylabel("Probability Density (1/min)") + + x_min = float(left.min()) + x_max = float((left + width).max()) + if plot_upper_limit_minutes is not None: + x_max = min(x_max, float(plot_upper_limit_minutes)) + ax.set_xlim(x_min, x_max) + + ax.xaxis.set_major_locator(MaxNLocator(nbins=9)) + ax.xaxis.set_major_formatter(FuncFormatter(format_minutes_tick)) + ax.grid(axis="y", alpha=0.25, linewidth=0.8) + ax.spines["top"].set_visible(False) + ax.spines["right"].set_visible(False) + + if log_y: + ax.set_yscale("log") + + marker_label = f"CDF <= {format_bin_bound(cdf_marker_minutes)} min" + if cdf_at_marker is not None: + marker_label = f"{marker_label}: {cdf_at_marker * 100:.1f}%" + ax.axvline( + cdf_marker_minutes, + color="#E45756", + linestyle="--", + linewidth=1.6, + label=marker_label, + ) + ax.legend(loc="upper right", frameon=False, fontsize=9) + + # Skip dense labeling when there are many bins to keep figure readable. + annotate_bars = len(summary_df) <= 40 + if annotate_bars: + for bar, pct in zip(bars, summary_df["percentage"]): + if pct < 1.0: + continue + h = bar.get_height() + if h <= 0: + continue + ax.annotate( + f"{pct:.1f}%", + xy=(bar.get_x() + bar.get_width() / 2.0, h), + xytext=(0, 3), + textcoords="offset points", + ha="center", + va="bottom", + fontsize=8, + ) + + plt.tight_layout() + fig.savefig(output_path, dpi=400, bbox_inches="tight") + plt.close(fig) + + +def main() -> None: + args = parse_args() + + if not args.interactions_path.exists(): + raise FileNotFoundError( + f"Interactions file not found: {args.interactions_path}" + ) + + if args.plot_upper_limit_minutes is not None and args.plot_upper_limit_minutes <= 0: + raise ValueError("--plot-upper-limit-minutes must be a positive number.") + if args.bin_time is not None and args.bin_time <= 0: + raise ValueError("--bin-time must be a positive number.") + if args.cdf_marker_minutes <= 0: + raise ValueError("--cdf-marker-minutes must be a positive number.") + + df = load_interactions(args.interactions_path, max_rows=args.max_rows) + total_times_minutes = compute_student_total_times_minutes(df) + + summary = summarize_binned_distribution( + total_times_minutes, + keep_nonpositive=args.keep_nonpositive_total_times, + bin_time_minutes=args.bin_time, + ) + summary.to_csv(args.output_counts, index=False) + + cdf_at_marker = cumulative_probability_at_minutes( + total_times_minutes=total_times_minutes, + threshold_minutes=args.cdf_marker_minutes, + keep_nonpositive=args.keep_nonpositive_total_times, + ) + + plot_distribution( + summary, + args.output_plot, + log_y=args.log_y, + plot_upper_limit_minutes=args.plot_upper_limit_minutes, + cdf_marker_minutes=args.cdf_marker_minutes, + cdf_at_marker=cdf_at_marker, + ) + + total_students = int(df["user_id"].nunique()) + students_used = int( + len( + filter_valid_total_times( + total_times_minutes, + keep_nonpositive=args.keep_nonpositive_total_times, + ) + ) + ) + print("Done.") + print(f"Interactions loaded: {len(df):,}") + print(f"Students observed: {total_students:,}") + print(f"Students used in distribution: {students_used:,}") + if args.bin_time is not None: + print(f"Bin width (min): {args.bin_time}") + print( + f"Cumulative P(total_time <= {format_bin_bound(args.cdf_marker_minutes)} min): " + f"{cdf_at_marker * 100:.2f}%" + ) + print(f"Saved plot: {args.output_plot}") + print(f"Saved bin counts: {args.output_counts}") + + +if __name__ == "__main__": + main() diff --git a/Code/process_to_single_file.py b/Code/process_to_single_file.py new file mode 100644 index 0000000000000000000000000000000000000000..fe283cc9876412514a71d3fdcf40bb4da6e411d8 --- /dev/null +++ b/Code/process_to_single_file.py @@ -0,0 +1,820 @@ +#!/usr/bin/env python3 +""" +Convert FoundationalASSIST CSV files to the CSEDM/OEKT JSON format. + +Inputs (under Data/ by default): + - Interactions.csv + - Problems.csv + - Skill_Set.csv + - Skills.csv + +Outputs (under src/data/FoundationalASSIST/ by default): + - dataset.json + - qmatrix.json + - trainset.json + - validset.json + - testset.json + +The produced dataset JSON follows the same schema used by src/data/CSEDM. +""" + +from __future__ import annotations + +import argparse +import json +import random +import re +from pathlib import Path +from typing import Literal, cast + +import pandas as pd +from tqdm import tqdm +from clean_utils import clean_problem_body + +PROJECT_ROOT = Path(__file__).resolve().parents[3] +DEFAULT_DATA_DIR = Path(__file__).resolve().parent.parent / "Data" +DEFAULT_OUTPUT_DIR = PROJECT_ROOT / "src" / "data" / "FoundationalASSIST" +GroupingMode = Literal["none", "1h", "halfday", "day", "week", "month", "year"] + + +def parse_grouping_mode(value: str) -> GroupingMode: + """Normalize grouping mode aliases used by --grouping-time.""" + normalized = value.strip().lower() + aliases: dict[str, GroupingMode] = { + "0": "none", + "0.0": "none", + "none": "none", + "off": "none", + "no": "none", + "1h": "1h", + "hour": "1h", + "halfday": "halfday", + "half-day": "halfday", + "day": "day", + "week": "week", + "month": "month", + "year": "year", + } + mode = aliases.get(normalized) + if mode is None: + valid_values = "1h, halfday, day, week, month, year, none" + raise argparse.ArgumentTypeError( + f"Invalid grouping mode '{value}'. Valid values: {valid_values}." + ) + return mode + + +def parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser( + description="Convert FoundationalASSIST to CSEDM/OEKT JSON format." + ) + parser.add_argument( + "--data-dir", + type=Path, + default=DEFAULT_DATA_DIR, + help="Directory containing Interactions.csv, Problems.csv, Skills.csv.", + ) + parser.add_argument( + "--output-dir", + type=Path, + default=DEFAULT_OUTPUT_DIR, + help="Directory to write dataset.json/qmatrix.json/split files.", + ) + parser.add_argument( + "--seed", + type=int, + default=42, + help="Random seed used for train/valid/test student split.", + ) + parser.add_argument( + "--train-ratio", + type=float, + default=0.8, + help="Fraction of students in train split.", + ) + parser.add_argument( + "--valid-ratio", + type=float, + default=0.1, + help="Fraction of students in valid split.", + ) + parser.add_argument( + "--test-ratio", + type=float, + default=0.1, + help="Fraction of students in test split.", + ) + parser.add_argument( + "--max-interactions", + type=int, + default=None, + help=( + "Optional cap on number of interaction rows after sorting. " + "Useful for quick smoke tests." + ), + ) + parser.add_argument( + "--grouping-time", + type=parse_grouping_mode, + default="none", + help=( + "Calendar grouping mode per student: 1h, halfday, day, week, " + "month, year, or none." + ), + ) + return parser.parse_args() + + +def _text(v: object) -> str: + if v is None: + return "" + if v is pd.NA: + return "" + if isinstance(v, float) and pd.isna(v): + return "" + return str(v) + + +def _as_int(v: object) -> int: + return int(float(_text(v))) + + +def _as_float(v: object) -> float: + return float(_text(v)) + + +def label_answer_options(answer_string: object) -> dict[str, str] | None: + """Convert pipe-delimited answers to lettered format.""" + answer_text = _text(answer_string).strip() + if not answer_text: + return None + + options = [opt.strip() for opt in answer_text.split("||")] + letters = ["A", "B", "C", "D", "E", "F", "G", "H", "I", "J"] + return {letters[i]: opt for i, opt in enumerate(options) if i < len(letters)} + + +def clean_html_and_normalize(text: object) -> str: + """Remove HTML tags and normalize text for reliable comparisons.""" + normalized = _text(text) + if not normalized: + return "" + + normalized = re.sub(r"<[^>]+>", "", normalized) + normalized = " ".join(normalized.split()) + normalized = re.sub(r"\s*:\s*", ":", normalized) + return normalized.strip() + + +def match_student_answer_to_letters( + student_answer_text: object, + answer_options_dict: dict[str, str] | None, +) -> str: + """Map student multiple-choice answer text(s) to letter labels.""" + answer_text = _text(student_answer_text) + if not answer_text or not answer_options_dict: + return answer_text + + student_answers = [ans.strip() for ans in answer_text.split(" , ")] + normalized_options = { + letter: clean_html_and_normalize(text) + for letter, text in answer_options_dict.items() + } + + matched_letters: list[str] = [] + for student_ans in student_answers: + normalized_student = clean_html_and_normalize(student_ans) + + for letter, normalized_option in normalized_options.items(): + if normalized_student == normalized_option: + matched_letters.append(letter) + break + else: + for letter, normalized_option in normalized_options.items(): + if ( + normalized_student in normalized_option + or normalized_option in normalized_student + ): + matched_letters.append(letter) + break + + if matched_letters: + return ", ".join(sorted(set(matched_letters))) + return answer_text + + +def get_correct_option_letters( + answer_options: dict[str, str] | None, + correct_answers: object, +) -> str: + """Resolve the correct answer text(s) to option letters for MC items.""" + correct_answer_text = _text(correct_answers).strip() + if not answer_options or not correct_answer_text: + return correct_answer_text + + correct_list = [ans.strip() for ans in correct_answer_text.split("||")] + correct_letters = [ + letter for letter, text in answer_options.items() if text in correct_list + ] + return ( + ", ".join(sorted(correct_letters)) if correct_letters else correct_answer_text + ) + + +def format_answer_options_for_prompt(answer_options: dict[str, str] | None) -> str: + """Format answer options dictionary for human-readable prompt text.""" + if not answer_options: + return "" + return "\n".join([f"{letter}) {text}" for letter, text in answer_options.items()]) + + +def load_and_preprocess_problems(problems_path: Path) -> pd.DataFrame: + """Load and preprocess problems with the same answer handling as KT inference.""" + problems_df = pd.read_csv(problems_path, low_memory=False) + problems_df["problem_id"] = pd.to_numeric( + problems_df["problem_id"], errors="coerce" + ) + problems_df = problems_df.dropna(subset=["problem_id"]).copy() + problems_df["problem_id"] = problems_df["problem_id"].astype(int) + + problems_df = problems_df.sort_values(["problem_id"]).drop_duplicates( + subset=["problem_id"], keep="first" + ) + + problems_df["cleaned body"] = problems_df["Problem Body"].apply(clean_problem_body) + problems_df["answer_options"] = problems_df["Multiple Choice Options"].apply( + label_answer_options + ) + + mc_types = {"Multiple Choice (select 1)", "Multiple Choice (select all)"} + problems_df["correct_answers"] = problems_df.apply( + lambda row: ( + get_correct_option_letters( + row["answer_options"], + row["Multiple Choice Answers"], + ) + if _text(row["Problem Type"]).strip() in mc_types + else _text(row.get("Fill-in Answers", "")) + ), + axis=1, + ) + problems_df["answer_options_formatted"] = problems_df["answer_options"].apply( + format_answer_options_for_prompt + ) + return problems_df + + +def load_skill_tables( + skills_path: Path, + skill_set_path: Path, +) -> tuple[list[dict], dict[int, list[int]], int]: + """Load skills and build a problem_id -> skill_ids mapping. + + Returns: + skills: OEKT skill list. + problem_to_skills: Mapping from original problem_id to contiguous skill IDs. + fallback_skill_id: Skill ID for untagged problems. + """ + usecols = ["problem_id", "node_code", "node_name"] + skills_df = pd.read_csv(skills_path, usecols=usecols, low_memory=False) + + skills_df["problem_id"] = pd.to_numeric(skills_df["problem_id"], errors="coerce") + skills_df = skills_df.dropna(subset=["problem_id"]).copy() + skills_df["problem_id"] = skills_df["problem_id"].astype(int) + skills_df["node_code"] = skills_df["node_code"].apply(lambda v: _text(v).strip()) + skills_df["node_name"] = skills_df["node_name"].apply(lambda v: _text(v).strip()) + skills_df = skills_df[skills_df["node_code"] != ""].copy() + + skill_set_df = pd.read_csv( + skill_set_path, + usecols=["index", "skill_code", "full_description"], + low_memory=False, + ) + skill_set_df["index"] = pd.to_numeric(skill_set_df["index"], errors="coerce") + skill_set_df = skill_set_df.dropna(subset=["index"]).copy() + skill_set_df["index"] = skill_set_df["index"].astype(int) + skill_set_df["skill_code"] = skill_set_df["skill_code"].apply( + lambda v: _text(v).strip() + ) + skill_set_df["full_description"] = skill_set_df["full_description"].apply( + lambda v: _text(v).strip() + ) + skill_set_df = skill_set_df[skill_set_df["skill_code"] != ""].copy() + skill_set_df = ( + skill_set_df.sort_values(["index", "skill_code"]) + .drop_duplicates(subset=["skill_code"], keep="first") + .copy() + ) + + node_name_by_code = ( + skills_df.sort_values(["node_code", "node_name"]) + .drop_duplicates(subset=["node_code"], keep="first") + .set_index("node_code")["node_name"] + .to_dict() + ) + + skill_rows: list[tuple[str, int, str, str]] = [] + skill_id_map: dict[str, int] = {} + for row in skill_set_df.itertuples(index=False): + node_code = _text(row.skill_code).strip() + skill_id = _as_int(row.index) - 1 + skill_id_map[node_code] = skill_id + + node_name = _text(node_name_by_code.get(node_code, "")).strip() + name = node_name if node_name else node_code + description = _text(row.full_description).strip() + if not description: + print( + f"Warning: Missing description for skill '{node_code}' in Skill_Set.csv. " + f"Using default description." + ) + + description = ( + f"Common Core State StandardS for Mathematics: Skill {node_code}" + ) + + skill_rows.append((node_code, skill_id, name, description)) + + # max_skill_id = max(skill_id_map.values(), default=-1) + missing_node_codes = sorted( + set(skills_df["node_code"].tolist()) - set(skill_id_map) + ) + # for node_code in missing_node_codes: + # max_skill_id += 1 + # skill_id_map[node_code] = max_skill_id + + # node_name = _text(node_name_by_code.get(node_code, "")).strip() + # name = node_name if node_name else node_code + # description = ( + # node_name + # if node_name + # else f"Common Core State StandardS for Mathematics: Skill {node_code}" + # ) + + # skill_rows.append((node_code, max_skill_id, name, description)) + + if missing_node_codes: + raise ValueError( + f"Error: Found {len(missing_node_codes)} node_code(s) in Skills.csv that are missing from Skill_Set.csv. " + f"Please ensure all node_code values in Skills.csv have a corresponding skill_code in Skill_Set.csv. " + f"Missing node_codes: {missing_node_codes}" + ) + + skills: list[dict] = [] + for _, skill_id, name, description in sorted(skill_rows, key=lambda r: r[0]): + skills.append( + { + "id": skill_id, + "name": name, + "description": description, + "prerequisites": [], + } + ) + + fallback_skill_id = max([s["id"] for s in skills], default=-1) + 1 + skills.append( + { + "id": fallback_skill_id, + "name": "UnmappedSkill", + "description": "Fallback skill for questions without explicit skill tags.", + "prerequisites": [], + } + ) + + problem_to_skills: dict[int, list[int]] = {} + pairs = skills_df[["problem_id", "node_code"]].drop_duplicates() + for row in pairs.itertuples(index=False): + pid = _as_int(row.problem_id) + sid = skill_id_map[_text(row.node_code).strip()] + problem_to_skills.setdefault(pid, []).append(sid) + + for pid, sids in problem_to_skills.items(): + if len(sids) == 0: + print(f"Warning: Problem {pid} has no valid skill mappings.") + problem_to_skills[pid] = sorted(set(sids)) + + return skills, problem_to_skills, fallback_skill_id + + +def build_question_content(problem_row: pd.Series) -> tuple[str, str]: + """Create question content and canonical correct answer from preprocessed fields.""" + body = _text(problem_row.get("cleaned body", "")).strip() + problem_type = _text(problem_row.get("Problem Type", "")).strip() + answer_options_formatted = _text( + problem_row.get("answer_options_formatted", "") + ).strip() + correct_answer = _text(problem_row.get("correct_answers", "")).strip() + + body_parts: list[str] = [] + if body: + body_parts.append(body) + if problem_type: + body_parts.append(f"Problem Type: {problem_type}") + if answer_options_formatted: + body_parts.append(f"Answer Options:\n{answer_options_formatted}") + + if not body_parts: + problem_id = problem_row.get("problem_id", "unknown") + return f"Problem {problem_id}", correct_answer + + return "\n\n".join(body_parts), correct_answer + + +def load_questions( + problems_df: pd.DataFrame, + problem_to_skills: dict[int, list[int]], + fallback_skill_id: int, +) -> tuple[list[dict], dict[int, str], int]: + """Build OEKT question objects from preprocessed Problems data.""" + + questions: list[dict] = [] + problem_to_qid: dict[int, str] = {} + unmapped_questions = 0 + + for row in problems_df.to_dict(orient="records"): + pid = _as_int(row["problem_id"]) + qid = f"q_{pid}" + skill_ids = problem_to_skills.get(pid, []) + if not skill_ids: + skill_ids = [fallback_skill_id] + unmapped_questions += 1 + content, correct_answer = build_question_content(pd.Series(row)) + question = { + "id": qid, + "content": content, + "skill_ids": skill_ids, + "rubrics": [ + { + "id": f"r_{pid}_0", + "description": (f"Match the correct answer: {correct_answer}"), + "skill_ids": skill_ids, + } + ], + } + + questions.append(question) + problem_to_qid[pid] = qid + + return questions, problem_to_qid, unmapped_questions + + +def load_interactions( + interactions_path: Path, + problem_meta_df: pd.DataFrame, + max_interactions: int | None = None, +) -> pd.DataFrame: + """Load and normalize interaction logs used to build student trajectories.""" + usecols = [ + "id", + "problem_id", + "answer_text", + "discrete_score", + "end_time", + "user_id", + ] + df = pd.read_csv(interactions_path, usecols=usecols, low_memory=False) + + df["problem_id"] = pd.to_numeric(df["problem_id"], errors="coerce") + df["discrete_score"] = pd.to_numeric(df["discrete_score"], errors="coerce") + df["id"] = pd.to_numeric(df["id"], errors="coerce") + df["end_time"] = pd.to_datetime(df["end_time"], errors="coerce", utc=True) + + df = df.dropna(subset=["user_id", "problem_id", "discrete_score"]).copy() + df["user_id"] = df["user_id"].astype(str) + df["problem_id"] = df["problem_id"].astype(int) + df["id"] = df["id"].fillna(-1).astype(int) + + answer_meta = problem_meta_df[ + ["problem_id", "Problem Type", "answer_options"] + ].copy() + df = df.merge(answer_meta, on="problem_id", how="left") + + mc_types = {"Multiple Choice (select 1)", "Multiple Choice (select all)"} + df["answer_text"] = df.apply( + lambda row: ( + match_student_answer_to_letters(row["answer_text"], row["answer_options"]) + if _text(row.get("Problem Type", "")).strip() in mc_types + and isinstance(row.get("answer_options"), dict) + else _text(row["answer_text"]) + ), + axis=1, + ) + + df = df.drop(columns=["Problem Type", "answer_options"]) + + df = df.sort_values(["user_id", "end_time", "id"], kind="mergesort") + if max_interactions is not None: + if max_interactions <= 0: + raise ValueError("--max-interactions must be a positive integer.") + df = df.head(max_interactions).copy() + return df + + +def build_qmatrix(questions: list[dict], num_skills: int) -> list[list[float]]: + """Build a rubric x skill matrix consistent with question/rubric ordering.""" + qmatrix: list[list[float]] = [] + for question in questions: + for rubric in question["rubrics"]: + row = [0.0] * num_skills + for sid in rubric["skill_ids"]: + row[int(sid)] = 1.0 + qmatrix.append(row) + return qmatrix + + +def split_student_ids( + student_ids: list[str], + train_ratio: float, + valid_ratio: float, + test_ratio: float, + seed: int, +) -> tuple[list[str], list[str], list[str]]: + """Create deterministic train/valid/test split lists at the student level.""" + if train_ratio < 0 or valid_ratio < 0 or test_ratio < 0: + raise ValueError("Split ratios must be non-negative.") + + total = train_ratio + valid_ratio + test_ratio + if total <= 0: + raise ValueError("At least one split ratio must be > 0.") + + ids = list(student_ids) + ids.sort() + rng = random.Random(seed) + rng.shuffle(ids) + + train_count = int(len(ids) * (train_ratio / total)) + valid_count = int(len(ids) * (valid_ratio / total)) + + train_ids = ids[:train_count] + valid_ids = ids[train_count : train_count + valid_count] + test_ids = ids[train_count + valid_count :] + return train_ids, valid_ids, test_ids + + +def get_calendar_group_key( + end_time: pd.Timestamp | None, + grouping_mode: GroupingMode, + missing_idx: int, +) -> tuple[object, ...]: + """Return a stable calendar bucket key for an interaction timestamp.""" + if end_time is None: + return ("missing", missing_idx) + + ts = end_time + if ts.tzinfo is None: + ts = ts.tz_localize("UTC") + else: + ts = ts.tz_convert("UTC") + + if grouping_mode == "1h": + return ("1h", ts.year, ts.month, ts.day, ts.hour) + if grouping_mode == "halfday": + return ("halfday", ts.year, ts.month, ts.day, 0 if ts.hour < 12 else 1) + if grouping_mode == "day": + return ("day", ts.year, ts.month, ts.day) + if grouping_mode == "week": + iso = ts.isocalendar() + return ("week", int(iso.year), int(iso.week)) + if grouping_mode == "month": + return ("month", ts.year, ts.month) + if grouping_mode == "year": + return ("year", ts.year) + + raise ValueError(f"Unsupported grouping mode: {grouping_mode}") + + +def write_dataset_json( + dataset_path: Path, + skills: list[dict], + questions: list[dict], + interactions_df: pd.DataFrame, + problem_to_qid: dict[int, str], + grouping_mode: GroupingMode = "none", + save_unmapped_skills: bool = False, +) -> tuple[list[str], int, int, int, int]: + """Stream-write dataset.json while optionally grouping by calendar buckets.""" + dataset_path.parent.mkdir(parents=True, exist_ok=True) + + student_ids: list[str] = [] + num_students = 0 + num_time_steps = 0 + num_questions = 0 + skipped_interactions = 0 + + with open(dataset_path, "w", encoding="utf-8") as f: + f.write("{") + f.write('"skills":') + if not save_unmapped_skills: + saving_skills = ( + skills[:-1] + if skills and skills[-1]["name"] == "UnmappedSkill" + else skills + ) + else: + saving_skills = skills + json.dump(saving_skills, f, ensure_ascii=False) + f.write(',"questions":') + json.dump(questions, f, ensure_ascii=False) + f.write(',"students":[') + + first_student = True + for user_id, student_df in tqdm(interactions_df.groupby("user_id", sort=False)): + time_steps: list[dict] = [] + current_group_key: tuple[object, ...] | None = None + + for row_idx, row in enumerate(student_df.itertuples(index=False)): + pid = _as_int(row.problem_id) + qid = problem_to_qid.get(pid) + if qid is None: + skipped_interactions += 1 + continue + + score = 1 if _as_float(row.discrete_score) >= 1.0 else 0 + answer_text = _text(row.answer_text) + response = { + "question_id": qid, + "answer_text": answer_text, + "rubric_scores": [score], + } + num_questions += 1 + + if grouping_mode == "none": + time_steps.append( + { + "t": len(time_steps), + "responses": [response], + } + ) + continue + + row_end_time_raw = row.end_time + row_end_time: pd.Timestamp | None = ( + None + if pd.isna(row_end_time_raw) + else cast(pd.Timestamp, row_end_time_raw) + ) + + group_key = get_calendar_group_key( + end_time=row_end_time, + grouping_mode=grouping_mode, + missing_idx=row_idx, + ) + if time_steps and current_group_key == group_key: + time_steps[-1]["responses"].append(response) + continue + + time_steps.append( + { + "t": len(time_steps), + "responses": [response], + } + ) + current_group_key = group_key + + if not time_steps: + continue + + student_obj = { + "student_id": user_id, + "time_steps": time_steps, + } + + if not first_student: + f.write(",") + json.dump(student_obj, f, ensure_ascii=False) + first_student = False + + student_ids.append(str(user_id)) + num_students += 1 + num_time_steps += len(time_steps) + + f.write("]}") + + return ( + student_ids, + num_students, + num_time_steps, + num_questions, + skipped_interactions, + ) + + +def save_json(path: Path, obj: object) -> None: + path.parent.mkdir(parents=True, exist_ok=True) + with open(path, "w", encoding="utf-8") as f: + json.dump(obj, f, indent=2, ensure_ascii=False) + + +def main() -> None: + args = parse_args() + + data_dir = args.data_dir + output_dir = args.output_dir + + interactions_path = data_dir / "Interactions.csv" + problems_path = data_dir / "Problems.csv" + skill_set_path = data_dir / "Skill_Set.csv" + skills_path = data_dir / "Skills.csv" + + for p in [interactions_path, problems_path, skill_set_path, skills_path]: + if not p.exists(): + raise FileNotFoundError(f"Required input file not found: {p}") + + print("Loading skills...") + skills, problem_to_skills, fallback_skill_id = load_skill_tables( + skills_path=skills_path, + skill_set_path=skill_set_path, + ) + + print("Loading and preprocessing problems...") + problems_df = load_and_preprocess_problems(problems_path) + + print("Loading questions...") + questions, problem_to_qid, unmapped_questions = load_questions( + problems_df=problems_df, + problem_to_skills=problem_to_skills, + fallback_skill_id=fallback_skill_id, + ) + + print("Loading interactions...") + interactions_df = load_interactions( + interactions_path, + problem_meta_df=problems_df, + max_interactions=args.max_interactions, + ) + + print("Writing dataset.json...") + dataset_path = output_dir / "dataset.json" + ( + student_ids, + num_students, + num_time_steps, + num_questions, + skipped_interactions, + ) = write_dataset_json( + dataset_path=dataset_path, + skills=skills, + questions=questions, + interactions_df=interactions_df, + problem_to_qid=problem_to_qid, + grouping_mode=args.grouping_time, + save_unmapped_skills=(unmapped_questions > 0), + ) + + print("Building qmatrix.json...") + num_skills = len(skills) - int(unmapped_questions == 0) + qmatrix = build_qmatrix(questions, num_skills=num_skills) + save_json(output_dir / "qmatrix.json", qmatrix) + + print("Building train/valid/test split files...") + train_ids, valid_ids, test_ids = split_student_ids( + student_ids=student_ids, + train_ratio=args.train_ratio, + valid_ratio=args.valid_ratio, + test_ratio=args.test_ratio, + seed=args.seed, + ) + save_json(output_dir / "trainset.json", train_ids) + save_json(output_dir / "validset.json", valid_ids) + save_json(output_dir / "testset.json", test_ids) + + total_rubrics = sum(len(q["rubrics"]) for q in questions) + question_skill_counts = [len(q.get("skill_ids", [])) for q in questions] + rubric_skill_counts = [ + len(r.get("skill_ids", [])) for q in questions for r in q.get("rubrics", []) + ] + avg_skills_per_question = ( + sum(question_skill_counts) / len(question_skill_counts) + if question_skill_counts + else 0.0 + ) + avg_skills_per_rubric = ( + sum(rubric_skill_counts) / len(rubric_skill_counts) + if rubric_skill_counts + else 0.0 + ) + avg_time_steps_per_student = ( + num_time_steps / num_students if num_students > 0 else 0.0 + ) + avg_questions_per_timestep = ( + num_questions / num_time_steps if num_time_steps > 0 else 0.0 + ) + + print("\n=== Conversion Summary ===") + print(f"Skills: {num_skills}") + print(f"Questions: {len(questions)}") + print(f"Rubrics: {total_rubrics}") + print(f"Avg skills/question: {avg_skills_per_question:.3f}") + print(f"Avg skills/rubric: {avg_skills_per_rubric:.3f}") + print(f"Students: {num_students}") + print(f"Time steps: {num_time_steps}") + print(f"Avg timesteps/student: {avg_time_steps_per_student:.3f}") + print(f"Avg questions/timestep: {avg_questions_per_timestep:.3f}") + print(f"Grouping mode: {args.grouping_time}") + print(f"Unmapped questions: {unmapped_questions}") + print(f"Skipped interactions:{skipped_interactions}") + print(f"Output directory: {output_dir}") + + +if __name__ == "__main__": + main() diff --git a/Code/qwen3next80bvllm_instruct.py b/Code/qwen3next80bvllm_instruct.py new file mode 100644 index 0000000000000000000000000000000000000000..b33a8729249955c2f9b0bd4d282ccdc3cf9bb9c0 --- /dev/null +++ b/Code/qwen3next80bvllm_instruct.py @@ -0,0 +1,35 @@ +""" +Knowledge Tracing inference with Qwen3-Next-80B-A3B-Instruct model. + +This is the standard instruction-following model (no thinking blocks). +Recommended sampling: temperature=0.7, top_p=0.8, top_k=20, min_p=0 + +Usage: + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80bvllm_instruct.py \ + --data-dir foundationalktdataset/ \ + --num-gpus 4 \ + --batch-size 10 \ + --cache-dir /data1/ \ + --num-students 500 \ + --bin-size 50 \ + --min-history 50 +""" + +from kt_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "Qwen/Qwen3-Next-80B-A3B-Instruct", + "gen_configs": { + "temperature": 0.7, + "top_p": 0.8, + "top_k": 20, + "min_p": 0.0, + "max_tokens": 32768, + "repetition_penalty": 1.0, + }, + "output_prefix": "qwen3next80binstruct", + "system_prompt_prefix": "", # No prefix - standard instruct model +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Code/qwen3next80bvllm_thinking.py b/Code/qwen3next80bvllm_thinking.py new file mode 100644 index 0000000000000000000000000000000000000000..2cae5e6c48cc88f290388663c8b98d3fc5719d40 --- /dev/null +++ b/Code/qwen3next80bvllm_thinking.py @@ -0,0 +1,35 @@ +""" +Knowledge Tracing inference with Qwen3-Next-80B-A3B-Thinking model. + +This model has native thinking mode - it automatically generates ... blocks. +Recommended sampling: temperature=0.6, top_p=0.95, top_k=20, min_p=0 + +Usage: + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80bvllm_thinking.py \ + --data-dir foundationalktdataset/ \ + --num-gpus 4 \ + --batch-size 10 \ + --cache-dir /data1/ \ + --num-students 500 \ + --bin-size 50 \ + --min-history 50 +""" + +from kt_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "Qwen/Qwen3-Next-80B-A3B-Thinking", + "gen_configs": { + "temperature": 0.6, + "top_p": 0.95, + "top_k": 20, + "min_p": 0.0, + "max_tokens": 32768, + "repetition_penalty": 1.0, + }, + "output_prefix": "qwen3next80bthinking", + "system_prompt_prefix": "", # No prefix - model has native thinking +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Code/scripts.sh b/Code/scripts.sh new file mode 100644 index 0000000000000000000000000000000000000000..898f2bb528ddd9dc5b864880fb03f46cb6418822 --- /dev/null +++ b/Code/scripts.sh @@ -0,0 +1,24 @@ +# !/bin/bash + +# Student Time Gap Distribution +python plot_timegap_distribution.py \ + --bin-time 5 \ + --plot-upper-limit-minutes 240 + +# Student Attempt Distribution +python plot_student_attempt_distribution.py \ + --bin-time 1440 + +python plot_student_attempt_distribution.py \ + --bin-time 10800 + +python plot_student_attempt_distribution.py \ + --bin-time 43200 + +# Total Time Distribution +python plot_totaltime_distribution.py \ + --bin-time 10800 + +# Preprocess +python process_to_single_file.py \ + --grouping-time 10800 \ No newline at end of file diff --git a/Data/CASE-Common Core State Standards for Math.json b/Data/CASE-Common Core State Standards for Math.json new file mode 100644 index 0000000000000000000000000000000000000000..1c2e5c078b66bd0be8a00cc24bd54e1e12c580db --- /dev/null +++ b/Data/CASE-Common Core State Standards for Math.json @@ -0,0 +1,32812 @@ +{ + "CFDocument": { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFDocuments/c6496676-d7cb-11e8-824f-0242ac160002", + "identifier": "c6496676-d7cb-11e8-824f-0242ac160002", + 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Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student's mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y). 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(2022). *Correspondences [Associations] between the Common Core State Standards for Mathematics and the WIDA English Language Development Standards Framework, 2020 Edition: Kindergarten-grade 12.* Board of Regents of the University of Wisconsin System. \n", + "caseVersion": "1.1" + }, + "CFItems": [ + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9a3274-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9a3274-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Domain", + "CFItemTypeURI": { + "title": "Domain", + "identifier": "89d67580-f024-5f77-abd7-acfaef39b204", + "uri": "https://case.georgiastandards.org/uri/89d67580-f024-5f77-abd7-acfaef39b204" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "fullStatement": "The Real Number System", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9a351a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9a351a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Domain", + "CFItemTypeURI": { + "title": "Domain", + "identifier": "89d67580-f024-5f77-abd7-acfaef39b204", + "uri": "https://case.georgiastandards.org/uri/89d67580-f024-5f77-abd7-acfaef39b204" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "fullStatement": "Quantities", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. 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In this range, read and write numerals and represent a number of objects with a written numeral.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9bdee1-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9bdee1-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "01" + ], + "humanCodingScheme": "1.OA.A.1", + "listEnumeration": "1.", + "fullStatement": "Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9be213-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9be213-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.", + "notes": "Sizes are compared directly or visually, not compared by measuring.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9be543-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9be543-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.MD.A.1", + "listEnumeration": "1.", + "fullStatement": "Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9be86e-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9be86e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.NBT.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9beba4-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9beba4-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.OA.A.1", + "listEnumeration": "1.", + "fullStatement": "Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9beecd-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9beecd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9bf1fd-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9bf1fd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.MD.A.1", + "listEnumeration": "1.", + "fullStatement": "Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9bf525-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9bf525-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.NBT.A.1", + "listEnumeration": "1.", + "fullStatement": "Use place value understanding to round whole numbers to the nearest 10 or 100.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9bf846-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9bf846-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.NF.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9bfb73-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9bfb73-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.OA.A.1", + "listEnumeration": "1.", + "fullStatement": "Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9bfea2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9bfea2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c02b9-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c02b9-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.MD.A.1", + "listEnumeration": "1.", + "fullStatement": "Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c0660-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c0660-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NBT.A.1", + "listEnumeration": "1.", + "fullStatement": "Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c09e2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c09e2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NF.A.1", + "listEnumeration": "1.", + "fullStatement": "Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c0d77-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c0d77-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.OA.A.1", + "listEnumeration": "1.", + "fullStatement": "Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c10a6-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c10a6-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c13e2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c13e2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.A.1", + "listEnumeration": "1.", + "fullStatement": "Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c1708-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c1708-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.A.1", + "listEnumeration": "1.", + "fullStatement": "Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c1a30-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c1a30-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.A.1", + "listEnumeration": "1.", + "fullStatement": "Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c1d5d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c1d5d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.OA.A.1", + "listEnumeration": "1.", + "fullStatement": "Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c2095-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c2095-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.EE.A.1", + "listEnumeration": "1.", + "fullStatement": "Write and evaluate numerical expressions involving whole-number exponents.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c2393-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c2393-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c26ca-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c26ca-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.A.1", + "listEnumeration": "1.", + "fullStatement": "Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c2b26-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c2b26-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.RP.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, \"The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.\" \"For every vote candidate A received, candidate C received nearly three votes.\"", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c2e34-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c2e34-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.A.1", + "listEnumeration": "1.", + "fullStatement": "Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, \"How old am I?\" is not a statistical question, but \"How old are the students in my school?\" is a statistical question because one anticipates variability in students' ages.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c313b-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c313b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.EE.A.1", + "listEnumeration": "1.", + "fullStatement": "Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c342f-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c342f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c3725-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c3725-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.1", + "listEnumeration": "1.", + "fullStatement": "Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c3a21-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c3a21-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.RP.A.1", + "listEnumeration": "1.", + "fullStatement": "Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c3d7d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c3d7d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c4078-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c4078-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.A.1", + "listEnumeration": "1.", + "fullStatement": "Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c4367-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c4367-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.F.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.", + "notes": "Function notation is not required in Grade 8.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c465b-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c465b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Verify experimentally the properties of rotations, reflections, and translations:", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c4a58-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c4a58-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.NS.A.1", + "listEnumeration": "1.", + "fullStatement": "Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c4d6c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c4d6c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.SP.A.1", + "listEnumeration": "1.", + "fullStatement": "Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c5182-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c5182-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-APR.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c54a3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c54a3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-CED.A.1", + "listEnumeration": "1.", + "fullStatement": "Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c57c7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c57c7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.A.1", + "listEnumeration": "1.", + "fullStatement": "Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c5ae5-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c5ae5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-SSE.A.1", + "listEnumeration": "1.", + "fullStatement": "Interpret expressions that represent a quantity in terms of its context", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c5e16-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c5e16-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-BF.A.1", + "listEnumeration": "1.", + "fullStatement": "Write a function that describes a relationship between two quantities", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c6130-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c6130-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-IF.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c644f-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c644f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-LE.A.1", + "listEnumeration": "1.", + "fullStatement": "Distinguish between situations that can be modeled with linear functions and with exponential functions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c675d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c675d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-TF.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c6a73-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c6a73-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-C.A.1", + "listEnumeration": "1.", + "fullStatement": "Prove that all circles are similar.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c6d88-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c6d88-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.A.1", + "listEnumeration": "1.", + "fullStatement": "Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c70b3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c70b3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GMD.A.1", + "listEnumeration": "1.", + "fullStatement": "Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.", + "notes": "Use dissection arguments, Cavalieri's principle, and informal limit arguments.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c73d2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c73d2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GPE.A.1", + "listEnumeration": "1.", + "fullStatement": "Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c77f2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c77f2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-MG.A.1", + "listEnumeration": "1.", + "fullStatement": "Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c7b3d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c7b3d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.A.1", + "listEnumeration": "1.", + "fullStatement": "Verify experimentally the properties of dilations given by a center and a scale factor:", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c7e76-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c7e76-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-CN.A.1", + "listEnumeration": "1.", + "fullStatement": "Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c8254-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c8254-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-Q.A.1", + "listEnumeration": "1.", + "fullStatement": "Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c859b-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c859b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-RN.A.1", + "listEnumeration": "1.", + "fullStatement": "Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)³ = 5(1/3)³ to hold, so (51/3)³ must equal 5.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c8813-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c8813-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.A.1", + "listEnumeration": "1.", + "fullStatement": "(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c8a61-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c8a61-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-CP.A.1", + "listEnumeration": "1.", + "fullStatement": "Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (\"or,\" \"and,\" \"not\").", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c8d00-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c8d00-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-IC.A.1", + "listEnumeration": "1.", + "fullStatement": "Understand statistics as a process for making inferences about population parameters based on a random sample from that population.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c8faf-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c8faf-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-ID.A.1", + "listEnumeration": "1.", + "fullStatement": "Represent data with plots on the real number line (dot plots, histograms, and box plots).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c93ca-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c93ca-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-MD.A.1", + "listEnumeration": "1.", + "fullStatement": "(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c9637-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c9637-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG" + ], + "humanCodingScheme": "K.CC.A.1", + "listEnumeration": "1.", + "fullStatement": "Count to 100 by ones and by tens.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c9896-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c9896-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG" + ], + "humanCodingScheme": "K.G.A.1", + "listEnumeration": "1.", + "fullStatement": "Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c9af3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c9af3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG" + ], + "humanCodingScheme": "K.MD.A.1", + "listEnumeration": "1.", + "fullStatement": "Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9c9da7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9c9da7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG" + ], + "humanCodingScheme": "K.NBT.A.1", + "listEnumeration": "1.", + "fullStatement": "Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ca104-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ca104-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG" + ], + "humanCodingScheme": "K.OA.A.1", + "listEnumeration": "1.", + "fullStatement": "Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.", + "notes": "Drawings need not show details, but should show the mathematics in the problem (This applies wherever drawings are mentioned in the Standards.)", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ca36a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ca36a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2020-06-20T13:27:27+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG", + "01", + "02", + "03", + "04", + "05", + "06", + "07", + "08", + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "MP1", + "listEnumeration": "1.", + "fullStatement": "Make sense of problems and persevere in solving them.", + "notes": "Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ca5d9-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ca5d9-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.MD.D.10", + "listEnumeration": "10.", + "fullStatement": "Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ca838-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ca838-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.D.10", + "listEnumeration": "10.", + "fullStatement": "Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9caa8d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9caa8d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.C.10", + "listEnumeration": "10.", + "fullStatement": "Prove theorems about triangles.", + "notes": "Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cacdd-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cacdd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.D.10", + "listEnumeration": "10.", + "fullStatement": "(+) Prove the Laws of Sines and Cosines and use them to solve problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9caf2d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9caf2d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.C.10", + "listEnumeration": "10.", + "fullStatement": "(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cb182-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cb182-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.D.11", + "listEnumeration": "11.", + "fullStatement": "Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cb3ef-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cb3ef-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.C.11", + "listEnumeration": "11.", + "fullStatement": "Prove theorems about parallelograms.", + "notes": "Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cb64c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cb64c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.D.11", + "listEnumeration": "11.", + "fullStatement": "(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cb89d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cb89d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.C.11", + "listEnumeration": "11.", + "fullStatement": "(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cbaef-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cbaef-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "educationLevel": [ + "KG", + "01", + "02", + "03", + "04", + "05", + "06", + "07", + "08" + ], + "listEnumeration": "12", + "fullStatement": "Standards for Math Content", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cbd4d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cbd4d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.D.12", + "listEnumeration": "12.", + "fullStatement": "Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cbfa5-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cbfa5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.D.12", + "listEnumeration": "12.", + "fullStatement": "Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cc214-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cc214-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.C.12", + "listEnumeration": "12.", + "fullStatement": "(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cc50c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cc50c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "listEnumeration": "13", + "fullStatement": "Standards for HS Math Content", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9cc7dc-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9cc7dc-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": 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"listEnumeration": "2", + "fullStatement": "Use functions to model relationships between quantities.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d1b5c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d1b5c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Cluster", + "CFItemTypeURI": { + "title": "Cluster", + "identifier": "d77602ec-0098-5b60-b0c0-531cc61709e3", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/d77602ec-0098-5b60-b0c0-531cc61709e3" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.B", + "listEnumeration": "2", + "fullStatement": "Understand and apply the Pythagorean Theorem.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d1dd5-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d1dd5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "01" + ], + "humanCodingScheme": "1.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.", + "notes": "Students do not need to learn formal names such as \"right rectangular prism.\"", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d205c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d205c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "01" + ], + "humanCodingScheme": "1.MD.A.2", + "listEnumeration": "2.", + "fullStatement": "Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.", + "notes": "Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d22e5-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d22e5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "01" + ], + "humanCodingScheme": "1.NBT.B.2", + "listEnumeration": "2.", + "fullStatement": "Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d25bb-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d25bb-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "01" + ], + "humanCodingScheme": "1.OA.A.2", + "listEnumeration": "2.", + "fullStatement": "Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d290b-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d290b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d2bdf-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d2bdf-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.MD.A.2", + "listEnumeration": "2.", + "fullStatement": "Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d2e64-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d2e64-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.NBT.A.2", + "listEnumeration": "2.", + "fullStatement": "Count within 1000; skip-count by 5s, 10s, and 100s.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d30e1-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d30e1-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.OA.B.2", + "listEnumeration": "2.", + "fullStatement": "Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.", + "notes": "See standard 1.OA.6 for a list of mental strategies.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d3367-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d3367-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d3655-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d3655-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.MD.A.2", + "listEnumeration": "2.", + "fullStatement": "Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.", + "notes": "Excludes multiplicative comparison problems (problems involving notions of \"times as much\";", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d3a38-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d3a38-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.NBT.A.2", + "listEnumeration": "2.", + "fullStatement": "Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d400d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d400d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.NF.A.2", + "listEnumeration": "2.", + "fullStatement": "Understand a fraction as a number on the number line; represent fractions on a number line diagram.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d430d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d430d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.OA.A.2", + "listEnumeration": "2.", + "fullStatement": "Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d45b3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d45b3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d484a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d484a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.MD.A.2", + "listEnumeration": "2.", + "fullStatement": "Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d4b33-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d4b33-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NBT.A.2", + "listEnumeration": "2.", + "fullStatement": "Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d4e66-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d4e66-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NF.A.2", + "listEnumeration": "2.", + "fullStatement": "Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d51bd-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d51bd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.OA.A.2", + "listEnumeration": "2.", + "fullStatement": "Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d5464-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d5464-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d5741-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d5741-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.B.2", + "listEnumeration": "2.", + "fullStatement": "Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d59e4-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d59e4-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.A.2", + "listEnumeration": "2.", + "fullStatement": "Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d5c8c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d5c8c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.A.2", + "listEnumeration": "2.", + "fullStatement": "Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d5f43-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d5f43-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.OA.A.2", + "listEnumeration": "2.", + "fullStatement": "Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation \"add 8 and 7, then multiply by 2\" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d6298-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d6298-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.EE.A.2", + "listEnumeration": "2.", + "fullStatement": "Write, read, and evaluate expressions in which letters stand for numbers.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d6553-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d6553-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d680b-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d680b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.B.2", + "listEnumeration": "2.", + "fullStatement": "Fluently divide multi-digit numbers using the standard algorithm.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d6aa3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d6aa3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.RP.A.2", + "listEnumeration": "2.", + "fullStatement": "Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.", + "notes": "Expectations for unit rates in this grade are limited to non-complex fractions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d6d44-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d6d44-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.A.2", + "listEnumeration": "2.", + "fullStatement": "Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d6fe1-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d6fe1-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.EE.A.2", + "listEnumeration": "2.", + "fullStatement": "Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that \"increase by 5%\" is the same as \"multiply by 1.05.\"", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d73cd-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d73cd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d769c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d769c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.2", + "listEnumeration": "2.", + "fullStatement": "Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d7951-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d7951-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.RP.A.2", + "listEnumeration": "2.", + "fullStatement": "Recognize and represent proportional relationships between quantities.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d7bf7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d7bf7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.A.2", + "listEnumeration": "2.", + "fullStatement": "Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d7eb3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d7eb3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.A.2", + "listEnumeration": "2.", + "fullStatement": "Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d816d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d816d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.F.A.2", + "listEnumeration": "2.", + "fullStatement": "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d8424-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d8424-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.A.2", + "listEnumeration": "2.", + "fullStatement": "Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d86d6-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d86d6-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.NS.A.2", + "listEnumeration": "2.", + "fullStatement": "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d89d9-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d89d9-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.SP.A.2", + "listEnumeration": "2.", + "fullStatement": "Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d8c97-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d8c97-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-APR.B.2", + "listEnumeration": "2.", + "fullStatement": "Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d8f41-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d8f41-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-CED.A.2", + "listEnumeration": "2.", + "fullStatement": "Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d91e7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d91e7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.A.2", + "listEnumeration": "2.", + "fullStatement": "Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d9496-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d9496-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-SSE.A.2", + "listEnumeration": "2.", + "fullStatement": "Use the structure of an expression to identify ways to rewrite it. For example, see x4 — y4 as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d974a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d974a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-BF.A.2", + "listEnumeration": "2.", + "fullStatement": "Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d99ff-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d99ff-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-IF.A.2", + "listEnumeration": "2.", + "fullStatement": "Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d9ca7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d9ca7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-LE.A.2", + "listEnumeration": "2.", + "fullStatement": "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9d9f54-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9d9f54-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-TF.A.2", + "listEnumeration": "2.", + "fullStatement": "Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9da1fd-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9da1fd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-C.A.2", + "listEnumeration": "2.", + "fullStatement": "Identify and describe relationships among inscribed angles, radii, and chords.", + "notes": "Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9da4ac-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9da4ac-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.A.2", + "listEnumeration": "2.", + "fullStatement": "Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9da784-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9da784-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GMD.A.2", + "listEnumeration": "2.", + "fullStatement": "(+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9daa46-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9daa46-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GPE.A.2", + "listEnumeration": "2.", + "fullStatement": "Derive the equation of a parabola given a focus and directrix.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9dacf0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9dacf0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-MG.A.2", + "listEnumeration": "2.", + "fullStatement": "Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9db04d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9db04d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.A.2", + "listEnumeration": "2.", + "fullStatement": "Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9db316-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9db316-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-CN.A.2", + "listEnumeration": "2.", + "fullStatement": "Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9db5bb-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9db5bb-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-Q.A.2", + "listEnumeration": "2.", + "fullStatement": "Define appropriate quantities for the purpose of descriptive modeling.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9db867-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9db867-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-RN.A.2", + "listEnumeration": "2.", + "fullStatement": "Rewrite expressions involving radicals and rational exponents using the properties of exponents.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9dbb12-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9dbb12-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.A.2", + "listEnumeration": "2.", + "fullStatement": "(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9dbdbf-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9dbdbf-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-CP.A.2", + "listEnumeration": "2.", + "fullStatement": "Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and 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For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e2a5e-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e2a5e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NBT.A.3", + "listEnumeration": "3.", + "fullStatement": "Use place value understanding to round multi-digit whole numbers to any place.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e2c7a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e2c7a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NF.B.3", + "listEnumeration": "3.", + "fullStatement": "Understand a fraction a/b with a > 1 as a sum of fractions 1/b.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e2e91-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e2e91-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.OA.A.3", + "listEnumeration": "3.", + "fullStatement": "Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e30b9-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e30b9-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.G.B.3", + "listEnumeration": "3.", + "fullStatement": "Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e32dc-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e32dc-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.C.3", + "listEnumeration": "3.", + "fullStatement": "Recognize volume as an attribute of solid figures and understand concepts of volume measurement.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e34fb-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e34fb-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.A.3", + "listEnumeration": "3.", + "fullStatement": "Read, write, and compare decimals to thousandths.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e3712-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e3712-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.3", + "listEnumeration": "3.", + "fullStatement": "Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e3939-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e3939-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.OA.B.3", + "listEnumeration": "3.", + "fullStatement": "Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule \"Add 3\" and the starting number 0, and given the rule \"Add 6\" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e3b67-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e3b67-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.EE.A.3", + "listEnumeration": "3.", + "fullStatement": "Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e3d90-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e3d90-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.G.A.3", + "listEnumeration": "3.", + "fullStatement": "Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e3fc3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e3fc3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.B.3", + "listEnumeration": "3.", + "fullStatement": "Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e41ee-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e41ee-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.RP.A.3", + "listEnumeration": "3.", + "fullStatement": "Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e441c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e441c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.A.3", + "listEnumeration": "3.", + "fullStatement": "Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e464c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e464c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.EE.B.3", + "listEnumeration": "3.", + "fullStatement": "Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e4885-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e4885-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.G.A.3", + "listEnumeration": "3.", + "fullStatement": "Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e4aa8-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e4aa8-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.3", + "listEnumeration": "3.", + "fullStatement": "Solve real-world and mathematical problems involving the four operations with rational numbers.", + "notes": "Computations with rational numbers extend the rules for manipulating fractions to complex fractions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e4d0c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e4d0c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.RP.A.3", + "listEnumeration": "3.", + "fullStatement": "Use proportional relationships to solve multistep ratio and percent problems.", + "notes": "Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e4f3a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e4f3a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.B.3", + "listEnumeration": "3.", + "fullStatement": "Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e5169-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e5169-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.A.3", + "listEnumeration": "3.", + "fullStatement": "Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e5396-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e5396-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.F.A.3", + "listEnumeration": "3.", + "fullStatement": "Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e55c9-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e55c9-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.A.3", + "listEnumeration": "3.", + "fullStatement": "Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e5802-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e5802-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.SP.A.3", + "listEnumeration": "3.", + "fullStatement": "Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e763a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e763a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-MG.A.3", + "listEnumeration": "3.", + "fullStatement": "Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).", + "language": 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"educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-Q.A.3", + "listEnumeration": "3.", + "fullStatement": "Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9e7ef2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9e7ef2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-RN.B.3", + "listEnumeration": "3.", + "fullStatement": "Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational 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Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ec6c0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ec6c0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.OA.A.4", + "listEnumeration": "4.", + "fullStatement": "Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ec90c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ec90c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.MD.B.4", + "listEnumeration": "4.", + "fullStatement": "Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ecb67-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ecb67-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NBT.B.4", + "listEnumeration": "4.", + "fullStatement": "Fluently add and subtract multi-digit whole numbers using the standard algorithm.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ecdc0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ecdc0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NF.B.4", + "listEnumeration": "4.", + "fullStatement": "Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ed00e-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ed00e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.OA.B.4", + "listEnumeration": "4.", + "fullStatement": "Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ed262-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ed262-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.G.B.4", + "listEnumeration": "4.", + "fullStatement": "Classify two-dimensional figures in a hierarchy based on properties.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ed5fc-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ed5fc-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.C.4", + "listEnumeration": "4.", + "fullStatement": "Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ed865-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ed865-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.A.4", + "listEnumeration": "4.", + "fullStatement": "Use place value understanding to round decimals to any place.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9edad5-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9edad5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.4", + "listEnumeration": "4.", + "fullStatement": "Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9edd45-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9edd45-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.EE.A.4", + "listEnumeration": "4.", + "fullStatement": "Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9edfbc-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9edfbc-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.G.A.4", + "listEnumeration": "4.", + "fullStatement": "Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ee241-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ee241-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.B.4", + "listEnumeration": "4.", + "fullStatement": "Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ee4bb-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ee4bb-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.B.4", + "listEnumeration": "4.", + "fullStatement": "Display numerical data in plots on a number line, including dot plots, histograms, and box plots.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ee71f-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ee71f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.EE.B.4", + "listEnumeration": "4.", + "fullStatement": "Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9eebe1-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9eebe1-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.G.B.4", + "listEnumeration": "4.", + "fullStatement": "Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9eee6f-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9eee6f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.B.4", + "listEnumeration": "4.", + "fullStatement": "Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ef0eb-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ef0eb-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.A.4", + "listEnumeration": "4.", + "fullStatement": "Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ef36a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ef36a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.F.B.4", + "listEnumeration": "4.", + "fullStatement": "Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ef5f0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ef5f0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.A.4", + "listEnumeration": "4.", + "fullStatement": "Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9ef861-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9ef861-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.SP.A.4", + "listEnumeration": "4.", + "fullStatement": "Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. 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Is there evidence that those who have a curfew also tend to have chores?", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9efad6-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9efad6-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-APR.C.4", + "listEnumeration": "4.", + "fullStatement": "Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)2 = (x² — y²)² + (2xy)² can be used to generate Pythagorean triples.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9efd43-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9efd43-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-CED.A.4", + "listEnumeration": "4.", + "fullStatement": "Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9effbc-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9effbc-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.B.4", + "listEnumeration": "4.", + "fullStatement": "Solve quadratic equations in one variable.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f0232-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f0232-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-SSE.B.4", + "listEnumeration": "4.", + "fullStatement": "Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f04ba-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f04ba-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-BF.B.4", + "listEnumeration": "4.", + "fullStatement": "Find inverse functions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f0737-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f0737-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-IF.B.4", + "listEnumeration": "4.", + "fullStatement": "For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.", + "notes": "Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f09b7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f09b7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-LE.A.4", + "listEnumeration": "4.", + "fullStatement": "For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f0c6f-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f0c6f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-TF.A.4", + "listEnumeration": "4.", + "fullStatement": "(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f0f18-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f0f18-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-C.A.4", + "listEnumeration": "4.", + "fullStatement": "(+) Construct a tangent line from a point outside a given circle to the circle.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f119a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f119a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.A.4", + "listEnumeration": "4.", + "fullStatement": "Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f140d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f140d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GMD.B.4", + "listEnumeration": "4.", + "fullStatement": "Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f16e0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f16e0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GPE.B.4", + "listEnumeration": "4.", + "fullStatement": "Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f195e-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f195e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.B.4", + "listEnumeration": "4.", + "fullStatement": "Prove theorems about triangles.", + "notes": "Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f1bd7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f1bd7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-CN.B.4", + "listEnumeration": "4.", + "fullStatement": "(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f1e55-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f1e55-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.B.4", + "listEnumeration": "4.", + "fullStatement": "(+) Add and subtract vectors.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f20d2-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f20d2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-CP.A.4", + "listEnumeration": "4.", + "fullStatement": "Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f235a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f235a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-IC.B.4", + "listEnumeration": "4.", + "fullStatement": "Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f25df-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f25df-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-ID.A.4", + "listEnumeration": "4.", + "fullStatement": "Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f286a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f286a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-MD.A.4", + "listEnumeration": "4.", + "fullStatement": "(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. 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In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f375c-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f375c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Conceptual Category", + "CFItemTypeURI": { + "title": "Conceptual Category", + "identifier": "bb2b7874-ca3b-4a28-bdf9-4ab9b6bdaa3f", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/bb2b7874-ca3b-4a28-bdf9-4ab9b6bdaa3f" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "listEnumeration": "5", + "fullStatement": "Statistics & Probability", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f3a16-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f3a16-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Domain", + "CFItemTypeURI": { + "title": "Domain", + "identifier": "89d67580-f024-5f77-abd7-acfaef39b204", + "uri": "https://case.georgiastandards.org/uri/89d67580-f024-5f77-abd7-acfaef39b204" + }, + "educationLevel": [ + "KG" + ], + "listEnumeration": "5", + "fullStatement": "Geometry", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f3cb3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f3cb3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Grade Level", + "CFItemTypeURI": { + 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"listEnumeration": "5.", + "fullStatement": "Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f552e-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f552e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.MD.B.5", + "listEnumeration": "5.", + "fullStatement": "Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f57e3-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f57e3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "02" + ], + "humanCodingScheme": "2.NBT.B.5", + "listEnumeration": "5.", + "fullStatement": "Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f5a86-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f5a86-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": 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But addition and subtraction with unlike denominators in general is not a requirement at this grade.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f6853-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f6853-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.OA.C.5", + "listEnumeration": "5.", + "fullStatement": "Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 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Explain informally why the numbers will continue to alternate in this way.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f6b11-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f6b11-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.C.5", + "listEnumeration": "5.", + "fullStatement": "Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f6e17-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f6e17-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.B.5", + "listEnumeration": "5.", + "fullStatement": "Fluently multiply multi-digit whole numbers using the standard algorithm.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f70d0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f70d0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.5", + "listEnumeration": "5.", + "fullStatement": "Interpret multiplication as scaling (resizing), by:", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f74c0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f74c0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.EE.B.5", + "listEnumeration": "5.", + "fullStatement": "Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f77af-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f77af-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.C.5", + "listEnumeration": "5.", + "fullStatement": "Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f7a96-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f7a96-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.B.5", + "listEnumeration": "5.", + "fullStatement": "Summarize numerical data sets in relation to their context, such as by:", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f7d68-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f7d68-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.G.B.5", + "listEnumeration": "5.", + "fullStatement": "Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f803d-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f803d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.C.5", + "listEnumeration": "5.", + "fullStatement": "Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f8362-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f8362-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.B.5", + "listEnumeration": "5.", + "fullStatement": "Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f86d5-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f86d5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.F.B.5", + "listEnumeration": "5.", + "fullStatement": "Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f89a0-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f89a0-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.A.5", + "listEnumeration": "5.", + "fullStatement": "Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f8c74-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f8c74-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-APR.C.5", + "listEnumeration": "5.", + "fullStatement": "(+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.", + "notes": "The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f8f43-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f8f43-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.C.5", + "listEnumeration": "5.", + "fullStatement": "Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f920f-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f920f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-BF.B.5", + "listEnumeration": "5.", + "fullStatement": "(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f94e7-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f94e7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-IF.B.5", + "listEnumeration": "5.", + "fullStatement": "Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f97c6-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f97c6-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-LE.B.5", + "listEnumeration": "5.", + "fullStatement": "Interpret the parameters in a linear or exponential function in terms of a context.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f9a9b-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f9a9b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-TF.B.5", + "listEnumeration": "5.", + "fullStatement": "Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9f9d82-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9f9d82-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-C.B.5", + "listEnumeration": "5.", + "fullStatement": "Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9fa05a-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9fa05a-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-CO.A.5", + "listEnumeration": "5.", + "fullStatement": "Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9fa334-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9fa334-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-GPE.B.5", + "listEnumeration": "5.", + "fullStatement": "Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9fa609-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9fa609-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.B.5", + "listEnumeration": "5.", + "fullStatement": "Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6b9fa8da-d7cc-11e8-824f-0242ac160002", + "identifier": "6b9fa8da-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-CN.B.5", + "listEnumeration": "5.", + "fullStatement": "(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. 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For example, find the points of intersection between the line y = -3x and the circle x² + y² = 3.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba06d60-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba06d60-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-IF.C.7", + "listEnumeration": "7.", + "fullStatement": "Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.", + "notes": "Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). 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The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba07a82-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba07a82-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSG-SRT.C.7", + "listEnumeration": "7.", + "fullStatement": "Explain and use the relationship between the sine and cosine of complementary angles.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba07db3-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba07db3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-CN.C.7", + "listEnumeration": "7.", + "fullStatement": "Solve quadratic equations with real coefficients that have complex solutions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba080f8-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba080f8-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.C.7", + "listEnumeration": "7.", + "fullStatement": "(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba08433-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba08433-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-CP.B.7", + "listEnumeration": "7.", + "fullStatement": "Apply the Addition Rule, P(A or B) = P(A) + P(B) - 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Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0948b-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0948b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Grade Level", + "CFItemTypeURI": { + "title": "Grade Level", + "identifier": "8047d85d-6c8e-5231-bd6d-050731684413", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/8047d85d-6c8e-5231-bd6d-050731684413" + }, + "educationLevel": [ + "07" + ], + "listEnumeration": "8", + "fullStatement": "Grade 7", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba09818-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba09818-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "01" + ], + "humanCodingScheme": "1.OA.D.8", + "listEnumeration": "8.", + "fullStatement": "Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. 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Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0ab8d-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0ab8d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.C.8", + "listEnumeration": "8.", + "fullStatement": "Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0aeb7-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0aeb7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.C.8", + "listEnumeration": "8.", + "fullStatement": "Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0b1df-d7cc-11e8-824f-0242ac160002", + 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Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0c91e-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0c91e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-CN.C.8", + "listEnumeration": "8.", + "fullStatement": "(+) Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x - 2i).", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0ccae-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0ccae-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSN-VM.C.8", + "listEnumeration": "8.", + "fullStatement": "(+) Add, subtract, and multiply matrices of appropriate dimensions.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0cfe5-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0cfe5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-CP.B.8", + "listEnumeration": "8.", + "fullStatement": "(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0d319-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0d319-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSS-ID.C.8", + "listEnumeration": "8.", + "fullStatement": "Compute (using technology) and interpret the correlation coefficient of a linear fit.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0d653-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0d653-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2020-06-20T13:29:03+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "KG", + "01", + "02", + "03", + "04", + "05", + "06", + "07", + "08", + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "MP8", + "listEnumeration": "8.", + "fullStatement": "Look for and express regularity in repeated reasoning.", + "notes": "Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. 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Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0e7f4-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0e7f4-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.G.C.9", + "listEnumeration": "9.", + "fullStatement": "Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0ea6e-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0ea6e-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSA-REI.C.9", + "listEnumeration": "9.", + "fullStatement": "(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba0ece8-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba0ece8-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Standard", + "CFItemTypeURI": { + "title": "Standard", + "identifier": "88e14be5-f7f3-4e67-b4a2-d621eaa49d48", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/88e14be5-f7f3-4e67-b4a2-d621eaa49d48" + }, + "educationLevel": [ + "09", + "10", + "11", + "12" + ], + "humanCodingScheme": "HSF-IF.C.9", + "listEnumeration": "9.", + "fullStatement": "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 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Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba10e51-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba10e51-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "03" + ], + "humanCodingScheme": "3.NF.A.3.a", + "listEnumeration": "a.", + "fullStatement": "Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba110dd-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba110dd-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.MD.C.5.a", + "listEnumeration": "a.", + "fullStatement": "An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a \"one-degree angle,\" and can be used to measure angles.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1136b-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1136b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NF.B.3.a", + "listEnumeration": "a.", + "fullStatement": "Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba115f2-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba115f2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "04" + ], + "humanCodingScheme": "4.NF.B.4.a", + "listEnumeration": "a.", + "fullStatement": "Understand a fraction a/b as a multiple of 1/b. 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Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba11dd3-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba11dd3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.A.3.a", + "listEnumeration": "a.", + "fullStatement": "Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba12074-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba12074-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.4.a", + "listEnumeration": "a.", + "fullStatement": "Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. 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(In general, (a/b) × (c/d) = ac/bd.)", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1231f-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1231f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.5.a", + "listEnumeration": "a.", + "fullStatement": "Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba125cb-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba125cb-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.7.a", + "listEnumeration": "a.", + "fullStatement": "Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. 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Use tables to compare ratios.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1331c-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1331c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.B.5.a", + "listEnumeration": "a.", + "fullStatement": "Reporting the number of observations.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1361d-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1361d-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.EE.B.4.a", + "listEnumeration": "a.", + "fullStatement": "Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba138d5-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba138d5-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.1.a", + "listEnumeration": "a.", + "fullStatement": "Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba13b7c-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba13b7c-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.2.a", + "listEnumeration": "a.", + "fullStatement": "Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba13e2b-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba13e2b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.RP.A.2.a", + "listEnumeration": "a.", + "fullStatement": "Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba141ef-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba141ef-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.C.7.a", + "listEnumeration": "a.", + "fullStatement": "Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba14563-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba14563-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.C.8.a", + "listEnumeration": "a.", + "fullStatement": "Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1486b-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1486b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.C.7.a", + "listEnumeration": "a.", + "fullStatement": "Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. 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For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1938b-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1938b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.C.3.b", + "listEnumeration": "b.", + "fullStatement": "A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1965f-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1965f-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.MD.C.5.b", + "listEnumeration": "b.", + "fullStatement": "Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba19ae2-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba19ae2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NBT.A.3.b", + "listEnumeration": "b.", + "fullStatement": "Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba19dde-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba19dde-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.4.b", + "listEnumeration": "b.", + "fullStatement": "Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1a0ce-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1a0ce-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.5.b", + "listEnumeration": "b.", + "fullStatement": "Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1a3cc-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1a3cc-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "05" + ], + "humanCodingScheme": "5.NF.B.7.b", + "listEnumeration": "b.", + "fullStatement": "Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1a6b3-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1a6b3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.EE.A.2.b", + "listEnumeration": "b.", + "fullStatement": "Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1a9ea-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1a9ea-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.C.6.b", + "listEnumeration": "b.", + "fullStatement": "Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1acd4-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1acd4-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.NS.C.7.b", + "listEnumeration": "b.", + "fullStatement": "Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer than -7 °C.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1afb9-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1afb9-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.RP.A.3.b", + "listEnumeration": "b.", + "fullStatement": "Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1b2b7-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1b2b7-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "06" + ], + "humanCodingScheme": "6.SP.B.5.b", + "listEnumeration": "b.", + "fullStatement": "Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1b5b2-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1b5b2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.EE.B.4.b", + "listEnumeration": "b.", + "fullStatement": "Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1b8b8-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1b8b8-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.1.b", + "listEnumeration": "b.", + "fullStatement": "Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1bbb1-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1bbb1-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.NS.A.2.b", + "listEnumeration": "b.", + "fullStatement": "Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1beae-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1beae-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.RP.A.2.b", + "listEnumeration": "b.", + "fullStatement": "Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1c19b-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1c19b-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.C.7.b", + "listEnumeration": "b.", + "fullStatement": "Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?", + "notes": "", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1c4a2-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1c4a2-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "07" + ], + "humanCodingScheme": "7.SP.C.8.b", + "listEnumeration": "b.", + "fullStatement": "Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., \"rolling double sixes\"), identify the outcomes in the sample space which compose the event.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1c7ad-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1c7ad-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.C.7.b", + "listEnumeration": "b.", + "fullStatement": "Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.", + "language": "en" + }, + { + "uri": "https://casenetwork.imsglobal.org/ims/case/v1p0/CFItems/6ba1caa3-d7cc-11e8-824f-0242ac160002", + "identifier": "6ba1caa3-d7cc-11e8-824f-0242ac160002", + "lastChangeDateTime": "2018-10-24T20:56:19+00:00", + "CFItemType": "Component", + "CFItemTypeURI": { + "title": "Component", + "identifier": "1f1afd62-66cd-51cb-8299-1fe5ced9df16", + "uri": "https://api.standards.isbe.net/server/api/v1/ISBOE/ims/case/v1p0/CFItemTypes/1f1afd62-66cd-51cb-8299-1fe5ced9df16" + }, + "educationLevel": [ + "08" + ], + "humanCodingScheme": "8.EE.C.8.b", + "listEnumeration": "b.", + "fullStatement": "Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. 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28 is 7 times what number?

+

 

+

",4,4,,,151389 +PSBM5G,2,Fill-in-the-blank(s),Numeric,"

Evaluate 103.

+

 

+

","1,000","1,000",,,58180 +PSBM5G,1,Fill-in-the-blank(s),Numeric,"

Evaluate 53 ⋅ 23.

+

 

+

","1,000","1,000",,,58041 +PSBB9,1,Fill-in-the-blank(s),Numeric,"

There are 12 inches in 1 foot and 5,280 feet in 1 mile. Jada ran 314 miles.

+

 

+

How many feet is that?  

+

 

+

feet

",17160,17160,,,95 +PSBCC,1,Fill-in-the-blank(s),Numeric,"

Given the equation y = ‐3x + 2.5:

+

 

+

When x is 1, what value of y makes the equation true?

+
 
+

 

+

y =

",-0.5,-0.5,,,93 +PSBFF,1,Fill-in-the-blank(s),Drop Down,"

Diego has $11 and begins saving $5 each week toward buying a new phone. At the same time that Diego begins saving, Lin has $60 and begins spending $2 per week on supplies for her art class.

+

 

+

Is there a week when they have the same amount of money? 

+

 

+

","

No

,

Yes

",

Yes

,,,253 +PRABQMA9,1,Fill-in-the-blank(s),Numeric,"

Divide.

+

 

+

49÷815

+

 

+

",6-May,6-May,,,320140 +PSBXG,2,Fill-in-the-blank(s),Numeric,"

What is the scale factor?

+

 

+

",3,3,,,2532 +PRABG43A,1,Fill-in-the-blank(s),Algebraic Expression,"

Factor to write an equivalent expression: 26a-10

+

 

+

If you get stuck, use a diagram to organize your work.

+

 

+

",2(13a-5),2(13a-5),,,3056 +PSBB5WF,3,Fill-in-the-blank(s),Numeric,"

Lin’s second pan has a length of 83 inches, a width of 154 inches, and a height of 32 inches. What is the volume of the second pan?  

+

 

+

 cubic inches

",15,15,,,319193 +PSBBEUD,3,Fill-in-the-blank(s),Numeric,"

How many days of the week is Noah considering?

+

 

+

days of the week

+

 

+

",3,3,,,195315 +PSBYY,4,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

6.08 + 2.02

+

 

+

",8.1,8.1,,,3036 +PSBYY,5,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

35 - 0.02

+

 

+

",34.98,34.98,,,3201 +PSBYY,2,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

7 - 0.18

+

 

+

",6.82,6.82,,,2812 +PSBYY,3,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

13.23 + 2.67

+

 

+

",15.9,15.9,,,2930 +PSBYY,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

11 - 4.9 

+

 

+

",6.1,6.1,,,2695 +PSB4G,1,Fill-in-the-blank(s),Numeric,"

Andre is reviewing proportional relationships. He wants to practice using a graph that goes through a point so that each coordinate is between 1 and 10.

+

 

+

For the point, how many outcomes are in the sample space?

+

 

+

",100,100,,,3566 +PSB4G,2,Fill-in-the-blank(s),Numeric,"

For how many outcomes are the x-coordinate and the y-coordinate the same number?

+

 

+

",10,10,,,3705 +PRABG429,1,Fill-in-the-blank(s),Algebraic Expression,"

Expand to write an equivalent expression: -12(-2x+4y)

+

 

+

If you get stuck, use a diagram to organize your work.

+

 

+

",x-2y,x-2y,,,2894 +PSBBEUD,2,Fill-in-the-blank(s),Numeric,"

How many locations is Noah considering?

+

 

+

locations

+

 

+

",2,2,,,194852 +PSB25V,3,Fill-in-the-blank(s),Numeric,"

Divide 412 by the following unit fraction.

+

 

+

16

+

 

+

",27,27,,,131506 +PRABFCKF,1,Order / Sort,Ordering,

Order from smallest to largest:

,"Number of slices of bread in a stack that is 1 ft high, Number of books in a stack that is 1 ft high, Number of dollar bills in a stack that is 1 ft high, Number of pennies in a stack that is 1 ft high","Number of slices of bread in a stack that is 1 ft high, Number of books in a stack that is 1 ft high, Number of dollar bills in a stack that is 1 ft high, Number of pennies in a stack that is 1 ft high",,,238362 +PRABFG5X,1,Order / Sort,Ordering,"

The table shows five states and the lowest point in each state.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
StateLowest Elevation (feet)
California-282
Colorado3,350
Louisiana-8
New Mexico2,842
Wyoming3,099
+

 

+

Put the states in order by their lowest elevation, from least (1) to greatest (5).

","California, Louisiana, Wyoming, New Mexico, Colorado","California, Louisiana, Wyoming, New Mexico, Colorado",,,5669 +PSBBFD5,1,Fill-in-the-blank(s),Numeric,"

Find the value of 2425÷45.

+

 

+

 

+

",5-Jun,5-Jun,,,199749 +PSBRQK,2,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

5÷310

+

 

+

","16 2/3, 50/3","16 2/3, 50/3",,,76591 +PSBRQK,3,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

5÷910

+

 

+

","50/9, 5 5/9","50/9, 5 5/9",,,76716 +PSBDP4S,1,Fill-in-the-blank(s),Numeric,"

Find 12÷35. Try not to use a diagram, if possible. 

+

 

+

",20,20,,,594494 +PSBG4B,2,Fill-in-the-blank(s),Numeric,"

A rectangular bathroom floor is covered with square tiles that are 112 feet by 112 feet. The length of the bathroom floor is 1012 feet and the width is 612 feet.

+

 

+

How many tiles does it take to cover the width of the floor?

+

 

+

  tiles

+

Express your answer in fraction form.

",4 1/3,4 1/3,,,36911 +PSBCY9G,2,Fill-in-the-blank(s),Numeric,"

Find the correct quotient.

+

 

+

",15-Aug,15-Aug,,,469563 +PSB222,1,Fill-in-the-blank(s),Numeric,"

Find the value of 154 ÷ 58.

+

 

+

",6,6,,,130932 +PSB25V,1,Fill-in-the-blank(s),Numeric,"

Divide 412 by the following unit fraction.

+

18

+

 

+

",36,36,,,131258 +PSB25V,2,Fill-in-the-blank(s),Numeric,"

Divide 412 by the following unit fraction.

+

 

+

 14

+

 

+

",18,18,,,131386 +PSBBT7,1,Fill-in-the-blank(s),Numeric,"

Han found a way to compute complicated expressions more easily. Since 2 ⋅ 5=10, he looks for pairings of 2s and 5s that he knows equal 10. For example,

+

3 · 24 · 55 = 3 · 24 · 54 · 5 = (3 · 5) · (2 · 5)4 = 15 · 104 = 150,000.

+

 

+

Use Han's technique to compute the following:

+

 

+

24 · 5 · (3 · 5)3

+

 

+

 

+

",270000,270000,,,7635 +PSBBT7,2,Fill-in-the-blank(s),Numeric,"

Han found a way to compute complicated expressions more easily. Since 2 ⋅ 5=10, he looks for pairings of 2s and 5s that he knows equal 10. For example,

+

3 · 24 · 55 = 3 · 24 · 54 · 5 = (3 · 5) · (2 · 5)4 = 15 · 104 = 150,000.

+

 

+

Use Han's technique to compute the following:

+

 

+

+

 

+

",180000,180000,,,7829 +PSBGZP,2,Fill-in-the-blank(s),Numeric,"

A zookeeper is 614 feet tall. A young giraffe in his care is 938 feet tall.

+

 

+

What fraction of the giraffe’s height is the zookeeper’s height?  

+

 

+

+

Express your answer in fraction form.

",3-Feb,3-Feb,,,36501 +PSBDK49,1,Fill-in-the-blank(s),Numeric,"

Here is a right triangle. What is its area?

+

 

+

cm2

+

 

+

",8-Mar,8-Mar,,,577269 +PRABJCHV,1,Fill-in-the-blank(s),Numeric,"

A train moves at constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?

+

 

+

 miles per minute

",2-Mar,2-Mar,,,9567 +PRABJCHW,1,Fill-in-the-blank(s),Numeric,"

A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?

+

 

+

hours

",4,4,,,9673 +PSBB8W,4,Fill-in-the-blank(s),Numeric,"

If you are standing on a beach right next to the ocean, what is your elevation?

+

 

+

",0,0,,,9946 +PSBBPYX,2,Fill-in-the-blank(s),Numeric,"

The area of a rectangle is 1712 in2 and its shorter side is 312 in.

+

 

+

What is the length of the longer side?  

+

 

+

in

",5,5,,,242315 +PSBBP6G,1,Fill-in-the-blank(s),Numeric,"

Find the value of 532÷254. 

+

 

+

",Jan-40,Jan-40,,,243107 +PSBCAR,3,Fill-in-the-blank(s),Numeric,"

Use Priya’s method to calculate 0.0015 · 0.024.

+

 

+

",0.000036,0.000036,,,10585 +PSB2GF,2,Fill-in-the-blank(s),Numeric,"

A bucket contains 1123 gallons of water and is 56 full. How many gallons of water would be in a full bucket? 

+

 

+

Find the answer.

+

 

+

gallons

",14,14,,,127330 +PSBB72,3,Fill-in-the-blank(s),Numeric,"

What is the measure of angle AEB?

+

 

+

°

",60,60,,,10007 +PSBCCG,1,Fill-in-the-blank(s),Numeric,"

The scale of a map says that 8 cm represents 5 km.

+


What distance on the map (in centimeters) represents an actual distance of 8 kilometers?  

+

 

+

centimeters

",12.8,12.8,,,10706 +PSBCBU,1,Fill-in-the-blank(s),Algebraic Expression,"

A right triangle has side lengths of a, b, and c units. The longest side has a length of c units. Complete the equations to show three relations among  a, b, and c.

+

 

+

c2=

+

 

+

Use the ^ symbol to represent an exponent.

+

For example: 52 should be typed as 5^2

+

 

",a^2+b^2,a^2+b^2,,,10412 +PSBV2W,2,Fill-in-the-blank(s),Numeric,"

A sixth-grade science club needs $180 to pay for the tickets to a science museum. All tickets cost the same amount.

+

 

+

Find the quotient.

+

 

+

",12,12,,,102028 +PSBBEUD,5,Fill-in-the-blank(s),Numeric,"

How many different possible outcomes are in the sample space?

+

 

+

possible outcomes

+

 

+

",18,18,,,196019 +PSBWAZ,2,Fill-in-the-blank(s),Numeric,"

Find a value for a that makes the statement true.

+

 

+

a ÷ 6 is equal to 1

+

 

+

",6,6,,,103383 +PSBCMS,2,Fill-in-the-blank(s),Numeric,"

Evaluate:

+

 

+

12-3

+

 

+

",8,8,,,12381 +PRABQAC2,1,Fill-in-the-blank(s),Numeric,"

 

+

Find the sum without a calculator.

+

+

 

+

",0,0,,,14063 +PSBC62,2,Fill-in-the-blank(s),Numeric,"

A gas company’s delivery truck has a cylindrical tank that is 14 feet in diameter and 40 feet long.

+

 

+

How much gas can fit in the tank? 

+

 

+

cubic feet

+

Use 3.14 as an approximation for pi.  Round your answer to the nearest whole.

+

 

+

 

","6154, 6158","6154, 6158",,,15627 +PSBC6R,4,Fill-in-the-blank(s),Numeric,"

A child’s pass costs $15. How many dollars does an adult pass cost? 

+

 

+

$

",24,24,,,15569 +PSBC2Q,1,Fill-in-the-blank(s),Numeric,"

Calculate the product. If you get stuck, draw an area diagram to help.

+

 

+

(5.6) ⋅ (1.8)

+

 

+

",10.08,10.08,,,14749 +PSBC39,1,Fill-in-the-blank(s),Numeric,"

Calculate the product. If you get stuck, draw an area diagram to help.

+

 

+

(0.008) ⋅ (7.2)

+

 

+

",0.0576,0.0576,,,15038 +PRABHX6P,1,Fill-in-the-blank(s),Numeric,"

A salesperson sold a car for $18,250 and their commission is $693.50. What percentage of the sale price is their commission?

+

 

+

%

",3.8,3.8,,,15760 +PSBC4Z,3,Fill-in-the-blank(s),Numeric,"

Three cylinders have a volume of 2826 cm3.

+

Cylinder A has a height of 900 cm.

+

Cylinder B has a height of 225 cm.

+

Cylinder C has a height of 100 cm.

+

Find the radius of the cylinder. Use 3.14 as an approximation for π.

+

 

+

Cylinder C has a radius of cm

",3,3,,,15234 +PSBD8C,4,Fill-in-the-blank(s),Algebraic Expression,"

How much will a car be worth after one year if its initial value was x dollars? If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

dollars

+

Use x as your variable.

",0.85x,0.85x,,,21347 +PSBEBS,1,Fill-in-the-blank(s),Exact Match,"

Write the expression with fewer terms. 

+

 

+

10x − 2x

+
 
+

 

+

",8x,8x,,,21711 +PSBEEZ,2,Fill-in-the-blank(s),Numeric,"

How far are the hurdles from one another? 

+

 

+

 

+

meters

",9.14,9.14,,,22078 +PSBEGN,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

(-1) · 2 · 3

+

 

+

",-6,-6,,,22023 +PSBEED,1,Order / Sort,Ordering,"

Here are some scenarios:

+
    +
  • According to market research, a business has a 75% chance of making money in the first 3 years.
    • +
  • According to lab testing,  of a certain kind of experimental light bulb will work after 3 years.
    • +
  • According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
    • +
+


Order the scenarios in order of likelihood from least (1) to greatest (3) after three years.

","the business makes money, the light bulb still works, the car needs major repairs","the business makes money, the light bulb still works, the car needs major repairs",,,22103 +PSBEGN,2,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

+

 

+

",6,6,,,22322 +PSBEGN,3,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

+

 

+

",-6,-6,,,22552 +PSBESA,2,Fill-in-the-blank(s),Numeric,"

The equation d = 3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.

+

 

+

How many minutes does it take the snail to get 9 inches from the rock?  

+

 

+

minutes

",3,3,,,23822 +PRABTS95,1,Fill-in-the-blank(s),Numeric,"

Find the area of the rectangle with the following side lengths.

+

 

+

 

+

76 in and 67in

+

 

+

 

+

square inch

",1,1,,,25949 +PRABEV4K,1,Fill-in-the-blank(s),Numeric,"

A random sample of people were asked which hand they prefer to write with.

+

l means they prefer to use their left hand.

+

r means they prefer to use their right hand.

+

 

+

l     r     r     r     r     r     r     r     r     r     l     r     r     r     r

+

 

+

Based on this sample, estimate the proportion of the population that prefers to write with their left hand.

+

 

+

 

+

",15-Feb,15-Feb,,,24873 +PRABMSEU,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+

 

+

-25 · -34

+

 

+

",10-Mar,10-Mar,,,26005 +PRABESKQ,1,Fill-in-the-blank(s),Numeric,"

The graph of a proportional relationship contains the point with coordinates (3, 12). What is the constant of proportionality of the relationship?

+

 

+

",4,4,,,25520 +PSBEXG,3,Fill-in-the-blank(s),Numeric,"

What is the constant of proportionality?  

+

 

+

 sale dollars per original dollar

",0.8,0.8,,,24963 +PRABMSEV,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+

 

+

83 · -42

+

 

+

",-112,-112,,,26296 +PSBFCE,4,Fill-in-the-blank(s),Numeric,"

What is the value of c?

+

 

+

",4,4,,,27276 +PSBFCE,1,Fill-in-the-blank(s),Numeric,"

All of the points in the picture are on the same line.

+

 

+

+

 

+

Find the slope of the line.

+

 

+

",3,3,,,27019 +PSBC9S5,1,Fill-in-the-blank(s),Numeric,"

What is 56 ÷ 112?

+

 

+

",10,10,,,517656 +PSBGGY,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

21 is what percentage of 30?  

+

 

+

%

",70,70,,,33653 +PSBCBEC,2,Fill-in-the-blank(s),Numeric,"

Find the answer. Draw a diagram, if needed.

+

 

+

A set of books that are each 1.5 inches wide are being organized on a bookshelf that is 36 inches wide. How many books can fit on the shelf?

+

 

+

books

",24,24,,,351353 +PRABEGMJ,1,Fill-in-the-blank(s),Numeric,"

A cone has volume 12π cubic inches. Its height is 4 inches. What is its radius?

+

 

+

inches

",3,3,,,27930 +PSBFVZ,1,Fill-in-the-blank(s),Numeric,"

Diego made 6 boxes of spaghetti to feed 20 people who attended his dinner party. Next time, 50 people are coming! How many boxes of spaghetti should Diego buy to feed all those people?  

+

 

+

boxes of spaghetti

",15,15,,,30276 +PSBFYQ,2,Fill-in-the-blank(s),Numeric,"

Elena bought 8 tokens for $4.40. At this rate:

+

 

+

How much do 19 tokens cost?

+

 

+

$

",10.45,10.45,,,30779 +PSBFYQ,1,Fill-in-the-blank(s),Numeric,"

Elena bought 8 tokens for $4.40. At this rate:

+

 

+

How many tokens could she buy with $6.05?  

+

 

+

tokens

",11,11,,,30604 +PSBDNUV,1,Fill-in-the-blank(s),Numeric,"

What is 34÷18?

+

 

+

",6,6,,,587537 +PRABQMPS,1,Fill-in-the-blank(s),Numeric,"

Compute 4,803 · 95.

+

 

+

","456,285","456,285",,,284725 +PSBF75,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

What is 25% of 160?

+

 

+

",40,40,,,32069 +PSBF26,1,Fill-in-the-blank(s),Numeric,"

A snail travels 10 cm in 4 minutes. At this rate:

+

 

+

How long will it take the snail to travel 24 cm?

+

 

+

minutes

",9.6,9.6,,,31058 +PSBGBH,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

What is 150% of 32?

+

 

+

",48,48,,,32696 +PSBF9P,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

What is 39% of 200?

+

 

+

",78,78,,,32378 +PSBGC8,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

13 is 50% of what number?

+

 

+

",26,26,,,33021 +PSBGGX,2,Fill-in-the-blank(s),Numeric,"

What is the slope of the line you graphed?

+

 

+

",-1,-1,,,33513 +PSBGE8,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

18 is 120% of what number?

+

 

+

",15,15,,,33334 +PRABQKZE,1,Fill-in-the-blank(s),Numeric,"

Compute 3,902·85.

+

 

+

",331670,331670,,,457114 +PSBG2Q,2,Fill-in-the-blank(s),Algebraic Expression,"

What is the volume of the cone? Express your answer in terms of π.

+

 

+

cubic units

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",36pi,36pi,,,36673 +PSBG69,2,Fill-in-the-blank(s),Numeric,"

What fraction of the daily recommended value of iron is in 1 cup of oatmeal?

+

 

+

 

+

 

+

",15-Feb,15-Feb,,,37276 +PSBBZUE,1,Fill-in-the-blank(s),Exact Fraction,"

A teacher asked all the students in one class how many minutes it takes them to get to school. Here is a table of their responses:

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
2010158515105
2051510310185
2555121030510
+

 

+

 

+

What fraction of the students in this class say it takes them 5 minutes to get to school?

+

 

+

",24-Jul,24-Jul,,,297138 +PSB3AD,3,Fill-in-the-blank(s),Numeric,"

A line contains the points (-3, -2) and (7, 2).

+

 

+

Calculate the slope of the line.

+
 
+

 

+

",5-Feb,5-Feb,,,132337 +PSBG89,2,Fill-in-the-blank(s),Exact Fraction,"

What fraction of  is ?

+

 

+

 

+

Enter your answer as an exact fraction.

+

 

+

",3-Feb,3-Feb,,,37735 +PSBBWH7,2,Fill-in-the-blank(s),Numeric,"

A stack of 500 pieces of paper is 1.875 inches tall.

+

 

+

Compute the thickness of each piece of paper.

+

 

+

inches

",0.00375,0.00375,,,277925 +PRABHHQY,1,Fill-in-the-blank(s),Numeric,"

The two triangles shown are similar. Find the value of .

+

+
 
+

 

+

","3/2, 1.5","3/2, 1.5",,,37464 +PRABMSG5,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression. If the answer is not a whole number, write your answer as a fraction.

+

 

+

43 ÷ -24

+

 

+

",-0.055555556,-0.055555556,,,38766 +PSBHTM,2,Fill-in-the-blank(s),Algebraic Expression,"

Correct the error. What should the line actually be?

+

 

+

",4x-1,4x-1,,,40512 +PSBBZUE,2,Fill-in-the-blank(s),Exact Fraction,"

A teacher asked all the students in one class how many minutes it takes them to get to school. Here is a table of their responses:

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
2010158515105
2051510310185
2555121030510
+

 

+

 

+

What fraction of the students in this class say it takes them more than 10 minutes to get to school?

+

 

+

","9/24, 3/8","9/24, 3/8",,,297237 +PSBHPP,3,Fill-in-the-blank(s),Numeric,"

Strawberries cost $3.00 per pound. 

+

 

+

How many pounds of strawberries can you buy for $11.00?  

+

 

+

pounds of strawberries

",3-Nov,3-Nov,,,39959 +PSBHTH,1,Fill-in-the-blank(s),Numeric,"

An area of 6 square yards is equal to 54 square feet. 9 square yards is equal to how many square feet?  

+

 

+

square feet

",81,81,,,40656 +PSBH52,1,Fill-in-the-blank(s),Numeric,"

Another temperature scale frequently used in science is the Kelvin scale. In this scale, 0 is the lowest possible temperature of anything in the universe, and it is -273.15 degrees in the Celsius scale. Each 1 K is the same as 1°C so 10 K is the same as -263.15°C.

+

 

+

Water boils at 100°C. What is this temperature in K?

+

 

+

K

",373.15,373.15,,,42388 +PSBJDX,2,Order / Sort,Ordering,

Add the new set of cards to the first set so that all of the cards are ordered from least likely to most likely.

,"
+
+
+
+

The probability that a certain medical test gives the right result is 0.95. The chance that this medical test is correct for a random patient.

+
+
+
+
,
+
+
+
+

A fishbowl contains 5 balls where each one has an even number from 2 to 10 written on it and you choose one. The chance that you draw out of ball with the number 3 on it.

+
+
+
+
,

10% of people are left handed. The chance that a randomly chosen person is left handed.

,
+
+
+
+

In general English usage, 45 of words begin

+

with the letter T. The chance that a randomly chosen word in a novel begins with the letter T.

+
+
+
+
,

The weather report says there is a 20% chance of rain tomorrow. The chance of rain tomorrow.

,
+
+
+
+

The chance that your opponent will play rock first in a game of paper, rock, scissors.

+
+
+
+
,
+
+
+
+

2 out of every 5 dentists recommend a certain brand of toothpaste. The chance that a random dentist recommends the toothpaste.

+
+
+
+
,

Half of the cards in a deck are red and half are black. Shuffle the cards and select the first card. The chance that the card is red.

,

The offspring of two fruit flies in a science experiment have a 75% chance of having redeyes. The chance that the first fly to hatch has red eyes.

,
+
+
+
+

A pile contains 6 square pattern blocks and you choose one. The chance that the block you choose has 4 sides of the same length.

+
+
+
+
","
+
+
+
+

The probability that a certain medical test gives the right result is 0.95. The chance that this medical test is correct for a random patient.

+
+
+
+
,
+
+
+
+

A fishbowl contains 5 balls where each one has an even number from 2 to 10 written on it and you choose one. The chance that you draw out of ball with the number 3 on it.

+
+
+
+
,

10% of people are left handed. The chance that a randomly chosen person is left handed.

,
+
+
+
+

In general English usage, 45 of words begin

+

with the letter T. The chance that a randomly chosen word in a novel begins with the letter T.

+
+
+
+
,

The weather report says there is a 20% chance of rain tomorrow. The chance of rain tomorrow.

,
+
+
+
+

The chance that your opponent will play rock first in a game of paper, rock, scissors.

+
+
+
+
,
+
+
+
+

2 out of every 5 dentists recommend a certain brand of toothpaste. The chance that a random dentist recommends the toothpaste.

+
+
+
+
,

Half of the cards in a deck are red and half are black. Shuffle the cards and select the first card. The chance that the card is red.

,

The offspring of two fruit flies in a science experiment have a 75% chance of having redeyes. The chance that the first fly to hatch has red eyes.

,
+
+
+
+

A pile contains 6 square pattern blocks and you choose one. The chance that the block you choose has 4 sides of the same length.

+
+
+
+
",,,43887 +PSBJBR,1,Fill-in-the-blank(s),Numeric,"

Andre picks blocks out of a bag 60 times and notes that 43 of them were green.

+

 

+

What should Andre estimate for the probability of picking out a green block from this bag?

+

 

+

",43/60,43/60,,,43208 +PRABFERH,1,Fill-in-the-blank(s),Numeric,"

How many 15-liter glasses can Lin fill with a 112-liter bottle of water?

+

 

+

glasses

",7 1/2,7 1/2,,,275212 +PRABGJXG,1,Fill-in-the-blank(s),Numeric,"

Calculate the sum.

+

 

+

0.401 + 9.28

+

 

+

",9.681,9.681,,,9184 +PRABGJRS,1,Fill-in-the-blank(s),Numeric,"

How many 112-liter bottles of water does it take to fill a 16-liter jug? 

+

 

+

bottles of water

+

Express your answer in fraction form.

",10 2/3,10 2/3,,,275405 +PSBJQT,1,Fill-in-the-blank(s),Numeric,"

Answer the question below.

+

 

+

35% of f is 14. What is f?

+

 

+

",40,40,,,45372 +PRABD8HP,1,Fill-in-the-blank(s),Numeric,"

A restaurant offers delivery for their pizzas. The total cost is a delivery fee added to the price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. How many pizzas are delivered to a customer who pays $80?

+

 

+

pizzas

",7,7,,,43417 +PSBBVNT,3,Fill-in-the-blank(s),Numeric,"

Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets.  

+

 

+

If the family pays $25, what is the exact amount of change they should receive? 

+

 

+

$

",1.25,1.25,,,273269 +PSBSNF,3,Fill-in-the-blank(s),Numeric,"

A roll of ribbon was 12 meters long. Diego cut 9 pieces of ribbon that were 0.4 meter each to tie some presents. He then used the remaining ribbon to make some wreaths. Each wreath required 0.6 meter.  

+

 

+

How many wreaths could Diego make with the available ribbon?

+

 

+

wreaths

",14,14,,,81543 +PSBJNV,1,Fill-in-the-blank(s),Numeric,"

Answer the question below.

+

 

+

125% of e is 30. What is e?

+

 

+

",24,24,,,45043 +PSBJFK,2,Fill-in-the-blank(s),Algebraic Expression,"

Tyler needs some extra calories each day during his sports season. He wants to know how many servings he can have each day if all the extra calories come from the fruit snack. Write an equation that shows the number of servings, n, in terms of the number of calories, c.

+

 

+

n =

+

Use c as your variable.

",c/90,c/90,,,44015 +PRABMQK7,1,Fill-in-the-blank(s),Numeric,"

Noah enlarged a photograph by a scale factor of 6. The area of the enlarged photo is how many times as large as the area of the original?

+

 

+

times as many

",36,36,,,44380 +PSBJGY,3,Fill-in-the-blank(s),Numeric,"

A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages.

+

 

+

What is the probability that you turn to an even numbered page?

+

 

+

",214/428,214/428,,,44248 +PSBJM9,3,Fill-in-the-blank(s),Numeric,"

Now solve:  You need 34 yard of ribbon for one gift box. You have 3 yards of ribbon. How many gift boxes do you have ribbon for?  

+

 

+

gift boxes

",4,4,,,45097 +PSBJJW,3,Fill-in-the-blank(s),Numeric,"

How many times around the park did he ride?

+

 

+

 

+

",2,2,,,44687 +PSBJTA,2,Fill-in-the-blank(s),Numeric,"

How many of the values in this data set are between the first quartile and the median?

+

 

+

",5,5,,,45802 +PRABTTMR,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression when x is 4 and y is 6.

+

 

+

+

 

+

 

+

",4,4,,,46539 +PRABFG36,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

 

+

",15,15,,,46338 +PRABFG4A,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

",72,72,,,46909 +PRABTTMM,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression when x is 4 and y is 6.

+

 

+

+

 

+

",66,66,,,46425 +PRABFG38,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

 

+

",4,4,,,46711 +PRABTTMQ,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression when x is 4 and y is 6.

+

 

+

+

 

+

",1,1,,,46924 +PRABFG37,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

",27,27,,,46527 +PRABTTMP,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression when x is 4 and y is 6.

+

 

+

+

 

+

",17,17,,,46811 +PRABTTMN,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression when x is 4 and y is 6.

+

 

+

+

 

+

",16-Jan,16-Jan,,,46683 +PRABFG4B,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

",9,9,,,47289 +PRABFG4C,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

",1,1,,,47479 +PRABFK8X,1,Fill-in-the-blank(s),Numeric,"

There are 20 pennies in a jar. If 16% of the coins in the jar are pennies, how many coins are there in the jar?

+

 

+

coins

",125,125,,,47523 +PRABFG39,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression below.

+

 

+

+

 

+

",2,2,,,47109 +PSBUGJ,1,Fill-in-the-blank(s),Numeric,"

Use long division to find the quotient. Write your answer as a decimal.

+

99 ÷ 12

+

 

+

",8.25,8.25,,,92124 +PSBKEG,2,Fill-in-the-blank(s),Numeric,"

What value of d makes the equation true?

+

 

+

12+d=-4.8

+

 

+

d =

",-16.8,-16.8,,,48612 +PRABGZF4,1,Fill-in-the-blank(s),Numeric,"

A cube has side length of  10 inches. What is its volume?  

+

 

+

 

+

cubic inches

","1,000","1,000",,,48762 +PSBKG8,4,Fill-in-the-blank(s),Numeric,"

What value makes sense for the slope of the line that represents the amounts on Han’s fare card in July?

+

 

+

",0,0,,,49232 +PRABFG5C,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

15 = 23x

+

 

+

x =

+

If necessary, express your answer in fraction form.

",10-Mar,10-Mar,,,50865 +PSBSNF,1,Fill-in-the-blank(s),Numeric,"

A roll of ribbon was 12 meters long. Diego cut 9 pieces of ribbon that were 0.4 meter each to tie some presents. He then used the remaining ribbon to make some wreaths. Each wreath required 0.6 meter.  

+

 

+

How many meters of ribbon were available for making wreaths?

+

 

+

meters

",8.4,8.4,,,81261 +PSBK75,3,Fill-in-the-blank(s),Numeric,"

How many triangles can you fit together at one vertex? 

+

 

+

Do not include units (triangles) in your answer.

+

 

+

",6,6,,,53019 +PSBK75,1,Fill-in-the-blank(s),Numeric,"

 What is the measure of each angle in an equilateral triangle? 

+

 

+

Do not include units (degrees) in your answer.

+

 

+

",60,60,,,52844 +PSBMBT,4,Fill-in-the-blank(s),Numeric,"

Use any method to find the value for y that makes the equation true.

+

 

+

y=

",20,20,,,54008 +PSBMFR,4,Fill-in-the-blank(s),Numeric,"

How many students are in the school in 63 of them are sixth graders?

+

 

+

 students

",147,147,,,54666 +PSBBRP,1,Fill-in-the-blank(s),Numeric,"

Calculate the difference. 

+

 

+

13.2 − 1.78   

+

 

+

",11.42,11.42,,,7369 +PSBMFR,2,Fill-in-the-blank(s),Numeric,"

How many sixth graders are there if the school has 28 students?  

+

 

+

 sixth graders

",12,12,,,54441 +PSBMFR,3,Fill-in-the-blank(s),Algebraic Expression,"

If the school has x students, write an expression for the number of sixth graders in terms of x.  

+

 

+

","(3/7)x, 3x/7","(3/7)x, 3x/7",,,54562 +PSBBVU,1,Fill-in-the-blank(s),Numeric,"

Calculate the difference. 

+
 
+
0.9−0.245
+

 

+

",0.655,0.655,,,8064 +PSBBRFG,3,Fill-in-the-blank(s),Numeric,"

Calculate the sum vertically.

+

 

+

0.137+0.284.

+

 

+

",0.421,0.421,,,249867 +PSBBWPJ,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism measures 712 cm by 12 cm by 1512 cm.

+

 

+

Calculate the number of cubes with edge length 12 cm that fit in this prism.

+

 

+

cubes

","11,160","11,160",,,278504 +PSBBWPJ,2,Fill-in-the-blank(s),Numeric,"

A rectangular prism measures 712 cm by 12 cm by 1512 cm.

+

 

+

What is the volume of the prism in cm3?   If you are stuck, think about how many cubes with 12-cm edge lengths fit into 1 cm3.

+

 

+

cm3

",1395,1395,,,278648 +PSBM6G,1,Fill-in-the-blank(s),Numeric,"

. How many other whole numbers can you raise to a power and get 4,096?

+

 

+

 

+

",5,5,,,58258 +PSBNAB,3,Fill-in-the-blank(s),Algebraic Expression,"

A cone fits snugly inside a hemisphere, and they share a radius of 5.

+

 

+

+

 

+

What is the volume of the cone?

+

 

+

cubic units

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",125/3pi,125/3pi,,,58785 +PSBNQS,3,Fill-in-the-blank(s),Numeric,"

Find the value of the expression below.

+

 

+

+

 

+

",110,110,,,60862 +PRABGJXF,1,Fill-in-the-blank(s),Numeric,"

Calculate the sum.

+

 

+

1.075 + 27.105

+

 

+

",28.18,28.18,,,9017 +PSBNQS,4,Fill-in-the-blank(s),Numeric,"

Find the value of the expression below.

+

 

+

-22 ÷ 5

+
 
+

 

+

",-4.4,-4.4,,,61160 +PRABETNG,1,Fill-in-the-blank(s),Numeric,"

A shopper bought a watermelon, a pack of napkins, and some paper plates. In his state, there is no tax on food. The tax rate on non-food items is 5%. The total for the three items he bought was $8.25 before tax, and he paid $0.19 in tax. How much did the watermelon cost?

+

 

+

$

",4.45,4.45,,,62350 +PRABFFDZ,1,Fill-in-the-blank(s),Numeric,"

Calculate the sum.

+

 

+

33.1 + 1.95

+

 

+

",35.05,35.05,,,8869 +PSBBTU,1,Fill-in-the-blank(s),Numeric,"

Calculate the difference. 

+
 
+
23.11−0.376
+

 

+

",22.734,22.734,,,7710 +PSBPBA,2,Fill-in-the-blank(s),Numeric,"

Solve the equation to find their starting altitude.

+

 

+

feet

",-11,-11,,,64354 +PRABMSH6,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(-0.2) • (-0.3)

+

 

+

",0.06,0.06,,,65369 +PRABFJZP,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3a = 12

+

 

+

a =

+

 

",4,4,,,64054 +PSBCAR,2,Fill-in-the-blank(s),Numeric,"

Use Priya’s method to calculate 1.05 · 2.8. You can use the fact that105 · 28 = 2,940.

+

 

+

",2.94,2.94,,,10467 +PSBCMQV,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(0.64)⋅(0.81)

+

 

+

",0.5184,0.5184,,,403777 +PSB66B,2,Fill-in-the-blank(s),Numeric,"

There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.

+

 

+

How many kids rent instruments?  

+

 

+

kids

",72,72,,,153894 +PSBQMK,1,Fill-in-the-blank(s),Numeric,"

Find the difference. 

+

 

+

+

 

+

",1.7,1.7,,,70629 +PSBQJD,1,Fill-in-the-blank(s),Numeric,"

Find the difference. 

+

 

+

+

 

+

",0.25,0.25,,,70299 +PSBQRA,1,Fill-in-the-blank(s),Numeric,"

Find the difference. 

+

 

+

+

 

+

",0.013,0.013,,,71223 +PSBQPM,1,Fill-in-the-blank(s),Numeric,"

Find the difference. 

+

 

+

+

 

+

",0.97,0.97,,,70912 +PRABG6YN,1,Fill-in-the-blank(s),Numeric,"

Evaluate mentally: 

+

 

+

",1.4,1.4,,,71526 +PRABQBQM,1,Fill-in-the-blank(s),Numeric Expression,"

Another stack of books is 43 inches tall. Each book is -inch thick. 

+

 

+

Write an expression that represents the number of books in the stack.

+

 

+

",43/.5,43/.5,,,80072 +PRABFF2C,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(2.05)·(0.004)

+

 

+

",0.0082,0.0082,,,75309 +PSBRQK,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

5÷110

+

 

+

",50,50,,,76458 +PSBRUP,1,Fill-in-the-blank(s),Numeric,"

Compute the product using the equation 21 ⋅ 47 = 987 and what you know about fractions, decimals, and place value.

+

 

+

 (2.1) ⋅ (4.7)

+

 

+

",9.87,9.87,,,77299 +PSBRUJ,1,Fill-in-the-blank(s),Numeric,"

A scale drawing of a school bus has a scale of 12 inches to 5 feet. If the length of the school bus is 412 inches on the scale drawing, what is the actual length of the bus?

+

 

+

  feet

",45,45,,,77198 +PSBRWA,1,Fill-in-the-blank(s),Numeric,"

Compute the product using the equation 21 ⋅ 47 = 987 and what you know about fractions, decimals, and place value.

+

 

+

21 ⋅ (0.047)

+

 

+

",0.987,0.987,,,77578 +PSBR2P,1,Fill-in-the-blank(s),Numeric,"

Find the value of 36.8 ÷ 2.3.

+

 

+

",16,16,,,78269 +PSBRX3,1,Fill-in-the-blank(s),Numeric,"

Compute the product using the equation 21 ⋅ 47 = 987 and what you know about fractions, decimals, and place value.

+

 

+

(0.021) ⋅ (4.7)

+

 

+

",0.0987,0.0987,,,77861 +PSBRYP,1,Fill-in-the-blank(s),Numeric,"

A farm lets you pick 3 pints of raspberries for $12.00.

+

 

+

What is the cost per pint? 

+

 

+

$

",4,4,,,77528 +PSBRWS,1,Fill-in-the-blank(s),Numeric,"

A box contains  pounds of pancake mix. Jada used  pound for a recipe. What fraction of the pancake mix in the box did she use?

+

 

+

 

+

",2-Jan,2-Jan,,,77616 +PSBR72,2,Fill-in-the-blank(s),Numeric,"

Use the diagram to help you find (0.04) ⋅ (0.02). 

+

 

+

",0.0008,0.0008,,,79155 +PRABHHJ4,1,Fill-in-the-blank(s),Exact Fraction,"

Find the quotient. Write your answer as a fraction or a mixed number.

+

 

+

+

 

+

","2 1/35, 71/35","2 1/35, 71/35",,,81337 +PRABHHJ3,1,Fill-in-the-blank(s),Exact Fraction,"

Find the quotient. Write your answer as a fraction or a mixed number.

+

 

+

+

 

+

","25/8, 3 1/8","25/8, 3 1/8",,,81228 +PRABHNCG,1,Fill-in-the-blank(s),Numeric,"

A large bucket holds 5 gallons of water, which is about the same as 19 liters of water. 

+

 

+

A small bucket holds 2 gallons of water. About how many liters does it hold?

+

 

+

liters

",7.6,7.6,,,57665 +PSBTEW,1,Fill-in-the-blank(s),Numeric,"

A fence is being built around a rectangular garden that is  812 feet by  613 feet. Fencing comes in panels.  Each panel is 23 of a foot wide. How many panels are needed? 

+

 

+

 

+

panels

","45, 46","45, 46",,,86400 +PSBTTV,4,Fill-in-the-blank(s),Numeric,"

What is the slope of the graph between 0 and 10?

+

 

+

",10,10,,,87931 +PSBBH,1,Fill-in-the-blank(s),Numeric,"

Calculate (1.6) · (0.215).

+

 

+

",0.344,0.344,,,88 +PSBTT4,2,Fill-in-the-blank(s),Numeric,"

How many circles of radius 1 can you fit inside a circle of radius 3 units so that they do not overlap?

+

 

+

 

+
+

If you get stuck, consider using coins or other circular objects.

+
+

 

+

",7,7,,,88453 +PSBTUK,1,Fill-in-the-blank(s),Numeric,"

In her English class, Mai’s teacher gives 4 quizzes each worth 5 points. After 3 quizzes, she has the scores 4, 3, and 4. What does she need to get on the last quiz to have a mean score of 4?

+

 

+

",5,5,,,88478 +PSBTT4,1,Fill-in-the-blank(s),Numeric,"

How many circles of radius 1 can you fit inside a circle of radius 2 units so that they do not overlap?

+

 

+
+

If you get stuck, consider using coins or other circular objects.

+
+

 

+

",2,2,,,88342 +PSBTT4,3,Fill-in-the-blank(s),Numeric,"

How many circles of radius 1 can you fit inside a circle of radius 4 units so that they do not overlap?

+

 

+
+

If you get stuck, consider using coins or other circular objects.

+
+

 

+

",11,11,,,88561 +PSBTTV,6,Fill-in-the-blank(s),Numeric,"

What is the slope of the graph between 11 and 15?

+

 

+

",9,9,,,88244 +PRABKA6Z,1,Fill-in-the-blank(s),Numeric,"

What is the value of the expression?

+

 

+
+

 

+

",1,1,,,91640 +PSBUDU,3,Fill-in-the-blank(s),Numeric,"

Based on the information in the table, what do you think the inventory will be at on Saturday morning? Explain your reasoning.

+

 

+

",18,18,,,91688 +PSBUDU,4,Fill-in-the-blank(s),Numeric,"

What is the difference between greatest and least inventory?

+

 

+

",20,20,,,91790 +PSBUMJ,1,Fill-in-the-blank(s),Numeric,"

Find the product of 12 and 8.

+

 

+

",96,96,,,92205 +PSBUJG,1,Fill-in-the-blank(s),Numeric,"

Use long division to find the quotient. Write your answer as a decimal.

+

 

+

216 ÷ 5

+

 

+

",43.2,43.2,,,92479 +PSBUMJ,3,Fill-in-the-blank(s),Numeric,"

Find the least common multiple of 12 and 8.

+

 

+

",24,24,,,92518 +PSBUMJ,2,Fill-in-the-blank(s),Numeric,"

Find the greatest common factor of 12 and 8.

+

 

+

",4,4,,,92361 +PSBUMJ,4,Fill-in-the-blank(s),Numeric,"

Find the product of the greatest common factor and the least common multiple of 12 and 8.

+

 

+

",96,96,,,92677 +PSBU8Y,2,Fill-in-the-blank(s),Numeric,"

What is the probability the computer produces the first letter of your first name?

+

 

+

",26-Jan,26-Jan,,,96902 +PSBU9K,2,Fill-in-the-blank(s),Numeric,"

Find the area of each parallelogram.

+

 

+

+

 

+

 

+

Parallelogram B: square units.

",6,6,,,97230 +PSBVBE,2,Fill-in-the-blank(s),Numeric,"

The store bought a table for $200 and sold it for $350. What percentage was the markup?

+

 

+

 %

",75,75,,,97533 +PRABEUB8,1,Fill-in-the-blank(s),Numeric,"

What is the probability of selecting a random month of the year and getting a month that starts with the letter “J?”  If you get stuck, consider listing the sample space.

+

 

+

",12-Mar,12-Mar,,,97915 +PRABQN7G,1,Fill-in-the-blank(s),Numeric,"

A practice field is 250 feet long. The game field is 40% longer than the practice field. How long is the game field?  

+

 

+

feet

",350,350,,,98095 +PSBVQX,1,Fill-in-the-blank(s),Numeric,"

A school’s art club holds a bake sale on Fridays to raise money for art supplies. Here are the number of cookies they sold each week in the fall and in the spring:

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
fall20262524292019192424
spring19272921252226212525
+

 

+

Find the mean number of cookies sold in the fall.

+

 

+

",23,23,,,99247 +PSBJWY,3,Fill-in-the-blank(s),Numeric,"

What is the third quartile (Q3)?  

+

",8,8,,,46235 +PSBVQX,3,Fill-in-the-blank(s),Numeric,"

The MAD for the fall data is 2.8 cookies. The MAD for the spring data is 2.6 cookies. Express the difference in means as a multiple of the larger MAD.

+

 

+

Round your answer to the hundredth place.

+

 

+

",0.36,0.36,,,99939 +PRABEU7C,1,Fill-in-the-blank(s),Numeric,"

If 6 coins are flipped, find the probability that there is at least 1 heads.

+
 
+

 

+

",63/64,63/64,,,100714 +PSBVQX,2,Fill-in-the-blank(s),Numeric,"

Find the mean number of cookies sold in the spring.

+

 

+

",24,24,,,99606 +PRABHUGD,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?

+

 

+

ounces of cereal

+
",22.2,22.2,,,100544 +PSBVWT,4,Fill-in-the-blank(s),Numeric,"

Here are several recipes for sparkling lemonade. For each recipe, describe how many tablespoons of lemonade mix it takes per cup of sparkling water.

+

 

+

12 tablespoon of lemonade mix and 34 cups of sparkling water.

+

 

+

tablespoons lemonade mix per cup of sparkling water

+

Write your answer as a fraction.

",3-Feb,3-Feb,,,101254 +PSBWMQ,1,Fill-in-the-blank(s),Numeric,"

Tyler wonders what proportion of students at his school would dye their hair blue if their parents would let them. He surveyed a random sample of 10 students at his school, and 2 of them said they would. Kiran didn’t think Tyler’s estimate was very accurate, so he surveyed a random sample of 100 students, and 17 of them said they would.

+

 

+

Based on Tyler's sample, what proportion of the students would dye their hair blue?

+

 

+

",10-Feb,10-Feb,,,104881 +PSBWJZ,4,Fill-in-the-blank(s),Numeric,"

Use the graph to determine how much total rain fell on Tuesday.

+

 

+

cm 

",10,10,,,105377 +PRABTVKN,1,Fill-in-the-blank(s),Numeric,"

Un funcionario de tren analiza la ruta de un viaje y registra la distancia que recorre el tren en ciertos intervalos de tiempo.

+

 

+ + + + + + + + + + + + + + + + + + + +
tiempo (horas)distancia (millas)
0.522.5
145
1.567.5
+

 

+

 

+

El tren viaja a una rapidez constante. ¿Cuál es su rapidez?

+

 

+

 

+

millas por hora

",45,45,,,320443 +PRABJDMS,1,Fill-in-the-blank(s),Numeric,"

The population of city B was approximately 7,150,000, and it increased by 0.8% in one year. What was the new population?

+

 

+

Approximately people

","7207200, 7210000 ","7207200, 7210000 ",,,318309 +PSBEB6,2,Fill-in-the-blank(s),Numeric,"

What percentage of the students have more than one child in the family?

+

 

+

%

+

 

+

",75,75,,,21866 +PRABTVKQ,1,Fill-in-the-blank(s),Numeric,"

Noah y Andre están a 15 millas de distancia por un camino y comienzan a andar en bicicleta el uno hacia el otro. Noah pedalea a una rapidez constante de 4 millas por hora y Andre a una rapidez constante de 2 millas por hora. ¿Cuánto tiempo tardan en encontrarse?

+

 

+

horas

",2.5,2.5,,,320538 +PSBW4V,2,Fill-in-the-blank(s),Numeric,"

What value could you write in after 3x that would make the equation true for all values of x?

+

 

+

3x + 8 = 3x +  

+

 

+

",8,8,,,108574 +PRABHKBS,1,Fill-in-the-blank(s),Exact Fraction,"

Find the value of 

+

 

+

","21/4, 5 1/4","21/4, 5 1/4",,,111092 +PSBXC8,2,Fill-in-the-blank(s),Numeric,"

After how many months will the bamboo plant be 66 inches tall? months

",18,18,,,110017 +PSBXTM,2,Fill-in-the-blank(s),Numeric,"

Calculate the value of the expression below.

+

 

+

+

 

+

","16/3, 5 1/3","16/3, 5 1/3",,,112497 +PSBXTM,1,Fill-in-the-blank(s),Numeric,"

Calculate the value of the expression below.

+

 

+

+
 
+

 

+

","-16/3, -5 1/3","-16/3, -5 1/3",,,112290 +PSBXTM,4,Fill-in-the-blank(s),Numeric,"

Calculate the value of the expression below.

+

 

+

 

+

 

+

",-6,-6,,,112797 +PSBXSP,2,Fill-in-the-blank(s),Numeric,"

What is the coefficient of the variable?

+

 

+

",2,2,,,112511 +PSBYB5,6,Fill-in-the-blank(s),Numeric,"

Use the sample space to determine the probability that a fifth person would get the same outcome as person 1.

+

 

+

",15-Jan,15-Jan,,,115723 +PSBX7V,3,Fill-in-the-blank(s),Numeric,"

Teachers held a basketball shooting contest. Their goal was to make 60 baskets. For the teacher, determine what percentage of the goal they achieved.

+

 

+

Teacher C made 66 baskets.

+

 

+

%

",110,110,,,114889 +PSBX7V,4,Fill-in-the-blank(s),Numeric,"

Teachers held a basketball shooting contest. Their goal was to make 60 baskets. For the teacher, determine what percentage of the goal they achieved.

+

 

+

Teacher D made 9 baskets.  

+

 

+

%

",15,15,,,115027 +PSBYAA,2,Fill-in-the-blank(s),Numeric,"

What is the height of the 500 ml mark? Recall that 1 liter (L) is equal to 1000 milliliters (ml), and that 1 liter (L) is equal to 1,000 cm3.

+

 

+

cm

",12,12,,,115187 +PSBYTP,1,Order / Sort,Ordering,

Order the following pairs of coordinates from closest to farthest apart. Be prepared to explain your reasoning.

,"(7, 0) and (7, -9), (-3, 6) and (5, 6), (2, 4) and (2, 10), (1, -10) and (-4, -10), (-12, -12) and (-12, -1)","(7, 0) and (7, -9), (-3, 6) and (5, 6), (2, 4) and (2, 10), (1, -10) and (-4, -10), (-12, -12) and (-12, -1)",,,117898 +PSBYQW,2,Fill-in-the-blank(s),Numeric,"

What is the common value?

+

 

+

",50,50,,,117528 +PSBYTD,3,Fill-in-the-blank(s),Numeric Expression,"

Calculate the quotient of 109.2 ÷ 6 using any method of your choice.

+

 

+

",18.2,18.2,,,117994 +PSBYUC,7,Fill-in-the-blank(s),Numeric,"

The machine must be emptied to be serviced. If there are 40 bottles in the machine when it is to be serviced, what number will go in the second column in the table?

+

 

+

",-40,-40,,,118176 +PSBYX9,2,Fill-in-the-blank(s),Numeric Expression,"

Find the value of 61.12 ÷ 3.2.

+

 

+

",19.1,19.1,,,118786 +PSBY5V,3,Fill-in-the-blank(s),Numeric,"

At a school, 460 of the students walk to school. 

+

 

+

The number of students who ride the school bus is 110% of the number of students who walk. How many students ride the school bus?

+

 

+

students

",506,506,,,119945 +PRABETC2,1,Fill-in-the-blank(s),Numeric,"

It takes an ant farm 3 days to consume 12 of an apple. At that rate, in how many days will the ant farm consume 3 apples?  

+

 

+

days

",18,18,,,121533 +PSBZRX,1,Fill-in-the-blank(s),Numeric,"

Figures R, S, and T are all scaled copies of one another. Figure S is a scaled copy of R using a scale factor of 3. Figure T is a scaled copy of S using a scale factor of 2.

+

 

+

Find the scale factor from T to S.

+

 

+

",2-Jan,2-Jan,,,122745 +PSBZRX,3,Fill-in-the-blank(s),Numeric,"

Find the scale factor from R to T.

+

 

+

",6,6,,,123335 +PSBZRX,4,Fill-in-the-blank(s),Numeric,"

Find the scale factor from T to R.

+

 

+

",6-Jan,6-Jan,,,123444 +PSBZT4,2,Fill-in-the-blank(s),Numeric,"

What is the constant of proportionality?

+

 

+

 wheels per bus

",6,6,,,123500 +PSB2MF,1,Fill-in-the-blank(s),Numeric Expression,"

A cube has edge length 11 inches.

+

 

+

 

+

Write an expression for its volume.

+

 

+

V =

",11^3,11^3,,,128141 +PSBZWG,2,Fill-in-the-blank(s),Numeric,"

You spin the spinner 80 times. About how many times do you expect it will land on something other than A?

+

 

+

times

",60,60,,,124041 +PRABEQD2,1,Fill-in-the-blank(s),Numeric,"

Polygon B is a scaled copy of Polygon A using a scale factor of 5. Polygon A’s area is what fraction of Polygon B’s area?

+

 

+

",25-Jan,25-Jan,,,124672 +PSBZRX,2,Fill-in-the-blank(s),Numeric,"

Find the scale factor from S to R.

+

 

+

",3-Jan,3-Jan,,,123193 +PSBZ6U,2,Fill-in-the-blank(s),Numeric,"

After the discount, how much would the book cost? 

+

 

+

$

",15.3,15.3,,,125385 +PRABESEN,1,Fill-in-the-blank(s),Numeric,"

Noah was assigned to make 64 cookies for the bake sale. He made 125% of that number. 90% of the cookies he made were sold. How many of Noah's cookies were left after the bake sale?  

+

 

+

 

+

cookies

",8,8,,,123995 +PSB2CK,6,Fill-in-the-blank(s),Numeric,"

What is its answer?

+

 

+

",2.64,2.64,,,126628 +PSB2FK,2,Fill-in-the-blank(s),Numeric,"

What is the probability Mai will win the game? 

+

 

+

",3-Jan,3-Jan,,,126669 +PSB2CK,2,Fill-in-the-blank(s),Numeric,"

What is its answer?

+

 

+

",264,264,,,126091 +PSB2CK,4,Fill-in-the-blank(s),Numeric,"

What is its answer?

+

 

+

",26.4,26.4,,,126362 +PSB2CN,3,Fill-in-the-blank(s),Numeric,"

What value did Lin find for 62 ÷ 5?

+

 

+

",12.4,12.4,,,126648 +PRABFF2B,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(21.2)·(0.02)

+
 
+

 

+

",0.424,0.424,,,75189 +PSB2HQ,2,Fill-in-the-blank(s),Numeric,"

What percentage remains?  

",50,50,,,127791 +PSB2J8,1,Fill-in-the-blank(s),Numeric,"

Noah wants to save $60 so that he can purchase a concert ticket. If he has saved $45 so far, what percentage of his goal has he saved? 

+

 

+

%

",75,75,,,128001 +PSB2MG,2,Fill-in-the-blank(s),Numeric,"

 How many pages are in the book?

+

 

+

pages

",175,175,,,128305 +PSB2UR,5,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation representing this relationship. Use c for cups and t for tablespoons.

+

 

+

c =

+

Use t as your variable.

",(1/16)t,(1/16)t,,,129738 +PSB26A,1,Fill-in-the-blank(s),Numeric,"

The temperature in degrees Fahrenheit, F, is related to the temperature in degrees Celsius, C, by the equation F=95C+32,

+

 

+

In the Sahara desert, temperatures often reach 50 degrees Celsius. How many degrees Fahrenheit is this?

+

 

+

degrees Fahrenheit

",122,122,,,131112 +PSB2UR,4,Fill-in-the-blank(s),Numeric,"

What is the constant of proportionality for this relationship?

+

 

+

  cups per tablespoon

",16-Jan,16-Jan,,,129451 +PSB2WS,1,Fill-in-the-blank(s),Numeric,"

Find (4.2) · (1.6) by drawing an area diagram or using another method.

+

 

+

",6.72,6.72,,,130191 +PSBXSP,1,Fill-in-the-blank(s),Exact Match,"

For the equation 2n−3=7

+


What is the variable?

+

 

+

",n,n,,,112350 +PSB2Z9,2,Fill-in-the-blank(s),Numeric,"

Now find x when y = 2.

+

 

+

y = 6x + 8

+

 

+

x =

",-1,-1,,,130824 +PSB3A4,1,Fill-in-the-blank(s),Numeric,"

Tyler orders a meal that costs $15. 

+

 

+

If the tax rate is 6.6%, how much will the sales tax be on Tyler’s meal? 

+

 

+

$

",0.99,0.99,,,131934 +PSB3BJ,2,Fill-in-the-blank(s),Numeric,"

Now find x when y = 2.

+

 

+

y = 34x - 212

+

 

+

x =

",6,6,,,132416 +PSB3BX,2,Fill-in-the-blank(s),Numeric,"

At a used book sale, 5 books cost $15.  

+

 

+

At this rate, how many books can you buy for $21?  

+

 

+

books

",7,7,,,132567 +PSB3BJ,1,Fill-in-the-blank(s),Numeric,"

For the following equation, find y when x=-3.

+

 

+

y = 34x - 212

+

 

+

y =

",-4.75,-4.75,,,132200 +PSB3CC,1,Fill-in-the-blank(s),Numeric,"

Find 1.8 ÷ 0.004. If you get stuck, think about what equivalent division expression you could write.

+

 

+

",450,450,,,132551 +PSB3EU,1,Fill-in-the-blank(s),Numeric,"

For the following equation, find y when x = -3.

+

 

+

y = 1.5x + 11

+

 

+

y =

",6.5,6.5,,,132688 +PRABG2SM,1,Fill-in-the-blank(s),Numeric,"

Find the quotient mentally.

+

 

+

246 ÷ 12

+

 

+

",20.5,20.5,,,133100 +PRABQKSH,1,Order / Sort,Ordering,

Order these numbers from least to greatest.

,"

1

,

49100

,

113

,

89

,

12

,

1120

,

0

","

1

,

49100

,

113

,

89

,

12

,

1120

,

0

",,,133338 +PSB3SQ,1,Order / Sort,Ordering,"

Without calculating, order the quotients of these expressions from least to greatest.

","42.6 ÷ 70, 42.6 ÷ 0.07, 42.6 ÷ 0.7, 426 ÷ 70","42.6 ÷ 70, 42.6 ÷ 0.07, 42.6 ÷ 0.7, 426 ÷ 70",,,134784 +PSB3SQ,3,Fill-in-the-blank(s),Numeric,"

Use this answer to find the quotient of one of the previous expressions.

+

 

+

","6.08571, 0.608571, 60.8571, 608.571","6.08571, 0.608571, 60.8571, 608.571",,,135051 +PSB35V,7,Fill-in-the-blank(s),Numeric,"

Copy and paste the formula to check your prediction.

+

 

+

What number does cell D2 display?

+

 

+

",15.3,15.3,,,137401 +PSB3X8,4,Fill-in-the-blank(s),Numeric,"

What is the value of |1.8|?

+

 

+

",1.8,1.8,,,136203 +PSB3X8,2,Fill-in-the-blank(s),Numeric,"

What is the value of |-7|?

+

 

+

",7,7,,,135943 +PSBBP4J,2,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.

+

 

+

square units.

+

 

+

",11,11,,,242640 +PSBBP4J,2,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.

+

 

+

square units.

+

 

+

",11,11,,,242640 +PRABGKQY,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

0.24 ÷ 0.015

+

 

+

",16,16,,,137016 +PSB35V,3,Fill-in-the-blank(s),Numeric,"

Type in the formula, and press enter to check your prediction.

+

 

+

What number does cell C2 display?

+

 

+

",16,16,,,137056 +PSB35V,5,Fill-in-the-blank(s),Numeric,"

Replace the formula with the number, and press enter to check your prediction.

+

 

+

What number does cell C2 now display?

+

 

+

",200,200,,,137232 +PSB4DY,3,Fill-in-the-blank(s),Numeric,"

What is the area of the triangle?  

+

 

+

square units

",3,3,,,138605 +PSB4FT,5,Fill-in-the-blank(s),Numeric,"

At this rate, how much would Lin be paid for 2.1 hours of work? 

+

 

+

$

",37.8,37.8,,,139112 +PSB4C3,2,Fill-in-the-blank(s),Numeric,"

Another cone has quadruple the radius, and the same height. How many times larger is the new cone’s volume?

+

 

+

times larger

",16,16,,,138533 +PSB4CN,1,Fill-in-the-blank(s),Numeric,"

Use the table to help you solve the following problems. 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
number of tacosprice in dollars
  
  
  
  
  
+

 

+

Noah bought 4 tacos and paid $6. At this rate, how many tacos could he buy for $15?

+

 

+

",10,10,,,138263 +PSBMJG,2,Fill-in-the-blank(s),Numeric,"

Find the surface area of the polyhedron in square centimeters.

+

 

+

+

 

+

 square centimeters

",84,84,,,54974 +PSBEWK,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shape.

+

 

+

+

 

+

square units

",19,19,,,24929 +PSB5NC,2,Order / Sort,Ordering,

Order the people from greatest to least in terms of how fast they checked the comments.

,"Person 4, Person 1, Person 3, Person 2","Person 4, Person 1, Person 3, Person 2",,,146150 +PSB5NC,1,Order / Sort,Ordering,"

A company is hiring people to read through all the comments posted on their website to make sure they are appropriate. Four people applied for the job and were given one day to show how quickly they could check comments.

+

 

+
    +
  • Person 1 worked for 210 minutes and checked a total of 50,000 comments.
    • +
  • Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes.
    • +
  • Person 3 worked for 120 minutes, at a rate represented by c = 331t,
    where c is the number of comments checked and t is the time in minutes.
    • +
  • Person 4 worked for 150 minutes, at a rate represented by 
    • +
+

 

+

Order the people from greatest to least in terms of total number of comments checked.

","Person 1, Person 2, Person 4, Person 3","Person 1, Person 2, Person 4, Person 3",,,146018 +PSBXNS,2,Fill-in-the-blank(s),Numeric,"

Use your equation to find x.

+

 

+

x =  

",65,65,,,111728 +PSB3DP,1,Fill-in-the-blank(s),Numeric,"

Neon bracelets cost $1 for 4.

+

 

+

What is the cost per bracelet? 

+

 

+

$

+

 

+

",0.25,0.25,,,132758 +PSB6N4,3,Fill-in-the-blank(s),Numeric,"

4000 is 4 times what number?

+

 

+

",1000,1000,,,151647 +PSB6N4,2,Fill-in-the-blank(s),Numeric,"

8 is 32 times what number?

+

 

+

",4-Jan,4-Jan,,,151533 +PRABG42R,1,Fill-in-the-blank(s),Numeric,"

Solve the equation. If you get stuck, try using a diagram.

+

 

+

5x + 14 = 614

+

 

+

x =

",3,3,,,153281 +PRABG4ZF,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Find the sum.

+

 

+
+
+
+

-5.7 + (-4.2) 

+

 

+

",-9.9,-9.9,,,154547 +PRABMSJP,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

-3d + 7 = 1

+

 

+

d =

",2,2,,,155769 +PRABMT58,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

4w−7=6w+31

+

 

+

w=

",-19,-19,,,155730 +PSB7T9,4,Fill-in-the-blank(s),Numeric,"

What is the slope of this line? 

+

 

+

",-1,-1,,,157579 +PSBBVMH,1,Fill-in-the-blank(s),Numeric,"

Find the area of triangle MOQ in square units. 

+

 

+

 

+

+

 

+

 

+

square units

",20,20,,,272768 +PSBBVP2,1,Fill-in-the-blank(s),Numeric,"

Find the area of this shape. 

+

 

+

+

 

+

square units

",15,15,,,273241 +PRABQP5X,1,Fill-in-the-blank(s),Numeric,"

A population of red ants was 640. After a season of heavy rainfall, the ant population decreased by 50%. In the following dry season, the population increased by 5%. What is the ant population after the increase?

+

 

+

red ants

",336,336,,,156692 +PSBYW,2,Fill-in-the-blank(s),Numeric,"

The two triangles displayed are scaled copies of one another.

+

 

+

+

 

+

 

+

What is the value of x?

+

 

+

x=units

",10,10,,,3216 +PRABTGFK,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression if x is 25, y is -4, and z is -0.2.

+

 

+

2x - z

+

 

+

",1,1,,,158652 +PSB74P,1,Fill-in-the-blank(s),Numeric,"

Each square on a grid represents 1 unit on each side.

+

 

+

+

 

+

Calculate the slope of graph D.

+

 

+

",-4,-4,,,158484 +PSB74P,3,Fill-in-the-blank(s),Numeric,"

Each square on a grid represents 1 unit on each side.

+

 

+

+

 

+

Calculate the slope of graph E. 

+

 

+

",0,0,,,158769 +PSB76J,3,Fill-in-the-blank(s),Numeric,"

How many possible solutions make both inequalities true? 

+

 

+

",6,6,,,159292 +PSB75K,2,Fill-in-the-blank(s),Numeric,"

A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles.

+

 

+

At this rate, how many miles can it travel in 10 hours?  

+

 

+

miles

","5,600","5,600",,,159196 +PRABG44E,1,Fill-in-the-blank(s),Numeric,"

Lin plays a game that involves a standard number cube and a deck of ten cards numbered 1 through 10. If both the cube and card have the same number, Lin gets another turn. Otherwise, play continues with the next player.

+

 

+

What is the probability that Lin gets another turn?

+

 

+

",Jun-60,Jun-60,,,159519 +PRABFGZ7,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

100d = 13.71

+

 

+

d =

",0.1371,0.1371,,,298615 +PSB9AY,4,Fill-in-the-blank(s),Exact Fraction,"

Calculate the slope of this line.

+

 

+

",-1.285714286,-1.285714286,,,165287 +PRABFGZ4,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

a - 2.01 = 5.5

+

 

+

a =

",7.51,7.51,,,298057 +PRABFGZ6,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

10c = 13.71

+

 

+

c =

",1.371,1.371,,,298444 +PRABFGZ5,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

b + 2.01 = 5.5

+

 

+

b =

",3.49,3.49,,,298258 +PRABHN3P,1,Fill-in-the-blank(s),Numeric,"

Find the value of k so that the line passing through the pair of points has the given slope.

+

 

+

(3, 5) and (k, 9), slope = 

+

 

+

",11,11,,,165778 +PRABEHK3,1,Fill-in-the-blank(s),Numeric,"

A scoop of ice cream has a 3-inch diameter. How tall should the ice cream cone of the same diameter be in order to contain all of the ice cream inside the cone?

+

 

+

inches

",6,6,,,165245 +PRABHN3Q,1,Fill-in-the-blank(s),Numeric,"

Find the value of k so that the line passing through the pair of points has the given slope.

+

(-1, 4) and (-3, k), slope =

+

 

+

",5,5,,,165896 +PRABHN3N,1,Fill-in-the-blank(s),Numeric,"

Find the value of k so that the line passing through the pair of points has the given slope.

+

 

+

(1, k) and (4, 1), slope = -2

+

 

+

",7,7,,,165645 +PRABHN3M,1,Fill-in-the-blank(s),Numeric,"

Find the value of k so that the line passing through the pair of points has the given slope.

+

 

+

(k, 2) and (11, 14), slope = 2

+

 

+

",5,5,,,165535 +PSB94Q,2,Fill-in-the-blank(s),Numeric,"

What is the value for the median for the data in the dot plot?

+

 

+

",2,2,,,169437 +PSBC8G,2,Fill-in-the-blank(s),Numeric,"

Jada reads 5 pages every 20 minutes. At this rate, how many pages can she read in 1 hour?

+

 

+

Use a table to find the answer.

+

 

+ + + + + + + + + + + + + + + + + + + +
Pages ReadTime in Minutes
520
  
  
+

 

+

Jada read pages.

",15,15,,,15930 +PSBBADX,1,Fill-in-the-blank(s),Numeric,"

Here is a tape diagram that shows how far two students walked.

+

 

+

 

+ + + + + + + + + + +
  Priya's distance (km) + + + + + + + + + +
+ + + + + + + + + + +
22222
+
+ + + + + + + + + +
2222
+
+
  Tyler's distance (km)
+

 

+

 

+

What percentage of Priya’s distance did Tyler walk?  %

",80,80,,,171639 +PSBJNT,1,Fill-in-the-blank(s),Numeric,"

Find (12.34) · (0.7).

+

 

+

",8.638,8.638,,,45068 +PSBJQG,2,Fill-in-the-blank(s),Numeric,"

Now find the quotient.

+

 

+

302.1÷.0.5

+

 

+

",604.2,604.2,,,45439 +PSBBAB5,1,Fill-in-the-blank(s),Numeric,"

At a sandwich shop, any sandwich costs $4.50, plus $0.25 for each extra topping.

+

 

+

How much does a sandwich cost with 3 extra toppings?

+

 

+

$

",5.25,5.25,,,171459 +PSBJSY,2,Fill-in-the-blank(s),Numeric,"

Now find the quotient.

+
 
+

 

+

12.15÷0.02

+

 

+

",607.5,607.5,,,45750 +PSBJUZ,2,Fill-in-the-blank(s),Numeric,"

Now find the quotient.

+
 
+

 

+

1.375÷0.11

+

 

+

",12.5,12.5,,,46049 +PSBBAK8,2,Fill-in-the-blank(s),Numeric,"

For radius and diameter of a circle, what is the constant of proportionality?

+

 

+

","1/2, 2","1/2, 2",,,172418 +PSBBABF,1,Fill-in-the-blank(s),Numeric,"

The bike store marks up the wholesale cost of all of the bikes they sell by 30%.

+

 

+

Andre wants to buy a bike that has a price tag of $125, what was the wholesale cost of this bike? 

+

 

+

$

",96.15,96.15,,,171238 +PRABHG8P,1,Fill-in-the-blank(s),Numeric,"

Parallel lines l and m are cut by two transversals which intersect l in the same point. Two angles are marked in the figure. Find the measure x of the third angle.

+

 

+

x =°

+

 

+

",65,65,,,174309 +PSBBBKT,2,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

-12 · (-13)

+

 

+

",4,4,,,177679 +PSBBBY4,5,Fill-in-the-blank(s),Numeric,"

What is the value of the other variable?

+

 

+

",4,4,,,180476 +PSBBBY4,3,Fill-in-the-blank(s),Numeric,"

What value of a would work with the given value for b?

+

 

+

",6,6,,,180143 +PSBBCP7,1,Fill-in-the-blank(s),Numeric,"

 

+

Find the value of the expression without a calculator.

+

 

+

(2)(-30) + (-3)(-20) + (-6)(-10) - (2)(3)(10) 

+

 

+

",0,0,,,184690 +PSBBCQT,2,Fill-in-the-blank(s),Numeric,"

What is the slope of this line?

+

 

+

+

",2,2,,,184366 +PSBBCNR,2,Fill-in-the-blank(s),Numeric,"

How many kilowatt-hours did they use?

+

 

+

About kilowatt-hours

+

Round your answer to the nearest whole number. 

",684,684,,,184392 +PSBBCQF,1,Fill-in-the-blank(s),Algebraic Expression,"

Use the distributive property to write an expression that is equivalent to 12 + 4x.

+

 

+

",4(3+x),4(3+x),,,184709 +PRABG4R9,1,Fill-in-the-blank(s),Exact Match,"

Kiran read for x minutes, and Andre read for 58 more than that. Write an equation that relates the number of minutes Kiran read with y, the number of minutes that Andre read. Use decimals in your equation.

+

 

+

y =

",1.625x,1.625x,,,202480 +PRABET5M,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression if x is 25, y is -4, and z is -0.2.

+

 

+
+

x + y

+
+

 

+

",-3 3/5,-3 3/5,,,158297 +PSBBC95,1,Fill-in-the-blank(s),Numeric,"

Noah's parents are interested in moving to another part of town. They look up all the prices of the homes for sale and record them in thousands of dollars.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Neighborhood 1805580120609060805570
Neighborhood 2110120160110100110140150120120
+

 

+

+

 

+

Find the mean of neighborhood 1.

+

 

+

 

+

",75,75,,,187130 +PSBBC95,2,Fill-in-the-blank(s),Numeric,"

Find the MAD (mean absolute deviation) of neighborhood 1.

+

 

+

 

+

",15,15,,,187306 +PSBBC95,4,Fill-in-the-blank(s),Numeric,"

Find the MAD (mean absolute deviation) of neighborhood 2.

+

 

+

 

+

",15.6,15.6,,,187602 +PSBBC95,3,Fill-in-the-blank(s),Numeric,"

Find the mean of neighborhood 2.

+

 

+

",124,124,,,187451 +PSBBDGB,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression equivalent to  6 - 2x + 5 + 4x that only has two terms. 

+

 

+

",2x+11,2x+11,,,188812 +PSBD56Z,1,Fill-in-the-blank(s),Numeric,"

Andre set up a lemonade stand last weekend. It cost him $0.15 to make each cup of lemonade, and he sold each cup for $0.35.

+

 

+

If Andre collects $9.80, how many cups did he sell? 

+

 

+

cups

",28,28,,,677527 +PSBBEDV,3,Fill-in-the-blank(s),Numeric,"

How many solutions are there?

+

 

+

",1,1,,,194106 +PRABTTEG,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

13s=7

+

 

+

s =

",21,21,,,194802 +PRABTTEK,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

6v = ‐9

+

 

+

v =

",-1.5,-1.5,,,195078 +PRABKC63,1,Fill-in-the-blank(s),Numeric,"

What is the value of 34?

+

 

+

",81,81,,,198429 +PSBBFAS,1,Fill-in-the-blank(s),Numeric,"

Find a four-digit number using only the digits 0, 1, 2, or 3 where:

+
    +
  • the first digit tells you how many zeros are in the number,

    • +
  • the second digit tells you how many ones are in the number,

    • +
  • the third digit tells you how many twos are in the number, and

    • +
  • the fourth digit tells you how many threes are in the number.
    • +
+

The number 2,100 is close, but doesn’t quite work. The first digit is 2, and there are 2 zeros. The second digit is 1, and there is 1 one. The fourth digit is 0, and there are no threes. But the third digit, which is supposed to count the number of 2’s, is zero.

+

 

+

","2020, 1210","2020, 1210",,,198955 +PRABKC64,1,Fill-in-the-blank(s),Numeric,"

How many times bigger is 315 compared to 312? 

+

 

+

times bigger

",27,27,,,198552 +PRABEUZ2,1,Fill-in-the-blank(s),Numeric,"

A simulation is done to represent kicking 5 field goals in a single game with a 72% probability of making each one. A 1 represents making the kick and a 0 represents missing the kick.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
trial result
110101
211010
300011
411111
510011
+

 

+

 

+

Based on these results, estimate the probability that 3 or more kicks are made.

+

 

+

",5-Apr,5-Apr,,,198767 +PSBBFAS,3,Fill-in-the-blank(s),Numeric,"

How many solutions are there to this problem?

+

 

+

",2,2,,,199191 +PRABG5ZJ,1,Fill-in-the-blank(s),Numeric,"

Answer the following question.  If you get stuck, consider using pattern blocks.

+

 

+

How many s are in 2?

+

 

+

",3,3,,,201709 +PRABG5ZK,1,Fill-in-the-blank(s),Numeric,"

Answer the following question.  If you get stuck, consider using pattern blocks.

+

 

+

How many s are in ?

+

 

+

",9,9,,,201829 +PRABG5ZH,1,Fill-in-the-blank(s),Numeric,"

Answer the following question.  If you get stuck, consider using pattern blocks.

+

 

+

How many s are in 4?

+

 

+

",8,8,,,201571 +PSBBGGE,2,Fill-in-the-blank(s),Numeric,"

If an employee sells a family pass for $135, what is the amount of the commission they get to keep?

+

 

+

$

",21.6,21.6,,,205959 +PSBBGN8,3,Fill-in-the-blank(s),Numeric,"

How many dogs weigh at least 120 and less than 160 pounds?

+

 

+

dogs

",8,8,,,206824 +PSBBG4V,2,Fill-in-the-blank(s),Numeric,"

+

What is the distance between P and R?   units

",6,6,,,208077 +PSBES8,2,Fill-in-the-blank(s),Numeric,"

What is the area of the parallelogram?

+

 

+

square units

+

 

+

",45,45,,,24293 +PSB6EK,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region.

+

 

+

+

 

+

cm2

",96,96,,,150161 +PSB6CP,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region. 

+

 

+

+

 

+

cm2

",34,34,,,149829 +PSBBHYP,1,Order / Sort,Ordering,

Use the data from Station 4 to put the units of weight and mass in order from smallest to largest. 

,"Gram, Kilogram, Pound, Ounce","Gram, Kilogram, Pound, Ounce",,,213954 +PRABE3GY,1,Fill-in-the-blank(s),Numeric,"

The Dockland Building in Hamburg, Germany is shaped like a parallelogram.

+

 

+ + + + + + + +
If the length of the building is 86 meters and its height is 55 meters, what is the area of this face of the building?
+

 

+

square meters

","4,730","4,730",,,503982 +PSBCP64,1,Fill-in-the-blank(s),Numeric,"

For the triangle, a base and its corresponding height are labeled.

+

Find the area of the triangle.

+

 

+

+

 

+

square units

",12,12,,,417861 +PSBBPYN,1,Fill-in-the-blank(s),Numeric,"

Find the area of this trapezoid.

+

 

+

+

 

+

square units

",18,18,,,242072 +PSBBPYN,1,Fill-in-the-blank(s),Numeric,"

Find the area of this trapezoid.

+

 

+

+

 

+

square units

",18,18,,,242072 +PRABTTEJ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

79 + u = 65

+

 

+

u =

",-14,-14,,,194986 +PSBBH5N,2,Fill-in-the-blank(s),Numeric,"

A sea bird is 28 meters above the surface of the ocean. What is its elevation?

+


meters

",28,28,,,214460 +PRABFFGN,1,Fill-in-the-blank(s),Numeric,"

Use the partial quotients method to find 1,032 ÷ 43.

+

 

+

",24,24,,,215013 +PSBBJB3,1,Fill-in-the-blank(s),Numeric,"

A chemical engineer is trying to increase the amount of the useful product in a reaction. She performs the reaction with her new equipment 10 times and gets the following amounts of the useful product:

+ + + + + + + + + + + + + + + +
47.148.248.347.548.548.147.248.248.448.3
+

 

+

What proportion of the reactions were above the 48 grams threshold?

+

 

+

",0.7,0.7,,,215871 +PRABMTZU,1,Fill-in-the-blank(s),Numeric,"

Evaluate:

+

 

+

+

 

+

",1,1,,,221966 +PRABMTZV,1,Fill-in-the-blank(s),Numeric,"

Evaluate:

+

 

+

102 + 101 + 100

+

 

+

",111,111,,,222136 +PRABEH5H,1,Fill-in-the-blank(s),Numeric,"

Evaluate:

+

 

+

100

+

 

+

",1,1,,,221748 +PRABTTCZ,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+
 
+

+
 
+

 

+

",-25,-25,,,223225 +PRABTTC3,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+
 
+

+

 

+

",-1.5,-1.5,,,223453 +PRABTTCY,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+
 
+

+

 

+

",-11,-11,,,223087 +PRABTTC2,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+
 
+

+
 
+

 

+

",43,43,,,223345 +PSBBK3R,1,Fill-in-the-blank(s),Numeric,"

What is the smallest number that has a remainder of 1, 2, and 3 when divided by 2, 3, and 4, respectively?

+

 

+

",11,11,,,226035 +PSBBKZ8,1,Fill-in-the-blank(s),Numeric,"

A toaster has 4 slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 10 slices.

+

 

+

How long do you think it will take to make 20 slices?

+

 

+

seconds

",175,175,,,225766 +PSBBK68,1,Fill-in-the-blank(s),Numeric,"

A landscape architect is designing a pool that has this top view:

+

 

+

+

 

+

How much water will be needed to fill this pool 4 feet deep?

+

 

+

feet3

",486,486,,,226249 +PSBBMGT,3,Fill-in-the-blank(s),Numeric,"

Last Sunday 1,575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under.

+

 

+

Find the number of children that visited the park.

+

 

+

children

",441,441,,,228454 +PSBBMT8,1,Fill-in-the-blank(s),Numeric,"

In a basketball game, Elena scores twice as many points as Tyler. Tyler scores four points fewer than Noah, and Noah scores three times as many points as Mai. If Mai scores 5 points, how many points did Elena score? 

+

 

+

points

",22,22,,,230038 +PSBBM4Q,2,Fill-in-the-blank(s),Numeric,"

What is 4.4% of 625?

+

 

+

",27.5,27.5,,,231535 +PSBBM4Q,1,Fill-in-the-blank(s),Numeric,"

Find 44% of 625 using the facts that 40% of 625 is 250 and 4% of 625 is 25.

+

 

+

",275,275,,,231330 +PSBBM4Q,3,Fill-in-the-blank(s),Numeric,"

What is 0.44% of 625?

+

 

+

",2.75,2.75,,,231744 +PSBBMXK,3,Fill-in-the-blank(s),Numeric,"

Use the sample to estimate the measure of center that you chose for all the reviews.

+

 

+

",90,90,,,230731 +PSBBM3M,1,Fill-in-the-blank(s),Numeric,"

What is the last digit of 31000?

+
 
+

 

+

",1,1,,,231607 +PRABECCS,1,Fill-in-the-blank(s),Numeric,"

Clare asks Andre to play the following number puzzle:

+
+
+
+
+
+
+
    +
  • +

    Pick a number

    +
    • +
  • +

    Add 2

    +
    • +
  • +

    Multiply by 3

    +
    • +
  • +

    Subtract 7

    +
    • +
  • +

    Add your original number

    +
    • +
+

Andre’s final result is 27. Which number did he start with?

+
+
+
+
+
+
+

 

+

",7,7,,,231522 +PRABD526,1,Fill-in-the-blank(s),Numeric,"

The two triangles shown are similar.

+

 

+

+

 

+

Find the value of .

+

 

+

 

+

 

+

Write your answer as a fraction.

+

 

+

","0.83, 0.833, 5/6","0.83, 0.833, 5/6",,,232166 +PRABMTHB,1,Fill-in-the-blank(s),Numeric,"

For the pair of points, find the slope of the line that passes through both points.

+

If you get stuck, try plotting the points on graph paper and drawing the line through them with a ruler.

+

 

+

(1,1) and (5,7)

+

 

+

",2-Mar,2-Mar,,,236767 +PSBBNC8,2,Fill-in-the-blank(s),Algebraic Expression,"

A cone has a volume V, radius r, and a height of 12 cm.

+

 

+

A cone has the same height and 3 times the radius of the original cone. Write an expression for its volume.

+

 

+

",9V,9V,,,233520 +PRABMTHC,1,Fill-in-the-blank(s),Numeric,"

For the pair of points, find the slope of the line that passes through both points.

+

If you get stuck, try plotting the points on graph paper and drawing the line through them with a ruler.

+

 

+

(2,5) and (-1,2)

+

 

+

",1,1,,,236954 +PRABD5BN,1,Fill-in-the-blank(s),Numeric,"

For the pair of points, find the slope of the line that passes through both points.

+

If you get stuck, try plotting the points on graph paper and drawing the line through them with a ruler.

+

 

+

(1,1) and (7,5)

+

 

+

",3-Feb,3-Feb,,,236549 +PSBBN4D,1,Fill-in-the-blank(s),Numeric,"

Diego has 90 songs on his playlist. How many songs are there for the given genre?

+

 

+

40% rock

+

 

+

songs

",36,36,,,237164 +PRABMTHD,1,Fill-in-the-blank(s),Numeric,"

For the pair of points, find the slope of the line that passes through both points.

+

If you get stuck, try plotting the points on graph paper and drawing the line through them with a ruler.

+

 

+

(2,5) and (-7,-4)

+

 

+

",1,1,,,237129 +PRABTSUT,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

25 · -34 =

",-0.3,-0.3,,,279032 +PRABG4SB,1,Fill-in-the-blank(s),Numeric,"

A company claims that their new bottle holds 25% more laundry soap. If their original container held 53 fluid ounces of soap, how much does the new container hold?  

+

 

+

 

+

fluid ounces

",66.25,66.25,,,238173 +PSBBPBT,1,Fill-in-the-blank(s),Numeric,"

What is the least common multiple of 6 and 9?

+

 

+

",18,18,,,238849 +PSBBRMP,1,Fill-in-the-blank(s),Numeric,"

The other day, you wrote the sample space for spinning each of these spinners once.

+

+

 

+
+
+
+
+

What is the probability of getting:

+

 

+

Green and 3?

+
+
+
+
+

 

+

",20-Jan,20-Jan,,,250608 +PSBBRMP,3,Fill-in-the-blank(s),Numeric,"

What is the probability of getting:

+

 

+

Any color other than red and any number other than 2?

+

 

+

",20-Dec,20-Dec,,,250867 +PSBBRMP,2,Fill-in-the-blank(s),Numeric,"

What is the probability of getting:

+

 

+

Blue and any odd number?

+

 

+

",20-Mar,20-Mar,,,250727 +PSBBRT6,2,Fill-in-the-blank(s),Numeric,"

Find the exact value of a+b+c by reasoning about the diagram.

+

 

+

°

",90,90,,,252146 +PSBBRWG,1,Fill-in-the-blank(s),Numeric,"

The mean of four numbers is 7. Three of the numbers are 5, 7, and 7. What is the fourth number? 

+

 

+

",9,9,,,252396 +PSBBSCK,4,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

+

 

+

","6.0, 6, 6.00","6.0, 6, 6.00",,,254589 +PSB6Q9,1,Fill-in-the-blank(s),Exact Fraction,"

Here is a number line:

+
+

Write the number at A as a fraction.

+

 

+

A= 

",4-Jan,4-Jan,,,151911 +PSBBXEP,1,Fill-in-the-blank(s),Numeric,"

A car travels at a constant speed, as shown on the double number line.

+

 

+

 

+

+

 

+

 

+

How far does the car travel in 14 hours?

+

 

+

kilometers

",980,980,,,282992 +PSBBXG7,2,Fill-in-the-blank(s),Numeric,"

At a school recess, there needs to be a ratio of 2 adults for every 24 children on the playground. The double number line represents the number of adults and children on the playground at recess.

+

 

+

+

 

+

 

+

How many adults are needed if there are 72 children?  

+

 

+

adults

",6,6,,,283575 +PSBBS9U,1,Fill-in-the-blank(s),Exact Fraction,"

Here is a number line:

+

 

+

+

 

+

Write the number at A as a fraction.

+

 

+

A=

","2/6, 1/3","2/6, 1/3",,,259422 +PSBBFFH,1,Fill-in-the-blank(s),Numeric,"

A recipe for 1 batch of spice mix says, “Combine 3 teaspoons of mustard seeds, 5 teaspoons of chili powder, and 1 teaspoon of salt.” How many batches are represented by the diagram? 

+

 

+

batches

+

 

+

",3,3,,,199800 +PSBBS8B,1,Fill-in-the-blank(s),Numeric,"

42 is 6 times what number?

+

 

+

",7,7,,,258849 +PSBRWT,1,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle. If you get stuck, consider drawing a rectangle around the triangle.

+

 

+

+

 

+

square units

",9.5,9.5,,,77648 +PSBBS8B,3,Fill-in-the-blank(s),Numeric,"

700 is 7 times what number?

+

 

+

",100,100,,,259128 +PSBBS8M,2,Fill-in-the-blank(s),Numeric,"

How many different triangles are there?

+

 

+

different triangles

",3,3,,,259177 +PSBBTKT,1,Fill-in-the-blank(s),Numeric,"

What is the greatest common factor of 24 and 64?

+

 

+

",8,8,,,261290 +PSBBS8B,2,Fill-in-the-blank(s),Numeric,"

4 is 28 times what number?

+

 

+

",7-Jan,7-Jan,,,258984 +PSBBTGY,2,Fill-in-the-blank(s),Numeric,"

What is the furthest their phone could be from them?

+

 

+

feet

",70,70,,,260726 +PSBBTRH,2,Fill-in-the-blank(s),Numeric,"

Mai has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy?

+

 

+

Find the answer.  Draw a diagram, if needed.

+

 

+

movie tickets

",8,8,,,262087 +PSBBTW4,2,Fill-in-the-blank(s),Numeric,"

Find the answer.

+

 

+

 How many groups of 2 are in 7?

+

 

+

",3.5,3.5,,,263156 +PRABE93H,1,Fill-in-the-blank(s),Numeric,"

A cargo ship traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour?

+

 

+

+

 

+

 

+

nautical miles

",25,25,,,67685 +PSBBTX3,3,Fill-in-the-blank(s),Numeric,"

Decide what power of 10 to put on the label for the rightmost tick mark of this number line so that all three countries’ populations can be distinguished.

+

 

+

 

+

 

+

",8,8,,,263239 +PSBBTVE,2,Fill-in-the-blank(s),Numeric,"

Find the answer.

+

 

+

How many groups of s are in 10?

+

 

+

",4,4,,,262837 +PSBBTY8,3,Fill-in-the-blank(s),Numeric,"

Find the answer.

+

How many s are in 1?

+

 

+

",3-Apr,3-Apr,,,263570 +PSBBT24,3,Fill-in-the-blank(s),Numeric,"

Find the answer.

+

How many s are in 3?

+

 

+

",2-Sep,2-Sep,,,263960 +PSBBT4X,3,Fill-in-the-blank(s),Numeric,"

Find the answer. 

+

How many s are in 5?

+

 

+

",3-Oct,3-Oct,,,264344 +PSBBN4D,3,Fill-in-the-blank(s),Numeric,"

Diego has 90 songs on his playlist. How many songs are there for the given genre?

+

 

+

30% hip-hop

+

 

+

songs

",27,27,,,237456 +PSBBUDT,7,Fill-in-the-blank(s),Numeric,"

Let's look at why the values tend to not change much after doing the simulation many times.

+

 

+

After doing the simulation 4 times, a group finds that Diego had to wait 3 times. What is an estimate for the probability Diego has to wait based on these results?

+

 

+

",4-Mar,4-Mar,,,265593 +PSBBT5X,3,Fill-in-the-blank(s),Numeric,"

Find the answer to your question:  If you get stuck, draw a diagram.

+

 

+

",3-Apr,3-Apr,,,264456 +PSBNJ6,1,Fill-in-the-blank(s),Numeric,"

In this cube, each small square has side length 1 unit. 

+

 

+

+

 

+

 

+

What is the surface area of this cube?

+

 

+

square units

",54,54,,,60186 +PSBCQR6,3,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

50 ÷ 4

+

 

+

","12.5, 12.50","12.5, 12.50",,,421448 +PRABFAHA,1,Fill-in-the-blank(s),Numeric,"

Kiran reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages? If you get stuck, consider using the table.

+

 

+

minutes

+

 

+ + + + + + + + + + + + + + + + + + + +
Time in MinutesNumber of Pages
205
 1
 11
",44,44,,,147031 +PSBBUDT,11,Fill-in-the-blank(s),Numeric,"

After doing the simulation 20 times, this group finds that Diego had to wait 15 times. What is an estimate for the probability Diego has to wait based on these results?

+

 

+

",15/20,15/20,,,265967 +PSBBYA9,1,Fill-in-the-blank(s),Numeric,"

A cashier worked an 8-hour day, and earned $58.00. The double number line shows the amount she earned for working different numbers of hours.

+

 

+

+

 

+

How much does the cashier earn per hour? 

+

 

+

$ 

",7.25,7.25,,,287601 +PSBBVCZ,2,Fill-in-the-blank(s),Numeric,"

Elena has some bottles of water that each holds 17 fluid ounces.

+

 

+

How much water is in 51 bottles?  

+

 

+

ounces

",867,867,,,271051 +PSBBVBU,2,Fill-in-the-blank(s),Numeric,"

80% of x is equal to 100. 

+

 

+

Use your equation to find the value of x.

+

 

+

x =

",125,125,,,271394 +PSBBVCY,2,Fill-in-the-blank(s),Numeric,"

The usual price of a sweatshirt is $18, what is its sale price?

+

 

+

$

",15.3,15.3,,,271538 +PSBBVFW,3,Fill-in-the-blank(s),Numeric,"

The distance from the tip of a slice of pizza to the crust is 7 in.

+

 

+

Estimate the circumference of the circle: 

+

 

+

inches

+

Use  3.14 for π.  

+

Round your answer to the nearest whole number.

",44,44,,,272056 +PSBBVHN,1,Fill-in-the-blank(s),Numeric,"

Elena is 56 inches tall. 

+

 

+

What is her height in centimeters? (Note: 100 inches = 254 centimeters)

+

 

+

centimeters

+

Round your answer to two decimal places.

",142.24,142.24,,,272220 +PSBBVT3,1,Fill-in-the-blank(s),Numeric,"

Chicken costs $3.20 per pound, and beef costs $4.59 per pound.  What is the exact cost of 3 pounds of chicken?

+

 

+

$

",9.6,9.6,,,273482 +PSBCRGJ,2,Fill-in-the-blank(s),Numeric,"

Here is an expression: 3 · 2t

+

 

+

Find the value of the expression when t is 4.

+

 

+

",48,48,,,425926 +PSBBWD2,1,Fill-in-the-blank(s),Numeric,"

Find the length of a side of a square if its area is 81 square inches.

+

 

+

inches

",9,9,,,276705 +PRABFBPA,1,Fill-in-the-blank(s),Numeric,"

Priya’s family exchanged 250 dollars for 4,250 pesos. Priya bought a sweater for 510 pesos. How many dollars did the sweater cost?

+

 

+

$

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
PesosDollars
4,250250
 25
 1
 3
510 
",30,30,,,42715 +PRABEU2C,1,Fill-in-the-blank(s),Numeric,"

A vending machine has 5 colors (white, red, green, blue, and yellow) of gumballs and an equal chance of dispensing each. A second machine has 4 different animal-shaped rubber bands (lion, elephant, horse, and alligator) and an equal chance of dispensing each. If you buy one item from each machine, what is the probability of getting a yellow gumball and a lion band?

+

 

+

",20-Jan,20-Jan,,,279365 +PSBC64M,2,Fill-in-the-blank(s),Numeric,"

What is the surface area of the polyhedron?

+

 

+

 cm2

+

 

+

",72,72,,,502515 +PRABEU2D,1,Fill-in-the-blank(s),Numeric,"

The numbers 1 through 10 are put in one bag, and the numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number?

+

 

+

",6/100,6/100,,,279742 +PSBBMNU,2,Fill-in-the-blank(s),Numeric,"

On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip.

+

 

+

How many children are there?  If you get stuck, consider using a tape diagram.

+

 

+

children

",80,80,,,229328 +PSBBYAG,2,Fill-in-the-blank(s),Numeric,"

What fraction of the teacher’s height is the student’s height?

+

 

+

",17-Dec,17-Dec,,,288005 +PSBBYDW,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

+

 

+

",2.5,2.5,,,288530 +PSBBYAG,1,Fill-in-the-blank(s),Numeric,"

A second-grade student is 4 feet tall. Her teacher is feet tall.

+

 

+

How many times as tall as the student is the teacher?

+

 

+

",17/12,17/12,,,287888 +PSBBYB9,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

+
 
+

 

+

",15,15,,,288230 +PSBBYD8,3,Fill-in-the-blank(s),Numeric,"

Find the mean. 

+

 

+

",2.4,2.4,,,288503 +PRABG6KV,1,Fill-in-the-blank(s),Numeric,"

Find the product mentally.

+

 

+

19 ⋅ 14

+

 

+

",266,266,,,289975 +PSBBYFM,1,Fill-in-the-blank(s),Numeric,"

Here is the data set on numbers of siblings from an earlier activity.

+ + + + + + + + + + + + + + + +
10217020110
+

 

+

Sort the data from least to greatest, and then find the median.

+
 
+

 

+

",1,1,,,288926 +PSBBZNB,2,Fill-in-the-blank(s),Numeric,"

 is equal to 1,024.

+

 

+

Evaluate the expression below.

+

 

+

44

+

 

+

 

+

",256,256,,,295883 +PSBBZNB,1,Fill-in-the-blank(s),Numeric,"

 is equal to 1,024.

+

 

+

Evaluate the expression below.

+

 

+

 

+
 
+

 

+

",4096,4096,,,295642 +PSBBZNB,3,Fill-in-the-blank(s),Numeric,"

 is equal to 1,024.

+

 

+

Evaluate the expression below.

+

 

+

43⋅42

+

 

+

 

+

",1024,1024,,,296064 +PSBBZZP,2,Fill-in-the-blank(s),Numeric,"

If there are 2,024 dedicated readers of The Adventures of Super Sam, estimate the number of readers who want the new hero to fly.

+

 

+

",810,810,,,298063 +PSBBZQT,2,Fill-in-the-blank(s),Numeric,"

A computer program found that the line c=2t-89 is a good fit for the data. Use this equation to predict how many cups of lemonade Lin might sell on a day when the high temperature is 74 degrees.

+

 

+

cups of lemonade

",59,59,,,296489 +PSBBZZP,1,Fill-in-the-blank(s),Numeric,"

Here are the results of a survey of 20 people who read The Adventures of Super Sam regarding what special ability they think the new hero should have.

+

 

+ + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
responsewhat new ability?
1fly
2freeze
3freeze
4fly
5fly
6freeze
7fly
8super strength
9freeze
10fly
+

 

+		 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
responsewhat new ability?
11freeze
12freeze
13fly
14invisibility
15freeze
16fly
17freeze
18fly
19super strength
20freeze
+

 

+
+

What proportion of this sample want the new hero to have the ability to fly?

+

 

+

",20-Aug,20-Aug,,,297976 +PSBC5ZP,2,Fill-in-the-blank(s),Numeric,"

Then solve the problem.

+

 

+

48 is what percent of 80?  

+

 

+

%

+

 

+

",28,28,,,496936 +PSBB2KM,2,Fill-in-the-blank(s),Exact Fraction,"

Triangle DEF is a scaled copy of triangle ABC with what scale factor?

+

 

+

",3-Feb,3-Feb,,,301410 +PRABMSJZ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

 57(e-9)=25

+

 

+

e =

",44,44,,,369146 +PSBCH75,2,Fill-in-the-blank(s),Numeric,"

Calculate its area. 

+

 

+

square centimeters

+

 

+

",88,88,,,390139 +PSBB2XS,3,Fill-in-the-blank(s),Numeric,"

How many customers would you seat at table C?

+

 

+

Do not include units (customers) in your answer

+

 

+

","4, 5","4, 5",,,303219 +PSBB2XS,1,Fill-in-the-blank(s),Numeric,"

Restaurant owners say it is good for each customer to have about 300 in2 of space at their table. How many customers would you seat at each table?

+

 

+

+

 

+

How many customers would you seat at table A?

+

 

+

Do not include units (customers) in your answer

+

 

+

 

+

",3,3,,,303079 +PSBB2R3,3,Fill-in-the-blank(s),Numeric,"

If the wire picture frame were stretched out to make one complete circle, what would its radius be?

+

 

+

inches

",10,10,,,302327 +PRABFG26,1,Fill-in-the-blank(s),Numeric,"

What is the volume of a cube with edge lengths of 23 units?

+

 

+

cubic units

+

Express your answer in fraction form.

",27-Aug,27-Aug,,,87339 +PSBB2XS,2,Fill-in-the-blank(s),Numeric,"

How many customers would you seat at table B?

+

 

+

Do not include units (customers) in your answer

+

 

+

","3, 4","3, 4",,,303155 +PSBB3M6,2,Fill-in-the-blank(s),Numeric,"

Use the fact that is a solution to the equation to find a decimal approximation of whose square is between 2.9 and 3.1.

+

 

+

",1.73,1.73,,,307502 +PSBBCG3,2,Fill-in-the-blank(s),Numeric,"

What fraction of 212 is 45?

+

 

+

Find the answer.

+

 

+

",25-Aug,25-Aug,,,183482 +PSBBJWZ,2,Fill-in-the-blank(s),Numeric,"

3 tickets to the museum cost $12.75. At this rate, what is the cost of 5 tickets?

+

 

+

$

",21.25,21.25,,,219244 +PSBC5,2,Fill-in-the-blank(s),Numeric,"

A builder was building a fence. In the morning, he worked for 25 of an hour. In the afternoon, he worked for 910 of an hour. How many times as long as in the morning did he work in the afternoon? 

+

 

+

Answer the question. 

+

 

+

times as long

",2 1/4,2 1/4,,,311 +PSBBV76,1,Fill-in-the-blank(s),Numeric,"

A school club sold 300 shirts. 31% were sold to fifth graders, 52% were sold to sixth graders, and the rest were sold to teachers. How many shirts were sold to fifth graders?

+

 

+

shirts

+

 

",93,93,,,275754 +PRABFEUM,1,Fill-in-the-blank(s),Numeric,"

At a constant speed, a car travels 75 miles in 60 minutes.

+

 

+

How far does the car travel in 18 minutes? If you get stuck, consider using the table.

+

 

+

miles

+

 

+ + + + + + + + + + + + + + + + + + + +
MinutesDistance in Miles
6075
6 
18 
",22.5,22.5,,,279063 +PSBB4KW,1,Fill-in-the-blank(s),Numeric,"

Elena notices a beaker in science class says it has a diameter of 9 cm and measures its circumference to be 28.3 cm.

+

 

+

What value do you get for  using these values and the equation for circumference, ?

+

 

+

",3.14,3.14,,,311896 +PSBB4KW,2,Fill-in-the-blank(s),Numeric,"

Diego learned that one of the space shuttle fuel tanks had a diameter of 840 cm and a circumference of 2,639 cm.

+

 

+

What value do you get for  using these values and the equation for circumference, ?

+

 

+

",3.1416,3.1416,,,312048 +PRABFFHT,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

12924   

",77,77,,,204768 +PSBB4YA,4,Fill-in-the-blank(s),Numeric,"

How much money will be left after buying the purchase? 

+

 

+

$

",0.14,0.14,,,314324 +PSBB5GF,3,Fill-in-the-blank(s),Numeric,"

20% of 5,000 is 1,000 and 21% of 5,000 is 1,050. Find each percentage of 5,000 and be prepared to explain your reasoning. If you get stuck, consider using the double number line diagram.

+

 

+

20.1% of 5,000

+

+

 

+

",1005,1005,,,316941 +PRABFFHS,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

5465   

",93,93,,,204595 +PSBB5GF,2,Fill-in-the-blank(s),Numeric,"

20% of 5,000 is 1,000 and 21% of 5,000 is 1,050. Find each percentage of 5,000 and be prepared to explain your reasoning. If you get stuck, consider using the double number line diagram.

+

 

+

0.1% of 5,000

+

+

 

+

",5,5,,,316809 +PSBB5JB,1,Fill-in-the-blank(s),Numeric,"

15% of 80 is 12 and 16% of 80 is 12.8. Find the percentage of 80 and be prepared to explain your reasoning.

+

 

+

15.1% of 80

+

 

+

",12.08,12.08,,,317307 +PSBB5DC,2,Fill-in-the-blank(s),Numeric,"

Find the area of the rectangle FROG. 

+

 

+

square units

",32,32,,,316462 +PSBB5GF,1,Fill-in-the-blank(s),Numeric,"

20% of 5,000 is 1,000 and 21% of 5,000 is 1,050. Find each percentage of 5,000 and be prepared to explain your reasoning. If you get stuck, consider using the double number line diagram.

+

 

+

1% of 5,000

+

 

+

 

+

 

+

",50,50,,,316680 +PRABFGZA,1,Fill-in-the-blank(s),Numeric,"

Complete the calculation so that the problem shows the correct difference.

+

 

+ + + + + + +
    1-      0.863
+

 

+

1 - = 0.863

",0.137,0.137,,,94419 +PSBB5GF,4,Fill-in-the-blank(s),Numeric,"

20% of 5,000 is 1,000 and 21% of 5,000 is 1,050. Find each percentage of 5,000 and be prepared to explain your reasoning. If you get stuck, consider using the double number line diagram.

+

 

+

20.4% of 5,000

+

+

 

+

",1020,1020,,,317074 +PSBB5JB,2,Fill-in-the-blank(s),Numeric,"

15% of 80 is 12 and 16% of 80 is 12.8. Find the percentage of 80 and be prepared to explain your reasoning.

+

 

+

15.7% of 80

+

 

+

",12.56,12.56,,,317429 +PRABQMA2,1,Fill-in-the-blank(s),Numeric,"

Divide.

+

 

+

34÷15

+

 

+

",3.75,3.75,,,319914 +PRABQMA8,1,Fill-in-the-blank(s),Numeric,"

Divide.

+

 

+

92÷34

+

 

+

",6,6,,,320033 +PRABQMBA,1,Fill-in-the-blank(s),Numeric,"

Divide.

+

 

+

523÷32

+

 

+

",34/9,34/9,,,320253 +PSBZKT,1,Fill-in-the-blank(s),Numeric,"

The area of a rectangle is 14 square units. It has side lengths x and y.  Given the value for x, find y.

+

 

+

x = 213

+

 

+

 

+

y =

",6,6,,,122331 +PSBB6UK,3,Fill-in-the-blank(s),Exact Match,"

Encuentra las coordenadas de punto C.

+

 

+

 

+

 

+

Escribe tu respuesta en el siguiente formato:

+

(x,y) sin espacios.

+

 

+

","(4,1)","(4,1)",,,324709 +PSBB6UK,2,Fill-in-the-blank(s),Exact Match,"

Encuentra las coordenadas de punto B.

+

 

+

 

+

 

+

Escribe tu respuesta en el siguiente formato:

+

(x,y) sin espacios.

+

 

+

","(5,3)","(5,3)",,,324631 +PSBB6UK,1,Fill-in-the-blank(s),Exact Match,"

Encuentra las coordenadas de cada punto.

+

+

Encuentra las coordenadas de punto A.

+

 

+

 

+

 

+

Escribe tu respuesta en el siguiente formato:

+

(x,y) sin espacios.

+

 

+

","(3,5)","(3,5)",,,324554 +PSBB6UK,5,Fill-in-the-blank(s),Exact Match,"

Encuentra las coordenadas de punto E.

+

 

+

 

+

 

+

Escribe tu respuesta en el siguiente formato:

+

(x,y) sin espacios.

+

 

+

","(3.5,0), (3 1/2,0), (7/2,0)","(3.5,0), (3 1/2,0), (7/2,0)",,,324900 +PSBB6UK,4,Fill-in-the-blank(s),Exact Match,"

Encuentra las coordenadas de punto D.

+

 

+

 

+

 

+

Escribe tu respuesta en el siguiente formato:

+

(x,y) sin espacios.

+

 

+

","(1,0)","(1,0)",,,324806 +PSBB6V4,1,Fill-in-the-blank(s),Numeric,"

Noah's oven thermometer gives a reading that is 2% greater than the actual temperature.

+

 

+

If the actual temperature is 325ºF, what will the thermometer reading be?

+

 

+

degrees

+

Round your answer to the nearest tenths place.

",331.5,331.5,,,324443 +PSBB694,2,Fill-in-the-blank(s),Numeric,"

Find the 10th term in this sequence.

+

 

+

",89/55,89/55,,,327384 +PRABG4SZ,1,Fill-in-the-blank(s),Numeric,"

With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount?  

+

 

+

%

+

Round your answer to the hundredth place.

",14.29,14.29,,,289043 +PRABH67G,1,Fill-in-the-blank(s),Numeric,"

The pressure on a bicycle tire is 63 psi. This is 5% higher than what the manual says is the correct pressure. What is the correct pressure?

+

 

+

psi

",60,60,,,51938 +PRABEQMG,1,Fill-in-the-blank(s),Algebraic Expression,"

What is the side length of a cube with a volume of v cubic units?

+

 

+

units

+

Type your answer in the following format:

+

cbrt(7) for 7 or 12cbrt(7) for127 

+

 

+

Use v as your variable.

+

 

+

 

",cbrt(v),cbrt(v),,,331115 +PRABETQ4,1,Fill-in-the-blank(s),Numeric,"

Lin is making a window covering for a window that has the shape of a half circle on top of a square of side length 3 feet. How much fabric does she need?  

+

 

+

square feet

+
+

Round your answer to the tenths place. 

+
",12.5,12.5,,,360704 +PSBB85Z,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

What is the area of this triangle, in square units?

+

 

+

square units

+
",9,9,,,337992 +PSBB9TM,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

+
 
+

 

+

",3.6,3.6,,,342027 +PSBB9VF,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

+
 
+

 

+

",2.45,2.45,,,342329 +PSBB9UV,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation for the line.

+

 

+

y=

+

Use x as your variable.

",4x+18,4x+18,,,342229 +PSBB9WZ,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

+
 
+

 

+

",0.18,0.18,,,342597 +PSBB9Z5,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

+
 
+

 

+

",0.092,0.092,,,343161 +PSBB9YF,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

+

 

+

",0.54,0.54,,,342865 +PSBBF6Y,1,Fill-in-the-blank(s),Numeric,"

The mass of one coin is 16.718 grams. The mass of a second coin is 27.22 grams. How much greater is the mass of the second coin than the first? 

+

 

+

grams

",10.502,10.502,,,204143 +PSBC9DA,1,Fill-in-the-blank(s),Numeric,"

The hexagon represents 1 whole. 

+

 

+

+

 

+

Use the diagram to answer the question: How many 13s are in 123? 

+

 

+

 

+

",5,5,,,515041 +PSBWCM,1,Fill-in-the-blank(s),Numeric,"

Jada walks at a speed of 3 miles per hour. Elena walks at a speed of 2.8 miles per hour. If they both begin walking along a walking trail at the same time, how much farther will Jada walk after 3 hours? 

+

 

+

miles

",0.6,0.6,,,103888 +PSBCAQB,1,Fill-in-the-blank(s),Numeric,"

Solve each of the problem and show your thinking. If you get stuck, consider drawing a tape diagram to represent the situation.

+

 

+

The ratio of students wearing sneakers to those wearing boots is 5 to 6.

+

 

+

If there are 33 students in the class, and all of them are wearing either sneakers or boots, how many of them are wearing sneakers?

+

 

+

students wearing sneakers

",15,15,,,347269 +PSBCAY5,1,Fill-in-the-blank(s),Exact Match,"

Write an expression equivalent to b + b + b + b + b that is a product of a coefficient and a variable.

+

 

+

","(5)(b), (5)b, 5(b), 5b, 5*b","(5)(b), (5)b, 5(b), 5b, 5*b",,,349044 +PSBCAYM,1,Fill-in-the-blank(s),Numeric,"

Calculate the quotient using your preferred strategy.

+
 
+

 

+

 

+

",9-Feb,9-Feb,,,348977 +PSBCAXG,1,Fill-in-the-blank(s),Numeric,"

Here is an expression: 2 + 3t

+

 

+

Evaluate the expression when t is 1.

+

 

+

",5,5,,,348715 +PSBCAWE,3,Fill-in-the-blank(s),Numeric,"

A vendor at a street fair sells popcorn in cones, all of height 9 inches. The sharing-size cone has 3 times the radius of the skinny-size cones. About how many times more popcorn does the sharing cone hold than the skinny cone? 

+

 

+

",9,9,,,348674 +PSBCA2E,1,Fill-in-the-blank(s),Numeric,"

Calculate the quotient using your preferred strategy.

+
 
+

  

+

 

+

",2-Mar,2-Mar,,,349260 +PSBCA5P,1,Fill-in-the-blank(s),Numeric,"

Calculate the quotient using your preferred strategy.

+
 
+

  

+

 

+

 

+

",12,12,,,349832 +PSBCAXG,2,Fill-in-the-blank(s),Numeric,"

Here is an expression: 2 + 3t

+

 

+

Evaluate the expression when t is 4.

+

 

+

",83,83,,,348833 +PSBCA7D,1,Fill-in-the-blank(s),Numeric,"

Calculate the quotient using your preferred strategy.

+

 

+

 

+

 

+

 

+

",32/15,32/15,,,350118 +PSBCAY5,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression equivalent b + b + b + b + b to that is a sum of two terms.

+

 

+

","b+4b, 3b+2b","b+4b, 3b+2b",,,349167 +PSBCA32,1,Fill-in-the-blank(s),Numeric,"

Calculate the quotient using your preferred strategy. 

+
 
+

 

+

 

+

",15,15,,,349546 +PRABUZ73,1,Fill-in-the-blank(s),Numeric,"

A frozen yogurt store sells 3 different flavors of yogurt: vanilla, chocolate, and strawberry. An order of frozen yogurt comes with 4 different topping choices: fudge, caramel, fruit, or plain. How many unique ways can you order a frozen yogurt? (You can only select one flavor of yogurt and one topping).

+

 

+

",12,12,,,350160 +PSBCBQB,6,Fill-in-the-blank(s),Numeric,"

Find the hemisphere’s radius if its diameter is 9.008 ft.

+

 

+

ft

",4.504,4.504,,,353101 +PRABER7F,1,Fill-in-the-blank(s),Numeric,"

Write the fraction as a decimal.

+
+

 

+

 9100

+
+

 

+

",".3, 0.3",".3, 0.3",,,355074 +PSBCBY8,2,Fill-in-the-blank(s),Numeric,"

What is the surface area of the pyramid?

+

 

+

square units 

+

 

+

",800,800,,,354813 +PRABESJA,1,Fill-in-the-blank(s),Exact Match,"

Write the decimal as a fraction.

+
+

  

+

10.01

+
+

 

+

","1001/100, 10 1/100","1001/100, 10 1/100",,,356245 +PSBBAQT,1,Fill-in-the-blank(s),Numeric,"

Find the area of this shape in two different ways.

+
+

 

+

+

 

+

What is the area?

+

 

+

 square meters

+
",10,10,,,173259 +PSBCCXG,3,Fill-in-the-blank(s),Numeric,"

What is the speed of the International Space Station?

+

 

+

kilometers per second

",8,8,,,360494 +PRABMPBN,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+


21  ÷  =  7

",3,3,,,361341 +PRABMPBQ,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+

 

+

21 · = 7

",3-Jan,3-Jan,,,361805 +PRABMPBM,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+


8 +   =  40

",32,32,,,361147 +PSBBQKA,1,Fill-in-the-blank(s),Numeric,"
The volume of both of these trapezoidal prisms is 24 cubic units. Their heights are 6 and 8 units, as labeled. What is the area of a trapezoidal base of the prism with a height of 6 units? 
+
+

 

+

units2

+

 

+

+
",4,4,,,244890 +PRABTTMK,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression when x is 4 and y is 6.

+

 

+

(6-x)3+y

+

 

+

",14,14,,,46285 +PSBCDQN,4,Fill-in-the-blank(s),Numeric,"

How many students are in the school if 42 of them are sixth graders? 

+

 

+

 students

",189,189,,,365306 +PSBCDR6,3,Fill-in-the-blank(s),Numeric,"

45% of z is 72. Find the value of z.

+

 

+

z =

",160,160,,,365680 +PRABEUP7,1,Fill-in-the-blank(s),Numeric,"

Edge lengths are given in units. Find the surface area in square units.  

+

 

+

square units

+

 

+

",340,340,,,155972 +PRABETYN,1,Fill-in-the-blank(s),Numeric,"

Andre wants to buy a backpack. The normal price of the backpack is $40. He notices that a store that sells the backpack is having a 30% off sale. What is the sale price of the backpack? 

+

 

+

$

",28,28,,,367113 +PSBE5U,2,Fill-in-the-blank(s),Numeric,"

This figure is made from part of a circle and part of a square.

+

 

+

+

 

+

 

+

What is the area of this figure, to the nearest square unit?

+

 

+

  square units

",23,23,,,26348 +PSBCEQE,1,Fill-in-the-blank(s),Numeric,"

How long is 10% of 60 minutes?

+

 

+

minutes

",6,6,,,370835 +PSBE5U,1,Fill-in-the-blank(s),Numeric,"

This figure is made from part of a circle and part of a square.

+

 

+

+

 

+

What is the perimeter of this figure, to the nearest unit?  

+

 

+

units

",19,19,,,26210 +PSBNQS,2,Fill-in-the-blank(s),Numeric,"

Find the value of the expression below.

+

 

+

-22 − (-5)

+

 

+

",-17,-17,,,60534 +PRABFH6S,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

62 ÷ 4

+

 

+

",9,9,,,373325 +PRABFH6R,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

+

 

+

",3,3,,,373136 +PRABFH43,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

23 · 3

+

 

+

",24,24,,,372761 +PRABFH44,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

+

 

+

",8,8,,,372951 +PRABFH6T,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

23 - 2

+

 

+

",6,6,,,373537 +PSBDBHH,1,Fill-in-the-blank(s),Numeric,"

What is the weight of a square if a triangle weighs 4 grams?

+

 

+

grams

+

 

+

",8,8,,,527725 +PSBCGRS,4,Fill-in-the-blank(s),Numeric,"

How many small faces would this bigger fractal have?

+

 

+

small faces

",256,256,,,382659 +PSBCGTP,2,Fill-in-the-blank(s),Numeric,"

A cyclist rode 3.75 miles in 0.3 hours. 

+

 

+

At that rate, how long (in hours) will it take her to go 4.5 miles?  

+

 

+

 hours

",0.36,0.36,,,382916 +PSBVZG,1,Fill-in-the-blank(s),Numeric,"

There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. The point (6, 47.94) is shown on the graph:

+

 

+

+

What is the constant of proportionality in this relationship? 

+

 

+

$

",7.99,7.99,,,101024 +PSBCHST,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2x − 23 = 0

+

 

+

x=

",3-Feb,3-Feb,,,387953 +PSBCJEN,4,Fill-in-the-blank(s),Numeric,"

Based on this simulation, what is the probability that at least two kittens will be chocolate brown.

+

 

+

",12-May,12-May,,,390823 +PSBCJEN,3,Fill-in-the-blank(s),Numeric,"

Based on this simulation, what is the probability that exactly two kittens will be chocolate brown.

+

 

+

",12-Mar,12-Mar,,,390558 +PSBCJEN,1,Fill-in-the-blank(s),Numeric,"

Priya’s cat is pregnant with a litter of 5 kittens. Each kitten has a 30% chance of being chocolate brown. Priya wants to know the probability that at least two of the kittens will be chocolate brown.

+
+
+
+
+

To simulate this, Priya put 3 white cubes and 7 green cubes in a bag. (This means that the white cubes represent the chances of a brown cat.) For each trial, Priya pulled out and returned a cube 5 times. Priya conducted 12 trials.

+

 

+

Here is a table with the results.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
trial numberoutcome
1ggggg
2gggwg
3wgwgw
4gwggg
5gggwg
6wwggg
7gwggg
8ggwgw
9wwwgg
10ggggw
11wggwg
12gggwg
+

 

+

How many successful trials were there?

+
+
+
+
+

 

+

",5,5,,,390129 +PSBDHKG,1,Fill-in-the-blank(s),Numeric,"

What is the value of 12÷13? 

+

 

+

+

 

+

Use pattern blocks to represent and find this value. The yellow hexagon represents 1 whole.

+

 

+

",1.5,1.5,,,562131 +PSBZ3C,1,Fill-in-the-blank(s),Numeric,"

The table represents a proportional relationship.  

+

 

+

Find the constant of proportionality.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
ay
223
31
10103
124
+

 

+

Constant of proportionality:  

+

Express your answer as a fraction.

",3-Jan,3-Jan,,,124164 +PSBCMNM,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(2.5)⋅(1.4)

+

 

+

",3.5,3.5,,,403421 +PRABFG57,1,Order / Sort,Ordering,

Order these numbers from least to greatest:

,"

-12

,

12

,

-1

,

-112

,

1

,

0

","

-12

,

12

,

-1

,

-112

,

1

,

0

",,,406337 +PSBCNEW,2,Fill-in-the-blank(s),Numeric,"

Students did push-ups for a fitness test. Their goal was 20 push-ups. For the student, determine what percentage of the goal they achieved.

+

 

+

Jada did 42 push-ups.

+

 

+

%

",210,210,,,407285 +PRABFKE2,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

125÷65

+

 

+

",2,2,,,416968 +PRABFKE4,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

910÷109

+

 

+

",0.81,0.81,,,417385 +PRABEVDT,1,Fill-in-the-blank(s),Numeric,"

Han surveys a random sample of students about their favorite pasta dish served by the cafeteria and makes a bar graph of the results.

+

 

+

+

 

+

Estimate the proportion of the students who like lasagna as their favorite pasta dish.

+

 

+

",20-Jun,20-Jun,,,106945 +PSBCQR6,2,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

2 ÷ 5

+

 

+

",".4, 0.4",".4, 0.4",,,421310 +PRABFG24,1,Fill-in-the-blank(s),Numeric,"

What is the area of a square with side lengths of 35 units?

+

 

+

square units

",25-Sep,25-Sep,,,86962 +PSBCQU6,4,Fill-in-the-blank(s),Numeric,"

Multiply. Express your answer as a decimal.

+

 

+

(0.75) · 40

+

 

+

",30,30,,,422237 +PSBCQU6,2,Fill-in-the-blank(s),Numeric,"

Multiply. Express your answer as a decimal.

+

 

+

34 · 400

+

 

+

",300,300,,,421967 +PSBCR8Q,1,Fill-in-the-blank(s),Numeric,"

 What is 0.5% of 75?

+

 

+

",0.375,0.375,,,429767 +PRABEPM6,1,Fill-in-the-blank(s),Numeric,"

Find the area of a square if its side length is 118 inches.

+

 

+

square inches

",121/64,121/64,,,424567 +PRABEPME,1,Fill-in-the-blank(s),Numeric,"

Write the exact value of the side length, in units, of a square whose area in square units is 1009.

+

 

+

units

",3-Oct,3-Oct,,,423601 +PSBCRGJ,1,Fill-in-the-blank(s),Numeric,"

Here is an expression: 3 · 2t

+

 

+

Evaluate the expression when t is 1.

+

 

+

",6,6,,,425797 +PSBCRJA,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression equivalent to m+m+m+m that is a sum of two terms.

+

 

+

","2m+2m, 3m+m","2m+2m, 3m+m",,,426220 +PSBCRJA,1,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression equivalent to m+m+m+m that is a product of a coefficient and a variable.

+

 

+

",4m,4m,,,426116 +PSBCRZ8,1,Fill-in-the-blank(s),Numeric,"

What is 10% of 75?

+

 

+

",7.5,7.5,,,428623 +PSBCR6G,1,Fill-in-the-blank(s),Numeric,"

 What is 0.1% of 75?

+

 

+

",0.075,0.075,,,429393 +PSBCR4G,1,Fill-in-the-blank(s),Numeric,"

What is 1% of 75?

+

 

+

",0.75,0.75,,,428993 +PSBCTGA,3,Fill-in-the-blank(s),Numeric,"

Identify the greatest common factor of 28 and 12.

+

 

+

",4,4,,,437180 +PSBCTEB,1,Fill-in-the-blank(s),Exact Match,"

Find all of the factors of 21.

+

 

+

List the factors in ascending (least to greatest) order, with a comma in between each of them, and with no spaces.

+

 

+

","1,3,7,21","1,3,7,21",,,436482 +PSBCTGA,1,Fill-in-the-blank(s),Exact Match,"

Find all of the factors of 28.

+

 

+

List the factors in ascending (least to greatest) order, with a comma in between each of them, and with no spaces.

+

 

+

","1,2,4,7,14,28","1,2,4,7,14,28",,,436921 +PSBCTEB,2,Fill-in-the-blank(s),Exact Match,"

Find all of the factors of 6.

+

 

+

List the factors in ascending (least to greatest) order, with a comma in between each of them, and with no spaces.

+

 

+

","1,2,3,6","1,2,3,6",,,436594 +PSBCTEB,3,Fill-in-the-blank(s),Numeric,"

Identify the greatest common factor of 21 and 6.

+

 

+

",3,3,,,436717 +PSBCTGA,2,Fill-in-the-blank(s),Exact Match,"

Find all of the factors of 12.

+

 

+

List the factors in ascending (least to greatest) order, with a comma in between each of them, and with no spaces.

+

 

+

","1,2,3,4,6,12","1,2,3,4,6,12",,,437042 +PSBCTHV,3,Fill-in-the-blank(s),Numeric,"

If the car wheel rotates 5 times per second, about how many miles does the car travel in one hour?

+

 

+

miles

+

Round your answer to the nearest tenth of a mile.

",18.5,18.5,,,437300 +PRABTTEH,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

15 = 1.5t

+

 

+

t =

",10,10,,,194900 +PRABTTEE,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

73=q+23

+

 

+

",3-May,3-May,,,194628 +PRABTTEF,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

90 = 20r

+

 

+

r =

",2-Sep,2-Sep,,,194712 +PSB7JA,2,Fill-in-the-blank(s),Numeric,"

The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is.

+

 

+

One rotation of the carousel takes 12 seconds. How much faster does Mai travel than Kiran?  

+

 

+

feet per second

+

Use 3.14 for π.

+

Round your answer to the tenths place.

",4.2,4.2,,,156264 +PRABETV3,1,Fill-in-the-blank(s),Numeric,"

The price of an ice cream cone is $3.25, but it costs $3.51 with tax. What is the sales tax rate?  

+

 

+

%

",8,8,,,61531 +PSBN64,1,Fill-in-the-blank(s),Numeric,"

Here is a diagram and its corresponding equation. Find the solution to the equation.

+

 

+

+

6x + 11 = 21

+

 

+

x =

","1.67, 1.7, 10/6","1.67, 1.7, 10/6",,,63291 +PSBCVNF,1,Fill-in-the-blank(s),Numeric,"

How many right angles need to be put together to make 360 degrees?

+

 

+

right angles

",4,4,,,448452 +PSBDRW4,2,Fill-in-the-blank(s),Algebraic Expression,"

The sides of a square have length s.

+

 

+

Write a formula for the area A of the square.

+

 

+

A =

+

Use s as your variable.

+

 

+

Use the ^ symbol to represent an exponent. 

+

For example:

+

52 should be typed as 5^2

+

(-5)2 should be typed as (-5)^2

",s^2,s^2,,,605052 +PSBCWN6,1,Fill-in-the-blank(s),Numeric,"

The diagram shows five small squares and one rectangle composed of 10 small squares.

+

+

Andre says this diagram can represent 1,500. What does a small square represent for Andre?

+

 

+

 

+

",100,100,,,454858 +PSBCAQG,2,Fill-in-the-blank(s),Numeric,"

A baker wants to reduce the amount of sugar in his cake recipes. He decides to reduce the amount used in 1 cake by 12 cup. He then uses 412 cups of sugar to bake 6 cakes.

+
+

 

+

+

 

+
+

How much sugar was originally in each cake recipe?  

+

 

+

cups of sugar

",1 1/4,1 1/4,,,347162 +PSBMD9,2,Fill-in-the-blank(s),Numeric,"

Andre wants to save $40 to buy a gift for his dad. Andre's neighbor will pay him weekly to mow the lawn, but Andre always gives a $2 donation to the food bank in weeks when he earns money. Andre calculates that it will take him 5 weeks to earn the money for his dad's gift. He draws a tape diagram to represent the situation.

+

 

+

+

 

+

How much does Andre's neighbor pay him in each week to mow the lawn? 

+

 

+

$

",10,10,,,54241 +PSBCY9Z,1,Fill-in-the-blank(s),Numeric,"

 There are four ways to make by multiplying powers of 10 with smaller, positive exponents.

+

+

(This list is complete if you don't pay attention to the order you write them in. For example, we are only counting and  once.)

+

 

+

How many ways are there to make by multiplying smaller powers of 10 together?

+

 

+

",10,10,,,469527 +PSBCY9Z,3,Fill-in-the-blank(s),Numeric,"

 

+

How many ways are there to make by multiplying smaller powers of 10 together?

+

 

+

",22,22,,,469703 +PSBCY9Z,2,Fill-in-the-blank(s),Numeric,"

 

+

How many ways are there to make by multiplying smaller powers of 10 together?

+

 

+

",14,14,,,469613 +PRABFG5A,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

5x = 27

+

 

+

x =

+

If necessary, express your answer in fraction form.

",Feb-35,Feb-35,,,50477 +PRABFG49,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

112 = 2x

+

 

+

x =

+

If necessary, express your answer in fraction form.

",4-Mar,4-Mar,,,50267 +PRABTGFC,1,Fill-in-the-blank(s),Numeric,"

Solve.

+

 

+

12 + p = -3

+

 

+

p =

",-3 1/2,-3 1/2,,,157401 +PSBC2PC,2,Fill-in-the-blank(s),Numeric,"

By what percentage did the price increase?

+

 

+

%

+

 

",20,20,,,477606 +PSBBBJQ,1,Fill-in-the-blank(s),Numeric,"

Here is a diagram and its corresponding equation. Find the solution to the equation.

+

 

+ + + + + + + +
6(x+1) = 24
+

 

+

x =

",3,3,,,178070 +PSBCZDE,1,Fill-in-the-blank(s),Numeric,"

Find the difference 0.2 - 0.05.

+

 

+

 

+

",0.15,0.15,,,470213 +PRABHR3H,1,Fill-in-the-blank(s),Numeric,"

Calculate 4,235 ÷ 11 using any method.

+

 

+

",385,385,,,473981 +PSBC2YF,2,Fill-in-the-blank(s),Numeric,"

At another sanctuary, the number of nesting turtles decreased by 10%. This year there were 234 nesting turtles. How many nesting turtles were at this sanctuary last year?

+

 

+

nesting turtles

",260,260,,,479240 +PSBC2S5,2,Fill-in-the-blank(s),Numeric,"

The population is now 6,600. What was the population last year?

+

 

+

people

",5280,5280,,,478342 +PRABG42S,1,Fill-in-the-blank(s),Numeric,"

Solve the equation 3(x + 4.5) = 36. If you get stuck, use the diagram.

+

 

+

x =

+

 

+

 

+

+

 

",7.5,7.5,,,55691 +PSBC4NU,3,Fill-in-the-blank(s),Numeric,"

Find the least common multiple of 10 and 8.

+

 

+

",40,40,,,489519 +PSBC4NU,5,Fill-in-the-blank(s),Numeric,"

Find the least common multiple of 7 and 9.

+

 

+

",63,63,,,489770 +PSBC4SY,2,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

60 ÷ 5 = 

+

 

+

",12,12,,,490267 +PSBGWX,3,Fill-in-the-blank(s),Exact Fraction,"

One inch is around 21120 centimeters.

+

 

+

+

 

+

What fraction of an inch is 1 centimeter?

+

 

+

inch

",20/51,20/51,,,35817 +PSBVZG,4,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation that represents the relationship between C, the total cost of the subscription, and m, the number of months.

+

 

+

C =

+

Use m as your variable.

",7.99m,7.99m,,,101733 +PSBV6V,2,Fill-in-the-blank(s),Numeric,"

Find the value of k.

+

 

+

",25,25,,,102385 +PSBC523,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

14 is 50% of what number?

+

 

+

",28,28,,,497078 +PSBZ6J,1,Fill-in-the-blank(s),Numeric,"

The triangle has an area of 778 cm2 and a base of 514 cm.  

+

 

+

What is the length of h?

+

 

+

cm

+

 

+

",3,3,,,125391 +PSBE7T,1,Fill-in-the-blank(s),Numeric,"

A painter needs to paint the bottom of a circular pool. The pool has a radius of 30 feet.

+

 

+

A store sells 5-gallon cans of paint. One gallon of paint covers 300 square feet.

+

 

+

What is the smallest number of 5-gallon cans the painter must buy to cover the bottom of the pool?

+

 

+

 5-gallon cans

",2,2,,,26568 +PSBH3U,1,Fill-in-the-blank(s),Numeric,"

The table below represents a proportional relationship.

+

 

+

Find the constant of proportionality.

+

 

+

Constant of proportionality:  

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
sP
28
312
520
1040
+

 

",4,4,,,42014 +PSBH3U,2,Fill-in-the-blank(s),Algebraic Expression,"

The table below represents a proportional relationship.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
sP
28
312
520
1040
+

 

+

Write an equation that represents the relationship.  

+

 

+

Equation: P =

","4*s, 4s","4*s, 4s",,,42156 +PSB5FH,1,Fill-in-the-blank(s),Numeric,"

The table below represents a proportional relationship.

+

 

+

Find the constant of proportionality.

+

 

+

Constant of proportionality:

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
dC
26.28
39.42
515.7
1031.4
+

 

",3.14,3.14,,,144794 +PSBC5YB,3,Fill-in-the-blank(s),Numeric,"

Tyler uses 20% of the remaining barbecue sauce. About how many ounces did he use the second time?  

+

 

+

ounces of barbecue sauce

",4.5,4.5,,,496551 +PSBC57S,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

What is 25% of 80?

+

 

+

",20,20,,,497933 +PSBBCFE,1,Fill-in-the-blank(s),Numeric,"

Snow is falling steadily in Syracuse, New York. After 2 hours, 4 inches of snow has fallen.

+

 

+

If it continues to snow at the same rate, how many inches of snow would you expect after 6.5 hours? If you get stuck, you can use the table to help.

+

 

+

inches

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
time (hours)snow (inches)
 1
1 
24
6.5 
x 
+

 

",13,13,,,182778 +PSBC59D,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

What is 41% of 200?

+

 

+

",82,82,,,498194 +PSBC77E,2,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

4 ÷ 5

+

 

+

",".8, 0.8",".8, 0.8",,,508172 +PSBC54T,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

24 is 120% of what number?

+

 

+

",20,20,,,497355 +PSBC556,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

18 is what percentage of 30?  

+

 

+

%

",60,60,,,497669 +PSBCXKJ,3,Fill-in-the-blank(s),Algebraic Expression,"

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information.

+

 

+

Each byte contains 8 bits of information. Write an equation to represent the relationship between the number of packets and the number of bits. 

+

 

+

x =

+

Use p as your variable.

","12,000p","12,000p",,,460374 +PSBBUMW,2,Fill-in-the-blank(s),Numeric,"

How far does a rider travel in one complete rotation around the Ferris wheel? 

+

 

+

meters

+

Use 3.14 for π. 

+

Round your answer to the nearest whole number.

",251,251,,,267619 +PRABQP6G,1,Fill-in-the-blank(s),Numeric,"

A new phone costs $450. There is a 40% discount on the price of the phone and an 8% sales tax on the discount price. What is the final cost of the phone after the discount and the sales tax?

+

 

+

$

",291.6,291.6,,,506119 +PSBC8GK,1,Fill-in-the-blank(s),Numeric,"

Here is an unlabeled polygon, along with its scaled copies Polygons A–D.

+

 

+

+

 

+

Determine the scale factor for copy C. 

+

 

+

",2-Mar,2-Mar,,,509883 +PSBDASC,2,Fill-in-the-blank(s),Numeric,"

What is the decimal representation of that number?

+

 

+

",0.5,0.5,,,522651 +PSBDASC,4,Fill-in-the-blank(s),Numeric,"

What is the decimal representation of that number?

+

 

+

 

+

",0.25,0.25,,,522897 +PSBDASC,6,Fill-in-the-blank(s),Numeric,"

What is the decimal representation of that number?

+

 

+

",0.125,0.125,,,523084 +PSBDAX7,3,Fill-in-the-blank(s),Numeric,"

If you were to sketch the graph of this linear equation, what would its slope be? 

+

 

+

",-2,-2,,,524173 +PSBDB29,1,Fill-in-the-blank(s),Numeric,"

Find the quotient of 1,332 ÷ 9 using one of the methods you have seen so far. 

+

 

+

",148,148,,,530879 +PSBDB7P,3,Fill-in-the-blank(s),Numeric,"

Find the quotient. 

+

 

+

665 ÷ 7

+

 

+

",95,95,,,531410 +PSBDB7P,5,Fill-in-the-blank(s),Numeric,"

Find the quotient. 

+

 

+

432 ÷ 16

+

 

+

",27,27,,,531647 +PRABTGFD,1,Fill-in-the-blank(s),Numeric,"

Solve.

+

 

+

-4.5 = a - 8

+

 

+

a =

",3.5,3.5,,,157262 +PSBDB7P,1,Fill-in-the-blank(s),Numeric,"

Find each quotient and show your reasoning. Use the partial quotients method at least once.

+
 
+
Find the quotient. 
+
 
+
 
+
1,115 ÷ 5 
+

 

+

",223,223,,,531190 +PSBCP4,2,Fill-in-the-blank(s),Numeric,"

Based on this model, how heavy would you expect a newborn Doberman to be?

+

 

+

pounds

+

 

+

",1.22,1.22,,,12777 +PSBBQXP,3,Fill-in-the-blank(s),Numeric,"

Tyler’s brother earns $12 per hour. The store offers him a raise—a 5% increase per hour. After the raise, how much will Tyler’s brother make per hour? 

+

 

+

$

",12.6,12.6,,,246966 +PSBVBE,3,Fill-in-the-blank(s),Numeric,"

Jada’s sister earns a commission. She makes 3.5% of the amount she sells. Last week, she sold $7,000 worth of furniture. How much was her commission?

+

 

+

 $

",245,245,,,97648 +PSBBKRM,1,Fill-in-the-blank(s),Algebraic Expression,"

Andre and Noah start tracking their savings at the same time.

+

 

+

Andre starts with $15 and deposits $5 per week.

+

 

+

Noah starts with $2.50 and deposits $7.50 per week. The graph of Noah's savings is given and his equation is y=7.5x+2.5, where x represents the number of weeks and y represents his savings.

+

 

+

+

 

+

Write the equation for Andre's savings.

+

 

+

y=

+

Use x as your variable.

",5x+15,5x+15,,,223780 +PSBC7QJ,2,Fill-in-the-blank(s),Numeric,"

A college student takes out a $7,500 loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet):

+

 

+

If the bank charges 5.3% interest each year? 

+

 

+

$

",7897.5,7897.5,,,505561 +PSBDFK7,3,Fill-in-the-blank(s),Numeric,"

Decide what power of 10 to put on the labeled tick mark on this number line so that all three countries’ populations can be distinguished.

+

 

+

+

 

+

",6,6,,,551805 +PSBDFVZ,2,Fill-in-the-blank(s),Numeric,"

How much will Noah spend for the belt buckle including tax? 

+

 

+

$

",26.56,26.56,,,553401 +PSBC7JE,1,Fill-in-the-blank(s),Numeric,"

Lin is shopping for a couch with her dad and hears him ask the salesperson, “How much is your commission?” The salesperson says that her commission is 512% of the selling price.

+

 

+

How much commission will the salesperson earn by selling a couch for $495? 

+

 

+

$

",27.23,27.23,,,504254 +PSBBWMY,3,Fill-in-the-blank(s),Numeric,"

For the event, tell how many outcomes there are.

+

 

+

Select a month. Then select 2020 or 2025.

+

 

+

outcomes

",24,24,,,278217 +PSBC4ET,2,Fill-in-the-blank(s),Numeric,"

Give the plant’s age and height at that time of Point D.

+

 

+

plant's age: weeks

+

 

+

height: inches

","5, 4","5, 4",,,488471 +PRABFG58,1,Order / Sort,Ordering,"

Here are the boiling points of certain elements in degrees Celsius:

+
    +
  • Argon: -185.8
    • +
  • Chlorine: -34
    • +
  • Fluorine: -188.1
    • +
  • Hydrogen: -252.87
    • +
  • Krypton: -153.2

    • +
+

List the elements from least (1) to greatest (5) boiling points.

","Hydrogen, Chlorine, Krypton, Argon, Flourine","Hydrogen, Chlorine, Krypton, Argon, Flourine",,,356879 +PSBDKXC,3,Fill-in-the-blank(s),Exact Fraction,"

Answer the question: What fraction of 9 is 3?

+

 

+

",3-Jan,3-Jan,,,576243 +PSBDKXC,6,Fill-in-the-blank(s),Exact Fraction,"

Answer the question: What fraction of 5 is ?

+

 

+

",10-Jan,10-Jan,,,576579 +PRABKCZR,1,Order / Sort,Ordering,

Some information is given about each sphere. Order them from least volume to greatest volume. You may sketch a sphere to help you visualize if you prefer.

,"

Sphere B has a diameter of 6.

,

Sphere C has a volume of 64π.

,

Sphere A has a radius of 4.

,

Sphere D has a radius double that of sphere B.

","

Sphere B has a diameter of 6.

,

Sphere C has a volume of 64π.

,

Sphere A has a radius of 4.

,

Sphere D has a radius double that of sphere B.

",,,154066 +PRABMSGY,1,Fill-in-the-blank(s),Numeric,"

Add.

+
+
+
+
+

-81.4 + (-12)

+
+
+
+
+

 

+

",-93.4,-93.4,,,586044 +PRABMSGX,1,Fill-in-the-blank(s),Numeric,"

Add.

+
+
+
+
+

-9.2 + 4.4

+
+
+
+
+

 

+

",-4.8,-4.8,,,585877 +PRABMSGZ,1,Fill-in-the-blank(s),Numeric,"

Add.

+
+
+
+
+

51.8 + (-0.8)

+
+
+
+
+

 

+

",51,51,,,586212 +PSBDPRR,3,Fill-in-the-blank(s),Numeric,"

What is the least common multiple of 10 and 15?

+

 

+

",30,30,,,592258 +PSBDHHQ,1,Fill-in-the-blank(s),Numeric,"

Use the tape diagram to represent and find the value of 12÷13.

+

 

+

+

 

+

",1.5,1.5,,,561849 +PRABFF3P,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

4 = 32b

+

 

+

b =

",8-Jan,8-Jan,,,223118 +PRABTGFM,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression if x is 25, y is -4, and z is -0.2.

+

 

+

x + y + z

+

 

+

",-3.8,-3.8,,,158771 +PSBU8Y,1,Fill-in-the-blank(s),Numeric,"

A computer randomly selects a letter from the alphabet.

+

 

+

How many different outcomes are in the sample space?

+

 

+

outcomes

",26,26,,,96485 +PSBZWG,1,Fill-in-the-blank(s),Numeric,"

A spinner has four equal sections, with one letter from the word “MATH” in each section.

+

 

+

You spin the spinner 20 times. About how many times do you expect it will land on A?

+

 

+

times

",5,5,,,123919 +PSBBWFQ,1,Fill-in-the-blank(s),Numeric,"

When rolling 3 standard number cubes, the probability of getting all three numbers to match is 6216. What is the probability that the three numbers do not all match?

+

 

+

",210/216,210/216,,,277185 +PSBBWMY,1,Fill-in-the-blank(s),Numeric,"

For the event, tell how many outcomes there are.

+

 

+

Roll a standard number cube. Then flip a quarter.

+

 

+

outcomes

",12,12,,,277725 +PSBNJW,2,Fill-in-the-blank(s),Numeric,"

According to the graph, where was Diego when he was going the slowest during the race?

+

 

+

kilometers into the race

+

 

+

",3,3,,,60170 +PSBNJW,1,Fill-in-the-blank(s),Numeric,"

Diego runs a 10-kilometer race and keeps track of his speed.

+

 

+

+

 

+

What was Diego's speed at the 5-kilometer mark in the race?

+

 

+

kilometers per hour

",10,10,,,60012 +PSBCD4,1,Fill-in-the-blank(s),Numeric,"

There are two different maps of California.

+

 

+
    +
  • On the first map, the scale is 1 cm to 20 km. The distance from Fresno to San Francisco is 15 cm.

    • +
  • On the second map, the scale is 1 cm to 100 km.
    • +
+

 

+

 

+

What is the distance from Fresno to San Francisco on the second map?

+

 

+

cm

",3,3,,,11049 +PSBFH9,6,Fill-in-the-blank(s),Numeric,"

These triangles are scaled copies of each other.

+

 

+

+

 

+

The area of the second triangle is how many times larger than the area of the first?

+

 

+

The area of Triangle H is times larger than the area of Triangle B.

",16-Sep,16-Sep,,,28347 +PSBFH9,5,Fill-in-the-blank(s),Numeric,"

These triangles are scaled copies of each other.

+

 

+

+

 

+

The area of the second triangle is how many times larger than the area of the first?

+

 

+

The area of Triangle G is times larger than the area of Triangle H.

",9-Apr,9-Apr,,,28087 +PSBFH9,2,Fill-in-the-blank(s),Numeric,"

These triangles are scaled copies of each other.

+

 

+

+

 

+

The area of the second triangle is how many times larger than the area of the first?

+

 

+

The area of Triangle G is times larger than the area of Triangle B.

",4-Jan,4-Jan,,,27332 +PSBFH9,3,Fill-in-the-blank(s),Numeric,"

These triangles are scaled copies of each other.

+

 

+

+

 

+

The area of the second triangle is how many times larger than the area of the first?

+

 

+

The area of Triangle B is times larger than the area of Triangle F.

",16,16,,,27571 +PSBFH9,4,Fill-in-the-blank(s),Numeric,"

These triangles are scaled copies of each other.

+

 

+

+

 

+

The area of the second triangle is how many times larger than the area of the first?

+

 

+

The area of Triangle F is times larger than the area of Triangle H.

",9-Jan,9-Jan,,,27844 +PSBZVR,2,Fill-in-the-blank(s),Numeric,"

Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units.

+

 

+

+

 

+

 

+

What scale factor did Lin apply to the Triangle A to create the copy?

+

 

+

",4,4,,,123600 +PSBZVR,3,Fill-in-the-blank(s),Numeric,"

Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units.

+

+

 

+

What is the length of the bottom side of the scaled copy?

+

 

+

  units

",12,12,,,123896 +PSBDXJH,2,Fill-in-the-blank(s),Numeric,"

Find the surface area of the rectangular prism.

+

 

+

 

+

square cm

",160,160,,,637195 +PSBC8C2,1,Fill-in-the-blank(s),Numeric,"

Here is an unlabeled polygon, along with its scaled copies Polygons A–D.

+

 

+

+

 

+

Determine the scale factor for copy A.

+

 

+

",2-Jan,2-Jan,,,509085 +PSBBG4V,6,Fill-in-the-blank(s),Numeric,"

Figure 2 is a scaled copy of Figure 1.

+

+

 

+

G and H are two points on Figure 1, but they are not shown. The distance between G and H is 1. What is the distance between the corresponding points on Figure 2?  

+

 

+

units

",3,3,,,209207 +PRABHR35,1,Fill-in-the-blank(s),Numeric,"

Use long division to find the value of 43.5 ÷ 3.

+

 

+

If you get stuck, you can draw base-ten diagrams. Be sure to say what each type of figure represents in your diagrams.

+

 

+

",14.5,14.5,,,641896 +PSBC8AA,1,Fill-in-the-blank(s),Numeric,"

Diego drew a scaled version of a Polygon P and labeled it Q.

+

 

+

+

 

+

If the area of Polygon P is 72 square units, what scale factor did Diego use to go from P to Q?

+

 

+

",4-Jan,4-Jan,,,508521 +PSBC8EN,1,Fill-in-the-blank(s),Numeric,"

Here is an unlabeled polygon, along with its scaled copies Polygons A–D.

+

 

+

+

 

+

Determine the scale factor for copy B.

+
 
+

 

+

",2,2,,,509539 +PSBC8JJ,1,Fill-in-the-blank(s),Numeric,"

Here is an unlabeled polygon, along with its scaled copies Polygons A–D.

+

 

+

+

 

+

Determine the scale factor for copy D.

+

 

+

",1,1,,,510249 +PRABMPB5,1,Fill-in-the-blank(s),Numeric,"

Solve the equation mentally.

+

 

+

1÷15 = x

+

 

+

",5,5,,,511103 +PSBB5YQ,1,Fill-in-the-blank(s),Numeric,"

A Andre le toma 4 minutos nadar 5 piscinas.

+

 

+

¿Esto equivale a cuántos piscinas por minuto?

+

 

+
 
+

 

+

piscinas por minuto

",4-May,4-May,,,319516 +PSBB5YQ,2,Fill-in-the-blank(s),Numeric,"

A Andre le toma 4 minutos nadar 5 piscinas.

+

 

+

¿Esto equivale a cuántos minutos por cada piscina?

+

 

+

 

+

minutos

",5-Apr,5-Apr,,,319607 +PSBB5YQ,3,Fill-in-the-blank(s),Numeric,"

Si Andre nadara 22 piscinas a esa misma tasa, ¿cuánto tiempo tardaría?

+

 

+
 
+

 

+

minutos

",17.6,17.6,,,319717 +PSBB6RP,1,Fill-in-the-blank(s),Numeric,"

Un lagarto y un caracol están uno al lado del otro en un tubo de drenaje. El lagarto sube 10 pulgadas y el caracol baja 4 pulgadas. Después de moverse, ¿a qué distancia están el uno del otro? 

+

 

+

 

+

pulgadas

",14,14,,,324288 +PSBD2MD,1,Fill-in-the-blank(s),Numeric,"

This diagram shows three small squares and two rectangles composed of 10 small squares.

+

 

+

+

 

+

Jada says this diagram can represent 230. What does a small square represent for Jada?

+

 

+

 

+

",10,10,,,654938 +PSB8P6,1,Fill-in-the-blank(s),Numeric,"

Here is a rectangular prism.

+

 

+

+

 

+

What is the surface area of the prism?

+

 

+

in2

",69.6,69.6,,,162087 +PSBD4PT,1,Fill-in-the-blank(s),Numeric,"

Elena measured the perimeter of a square desk and found 359 cm. Andre measured the perimeter of the same desk and found 3,579 mm.

+

 

+

By how many millimeters do these measurements differ?

+

 

+

  mm

",11,11,,,668634 +PRABEPF7,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

12(5 + 2y) = 4y − (6 − 9y)

+

 

+

y =

",-6,-6,,,331322 +PRABPNNB,1,Fill-in-the-blank(s),Numeric,"

Find the value of 4950 ÷ 76 using any method.

+

 

+

",21/25,21/25,,,10794 +PRABFH6U,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

102 + 52

+

 

+

",125,125,,,373740 +PSBZEG,1,Fill-in-the-blank(s),Numeric,"

Lin uses an app to graph the charge on her phone.

+

 

+

+

 

+

 

+

When did she start using her phone?

+

 

+

hours after noon

",2,2,,,121116 +PSBBVM4,1,Fill-in-the-blank(s),Numeric,"

Calculate 141.75 ÷ 2.5 using a method of your choice. 

+

 

+

",56.7,56.7,,,273049 +PSBDZ4,1,Fill-in-the-blank(s),Numeric,"

Elena donates some money to charity whenever she earns money as a babysitter. The table shows how much money, d, she donates for different amounts of money, m, that she earns.

+

 

+ + + + + + + + + + + + + + + + + + + +
d4.441.803.123.602.16
m3715263018
+

 

+

What percent of her income does Elena donate to charity? 

+

 

+

%

+

 

",12,12,,,19984 +PSBDP9E,1,Fill-in-the-blank(s),Numeric,"

Here is a rectangle:

+

+

 

+

What is the area of the rectangle?

+

 

+

cm2

",28,28,,,595379 +PRABEVTF,1,Fill-in-the-blank(s),Numeric,"

Elena goes for a long walk. This graph shows her time and distance traveled throughout the walk.

+

 

+

+

 

+

What was her fastest speed, in miles per hour?

+

 

+

miles per hour

",4,4,,,340581 +PSBC696,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region. All measurements are in centimeters.

+

 

+

+

 

+

 

+

square centimeters

",80,80,,,503274 +PRABTTCX,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+
+

 

+

12 + (-10)

+
+

 

+

",2,2,,,222978 +PRABPMQF,1,Fill-in-the-blank(s),Numeric,"

Lines s and t are parallel. Find the value of x.

+

 

+

+

 

+ + + + + + +
x = degrees
",50,50,,,189375 +PRABEQDF,1,Fill-in-the-blank(s),Numeric,"

If Quadrilateral Q is a scaled copy of Quadrilateral P created with a scale factor of 3, what is the perimeter of Q?

+

 

+

+
 
+

 

+

",186,186,,,413713 +PSB94Q,3,Fill-in-the-blank(s),Numeric,"

What is the value for the IQR for the data in the dot plot?

+

 

+

",2,2,,,169705 +PRABEUAG,1,Fill-in-the-blank(s),Numeric,"

Lin's puppy is gaining weight at a rate of 0.125 pounds per day. Describe the weight gain in days per pound.  

+

 

+

days per pound

",8,8,,,131274 +PRABEUGP,1,Fill-in-the-blank(s),Numeric,"

Segments AB, DC, and EC intersect at point C. Angle DCE measures 148°. Find the value of x.

+

 

+

+

 

+

x = °

",16,16,,,298893 +PSB9VY,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism is 3 units high, 2 units wide, and 5 units long. What is its surface area in square units? 

+

 

+

+

 

+

square units

",62,62,,,168559 +PRABFFUF,1,Fill-in-the-blank(s),Numeric,"

A diver is 25 feet below sea level. After he swims up 15 feet toward the surface, what is his elevation?

+

 

+

feet

",-10,-10,,,198319 +PSB33P,3,Fill-in-the-blank(s),Drop Down,"

Which is larger?

+

 

+

 

","

Line segment Line segment e

,

Line segment f

","

Line segment f

",,,136977 +PSBBEQB,1,Fill-in-the-blank(s),Numeric,"

A whale is at the surface of the ocean to breathe. What is the whale’s elevation?  

+

 

+

feet

",0,0,,,195392 +PSBBRCW,1,Fill-in-the-blank(s),Numeric,"

Use the given key to answer the questions.

+

+

 

+

What number does this diagram represent?

+

+

 

+

",0.025,0.025,,,249213 +PSBBRFG,1,Fill-in-the-blank(s),Numeric,"

Here are diagrams that represent 0.137 and 0.284.

+

 

+

+

 

+

Use the diagram to find the value of 0.137 + 0.284.

+

 

+

",0.421,0.421,,,249667 +PSBBF42,1,Fill-in-the-blank(s),Numeric,"

Han's calculation of 972 ÷ 9 is shown here.

+

 

+

+

 

+

Find 180 · 9.

+

 

+

",1620,1620,,,203679 +PSB3AB,1,Fill-in-the-blank(s),Numeric,"

What is 3÷4?

+

 

+

",4-Mar,4-Mar,,,132213 +PSBB6JQ,3,Fill-in-the-blank(s),Numeric,"

What is the measure of angle MOE?

+

 

+

°

+

 

+

",60,60,,,322590 +PSBBV5S,1,Fill-in-the-blank(s),Numeric,"

Here is a base-ten diagram that represents 1.13. Use the diagram to find 1.13 − 0.46.

+

 

+

+

 

+

+

 

",0.67,0.67,,,275825 +PSBCWN6,3,Fill-in-the-blank(s),Numeric,"

Clare says this diagram can represent 1.5. What does a small square represent for Clare?

+

 

+

+

 

+

",0.1,0.1,,,455078 +PSBD2MD,3,Fill-in-the-blank(s),Numeric,"

Lin says this diagram can represent 2.3. What does a small square represent for Lin?

+

 

+

+

 

+

",0.1,0.1,,,655039 +PSBB8P,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region. All angles are right angles. 

+

 

+

+

 

+

square units

","1,400","1,400",,,10047 +PRABEC2P,1,Fill-in-the-blank(s),Numeric,"

Solve 3(x - 4) = 12x

+

 

+

x =

",-1.333333333,-1.333333333,,,294102 +PSBNB,1,Fill-in-the-blank(s),Numeric,"

A train traveled at a constant speed. The graph shows how far the train traveled, in miles, during a given amount of time, in hours. 

+

 

+

+

 

+

The point (1, m) is on the graph. Find the value of m.

+

 

+

",80,80,,,1449 +PSBJGY,4,Fill-in-the-blank(s),Numeric,"

A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages.

+

 

+

If you repeat this experiment 50 times, about how many times do you expect you will turn to an even numbered page?

+

 

+

times

",25,25,,,44396 +PSBQQ6,3,Fill-in-the-blank(s),Numeric,"

On TUESDAY, the mother writes the word on a piece of paper and cuts it up so that each letter is on a separate piece of paper. She mixes up the papers and picks one. What is the probability that she will choose the piece of paper with the letter Y?

+

 

+

",7-Jan,7-Jan,,,71072 +PSBJGY,2,Fill-in-the-blank(s),Numeric,"

A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages.

+

 

+

What is the probability that you turn to page 45?

+

 

+

",1/428,1/428,,,44115 +PRABFG48,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

8x = 23

+

 

+

x =

+

If necessary, express your answer in fraction form.

",24-Feb,24-Feb,,,50042 +PSBBESV,2,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

How much does the bottle hold?  

+

 

+

ounces of water

",25,25,,,196111 +PRABFMBU,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

12 ÷ 2 

+

 

+

",4-Jan,4-Jan,,,407357 +PRABFG5B,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

14x = 5

+

 

+

x =

+

If necessary, express your answer in fraction form.

",20,20,,,50674 +PRABFMCN,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

2 ÷ 2

+

 

+

",1,1,,,407583 +PRABFMCP,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

12 ÷ 12

+
 
+

 

+

",1,1,,,407757 +PRABFMCQ,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

3879 ÷ 3879

+

 

+

",1,1,,,407929 +PSBUK7,1,Fill-in-the-blank(s),Numeric,"

Use long division to find the quotient. Write your answer as a decimal.

+

 

+

1,988 ÷ 8

+

 

+

",248.5,248.5,,,92835 +PSBBBRT,3,Fill-in-the-blank(s),Numeric,"

Apples cost $1.99 per pound.

+

 

+

Clare spent $5.17 on apples. How many pounds of apples did Clare buy?  

+

 

+

pounds

+

Round your answer to the nearest tenth of a pound.

",2.6,2.6,,,179199 +PRABHR3J,1,Fill-in-the-blank(s),Numeric,"

Use long division to find the value of 1,875÷15.

+

 

+

",125,125,,,262674 +PSBYW,1,Fill-in-the-blank(s),Numeric,"

The two triangles displayed are scaled copies of one another.

+

 

+

+

 

+

Find the scale factor.

+

 

+

","5/2, 2/5","5/2, 2/5",,,3108 +PSBZEG,2,Fill-in-the-blank(s),Numeric,"

When did she start charging her phone?

+

 

+

hours after noon

+

 

+

",8,8,,,121281 +PSBC6Q5,2,Fill-in-the-blank(s),Numeric,"

Here is an equation: 4x−4=4x+. What could you write in the blank so the equation would be true for:

+

 

+

All values of x

",-4,-4,,,500624 +PSBCGM8,3,Fill-in-the-blank(s),Numeric,"

What is the slope of the line?

+

 

+

Slope =

",-1,-1,,,381865 +PRABEUA4,1,Fill-in-the-blank(s),Numeric,"

Here is a diagram of a birdhouse Elena is planning to build. (It is a simplified diagram, since in reality, the sides will have a thickness.) About how many square inches of wood does she need to build this birdhouse?

+

 

+

+

 

+

 

+

square inches

",286,286,,,53415 +PSB6V2,1,Fill-in-the-blank(s),Numeric,"

The graph represents the average price of regular gasoline in the United States in dollars as a function of the number of months after January 2014.

+

 

+

+

 

+

How many months after January 2014 was the price of gas the greatest?  

+

 

+

months

",5,5,,,152409 +PSBCHP9,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3(x − 5) = 6

+

 

+

x=

",7,7,,,387531 +PRABHUKK,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

x - 5(x - 1) = x - (2x - 3)

+

 

+

x=

",3-Feb,3-Feb,,,191140 +PSBB7SQ,2,Fill-in-the-blank(s),Numeric,"

What is the solution to the equation?

+

 

+

y =

",-5.909090909,-5.909090909,,,330016 +PSB6YG,2,Fill-in-the-blank(s),Numeric,"

Solve the system of equations to find the number of bicycles in the store.

+

 

+

bicycles

",178,178,,,153081 +PRABJWEF,1,Fill-in-the-blank(s),Numeric,"

Imagine that you measure the length and width of a rectangle and you know the measurements are accurate within 5% of the actual measurements. If you use your measurements to find the area, what is the maximum percent error for the area of the rectangle?

+

 

+

%

",10.25,10.25,,,123066 +PSBZEG,3,Fill-in-the-blank(s),Numeric,"

While she was using her phone, at what rate was Lin’s phone battery dying?

+

 

+

% per hour

+

 

+

",30,30,,,121482 +PSBCGM8,1,Fill-in-the-blank(s),Numeric,"

A length of ribbon is cut into two pieces to use in a craft project. The graph shows the length of the second piece, x, for each length of the first piece, y.

+

 

+

+

 

+

How long is the ribbon?

+

 

+

feet

",15,15,,,381490 +PSBWF3,4,Fill-in-the-blank(s),Numeric,"

If this pattern continues, what should be the value of 5-1?

+

 

+

",5-Jan,5-Jan,,,104560 +PSBDV4,2,Fill-in-the-blank(s),Numeric,"

Lin’s family needs to travel 325 miles to reach her grandmother’s house.  

+

 

+

How far have they traveled when they have completed 72% of the trip’s distance?  

+

 

+

miles

",234,234,,,19578 +PSBDV4,3,Fill-in-the-blank(s),Numeric,"

Lin’s family needs to travel 325 miles to reach her grandmother’s house.  

+

 

+

At 377 miles, what percentage of the trip’s distance have they completed?  

+

 

+

%

",116,116,,,19738 +PSBBMNM,2,Fill-in-the-blank(s),Numeric,"

Compute the volume of the prism when d = 1.

+

 

+

cubic units

+

 

+

",4,4,,,228973 +PRABFJWS,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

0.024 ÷ 0.015

+

 

+

",1.6,1.6,,,136828 +PRABFKGS,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression mentally.

+

 

+

3.5 ⋅ 40 + 3.5 ⋅ 60

+

 

+

",350,350,,,94031 +PRABGKQZ,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

0.024 ÷ 0.15

+

 

+

",0.16,0.16,,,137139 +PRABGKQ2,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

24 ÷ 15

+

 

+

",1.6,1.6,,,137305 +PSBBMNM,1,Fill-in-the-blank(s),Algebraic Expression,"

Consider a rectangular prism with length 4 and width and height d.

+

 

+

+

 

+

 

+

Find an expression for the volume of the prism in terms of d.

+

 

+

","d x 4 x d, d x d x 4, dd4, d4d, 4d^2, 4 x d x d, 4dd","d x 4 x d, d x d x 4, dd4, d4d, 4d^2, 4 x d x d, 4dd",,,228800 +PSBBTPJ,1,Fill-in-the-blank(s),Numeric,"

Lin ran 29 meters in 10 seconds. She ran at a constant speed.  

+

 

+

How far did Lin run every second?

+

 

+

meters

",2.9,2.9,,,261537 +PSBBSCK,5,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

51 - 0.07

+

 

+

",50.93,50.93,,,254716 +PRABFKEU,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

17÷18

+

 

+

",7-Aug,7-Aug,,,416720 +PSBCPMQ,3,Fill-in-the-blank(s),Numeric,"

What is the greatest common factor of 42 and 50?

+

 

+

",2,2,,,414817 +PRABFKCS,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2e = 6.4

+

 

+

e =

",3.2,3.2,,,64813 +PSBB8WU,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

What is the area of this square, in square units?

+

 

+

square units

+
",10,10,,,336859 +PRABFKE3,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

 

+

110÷10

+

 

+

",1/100,1/100,,,417173 +PSBCPMQ,2,Fill-in-the-blank(s),Numeric,"

What is the greatest common factor of 42 and 15?

+

 

+

",3,3,,,414639 +PRABFKGR,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression mentally.

+

 

+

12 · 37 - 12 · 7

+

 

+

",15,15,,,93868 +PSBCPMQ,1,Fill-in-the-blank(s),Exact Match,"

List all the factors of 42.

+

 

+

List your answer in a numerical ordered list separated by commas and without extra spaces.

+

For example: 1,2,3

+

 

+

","1,2,3,6,7,14,21,42","1,2,3,6,7,14,21,42",,,414444 +PSBDPRR,1,Fill-in-the-blank(s),Exact Match,"

List all multiples of 10 up to 100.

+

 

+

List your answers in a list separated by commas and without extra spaces.

+

For example: 1,2,3,4,5

+

 

+

","10,20,30,40,50,60,70,80,90,100","10,20,30,40,50,60,70,80,90,100",,,591850 +PSBDPRR,2,Fill-in-the-blank(s),Exact Match,"

List all multiples of 15 up to 100.

+

 

+

List your answers in a list separated by commas and without extra spaces.

+

For example: 1,2,3,4,5

+

 

+

","15,30,45,60,75,90","15,30,45,60,75,90",,,592027 +PRABFKGT,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression mentally.

+

 

+

999 ⋅ 5

+

 

+

",4995,4995,,,94199 +PSBH52,2,Fill-in-the-blank(s),Numeric,"

Ammonia boils at -35.5°C. What is the boiling point of ammonia in K?

+

 

+

K

",237.65,237.65,,,42486 +PSBBSCK,3,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

11.26 + 5.34

+

 

+

","16.6, 16.60","16.6, 16.60",,,254457 +PSBBSCK,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

16 - 2.2

+
 
+

 

+

",13.8,13.8,,,254190 +PSBBSCK,2,Fill-in-the-blank(s),Numeric,"

Evaluate the expression.

+

 

+

3 - 0.26

+
 
+

 

+

",2.74,2.74,,,254319 +PSBJTA,1,Fill-in-the-blank(s),Numeric,"

Suppose that there are 20 numbers in a data set and that they are all different.

+

 

+

How many of the values in this data set are between the first quartile and the third quartile?

+

 

+

",10,10,,,45665 +PSBCMTY,2,Fill-in-the-blank(s),Numeric,"

Evaluate the expression 4x3 for the given value of x. 

+

 

+

x = 2

+

 

+

",32,32,,,404343 +PSBCMTY,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression 4x3 for the given value of x. 

+

 

+

x = 1

+

 

+

",4,4,,,404191 +PSBCMTY,3,Fill-in-the-blank(s),Numeric,"

Evaluate the expression 4x3 for the given value of x. 

+

 

+

x = 12

+

 

+

",0.5,0.5,,,404451 +PSBXZW,1,Fill-in-the-blank(s),Algebraic Expression,"

Two months ago, the price, in dollars, of a cell phone was c.

+

 

+

Last month, the price of the phone increased by 10%. Write an expression for the price of the phone last month. 

+

 

+

+

Use c as your variable

+

 

",1.1c,1.1c,,,113440 +PSBXZW,2,Fill-in-the-blank(s),Algebraic Expression,"

This month, the price of the phone decreased by 10%. Write an expression for the price of the phone this month.

+

 

+

+

Use c as your variable.

+

 

",0.9c,0.9c,,,113646 +PRABMSS2,1,Fill-in-the-blank(s),Numeric,"

Edge lengths are given in units. Find the surface area in square units.  

+

 

+

square units

+

 

+

",408,408,,,156219 +PRABMSS3,1,Fill-in-the-blank(s),Numeric,"

Edge lengths are given in units. Find the surface area in square units.

+

 

+

 square units

+

 

+

",274,274,,,156411 +PRABMSS7,1,Fill-in-the-blank(s),Numeric,"

Edge lengths are given in units. Find the surface area in square units.  

+

 

+

square units

+

",216,216,,,151997 +PSBBK68,3,Fill-in-the-blank(s),Numeric,"

Here are the prices for different amounts of plastic liner. How much will all the plastic liner for the pool cost?

+

 

+

$

+

 

+ + + + + + + + + + + + + + + + + + + +
plastic liner (ft2)cost ($)
253.75
507.50
7511.25
+

 

",44.75,44.75,,,226658 +PSBYCZ,5,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression for the volume.

+

 

+

+

 

+

Use the ^ symbol to represent an exponent. 

+

For example: 52 should be typed as 5^2

",s^3,s^3,,,115789 +PSBYCZ,4,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression for the surface area.

+

 

+

+

 

+

Use the ^ symbol to represent an exponent. 

+

 For example: 52 should be typed as 5^2

",6s^2,6s^2,,,115625 +PSBYCZ,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression for the area of each face.

+

 

+

+

 

+

Use the ^ symbol to represent an exponent. 

+

 For example: 52 should be typed as 5^2

",s^2,s^2,,,115417 +PRABHQG9,1,Fill-in-the-blank(s),Numeric,"

It takes Jada 20 minutes to walk to school. It takes Andre 80% as long to walk to school. How long does it take Andre to walk to school?

+

 

+

minutes

",16,16,,,418297 +PSBCEKU,1,Fill-in-the-blank(s),Numeric,"

How long is 50% of 60 minutes?

+

 

+

minutes

",30,30,,,370230 +PSBDPP7,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3y - 69 = 4 - 2y-3

+

 

+

y =

",2,2,,,592014 +PRABKC8H,1,Fill-in-the-blank(s),Numeric,"

Write (5.64) · 10-7 as a decimal.

+

 

+

",0.000000564,0.000000564,,,238057 +PRABET34,1,Fill-in-the-blank(s),Numeric,"

A small town had a population of 960 people last year. The population grew to 1200 people this year. By what percentage did the population grow?   %

+

 

+

",25,25,,,389538 +PRABET36,1,Fill-in-the-blank(s),Numeric,"

The gas tank of a truck holds 30 gallons. The gas tank of a passenger car holds 50% less. How many gallons does it hold?

+

 

+

gallons

+

 

+

",15,15,,,389890 +PRABEUAJ,1,Fill-in-the-blank(s),Numeric,"

Angles A and C are supplementary. Find the measure of angle C.

+

 

+

+

 

+

m∠C = °

",106,106,,,598936 +PRABG43H,1,Fill-in-the-blank(s),Numeric,"

Angle SPR and angle RPQ are complementary. Find the measure of angle RPQ.

+

 

+

+

 

+

m∠RPQ = °

",53,53,,,351786 +PRABEPPR,1,Fill-in-the-blank(s),Numeric,"

The points (12, 23) and (14, 45) lie on a line. What is the slope of the line?

+

 

+

",11,11,,,412814 +PSBB6KY,2,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.  (The side length of each square on the grid is 1 unit.)

+

 

+

+

 

+

square units

",22.5,22.5,,,323003 +PRABFB66,1,Fill-in-the-blank(s),Numeric,"

Solve the problem. If you get stuck, consider using the double number lines.

+

 

+

Yesterday, Priya successfully made 12 free throws. Today, she made 150% as many. How many successful free throws did Priya make today?

+

 

+

free throws

+

 

+

 

+

+

 

+

 

",18,18,,,324952 +PRABD46C,1,Fill-in-the-blank(s),Numeric,"

Triangle DEF is a right triangle, and the measure of angle D is 28°. What are the measures of the other two angles? 

+

 

+

° and °

","90, 62","90, 62",,,8680 +PSB6SM,3,Fill-in-the-blank(s),Numeric,"

Three cones have a volume of 192π cm3. Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm.

+

 

+

Find the height of each cone C.

+

 

+

cm

",36,36,,,152166 +PSBBK96,2,Fill-in-the-blank(s),Numeric,"

What is the area of the base you shaded?

+

 

+

square units

+

 

+

",26,26,,,227110 +PSBBK96,3,Fill-in-the-blank(s),Numeric,"

What is the volume of the trapezoidal prism below?

+

 

+

cubic units

+

 

+

",312,312,,,227295 +PRABKCY4,1,Fill-in-the-blank(s),Algebraic Expression,"

Recall that the volume of a sphere is given by the formula V=43πr3.

+

 

+

+

 

+

Here is a sphere with radius 4 feet. What is the volume of the sphere? Express your answer in terms of π.

+

 

+

cubic feet

+

Use pi to represent the symbol.  For example: 32π would be typed as 32pi

",256/3pi,256/3pi,,,125684 +PRABKCY5,1,Fill-in-the-blank(s),Numeric,"

Recall that the volume of a sphere is given by the formula V=43πr3.

+

 

+

A spherical balloon has a diameter of 4 feet. Approximate how many cubic feet of air this balloon holds. Use 3.14 as an approximation for π, and give a numerical answer.

+

 

+

cubic feet

+

Round your answer to the hundredths place.

",33.49,33.49,,,125853 +PSB6SM,1,Fill-in-the-blank(s),Numeric,"

Three cones have a volume of 192π cm3. Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm.

+

 

+

Find the height of each cone A.

+

 

+

cm

",144,144,,,151827 +PSBCCRU,2,Fill-in-the-blank(s),Numeric,"

Every animal has two parents. Each of its parents also has two parents.

+

 

+

We say that the animal’s eight great-grandparents are “three generations back” from the animal. At which generation back would an animal have 262,144 ancestors?

+

 

+

generations

",18,18,,,359589 +PSB6SM,2,Fill-in-the-blank(s),Numeric,"

Three cones have a volume of 192π cm3. Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm.

+

 

+

Find the height of each cone B.

+

 

+

cm

",64,64,,,151987 +PRABEPM2,1,Fill-in-the-blank(s),Algebraic Expression,"

Write the exact value of the side length, in units, of a square whose area in square units is  0.11.

+

 

+

units

+

 

+

Type your answer in the following format:

+

sqrt(7) for 7 or 12sqrt(7) for 127 

",sqrt(0.11),sqrt(0.11),,,424081 +PRABEPM4,1,Fill-in-the-blank(s),Numeric,"

Find the area of a square if its side length is 15 cm.

+

 

+

square centimeter

",25-Jan,25-Jan,,,424251 +PRABKAHJ,1,Fill-in-the-blank(s),Numeric,"

What is the volume of a giant cube that measures 10,000 km on each side?

+

 

+

km3

",1E+12,1E+12,,,58527 +PSBBWD2,4,Fill-in-the-blank(s),Algebraic Expression,"

Find the length of a side of a square if its area is m2 square units.

+

 

+

units

",m,m,,,277212 +PSBB6KY,4,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.  (The side length of each square on the grid is 1 unit.)

+

 

+

+

 

+

square units

",44,44,,,323128 +PSBS5V,2,Fill-in-the-blank(s),Algebraic Expression,"

Write a second equation whose graph goes through (0, 2) so that the system has no solutions.

+

 

+

y=

+

Use x as your variable.

",3/2x+2,3/2x+2,,,84475 +PSBS5V,3,Fill-in-the-blank(s),Algebraic Expression,"

Write a second equation whose graph goes through (2, 2) so that the system has one solution at (4, 3).

+

 

+

y=

+

Use x as your variable.

",1/2x+1,1/2x+1,,,84651 +PRABEPAU,1,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation for the line that passes through (-8.5,11) and (5,-2.5).

+

 

+

y=

+

Use x as your variable.

",#NAME?,#NAME?,,,18775 +PRABEQ3S,1,Order / Sort,Ordering,

Order the following expressions from least to greatest.

,"0.025 ÷ 1, 25 ÷ 10, 250,000 ÷ 1,000, 2.5 ÷ 1,000","0.025 ÷ 1, 25 ÷ 10, 250,000 ÷ 1,000, 2.5 ÷ 1,000",,,10115 +PSBB6KY,6,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.  (The side length of each square on the grid is 1 unit.)

+

 

+

+

 

+

square units

",36,36,,,323266 +PSBB6KY,8,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.  (The side length of each square on the grid is 1 unit.)

+

 

+

+

 

+

square units

",33,33,,,323410 +PRABTTCT,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

8v=-18

+

 

+

v =

",-2.25,-2.25,,,179341 +PRABTTCS,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

98+u=37

+

 

+

u =

",-61,-61,,,179212 +PSBBBRT,2,Fill-in-the-blank(s),Algebraic Expression,"

Apples cost $1.99 per pound.

+

 

+

How much do x pounds of apples cost?  

+

 

+

$

",1.99x,1.99x,,,178978 +PSBCNEW,3,Fill-in-the-blank(s),Numeric,"

Students did push-ups for a fitness test. Their goal was 20 push-ups. For the student, determine what percentage of the goal they achieved.

+

 

+

Lin did 13 push-ups.  

+

 

+

%

",65,65,,,407421 +PSBX7V,2,Fill-in-the-blank(s),Numeric,"

Teachers held a basketball shooting contest. Their goal was to make 60 baskets. For the teacher, determine what percentage of the goal they achieved.

+

 

+

Teacher B made 42 baskets.  

+

 

+

 %

",70,70,,,114762 +PSBCNEW,1,Fill-in-the-blank(s),Numeric,"

Students did push-ups for a fitness test. Their goal was 20 push-ups. For the student, determine what percentage of the goal they achieved.

+

 

+

Elena did 16 push-ups.  

+

 

+

%

",80,80,,,407150 +PSBCNEW,4,Fill-in-the-blank(s),Numeric,"

Students did push-ups for a fitness test. Their goal was 20 push-ups. For the student, determine what percentage of the goal they achieved.

+

 

+

Andre did 21 push-ups.  

+

 

+

%

",105,105,,,407530 +PSBDBNU,2,Fill-in-the-blank(s),Numeric,"

Ten students each attempted 10 free throws. This list shows how many free throws each student made.

+

 

+
8, 5, 6, 6, 4, 9, 7, 6, 5, 9
+
 
+

What is the IQR (interquartile range)?

+

 

+

free throws

",3,3,,,528780 +PRABEU7D,1,Fill-in-the-blank(s),Numeric,"

A school is selling candles for a fundraiser. They keep 40% of the total sales as their commission, and they pay the rest to the candle company.

+
+

 

+ + + + + + + + + + + + + + + + + + + +
price of candlenumber of candles sold
small candle: $1168
medium candle: $1845
large candle: $2521
+

 

+

How much money must the school pay to the candle company? 

+

 

+

$

+
",1249.8,1249.8,,,101005 +PSBBFST,1,Fill-in-the-blank(s),Numeric,"

Find the area of the parallelogram.

+

 

+

+

 

+

square units

",21,21,,,201855 +PRABMPB4,1,Fill-in-the-blank(s),Numeric,"

Solve the equation mentally.

+

 

+

x · 111 = 1

+

 

+

",11,11,,,510935 +PSBDUT,2,Fill-in-the-blank(s),Numeric,"

Find the perimeter of the polygon.

+

 

+

units

",22,22,,,19594 +PSBBBRT,1,Fill-in-the-blank(s),Numeric,"

Apples cost $1.99 per pound.

+

 

+

How much do 3.25 pounds of apples cost?

+

 

+

$

+

Round your answer to the nearest cent.

",6.47,6.47,,,178727 +PSBDWUR,1,Fill-in-the-blank(s),Numeric,"

How many different outcomes are in the sample space? You do not need to write out the actual options, just provide the number and your reasoning.

+

 

+

A letter of the English alphabet is followed by a digit from 0 to 9.

+

 

+

",260,260,,,632697 +PSBDWWG,1,Fill-in-the-blank(s),Numeric,"

How many different outcomes are in the sample space? You do not need to write out the actual options, just provide the number and your reasoning.

+

 

+

A baseball team’s cap is selected from 3 different colors, 2 different clasps, and 4 different locations for the team logo. A decision is made to include or not to include reflective piping.

+

 

+

",48,48,,,633159 +PSBDWYK,1,Fill-in-the-blank(s),Numeric,"

How many different outcomes are in the sample space? You do not need to write out the actual options, just provide the number and your reasoning.

+

 

+

A locker combination like 7-23-11 uses three numbers, each from 1 to 40.  Numbers can be used more than once, like 7-23-7. 

+

 

+

",64000,64000,,,633512 +PSBWF3,2,Fill-in-the-blank(s),Numeric,"

If this pattern continues, what should be the value of 50?

+

 

+

",1,1,,,104232 +PSBG9Y,3,Fill-in-the-blank(s),Numeric,"

A librarian is curious about the habits of the library's patrons. He records the type of item that the first 10 patrons check out from the library.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
patronitem type
1fiction book
2non-fiction book
3fiction book
4fiction book
5audiobook
6non-fiction book
7DVD
8non-fiction book
9fiction book
10DVD
+

 

+

Based on the information from these patrons, estimate the number of DVDs that will be checked out for every 100 patrons. 

+

 

+

DVDs

",20,20,,,37832 +PSBWMQ,2,Fill-in-the-blank(s),Numeric,"

Tyler wonders what proportion of students at his school would dye their hair blue if their parents would let them. He surveyed a random sample of 10 students at his school, and 2 of them said they would. Kiran didn’t think Tyler’s estimate was very accurate, so he surveyed a random sample of 100 students, and 17 of them said they would.

+

 

+

Based on Kiran's sample, what proportion of the students would dye their hair blue?

+

 

+

",17/100,17/100,,,105229 +PSBC55V,1,Fill-in-the-blank(s),Numeric,"

A stadium can seat 16,000 people at full capacity.  

+

 

+

If there are 13,920 people in the stadium, what percentage of the capacity is filled? 

+

 

+

%

",87,87,,,497385 +PSBC55V,3,Fill-in-the-blank(s),Numeric,"

What percentage of the capacity is not filled?

+

 

+

%

",13,13,,,497698 +PRABEPMF,1,Fill-in-the-blank(s),Algebraic Expression,"

Write the exact value of the side length, in units, of a square whose area in square units is 25.

+

 

+

units

+

If necessary type your answer in the following format:

+

sqrt(7) for 7 or 12sqrt(7) for 127 

",sqrt(2/5),sqrt(2/5),,,423768 +PSBBWD2,2,Fill-in-the-blank(s),Numeric,"

Find the length of a side of a square if its area is 425 square centimeters.

+

 

+

cm

",5-Feb,5-Feb,,,276874 +PRABESH7,1,Fill-in-the-blank(s),Exact Match,"

Write the decimal as a fraction.

+
+

 

+

0.81

+

 

+
+

",10-Sep,10-Sep,,,355769 +PSBCBW4,3,Fill-in-the-blank(s),Exact Match,"

Write 1720 as a decimal.

+

 

+

",".85, 0.85",".85, 0.85",,,354272 +PRABEQMH,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

 13

+
+
 
+

 

+

",1,1,,,331279 +PSBCMS,1,Fill-in-the-blank(s),Numeric,"

Evaluate:

+

 

+

123

+

 

+

",8-Jan,8-Jan,,,12211 +PSBCJK,1,Fill-in-the-blank(s),Numeric,"

In 2015, there were roughly 1 × 106 high school football players and 2 × 103professional football players in the United States. About how many times more high school football players are there? 

+

 

+

times more high school football players

",500,500,,,11875 +PRABEQDP,1,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation for the graph.

+

 

+

+

 

+

y=

+

Use x as your variable.

",2x+1.5,2x+1.5,,,2034 +PRABEQMM,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

1643

+
+
 
+

 

+

",4-Jan,4-Jan,,,331773 +PRABEQ7S,1,Fill-in-the-blank(s),Numeric,"

A standard city block in Manhattan is a rectangle measuring 80 m by 270 m. A resident wants to get from one corner of a block to the opposite corner of a block that contains a park. She wonders about the difference between cutting across the diagonal through the park compared to going around the park, along the streets.

+

 

+

How much shorter would her walk be going through the park? Round your answer to the nearest meter.

+

 

+

meters

",68,68,,,162829 +PRABEQMJ,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

2163

+
+
 
+

 

+

",6,6,,,331447 +PRABEQMK,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

80003

+
+
 
+

 

+

",20,20,,,331613 +PRABESH6,1,Fill-in-the-blank(s),Exact Match,"

Write the fraction as a decimal.

+
+

 

+

2310

+
+

 

+

",2.3,2.3,,,355634 +PRABEQMU,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

0.0273

+
+
 
+

 

+

",0.3,0.3,,,332084 +PRABESH5,1,Fill-in-the-blank(s),Exact Match,"

Write the fraction as a decimal.

+
+

 

+

 916

+
+

 

+

",".75, 0.75",".75, 0.75",,,355425 +PRABEQMV,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

0.0001253

+
+
 
+

 

+

",0.05,0.05,,,332235 +PRABEQ4D,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Find the positive solution to t3=216. If the solution is irrational, write the solution using cube root notation.

+

 

+

t=

+
+
+
+
+
+

If needed, type your answer in the following format:

+

sqrt(7) for 73v or 12sqrt(7) for 1273 

+
+
",6,6,,,161350 +PRABEQMT,1,Fill-in-the-blank(s),Numeric,"

Write an equivalent expression that doesn’t use a cube root symbol.

+
+

 

+

271253

+
+
 
+

 

+

",5-Mar,5-Mar,,,331947 +PRABESH9,1,Fill-in-the-blank(s),Numeric,"

Write the decimal as a fraction.

+
+

 

+

0.04

+
+

 

+

",5-Jan,5-Jan,,,356075 +PRABESH8,1,Fill-in-the-blank(s),Exact Match,"

Write the decimal as a fraction.

+
+

 

+

0.0276

+
+

 

+

",276/10000,276/10000,,,355920 +PRABESH4,1,Fill-in-the-blank(s),Exact Match,"

Write the fraction as a decimal.

+
+

 

+

99100

+
+

 

+

","0.99, .99","0.99, .99",,,355272 +PSB96F,7,Fill-in-the-blank(s),Numeric,"

+

 

+ + + + + + + + + + + +
For how many cars does the prediction made by the model in Diagram A differ by more than $3,000? cars
What about the model in Diagram B?cars
+

 

","4, 6","4, 6",,,170280 +PRABEQAW,1,Fill-in-the-blank(s),Numeric,"
+
+
+

a and b represent the length of a leg of a right triangle, and c represents the length of its hypotenuse. Find the missing length, given the other two lengths.

+

 

+

a=?, b=21, c=29

+

 

+

a=

+
+
+
",20,20,,,8050 +PRABGZFY,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 64 sq cm. What is its side length?  

+

 

+

centimeters

",8,8,,,48302 +PSBDHZF,4,Fill-in-the-blank(s),Numeric,"

A recipe uses 5 cups of flour for every 2 cups of sugar.

+

 

+

How much sugar is used with 6 cups of flour?  

+

 

+

cups

",2.4,2.4,,,564997 +PSBR5G,2,Fill-in-the-blank(s),Numeric,"

What is the area of each square?

+

 

+

 

+

square units

",100,100,,,78619 +PSBCDYX,3,Fill-in-the-blank(s),Numeric,"

Solve the equation you wrote.

+

 

+

x =

",7.8,7.8,,,366764 +PSBMSN,3,Fill-in-the-blank(s),Numeric,"

Solve the equation you wrote.

+

 

+

x =

",11.6,11.6,,,56163 +PSBC2CF,1,Fill-in-the-blank(s),Numeric,"

In this net, the two triangles are right triangles. All quadrilaterals are rectangles. What is its surface area in square units? 

+

 

+

+

 

+

 

+

square units

",168,168,,,475491 +PSBBQN7,3,Fill-in-the-blank(s),Numeric,"

The discounted price of a hat is $18. What is the regular price? 

+

 

+

$

",22.5,22.5,,,245546 +PSBGS5,2,Fill-in-the-blank(s),Numeric,"

A tugboat traveled -1.5 miles in 0.3 hours. What was its velocity?

+

 

+

miles per hour

",-5,-5,,,35010 +PRABETRY,1,Fill-in-the-blank(s),Numeric,"

A cookie recipe uses 3 cups of flour to make 15 cookies. How many cookies can you make with this recipe with 4 cups of flour? (Assume you have enough of the other ingredients.)

+

 

+

cookies

+

 

",20,20,,,37332 +PSBG5F,1,Fill-in-the-blank(s),Numeric,"

A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.

+

 

+

At what depth is it after 1 stage?

+

 

+

meters

",-280,-280,,,36149 +PSBG5F,2,Fill-in-the-blank(s),Numeric,"

At what depth is it after 2 stages?  

+

 

+

meters

",-220,-220,,,36440 +PSBG5F,3,Fill-in-the-blank(s),Numeric,"

At what depth is it after 4 stages?

+

 

+

meters

",-100,-100,,,36700 +PSBG5F,4,Fill-in-the-blank(s),Numeric,"

A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.

+

 

+

How many stages will it take to return to the surface?

+

 

+

stages of change

",6,6,,,36971 +PSBB2XW,2,Fill-in-the-blank(s),Numeric,"

A runner ran 23 of a 5-kilometer race in 21 minutes. They ran the entire race at a constant speed.

+

 

+

How many minutes did it take to run 1 kilometer?

+

 

+

minutes

",6.3,6.3,,,303033 +PRABEFVX,1,Fill-in-the-blank(s),Numeric,"

A cylinder has volume 45π and radius 3. What is its height?

+

 

+

units

",5,5,,,17475 +PSB5E8,2,Fill-in-the-blank(s),Numeric,"

Find the surface area of this polyhedron. 

+

 

+

square units

+

 

+

",72,72,,,144713 +PSBBN6Q,2,Fill-in-the-blank(s),Numeric,"

Find the distance between C and D.  

+

 

+

 units

",5,5,,,238060 +PSBH83,2,Fill-in-the-blank(s),Algebraic Expression,"

Write the equation of the line.

+

 

+

y=

+

Use x as your variable.

",(-2/3)x-3,(-2/3)x-3,,,43045 +PRABD3CT,1,Fill-in-the-blank(s),Numeric,"

Point A has coordinates (3, 4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, what are the coordinates of the image?

+

 

+

(,)

","-6, -1","-6, -1",,,351892 +PSBBSYB,2,Fill-in-the-blank(s),Numeric,"

If not, write it in scientific notation.

+

 

+

×10

","6, 3.6","6, 3.6",,,257604 +PSBBBZ6,2,Fill-in-the-blank(s),Numeric,"

Find the value after the change.

+

 

+

 

+

$

",18.08,18.08,,,180669 +PSBBK7H,2,Fill-in-the-blank(s),Numeric,"

Solve the system. 

+

 

+

(,)

+

 

+

 

","-6, 4","-6, 4",,,226545 +PSBBSWV,2,Fill-in-the-blank(s),Numeric,"

If not, write it in scientific notation.

+

 

+

×10

","-4, 9.9","-4, 9.9",,,257352 +PSBBSVC,2,Fill-in-the-blank(s),Numeric,"

If not, write it in scientific notation.

+

 

+

×10

","4, 4.82","4, 4.82",,,257097 +PRABEQMD,1,Fill-in-the-blank(s),"Algebraic Expression, Numeric","

What is the volume of a cube with a side length of s units?

+

 

+

 cubic units

+

 

+

Use s as your variable.

","3, s","3, s",,,330621 +PRABEGKP,1,Fill-in-the-blank(s),Numeric,"

Solve: y=6x-8y=-3x+10

+

 

+

(,)

","4, 2","4, 2",,,227799 +PSBBUFM,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region in square units.

+

 

+

+

 

+

square units

",40,40,,,266614 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","2, 4","2, 4",,,437233 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","2, 4","2, 4",,,437233 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","2, 4","2, 4",,,437233 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","4, 2","4, 2",,,437233 +PRABE6XQ,1,Fill-in-the-blank(s),Numeric,"

A square has side length 4 cm. What is its area?

+

 

+

square centimeters

",16,16,,,247357 +PSBR5G,3,Fill-in-the-blank(s),Numeric,"

Use the squares to help you find 40 ⋅ 20.

+

 

+

 

+

",800,800,,,78754 +PSB3DP,2,Fill-in-the-blank(s),Numeric,"

Neon bracelets cost $1 for 4.

+

 

+

At this rate, how much will 11 neon bracelets cost? 

+

 

+

$

",2.75,2.75,,,132877 +PSBNJ6,2,Fill-in-the-blank(s),Numeric,"

What is the volume of this cube?

+

 

+

+

 

+

cubic units

",27,27,,,60349 +PRABHNBP,1,Fill-in-the-blank(s),Numeric,"

In a sprint to the finish, a professional cyclist travels 380 meters in 20 seconds. At that rate, how far does the cyclist travel in 3 seconds?

+

 

+

meters

",57,57,,,306784 +PSBBMCP,1,Fill-in-the-blank(s),Numeric,"

Find the area of this polygon.

+

 

+

 

+

+

 

+

 

+

square units

",33,33,,,227577 +PSB5M9,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region. 

+

 

+

 

+

+

 

+

 

+

square centimeters

",31,31,,,145962 +PSBSB6,1,Fill-in-the-blank(s),Numeric,"

Twelve cubes are stacked to make this figure.

+

 

+

+

 

+

What is its surface area?

+

 

+

square units

",36,36,,,79708 +PSBBUFM,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region in square units.

+

 

+

+

 

+

square units

",40,40,,,266614 +PSBBVH2,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism is 4 units high, 2 units wide, and 6 units long. What is its surface area in square units?

+

 

+

square units

",88,88,,,272246 +PSBCMPS,1,Fill-in-the-blank(s),Numeric,"

A maritime flag is shown. What is the area of the shaded part of the flag?

+

 

+

+

square inches

",72,72,,,403617 +PSBQ5D,2,Fill-in-the-blank(s),Numeric,"

Find the solution.

+

 

+

Each notebook contains 60 sheets of paper. Andre has 5 notebooks. How many sheets of paper do Andre’s notebooks contain?

+

 

+

y = sheets

",300,300,,,73717 +PSBC6R,2,Fill-in-the-blank(s),Numeric,"

How many dollars does an adult pass cost if a child’s pass costs $10?

+

 

+

$

+

 

",16,16,,,15269 +PSBC6R,3,Fill-in-the-blank(s),Algebraic Expression,"

How many dollars does an adult pass cost if a child’s pass costs w dollars?

+

 

+

",1.6w,1.6w,,,15414 +PSBZKT,2,Fill-in-the-blank(s),Numeric,"

The area of a rectangle is 14 square units. It has side lengths x and y.  Given the value for x, find y.

+

 

+

x = 415

+

 

+

 

+

y =

+

 

+

Express your answer in fraction form.

",3 1/3,3 1/3,,,122450 +PSBQ3W,2,Fill-in-the-blank(s),Numeric,"

Find the solution.

+

 

+

x = pounds

",11,11,,,73395 +PSBB6NJ,1,Fill-in-the-blank(s),Numeric,"

Find the area of this triangle.

+

 

+

+

 

+

square units

",51,51,,,323746 +PSBN3A,3,Fill-in-the-blank(s),Numeric," + + + + + + +
+

How many ounces of meat were used?

+		ounces
",52,52,,,62872 +PSBN3A,4,Fill-in-the-blank(s),Numeric," + + + + + + +
+

How many ounces of cheese were used?

+		 ounces
",39,39,,,63037 +PSBB6JM,1,Fill-in-the-blank(s),Numeric,"

At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 100 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school? 

+

 

+

sixth-grade students

",250,250,,,323049 +PSB4YV,1,Fill-in-the-blank(s),Numeric,"

A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of her purchase? 

+

 

+

$

",65,65,,,142055 +PSB43J,1,Fill-in-the-blank(s),Numeric,"

The original price of a scarf was $16. During a store-closing sale, a shopper saved $12 on the scarf. What percentage discount did she receive?

+

 

+

%

",75,75,,,142483 +PSBCGRW,1,Fill-in-the-blank(s),Numeric,"

Han and Clare go shopping, and they each have a coupon. Answer each question and show your reasoning.

+

 

+ + + + + + + +
+

Han buys an item with a normal price of $15 and uses a 10% off coupon. How much does he save by using the coupon?

+

 

+

$

+
+

 

+

 

",1.5,1.5,,,382388 +PSB5DV,1,Fill-in-the-blank(s),Numeric,"

An ant travels at a constant rate of 30 cm every 2 minutes.

+

 

+

At what pace does the ant travel per centimeter?

+

 

+

minutes per inch

+

 

+

Express your answer in fraction form.

",15-Jan,15-Jan,,,144285 +PSB5DV,2,Fill-in-the-blank(s),Numeric,"

An ant travels at a constant rate of 30 cm every 2 minutes.

+

 

+

At what speed does the ant travel per minute?  

+

 

+

centimeters per inch

",15,15,,,144489 +PSBBP4N,1,Fill-in-the-blank(s),Numeric,"

A bookshelf is 42 inches long.  

+

 

+

How many books of length 112 inches will fit on the bookshelf? 

+

 

+

books

",28,28,,,242498 +PSBBBGJ,1,Fill-in-the-blank(s),Numeric,"

What is the volume of a rectangular prism that is 112 inches by 214 inches by 4 inches?

+

 

+

in3

",13 1/2,13 1/2,,,177695 +PSBBT6M,2,Fill-in-the-blank(s),Numeric,"

How many 38-inch thick books make a stack that is 6 inches tall?

+

 

+

38-inch thick books

",16,16,,,264639 +PRABHK6K,1,Fill-in-the-blank(s),Numeric,"

A cube has a volume of 73 cubic centimeters. What is its surface area?

+

 

+

 

+

square centimeters

",294,294,,,128547 +PSB2MF,2,Fill-in-the-blank(s),Numeric Expression,"

A cube has edge length 11 inches.

+

 

+

 

+

Write an expression for its surface area.

+

 

+

SA =

",6*11*11,6*11*11,,,128322 +PSBDGPV,1,Fill-in-the-blank(s),Numeric,"

A square has a side length 9 cm. What is its area?  

+

 

+

 square centimeters

",81,81,,,557307 +PSBDGPV,2,Fill-in-the-blank(s),Numeric,"

A square has an area of 9 cm2. What is its side length?

+

 

+

 centimeters

",3,3,,,557481 +PSBC62G,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism has dimensions of 3 cm by 2 cm by 2 cm. What is its surface area?   

+

 

+

+

 

+

cm2

",32,32,,,502164 +PSBBX54,1,Fill-in-the-blank(s),Numeric,"

Find the area of this shape.

+

 

+

+

 

+

square units

",18,18,,,287214 +PSB2GN,1,Fill-in-the-blank(s),Numeric,"

Four students set up a lemonade stand. At the end of the day, their profit is $17.52. How much money do they each have when the profit is split equally? 

+

 

+

$

",4.38,4.38,,,127324 +PSBBX2F,1,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle. If you get stuck, carefully consider which side of the triangle to use as the base.

+

 

+

 

+

+

 

+

 

+

square units

",12,12,,,286560 +PRABETEZ,1,Fill-in-the-blank(s),Numeric,"

A restaurant bill is $59 and you pay $72. What percentage gratuity did you pay?  

+

 

+

%

+

Round to the nearest whole percent.

",22,22,,,236501 +PRABMSJM,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

b - -6 = -2

+

 

+

b =

",-8,-8,,,155183 +PRABMSJN,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

-c + 4 = -9

+

 

+

c =

",13,13,,,155484 +PSBJ95,1,Fill-in-the-blank(s),Numeric,"

What is the smallest number of faces a polyhedron can possibly have? 

+

 

+

faces

",4,4,,,47990 +PRABQKVJ,1,Fill-in-the-blank(s),Numeric,"

Mai made 6 cups of vegetable soup and divided the soup equally among 8 containers. How much soup went in each container?

+

 

+

  cup of vegetable soup

",4-Mar,4-Mar,,,518962 +PRABQKSN,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism has dimensions of 8 cm by 9 cm by 10 cm. What is its volume?  

+

 

+

 cubic centimeters

",720,720,,,133518 +PSBR9P,1,Fill-in-the-blank(s),Numeric,"

A cereal box is 8 inches by 2 inches by 12 inches. What is its surface area? Show your reasoning. If you get stuck, consider drawing a sketch of the box or its net and labeling the edges with their measurements.

+

 

+

square inches

",272,272,,,79262 +PSBK3Q,3,Fill-in-the-blank(s),Numeric,"

Estimate the actual height of the spacecraft to the nearest meter.

+

 

+

meters

",7,7,,,51828 +PSBBTGY,1,Fill-in-the-blank(s),Numeric,"

Based on signal strength, a person knows their lost phone is exactly 47 feet from the nearest cell tower. The person is currently standing 23 feet from the same cell tower. What is the closest the phone could be to the person?

+

 

+

 feet

",24,24,,,260281 +PSBBT2C,2,Fill-in-the-blank(s),Numeric,"

Mai’s family is traveling in a car at a constant speed of 65 miles per hour.

+

 

+

How far do they travel in 25 minutes?  

+

 

+

miles

+

Round your answer to one decimal point.

",27.1,27.1,,,263683 +PSBBT2C,1,Fill-in-the-blank(s),Numeric,"

Mai’s family is traveling in a car at a constant speed of 65 miles per hour.

+

 

+

At that speed, how long will it take them to travel 200 miles?  

+

 

+

hours 

+

Submit your answer as a fraction.

",3 1/13,3 1/13,,,263438 +PSB2J8,2,Fill-in-the-blank(s),Numeric,"

What percentage remains?  %

",25,25,,,128108 +PSBBBBS,1,Fill-in-the-blank(s),Numeric,"

Your teacher will give you cubes that have edge lengths of 12 inch.

+

 

+

Here is a drawing of a cube with edge lengths of 1 inch.

+

 

+

+

 

+

How many cubes with edge lengths of 12 inch are needed to fill this cube?

+

 

+

cubes

",8,8,,,176751 +PSBBCJZ,1,Fill-in-the-blank(s),Numeric,"

A loaf of bread is cut into slices.

+

 

+

If each slice is 12 of a loaf, how many slices are there?

+

 

+

slices of bread

",2,2,,,183695 +PSBDK49,2,Fill-in-the-blank(s),Numeric,"
+

What is the height h for the base that is 54 units long?  

+

 

+

cm

+

 

+

+
",5-Mar,5-Mar,,,577430 +PSBBSVD,3,Fill-in-the-blank(s),Numeric,"

What is the volume, in cubic inches, of one cube with an edge length of 13 inch?

+

 

+

cubic inches

",27-Jan,27-Jan,,,256912 +PRABE6XG,1,Fill-in-the-blank(s),Numeric,"

What is the volume of this cube?

+

 

+

 

+

+

cubic centimeters

",8,8,,,247085 +PRABFFX3,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 49 m2. What is its side length?

+

 

+

meters

",7,7,,,247608 +PRABGZFX,1,Fill-in-the-blank(s),Numeric,"

A square has side length 7 in.  What is its area?  

+

 

+

square inches

+

 

+

 

",49,49,,,48123 +PSBCVNF,3,Fill-in-the-blank(s),Numeric,"

How many right angles need to be put together to make 270 degrees?

+

 

+

right angles

",3,3,,,449139 +PSBBS6F,2,Fill-in-the-blank(s),Numeric,"

How many different triangles are there?

+

 

+

different triangles

",4,4,,,258731 +PSBZ6U,1,Fill-in-the-blank(s),Numeric,"

A bookstore has marked down the price for all the books in a certain series by 15%.

+

 

+
+

How much is the discount on a book that normally costs $18.00? 

+

 

+

$

+
",2.7,2.7,,,125047 +PSBCVNF,4,Fill-in-the-blank(s),Numeric,"

How many right angles need to be put together to make a straight angle?

+

 

+

right angles

",2,2,,,449555 +PSBCVNF,2,Fill-in-the-blank(s),Numeric,"

How many right angles need to be put together to make 180 degrees?

+

 

+

right angles

",2,2,,,448806 +PRABFFX4,1,Fill-in-the-blank(s),Numeric,"

A cube has an edge length of 3 in. What is its volume?

+

 

+

cubic inches

",27,27,,,247781 +PSBCGVZ,1,Fill-in-the-blank(s),Numeric,"

The figure is a diagram of a sign. Lengths are given in inches.

+

 

+

+

 

+

What is the area of the sign?

+

 

+

square inches

",360,360,,,383334 +PSBTYT,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region(s) of the figure.

+

 

+

 

+

+

 

+

 

+

cm2

",24,24,,,89233 +PSBEUY,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shape.

+

 

+

+

 

+

square units

",12,12,,,24639 +PRABE3GJ,1,Fill-in-the-blank(s),Numeric,"

Find the area of the parallelogram.

+

 

+

 

+

+

 

+

 

+

square centimeters 

",30,30,,,25226 +PRABTS92,1,Fill-in-the-blank(s),Numeric,"

Find the area of the rectangle with the following side lengths.

+

 

+

 

+

5 in and 13 in 

+

 

+

 

+

square inches

",3-May,3-May,,,25576 +PRABTS93,1,Fill-in-the-blank(s),Numeric,"

Find the area of the rectangle with the following side lengths.

+

 

+

 

+

5 in and 43inches

+

 

+

 

+

square inches

+

 

+

Give your answer as a simplified fraction.

",20/3,20/3,,,25682 +PRABTS94,1,Fill-in-the-blank(s),Numeric,"

Find the area of the rectangle with the following side lengths.

+

 

+

 

+

52 in and 43in

+

 

+

 

+

square inches

+

 

+

Give your answer as a simplified fraction.

",3-Oct,3-Oct,,,25823 +PSBDD5N,1,Fill-in-the-blank(s),Numeric,"

The rectangle has sides measuring 7 cm and 4 cm. What is the area of this rectangle?   

+

 

+

cm2

+

 

+

",28,28,,,543579 +PRABFEPA,1,Fill-in-the-blank(s),Numeric,"

A parallelogram has an area of 7 square units. If the height that corresponds to a base is 14 unit, what is the base?

+

 

+

units

",28,28,,,42913 +PSBDH2W,2,Fill-in-the-blank(s),Numeric,"

Here are two copies of a parallelogram. Each copy has one side labeled as the base b and a segment drawn for its corresponding height and labeled h.

+

 

+

+

 

+

The height of the parallelogram on the right is 2 centimeters. How long is the base of that parallelogram? 

+

 

+

centimeters

",1.2,1.2,,,565173 +PRABE3F5,1,Fill-in-the-blank(s),Numeric,"

The area of a rectangular playground is 78 square meters. If the length of the playground is 13 meters, what is its width?

+

 

+

meters

",6,6,,,347425 +PSB9JU,1,Fill-in-the-blank(s),Numeric,"

The square in the middle has an area of 1 square unit. What is the area of the entire rectangle in square units? 

+

 

+

square units

+

 

+

",4,4,,,166613 +PSB75K,1,Fill-in-the-blank(s),Numeric,"

A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles.

+

 

+

What is the plane’s speed in miles per hour?  

+

 

+

miles per hour

+

 

+

 

+

 

+

 

",560,560,,,159000 +PRABFEN9,1,Fill-in-the-blank(s),Numeric,"

A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base?

+

 

+

units

",9-Dec,9-Dec,,,42671 +PSBT2R,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region(s) of the figure.

+

 

+

 

+

+

 

+

 

+

cm2

",21,21,,,89569 +PSB6F9,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region. 

+

+

 

+

cm2

",40,40,,,150514 +PRABE37P,1,Fill-in-the-blank(s),Numeric,"

A parallelogram has a base of 9 units and a corresponding height of 23units. What is its area?

+

 

+

square units

",18/3,18/3,,,42515 +PSBCFEV,1,Fill-in-the-blank(s),Numeric,"

A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.

+

 

+

What is the area, in square meters, of 6 triangles? If you get stuck, consider drawing a diagram.

+

 

+

square meters

+

 

+

Give your answer as a simplified fraction.

",18-Jun,18-Jun,,,375305 +PSBCFEV,2,Fill-in-the-blank(s),Numeric,"

How many triangles are needed to compose a region that is 112 square meters?

+

 

+

triangles

",27,27,,,375493 +PSBCWW,1,Fill-in-the-blank(s),Numeric,"

Here is a parallelogram composed of smaller parallelograms.  The shaded region is composed of four identical parallelograms.  All lengths are in inches.

+

 

+

+

 

+

What is the area of the unshaded parallelogram in the middle?

+

 

+

  in2

",3.2,3.2,,,14144 +PSBDH2W,1,Fill-in-the-blank(s),Numeric,"

Here are two copies of a parallelogram. Each copy has one side labeled as the base b and a segment drawn for its corresponding height and labeled h.

+

 

+

+

 

+

The base of the parallelogram is 2.4 centimeters; its corresponding height is 1 centimeter. Find its area in square centimeters.

+

 

+

square centimeters

",2.4,2.4,,,565046 +PRABQJVJ,1,Order / Sort,Ordering,

Here is a list of expressions. Order them from least to greatest.

,"

10³

,

8³

,

7 · 8²

,

40²

,

104

","

10³

,

8³

,

7 · 8²

,

40²

,

104

",,,503178 +PSBC6YQ,1,Fill-in-the-blank(s),Numeric,"

A square has an area of 16 cm2. What is the length of each of its sides?

+

 

+

 cm

",4,4,,,501827 +PSBC6YQ,2,Fill-in-the-blank(s),Numeric,"

A square has a side length of 8 cm. What is its area?

+

 

+

  cm2

",64,64,,,501955 +PSBCP64,3,Fill-in-the-blank(s),Numeric,"

For the triangle, a base and its corresponding height are labeled.

+

Find the area of the triangle.

+

 

+

+

 

+

square units

",12,12,,,418178 +PSBCGTY,1,Fill-in-the-blank(s),Numeric,"

Find the area of the figure. 

+

+

 

+

square units

",38,38,,,383037 +PSBV94,1,Fill-in-the-blank(s),Numeric,"

The rectangle below has sides measuring 6 cm and 5 cm. What is the area of this rectangle?   

+

 

+

cm2

+

 

+

",30,30,,,103462 +PSBCGVZ,3,Fill-in-the-blank(s),Numeric,"

A person is going to paint the sign, including both the front and back. How many square inches will they need to cover?  

+

 

+

square inches

",720,720,,,383524 +PSBN4,1,Fill-in-the-blank(s),Numeric,"

A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. How many blue marbles are in the bag?  

+

 

+

 blue marbles

",126,126,,,1638 +PRABHQGR,1,Fill-in-the-blank(s),Numeric,"

A large bottle of juice contains 500 milliliters of juice. A medium bottle contains 70% as much juice as the large bottle. How many milliliters of juice are in the medium bottle?

+

 

+

milliliters

+

 

+

 

+

",350,350,,,35357 +PSBNUC,1,Fill-in-the-blank(s),Numeric,"

The cost of 5 cans of dog food is $4.35. At this price, how much do 11 cans of dog food cost?   

+

 

+

$

",9.57,9.57,,,61761 +PSBNPV,1,Fill-in-the-blank(s),Numeric,"

An elevator travels 310 feet in 10 seconds. At that speed, how far can this elevator travel in 12 seconds? 

+

 

+

feet

",372,372,,,61003 +PSBN3A,1,Fill-in-the-blank(s),Numeric,"

A sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich. After making sandwiches for an hour, the shop owner has used 91 combined ounces of meat and cheese.

+

 

+

How many combined ounces of meat and cheese are used on each sandwich?

+

 

+

ounces

+

 

",7,7,,,62539 +PSBN3A,2,Fill-in-the-blank(s),Numeric," + + + + + + +
+

How many sandwiches were made in the hour?

+		sandwiches
",13,13,,,62707 +PSB28Z,1,Fill-in-the-blank(s),Numeric,"

Noah has 5 meters of rope. How many pieces of rope of length 12 meter can he cut from it?

+

 

+

pieces of rope

",10,10,,,131914 +PSBBAJK,2,Fill-in-the-blank(s),Numeric,"

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.

+

 

+

How many band members are seventh graders?  

+

 

+

seventh grade band members

",14,14,,,172318 +PRABFB67,1,Fill-in-the-blank(s),Numeric,"

A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?

+

 

+

milligrams

+

 

+

",80,80,,,325149 +PSB4FT,4,Fill-in-the-blank(s),Numeric,"

At this rate, how much would Lin be paid for 3 hours of work?   

+

 

+

$

",54,54,,,138970 +PSBMAP,1,Fill-in-the-blank(s),Numeric,"

Solve the problem, and show your thinking. Organize it so it can be followed by others. If you get stuck, consider drawing a double number line, table, or tape diagram.

+

 

+

Andre and Han are moving boxes. Andre can move 4 boxes every half hour. Han can move 5 boxes every half hour. How long will it take Andre and Han to move all 72 boxes?

+

 

+

hours

",4,4,,,53714 +PSBK84,1,Fill-in-the-blank(s),Numeric,"

Solve the problem, and show your thinking. Organize it so it can be followed by others. If you get stuck, consider drawing a double number line, table, or tape diagram.

+

 

+

A recipe for salad dressing calls for 4 parts oil for every 3 parts vinegar. How much oil should you use to make a total of 28 teaspoons of dressing?

+

 

+

teaspoons

",16,16,,,53422 +PSBCCUK,2,Fill-in-the-blank(s),Numeric,"

Priya’s neighbor has a dirt bike that can go 360 meters in 15 seconds. At this rate, how long would it take them to ride 3,000 meters?

+

 

+

seconds

",125,125,,,360123 +PSB3BX,1,Fill-in-the-blank(s),Numeric,"

At a used book sale, 5 books cost $15.  

+

 

+

What is the cost per book? 

+

 

+

$

",3,3,,,132432 +PSBNGY,1,Fill-in-the-blank(s),Numeric,"

A sports drink recipe calls for 53 tablespoons of powdered drink mix for every 12 ounces of water. How many batches can you make with 5 tablespoons of drink mix and 36 ounces of water? 

+

 

+

batches

",3,3,,,59778 +PSBCXN,1,Fill-in-the-blank(s),Numeric,"

Find the surface area of the polyhedron that can be assembled from this net. 

+

 

+

+

 

+

in2

",224,224,,,14173 +PSB4HP,2,Fill-in-the-blank(s),Numeric,"

Here is a table that represents the situation. Find the cost of 1 gigabyte. You can use as many rows as you need.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Memory (Gigabytes)Cost (Dollars)
12832
  
  
  
  
  
  
  
+

 

+

What is the cost of 1 gigabyte? 

+

 

+

$

+

 

",0.25,0.25,,,139424 +PRABFAG9,1,Fill-in-the-blank(s),Numeric,"

Priya collected 2,400 grams of pennies in a fundraiser. Each penny has a mass of 2.5 grams. How much money did Priya raise? If you get stuck, consider using the table. 

+

 

+

$

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Number of PenniesMass in Grams
12.5
  
  
  
  
 2,400
+

 

",9.6,9.6,,,146848 +PSB296,1,Fill-in-the-blank(s),Numeric,"

Four bags of chips cost $6.

+

 

+

What is the cost per bag? 

+

 

+

$

",1.5,1.5,,,132144 +PSBCCS2,2,Fill-in-the-blank(s),Numeric,"

Complete the last row with the missing number.

+

 

+ + + + + + + + + + + + + + + + + + + +
20100
1050
15
3,000
","15,000","15,000",,,359683 +PSBCCUK,1,Fill-in-the-blank(s),Numeric,"

Priya can bike 150 meters in 20 seconds.  At this rate, how long would it take her to bike 3,000 meters?

+

 

+

seconds

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
  
  
  
  
  
  
+

 

+

 

",400,400,,,360011 +PSB3NH,1,Fill-in-the-blank(s),Numeric,"

Mai is making friendship bracelets. Each bracelet is made from 24.3 cm of string. If she has 170.1 cm of string, how many bracelets can she make? 

+

 

+

bracelets

",7,7,,,134242 +PSBCATA,1,Fill-in-the-blank(s),Numeric,"

Solve the following problems and show your thinking. If you get stuck, consider drawing a tape diagram to represent the situation.

+

 

+

 

+

Elena makes fruit punch by mixing 4 parts cranberry juice to 3 parts apple juice to 2 parts grape juice. If one batch of fruit punch includes 30 cups of apple juice, how large is this batch of fruit punch?

+

 

+

cups of punch

",90,90,,,347969 +PSB873,2,Fill-in-the-blank(s),Numeric,"

Your friend offers to help you with the rest of the painting. It takes the two of you 150 more minutes of painting time to finish the entire room. How much time did your friend save you?

+

 

+

minutes

",154,154,,,164748 +PSBRUY,1,Fill-in-the-blank(s),Numeric,"

Andre paid $13 for 3 books. Diego bought 12 books priced at the same rate. How much did Diego pay for the 12 books? 

+

 

+

$

",52,52,,,77267 +PSB296,2,Fill-in-the-blank(s),Numeric,"

Four bags of chips cost $6.

+

 

+

At this rate, how much will 7 bags of chips cost? 

+

 

+

$

",10.5,10.5,,,132256 +PSBF26,2,Fill-in-the-blank(s),Numeric,"

A snail travels 10 cm in 4 minutes. At this rate:

+

 

+

How far does the snail travel in 6 minutes?

+

 

+

cm

",15,15,,,31250 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316 +PSBX32,1,Fill-in-the-blank(s),Numeric,"

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?  

+

 

+

 red marbles

",114,114,,,114344 +PSBNSD,1,Fill-in-the-blank(s),Numeric,"

Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 7 hours? 

+

 

+

$

",57.75,57.75,,,61363 +PSBB9H,1,Fill-in-the-blank(s),Numeric,"

During the first part of a hike, Andre drank 1.5 liters of the water he brought.

+

 

+

If this is 50% of the water he brought, how much water did he bring?

+

 

+

liters of water

+

 

+

 

",3,3,,,10241 +PSBB9H,2,Fill-in-the-blank(s),Numeric,"

If he drank 80% of his water on his entire hike, how much did he drink?

+

 

+

liters of water

",2.4,2.4,,,10342 +PSBBVCY,3,Fill-in-the-blank(s),Numeric,"

The usual price of a soccer ball is $24.80, what is its sale price?

+

 

+

$

",21.08,21.08,,,271644 +PRABFCHD,1,Fill-in-the-blank(s),Numeric,"

A bathtub can hold 80 gallons of water. The faucet flows at a rate of 4 gallons per minute. What percentage of the tub will be filled after 6 minutes?

+

 

+

%

",30,30,,,272713 +PSBBU72,1,Fill-in-the-blank(s),Numeric,"

A sign in front of a roller coaster says ""You must be 40 inches tall to ride.""  What percentage of this height is 34 inches?

+

 

+

%

",85,85,,,270541 +PSBCJ3Z,1,Fill-in-the-blank(s),Numeric,"

Tyler has a baseball bat that weighs 28 ounces. Find this weight in kilograms. (Note: 1 kilogram is approximately 35 ounces)

+

 

+

kilograms

+

 

",0.8,0.8,,,394487 +PSBQFE,1,Fill-in-the-blank(s),Numeric,"

The fastest elevators in the Burj Khalifa can travel 330 feet in just 10 seconds.

+

 

+

How far does the elevator travel in 11 seconds? 

+

 

+

feet

",363,363,,,69590 +PSBCJ8B,2,Fill-in-the-blank(s),Numeric,"

An ant can travel at a constant speed of 980 inches every 5 minutes.

+

 

+

At this rate, how far can the ant travel in 7 minutes?

+

 

+

inches

","1,372","1,372",,,395593 +PSBCJ8B,1,Fill-in-the-blank(s),Numeric,"

An ant can travel at a constant speed of 980 inches every 5 minutes.

+

 

+

How far does the ant travel in 1 minute?

+

 

+

inches

",196,196,,,395419 +PSB5BE,3,Fill-in-the-blank(s),Numeric,"

Han spent 75 minutes practicing the piano over the weekend.

+

 

+

Tyler practiced the clarinet for 64% as much time as Han practiced the piano. How long did he practice?

+

 

+

minutes

",48,48,,,143860 +PSBBU72,2,Fill-in-the-blank(s),Numeric,"

A sign in front of a roller coaster says ""You must be 40 inches tall to ride."" What percentage of this height is 54 inches?

+

 

+

%

",135,135,,,270745 +PSBBVAB,1,Fill-in-the-blank(s),Numeric,"

At a hardware store, a tool set normally costs $80. During a sale this week, the tool set costs $12 less than usual. What percentage of the usual price is the savings? 

+

 

+

%

",15,15,,,271030 +PSBCERJ,3,Fill-in-the-blank(s),Numeric,"

Next, use your double number line to answer the questions.

+

 

+

How much flour should be used with 10 pints of water?

+

 

+

cups

",40,40,,,370906 +PSBCERJ,4,Fill-in-the-blank(s),Numeric,"

How much water should be used with 24 cups of flour?

+

 

+

pints

",6,6,,,371046 +PSBCERJ,5,Fill-in-the-blank(s),Numeric,"

How much flour per pint of water does this recipe use?

+

 

+

cups

",4,4,,,371156 +PSBBADX,2,Fill-in-the-blank(s),Numeric,"

What percentage of Tyler’s distance did Priya walk?  %

",125,125,,,171838 +PSBCM3,3,Fill-in-the-blank(s),Numeric,"

Noah bought 15 baseball cards for $9.00. Assuming each baseball card costs the same amount.

+

 

+

At this rate, how much will 12 baseball cards cost? 

+

 

+

 $

",7.2,7.2,,,12177 +PSBCJ55,1,Fill-in-the-blank(s),Numeric,"

A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.) How many ounces of almonds would be in a one-pound bag of this trail mix?  

+

 

+

ounces of almonds

",9 1/3,9 1/3,,,395051 +PSBBCTV,2,Fill-in-the-blank(s),Numeric,"

Attendance at the drama play was 140% of attendance at the concert.

+

 

+

people attended the drama play

",350,350,,,185277 +PSBNWN,1,Fill-in-the-blank(s),Numeric,"

A restaurant has 26 tables in its dining room. It takes the waitstaff 10 minutes to clear and set 4 tables. At this rate, how long will it take the waitstaff to clear and set all the tables in the dining room? 

+

 

+

minutes

",65,65,,,62166 +PSBBA9D,1,Fill-in-the-blank(s),Numeric,"

The area of Triangle C is 545 square units. What is the length of h?

+

 

+

+

 

+

units

+

 

+

 

",6,6,,,176469 +PSB6H4,1,Fill-in-the-blank(s),Numeric,"

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches.  What is the height of the box?

+

 

+

inches

",3 1/2,3 1/2,,,150895 +PSB6H4,2,Fill-in-the-blank(s),Numeric,"

Lin’s teacher uses the box to store her set of cubes with an edge length of 12 inch. If the box is completely full, how many cubes are in the set?

+

 

+

cubes

",448,448,,,151049 +PSBBCTV,3,Fill-in-the-blank(s),Numeric,"

Attendance at literacy night was 44% of attendance at the concert.

+

 

+

people attended literacy night

",110,110,,,185395 +PSBBPDJ,1,Fill-in-the-blank(s),Numeric,"

6 is what percentage of 10?  

+

 

+

%

",60,60,,,239163 +PSBBCTV,1,Fill-in-the-blank(s),Numeric,"

A school held several evening activities last month—a music concert, a basketball game, a drama play, and literacy night. The music concert was attended by 250 people.  How many people came to each of the other activities? 

+

 

+

Attendance at a basketball game was 30% of attendance at the concert.

+

 

+

people attended the basketball game

",75,75,,,185126 +PRABP755,1,Fill-in-the-blank(s),Numeric,"

A jet plane can carry up to 200,000 liters of fuel. It used 130,000 liters of fuel during a flight. What percentage of the fuel capacity did it use on this flight?

+

 

+

%

+

 

",65,65,,,174579 +PSBBVCY,1,Fill-in-the-blank(s),Numeric,"

The sale price of every item in a store is 85% of its usual price.  The usual price of a backpack is $30, what is its sale price?

+

 

+

$

",25.5,25.5,,,271396 +PSB2RG,1,Fill-in-the-blank(s),Numeric,"

Water makes up about 71% of Earth’s surface, while the other 29% consists of continents and islands. 96% of all Earth’s water is contained within the oceans as salt water, while the remaining 4% is fresh water located in lakes, rivers, glaciers, and the polar ice caps.If the total volume of water on Earth is 1,386 million cubic kilometers, what is the volume of salt water?

+

 

+

cubic kilometers

","1,330,560,000","1,330,560,000",,,129075 +PSB2RG,2,Fill-in-the-blank(s),Numeric,"

What is the volume of fresh water?

+

 

+

cubic kilometers

","55,440,000","55,440,000",,,129183 +PSBBSVD,1,Fill-in-the-blank(s),Numeric,"

How many cubes with edge lengths of 13 inch are needed to build a cube with an edge length of 1 inch?

+

 

+

cubes

",27,27,,,256677 +PSBCENS,1,Fill-in-the-blank(s),Numeric,"

How long is 75% of 60 minutes?

+

 

+

minutes

",45,45,,,370522 +PSBCBSW,1,Fill-in-the-blank(s),Numeric,"

In 2011, a professional climber scaled the outside of the Burj Khalifa, making it all the way to 828 meters (the highest point on which a person can stand) in 6 hours. 

+

 

+

Assuming they climbed at the same rate the whole way:

+

 

+

How far did they climb in the first 2 hours?  

+

 

+

meters

",276,276,,,353327 +PSBCBSW,2,Fill-in-the-blank(s),Numeric,"

How far did they climb in 5 hours?

+

 

+

  meters

",690,690,,,353461 +PSBCBSW,3,Fill-in-the-blank(s),Numeric,"

How far did they climb in the final 15 minutes?  

+

 

+

meters

",34.5,34.5,,,353584 +PRABHQGM,1,Fill-in-the-blank(s),Numeric,"

Fill in the blank: The value of 8 dimes is % of the value of a dollar.

",80,80,,,515648 +PSBR46,2,Fill-in-the-blank(s),Numeric,"

If the small holds 36 units, how much does the large hold?

+

 

+

 units

",48,48,,,78711 +PSBBANS,1,Fill-in-the-blank(s),Numeric,"

Jada has a monthly budget for her cell phone bill. Last month she spent 120% of her budget, and the bill was $60. What is Jada’s monthly budget? 

+

 

+

$

",50,50,,,172957 +PSBBAJK,1,Fill-in-the-blank(s),Numeric,"

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.

+

 

+

How many band members are sixth graders?  

+

 

+

sixth grade band members

",28,28,,,172131 +PSBBAT4,2,Fill-in-the-blank(s),Numeric,"

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate:

+

 

+

How far can the athlete run in 1 hour?

+

 

+

miles

",9.6,9.6,,,174088 +PSBBAT4,1,Fill-in-the-blank(s),Numeric,"

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate:

+

 

+

How long will it take the athlete to run 9 miles?

+

 

+

minutes

",56.25,56.25,,,173863 +PSBBN93,1,Fill-in-the-blank(s),Numeric,"

15 is what percentage of 30?

+

 

+

%

",50,50,,,238558 +PSBBPBW,1,Fill-in-the-blank(s),Numeric,"

3 is what percentage of 12?

+

 

+

%

",25,25,,,238851 +PSBCJ3Z,2,Fill-in-the-blank(s),Numeric,"

Tyler has a baseball bat that weighs 28 ounces. Find this weight in grams. (Note: 1 kilogram is approximately 35 ounces)

+

 

+

grams

",800,800,,,394746 +PSBCGRW,3,Fill-in-the-blank(s),Numeric,"

Clare buys an item with a normal price of $24, but saves $6 by using a coupon. For what percentage off is this coupon?

+

 

+

%

+

 

",25,25,,,382646 +PSBBAJK,3,Fill-in-the-blank(s),Numeric,"

What percentage of the band members are eighth graders?  %

",40,40,,,172534 +PSBFMQ,3,Fill-in-the-blank(s),Numeric,"

Costs of homes can be very different in different parts of the United States.

+

 

+

A 2,100-square-foot home in Cheyenne, Wyoming, costs $110 per square foot. How much does this home cost? 

+

 

+

$

","231,000","231,000",,,28730 +PSBB6SK,1,Fill-in-the-blank(s),Numeric,"

It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

+

 

+

How many pounds of mashed potatoes can they make with 15 pounds of potatoes?  

+

 

+

pounds

",22 1/2,22 1/2,,,324260 +PSBB6SK,2,Fill-in-the-blank(s),Numeric,"

It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

+

 

+

How many pounds of potatoes are needed to make 50 pounds of mashed potatoes?  

+

 

+

pounds

+

 

+

Express your answer in fraction form.

",33 1/3,33 1/3,,,324446 +PSBCJWC,1,Fill-in-the-blank(s),Numeric,"

There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. 

+

 

+

How many milliliters are in 3 gallons?

+

 

+

  milliliters

","11,355","11,355",,,393425 +PSBCJWC,3,Fill-in-the-blank(s),Numeric,"

There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. 

+

 

+

How many milliliters are in 1 quart?

+

 

+

  milliliters

",946.25,946.25,,,393738 +PSB5BE,1,Fill-in-the-blank(s),Numeric,"

Han spent 75 minutes practicing the piano over the weekend.

+

 

+

Priya practiced the violin for 152% as much time as Han practiced the piano. How long did she practice?

+

 

+

minutes

",114,114,,,143514 +PRABFBDX,1,Fill-in-the-blank(s),Numeric,"

Lin bought 3 hats for $22.50. At this rate, how many hats could she buy with $60.00? If you get stuck, consider using the table.

+

 

+

hats

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
Number of HatsPrice in Dollars
  
  
  
  
",8,8,,,174455 +PSBCM3,1,Fill-in-the-blank(s),Numeric,"

Noah bought 15 baseball cards for $9.00. Assuming each baseball card costs the same amount, answer the following questions.

+

 

+

At this rate, how much will 30 baseball cards cost? 

+

 

+

$

",18,18,,,11914 +PSBC2V3,2,Fill-in-the-blank(s),Numeric,"

How far could he run in 30 minutes?

+

 

+

miles

",4.8,4.8,,,478871 +PRABFEJF,1,Fill-in-the-blank(s),Numeric,"

There are 80 kids in a gym. 75% are wearing socks. How many are not wearing socks? If you get stuck, consider using a tape diagram.

+

 

+

kids

",20,20,,,128360 +PRABFEJ2,1,Fill-in-the-blank(s),Numeric,"

A pool in the shape of a rectangular prism is being filled with water. The length and width of the pool is 24 feet and 15 feet. If the height of the water in the pool is 113 feet, what is the volume of the water in cubic feet?

+

 

+

cubic feet

",480,480,,,579223 +PSBZ4A,1,Fill-in-the-blank(s),Numeric,"

Clare is using little wooden cubes with edge length 12 inch to build a larger cube that has edge length 4 inches. How many little cubes does she need? 

+

 

+

cubes

",512,512,,,125069 +PSBBN69,2,Fill-in-the-blank(s),Numeric,"

A garden hose emits 9 quarts of water in 6 seconds. At this rate:

+

 

+

How much water does the hose emit in 10 seconds?

+

 

+

quarts

",15,15,,,238070 +PSBBMNU,1,Fill-in-the-blank(s),Numeric,"

On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip. Answer these questions. If you get stuck, consider using a tape diagram.

+

 

+

How many chaperones are there? chaperones

",12,12,,,229131 +PSBCNE9,2,Fill-in-the-blank(s),Numeric,"

Find the solution for the situation.

+

 

+

w =

",9,9,,,407575 +PSBCSBC,1,Fill-in-the-blank(s),Numeric,"

A penguin walks 10 feet in 6 seconds. At this speed:

+

 

+

How far does the penguin walk in 45 seconds?

+

 

+

  feet

",75,75,,,430257 +PSBCSBC,2,Fill-in-the-blank(s),Numeric,"

How long does it take the penguin to walk 45 feet?  

+

 

+

seconds

",27,27,,,430376 +PSBBKEC,2,Fill-in-the-blank(s),Numeric,"

In a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is red. There are 4 cups of blue paint used in a batch of lilac paint.  

+

 

+

How many cups of red paint are used?  If you get stuck, consider using a tape diagram.  

+

 

+

cups of red paint

",8,8,,,221830 +PSBCRM3,1,Fill-in-the-blank(s),Numeric,"

Jada makes sparkling juice by mixing 2 cups of sparkling water with every 3 cups of apple juice.

+

 

+

How much sparkling water does Jada need if she uses 15 cups of apple juice?

+

 

+

cups of sparkling water

",10,10,,,426461 +PSBBN69,1,Fill-in-the-blank(s),Numeric,"

A garden hose emits 9 quarts of water in 6 seconds. At this rate:

+

 

+

How long will it take the hose to emit 12 quarts?

+

 

+

seconds

",8,8,,,237868 +PSBCNC3,2,Fill-in-the-blank(s),Numeric,"

Find the solution for the situation.

+

 

+

z =

",186,186,,,407163 +PSBBKEC,1,Fill-in-the-blank(s),Numeric,"

In a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is red. There are 4 cups of blue paint used in a batch of lilac paint.  

+

 

+

How many cups of white paint are used?  If you get stuck, consider using a tape diagram.

+

 

+

cups of white paint

",8,8,,,221668 +PSBMJB,3,Fill-in-the-blank(s),Numeric,"

45% of c is 72. Find the value of c.

+

 

+

c =

",160,160,,,55067 +PSBBMGT,1,Fill-in-the-blank(s),Numeric,"

Last Sunday 1,575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under.

+

 

+

Find the number of adults that visited the park.

+

 

+

adults

",882,882,,,228118 +PSBCA2N,1,Fill-in-the-blank(s),Numeric,"

Two skateboarders start a race at the same time. Skateboarder A travels at a steady rate of 15 feet per second. Skateboarder B travels at a steady rate of 22 feet per second. After 4 minutes, how much farther will Skateboarder B have traveled? 

+

 

+

feet

","1,680","1,680",,,349252 +PSB857,1,Fill-in-the-blank(s),Numeric,"

Here is the floor plan for a bedroom:

+

 

+

 

+

+

 

+

 

+

Imagine you are planning to repaint all the walls in this room, including inside the closet.

+

 

+
    +
  • The east wall is 3 yards long.
    • +
+

 

+
    +
  • The south wall is 10 feet long but has a window, 5 feet by 3 feet, that does not need to be painted.
    • +
+

 

+
    +
  • The west wall is 3 yards long but has a door, 7 feet tall and 3 feet wide, that does not need to be painted.
    • +
+

 

+
    +
  • The north wall includes a closet, 6.5 feet wide, with floor-to-ceiling mirrored doors that do not need to be painted. There is, however, a smaller wall between the west wall and the closet that does need to be painted on all sides. The wall is 0.5 feet wide and extends 2 feet into the room.
    • +
+

 

+
    +
  • The ceiling in this room is 8 feet high.
    • +
+

 

+
    +
  • All of the corners are right angles.
    • +
+

 

+

If you paint all the walls in the room, how many square feet do you need to cover?  

+

 

+

square feet

",300,300,,,164090 +PSB857,2,Fill-in-the-blank(s),Numeric,"

An advertisement about the paint that you want to use reads: “Just 2 quarts covers 175 square feet!” If you need to apply two coats of paint on all the walls, how much paint do you need to buy?

+

 

+

quarts

",7,7,,,164198 +PSBRUT,2,Fill-in-the-blank(s),Numeric,"

Consider the problem: It takes one week for a crew of workers to pave 35 kilometer of a road. At that rate, how long will it take to pave 1 kilometer?

+

 

+

weeks

",1 2/3,1 2/3,,,77264 +PSBBBBS,2,Fill-in-the-blank(s),Numeric,"

What is the volume, in cubic inches, of a cube with edge lengths of 12 inch?

+

 

+

in3

",8-Jan,8-Jan,,,176895 +PSBBA7J,1,Fill-in-the-blank(s),Numeric,"

The area of Triangle B is 8 square units. Find the length of b.

+

 

+

+

 

+

units

",6,6,,,176215 +PSBBA5R,1,Fill-in-the-blank(s),Numeric,"

Find the area of Triangle A in square centimeters.

+

 

+

+

 

+

cm2

",10 1/8,10 1/8,,,175939 +PSBDGJU,2,Fill-in-the-blank(s),Numeric,"

Andre poured 27 ounces of rice into 6 containers. If all containers have the same amount of rice, how many ounces are in each container?

+

 

+

 

+

Find the unknown quantity.

+

 

+

 

+

? = ounces

",4 1/2,4 1/2,,,556824 +PSBBTZP,4,Fill-in-the-blank(s),Numeric,"

A family has a monthly budget of $2,400. How much money is spent on each category?

+

 

+

17% is spent on transportation.

+

 

+

$

",408,408,,,263496 +PSBDHZF,1,Fill-in-the-blank(s),Numeric,"

A recipe uses 5 cups of flour for every 2 cups of sugar.

+

 

+

How much sugar is used for 1 cup of flour?

+

 

+

cups

",5-Feb,5-Feb,,,564514 +PSBDHZF,2,Fill-in-the-blank(s),Numeric,"

A recipe uses 5 cups of flour for every 2 cups of sugar.

+

 

+

How much flour is used for 1 cup of sugar?

+


cups

",2.5,2.5,,,564678 +PSBFMQ,1,Fill-in-the-blank(s),Numeric,"

Costs of homes can be very different in different parts of the United States.

+

 

+

A 450-square-foot apartment in New York City costs $540,000. What is the price per square foot? 

+

 

+

$per square foot

",1200,1200,,,28432 +PSB82X,3,Fill-in-the-blank(s),Numeric,"

A box of pencils is 514 inches wide. Seven pencils, laid side by side, take up 258 inches of the width.

+

 

+

All 7 pencils have the same width. How wide is each pencil?

+

 

+

inch

",8-Mar,8-Mar,,,163759 +PSB82X,1,Fill-in-the-blank(s),Numeric,"

A box of pencils is 514 inches wide. Seven pencils, laid side by side, take up 258 inches of the width.

+

 

+

How many inches of the width of the box is not taken up by the pencils?  

+

 

+

inches

",2 5/8,2 5/8,,,163575 +PSBWZJ,1,Fill-in-the-blank(s),Numeric,"

For the situation, find the unit rates.

+

 

+

A cheesecake recipe says, “Mix 12 oz of cream cheese with 15 oz of sugar.”

+

 

+ + + + + + +
+

How many ounces of cream cheese are there for every ounce of sugar?

+

 

+

ounce of cream cheese per ounce of sugar

+
+

 

+

 

",5-Apr,5-Apr,,,108047 +PSBWZJ,2,Fill-in-the-blank(s),Numeric,"

How many ounces of sugar is that for every ounce of cream cheese?

+

 

+

ounces of sugar per ounce of cream cheese

",1.25,1.25,,,108169 +PSBW27,1,Fill-in-the-blank(s),Numeric,"

For the situation, find the unit rates.

+

 

+

Mai’s family drinks a total of 10 gallons of milk every 6 weeks.

+

 

+ + + + + + + + + +
+

How many gallons of milk does the family drink per week?   gallons per week

+
Express your answer in fraction form.
",1 2/3,1 2/3,,,108354 +PSBW27,2,Fill-in-the-blank(s),Numeric,"

How many weeks does it take the family to consume 1 gallon of milk?   weeks per gallon

",0.6,0.6,,,108478 +PSBVFK,1,Fill-in-the-blank(s),Numeric,"

A box of cereal weighs 600 grams. How much is this weight in pounds?  (Note: 1 kilogram = 2.2 pounds)

+

 

+

pounds

",1.32,1.32,,,98240 +PSB66B,3,Fill-in-the-blank(s),Numeric,"

There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.

+

 

+

What percentage of kids rent their instruments?  

+

 

+

%

",80,80,,,154014 +PSBDPZ5,2,Fill-in-the-blank(s),Numeric,"

A school wants to raise $2,500 to support its music program.  

+

 

+

If it raises 175% of its goal, how much money will the music program receive? 

+

 

+

$

","4,375","4,375",,,593802 +PSBCZEX,1,Fill-in-the-blank(s),Numeric,"

You need to be at least 39.37 inches tall (about a meter) to ride on a bumper car.  Diego’s cousin is 35.75 inches tall. How many more inches will he need to grow before Diego can take him on the bumper car ride? 

+

 

+

inches

",3.62,3.62,,,470590 +PSBVDH,3,Fill-in-the-blank(s),Numeric,"

A car can travel 35 miles per gallon of gas. It uses 135 of a gallon of gas to go 1 mile.

+

 

+

How much gas does the car use to go 100 miles? 

+

 

+

gallons

",100/35,100/35,,,97813 +PSBVDH,1,Fill-in-the-blank(s),Numeric,"

A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 135 of a gallon of gas to go 1 mile.

+

 

+

How far can the car travel with 15 gallons?

+

 

+

  miles

",525,525,,,97491 +PRABQB3W,1,Fill-in-the-blank(s),Numeric,"

The garden hose at Andre's house can fill a 5-gallon bucket in 2 minutes. The hose at his next-door neighbor’s house can fill a 10-gallon bucket in 8 minutes. If they use both their garden hoses at the same time, and the hoses continue working at the same rate they did when filling a bucket, how long will it take to fill a 750-gallon pool?

+

 

+

minutes

",200,200,,,149859 +PRABQB3V,1,Fill-in-the-blank(s),Numeric,"

Jada eats 2 scoops of ice cream in 5 minutes. Noah eats 3 scoops of ice cream in 5minutes. How long does it take them to eat 1 scoop of ice cream working together (if they continue eating ice cream at the same rate they do individually)?

+

 

+

minute(s)

",1,1,,,149750 +PSBCBCB,3,Fill-in-the-blank(s),Numeric,"

Answer the question.

+

 

+

45 ÷ 23 =

",5-Jun,5-Jun,,,351102 +PSBCZ5V,1,Fill-in-the-blank(s),Numeric,"

Noah would like to cover a rectangular tray with rectangular tiles. The tray has a width of 1114 inches and an area of 5058 square inches.

+

 

+

Find the length of the tray in inches.

+

 

+

inches

",4 1/2,4 1/2,,,474069 +PSBCZ5V,2,Fill-in-the-blank(s),Numeric,"

If the tiles are 34 inch by 910 inch, how many would Noah need to cover the tray completely, without gaps or overlaps?

+

 

+

tiles

",120,120,,,474198 +PSBCAVU,1,Fill-in-the-blank(s),Numeric,"

Mai runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4 laps of the track? 

+

 

+

minutes

",32/5,32/5,,,348393 +PSBUCB,3,Fill-in-the-blank(s),Numeric,"

How much does the trip cost?

+

 

+

$

",600,600,,,91335 +PRABFBZG,1,Fill-in-the-blank(s),Numeric,"

There are 4 tablespoons in 14 cup. There are 2 cups in 1 pint. How many tablespoons are there in 1 pint? If you get stuck, consider drawing a double number line or making a table.

+

 

+

tablespoons

",32,32,,,350310 +PSBCHS5,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

This package of sliced cheese costs $2.97.

+

 

+

 

+

 

+

 

+

How much would a package with 18 slices cost at the same price per slice? 

+

 

+

$

+
+

 

",4.86,4.86,,,387984 +PSBCHWW,3,Fill-in-the-blank(s),Numeric,"

A copy machine can print 480 copies every 4 minutes.

+

 

+

A teacher printed 720 copies. How long did it take to print?  

+

 

+

minutes

",6,6,,,388660 +PSBCHWW,1,Fill-in-the-blank(s),Numeric,"

A copy machine can print 480 copies every 4 minutes.

+

 

+

How many copies can it print in 10 minutes?

+

 

+

copies

","1,200","1,200",,,388358 +PSBC2V3,1,Fill-in-the-blank(s),Numeric,"

While training for a race, Andre’s dad ran 12 miles in 75 minutes on a treadmill. If he runs at that rate:

+

 

+

How long would it take him to run 8 miles?

+

 

+

minutes

",50,50,,,478760 +PSBBTZP,1,Fill-in-the-blank(s),Numeric,"

A family has a monthly budget of $2,400. How much money is spent on each category?

+

 

+

44% is spent on housing.

+

 

+

$

","1,056","1,056",,,262990 +PSBBN4D,4,Fill-in-the-blank(s),Numeric,"

Diego has 90 songs on his playlist. How many songs are there for the given genre?

+

 

+

The rest is electronica.

+

 

+

songs

",18,18,,,237612 +PRABQKR2,1,Fill-in-the-blank(s),Numeric,"

A ship captain is mapping a trip and wants to know the distance the ship will travel over certain time intervals.

+

 

+ + + + + + + + + + + + + + + + + + + +
time (hours)distance (miles)
0.512.5
125
1.537.5
+

 

+

Assuming that the ship travels at a constant speed, what is its speed?  

+

 

+

 miles per hour

",25,25,,,560590 +PRABQKR6,1,Fill-in-the-blank(s),Numeric,"

Elena and Jada are 12 miles apart on a path when they start moving toward each other. Elena runs at a constant speed of 5 miles per hour, and Jada walks at a constant speed of 3 miles per hour. How long does it take until Elena and Jada meet?

+

 

+

  hours

",1.5,1.5,,,560733 +PSBDG4M,1,Fill-in-the-blank(s),Numeric,"

Lin runs 5 laps around a track in 6 minutes.

+

 

+

How many minutes per lap is that?  

+

 

+

minutes per lap

",1.2,1.2,,,559407 +PSBBN4D,2,Fill-in-the-blank(s),Numeric,"

Diego has 90 songs on his playlist. How many songs are there for the given genre?

+

 

+

10% country

+

 

+

songs

",9,9,,,237316 +PSB2A,1,Fill-in-the-blank(s),Numeric,"

It takes Andre 4 minutes to swim 5 laps.

+

 

+

How many laps per minute is that?  

+

 

+

 laps per minute

",1.25,1.25,,,3098 +PRABQMXM,1,Fill-in-the-blank(s),Numeric,"

A conductor is mapping a trip and records the distance the train travels over certain time intervals.

+

 

+ + + + + + + + + + + + + + + + + + + +
time (hours)distance (miles)
0.522.5
145
1.567.5
+

 

+

The train travels at a constant speed. What is its speed?  

+

 

+

 miles per hour

",45,45,,,4213 +PRABQMXP,1,Fill-in-the-blank(s),Numeric,"

Noah and Andre are 15 miles apart on a bike path when they start biking toward each other. Noah rides at a constant speed of 4 miles per hour, and Andre rides at a constant speed of 2 miles per hour. How long does it take until Noah and Andre meet?  

+

 

+

 hours

",2.5,2.5,,,4344 +PSB2A,3,Fill-in-the-blank(s),Numeric,"

If Andre swims 22 laps at the same rate, how long does it take him?  

+

 

+

 minutes

",17.6,17.6,,,3418 +PSBBNVA,1,Fill-in-the-blank(s),Numeric,"

A rocking horse has a weight limit of 60 pounds.  What percentage of the weight limit is 33 pounds? %

",55,55,,,236051 +PSBBNVA,2,Fill-in-the-blank(s),Numeric,"

What percentage of the weight limit is 114 pounds?  %

",190,190,,,236208 +PSBBNVA,3,Fill-in-the-blank(s),Numeric,"

What weight is 95% of the limit?   pounds

",57,57,,,236371 +PSB2A,2,Fill-in-the-blank(s),Numeric,"

It takes Andre 4 minutes to swim 5 laps.

+

 

+

How many minutes per lap is that?

+

 

+

minutes per lap

",5-Apr,5-Apr,,,3256 +PSBBTWH,3,Fill-in-the-blank(s),Numeric,"

Find the answer:  

+

 

+

49 kilogram of baking soda costs $2. How much does 1 kilogram of baking soda cost?

+

 

+

$

",4.5,4.5,,,262987 +PSBBTY2,3,Fill-in-the-blank(s),Numeric,"

Find the answer: 

+

 

+

Diego can fill 115 bottles with 3 liters of water. How many liters of water fill 1 bottle?

+

 

+

liters of water

",2-May,2-May,,,263466 +PSBG4B,1,Fill-in-the-blank(s),Numeric,"

A rectangular bathroom floor is covered with square tiles that are 112 feet by 112 feet. The length of the bathroom floor is 1012 feet and the width is 612 feet.

+

 

+

How many tiles does it take to cover the length of the floor?  

+

 

+

tiles

",7,7,,,36743 +PSB2A9,1,Fill-in-the-blank(s),Numeric,"

A builder is building a fence with 614-inch-wide wooden boards, arranged side-by-side with no gaps or overlaps. How many boards are needed to build a fence that is 150 inches long? 

+

 

+

boards

",24,24,,,126203 +PSB2HQ,1,Fill-in-the-blank(s),Numeric,"

Lin wants to save $75 for a trip to the city. If she has saved $37.50 so far, what percentage of her goal has she saved? 

+

 

+

%

",50,50,,,127673 +PSBBTTZ,3,Fill-in-the-blank(s),Numeric,"

Find the answer:  

+

 

+

Jada bought 312 yards of fabric for $21. How much did each yard cost?

+

 

+

$

",6,6,,,262501 +PSB3AH,3,Fill-in-the-blank(s),Numeric,"

How much does Elena’s water weigh if her bucket is full and her bucket is identical to Noah’s?

+

 

+

pounds

",6 1/4,6 1/4,,,132330 +PSBBCJZ,2,Fill-in-the-blank(s),Numeric,"

If each slice is 15 of a loaf, how many slices are there?  

+

 

+

slices of bread

",5,5,,,183784 +PSBBTZP,2,Fill-in-the-blank(s),Numeric,"

A family has a monthly budget of $2,400. How much money is spent on each category?

+

 

+

23% is spent on food.

+

 

+

$

",552,552,,,263152 +PSBBTZP,3,Fill-in-the-blank(s),Numeric,"

A family has a monthly budget of $2,400. How much money is spent on each category?

+

 

+

6% is spent on clothing.

+

 

+

$

",144,144,,,263336 +PSBGZP,1,Fill-in-the-blank(s),Numeric,"

A zookeeper is 614 feet tall. A young giraffe in his care is 938 feet tall.

+

 

+

How many times as tall as the zookeeper is the giraffe?

+

 

+

times as tall

",1 1/2,1 1/2,,,36318 +PSBBX8F,1,Fill-in-the-blank(s),Numeric,"

Lin has a work of art that is 14 inches by 20 inches. She wants to frame it with large paper clips laid end to end.

+

 

+

If each paper clip is 134 inch long, how many paper clips would she need?

+

 

+

paper clips

",38,38,,,287470 +PSBBX8F,3,Fill-in-the-blank(s),Numeric,"

How many paper clips are needed if the paper clips are spaced 14 inch apart?

+

 

+

paper clips

",34,34,,,287627 +PSBBP4N,3,Fill-in-the-blank(s),Numeric,"

A bookcase has 5 of these bookshelves. How many feet of shelf space is there? 

+

 

+

feet

",17 1/2,17 1/2,,,242767 +PSBBPW6,1,Fill-in-the-blank(s),Numeric,"

A worker is tiling the floor of a rectangular room that is 12 feet by 15 feet. The tiles are square with side lengths 113 feet. How many tiles are needed to cover the entire floor? 

+

 

+

tiles

","102, 101 1/4","102, 101 1/4",,,241877 +PSBBP9C,1,Fill-in-the-blank(s),Numeric,"

How many groups of 123 are in 156?

+

 

+

groups

",10-Nov,10-Nov,,,243402 +PSBBP9C,2,Fill-in-the-blank(s),Numeric,"

How many groups of 123 are in 413?

+

 

+

groups

",2 3/5,2 3/5,,,243534 +PSBBP9C,3,Fill-in-the-blank(s),Numeric,"

How many groups of 123 are in 56?

+

 

+

groups

",2-Jan,2-Jan,,,243693 +PRABFEJZ,1,Fill-in-the-blank(s),Numeric,"

It takes 114 minutes to fill a 3-gallon bucket of water with a hose. At this rate, how long does it take to fill a 50-gallon tub? If you get stuck, consider using a table.

+

 

+

minutes

+

Express your answer in fraction form.

",125/6,125/6,,,43293 +PSBDHZF,3,Fill-in-the-blank(s),Numeric,"

A recipe uses 5 cups of flour for every 2 cups of sugar.

+

 

+

How much flour is used with 7 cups of sugar?

+


cups

",17.5,17.5,,,564837 +PSBBCFE,3,Fill-in-the-blank(s),Numeric,"

How many inches of snow will fall in 24 hours if it continues to snow at this rate?  

+

 

+

inches

",48,48,,,183159 +PSBBCFE,2,Fill-in-the-blank(s),Algebraic Expression,"

Snow is falling steadily in Syracuse, New York. After 2 hours, 4 inches of snow has fallen.

+

 

+

Write an equation that gives the amount of snow that has fallen after x hours at this rate. 

+

 

+

y =

",2x,2x,,,182948 +PRABMQK6,1,Fill-in-the-blank(s),Numeric,"

Lin has a drawing with an area of 20 in2.  If she increases all the sides by a scale factor of 4, what will the new area be?

+

 

+

 

+

 

+

  in2

",320,320,,,44235 +PSBBV76,3,Fill-in-the-blank(s),Numeric,"

A school club sold 300 shirts. 31% were sold to fifth graders, 52% were sold to sixth graders, and the rest were sold to teachers. How many shirts were sold to teachers?

+

 

+

shirts

",51,51,,,276105 +PSBD24,3,Fill-in-the-blank(s),Numeric,"

Elena paints the back of the second aquarium. It has a height of 134 feet. The painted area is 556 square feet. What is its length?

+

 

+

feet

",3-Oct,3-Oct,,,20500 +PSBBV76,2,Fill-in-the-blank(s),Numeric,"

A school club sold 300 shirts. 31% were sold to fifth graders, 52% were sold to sixth graders, and the rest were sold to teachers. How many shirts were sold to sixth graders?

+

 

+

shirts

",156,156,,,275922 +PRABEDFF,1,Order / Sort,Ordering,"

Cylinder A, B, and C have the same radius but different heights. Put the cylinders in order of their volume from least to greatest.

","

,

,

","

,

,

",,,157411 +PSBC2HZ,1,Fill-in-the-blank(s),Numeric,"

Mai, Kiran, and Clare are baking cookies together. They need 34 cup of flour and 13 cup of butter to make a batch of cookies. They each brought the ingredients they had at home.

+

 

+
    +
  • Mai brought 2 cups of flour and 14 cup of butter.
    • +
+

 

+
    +
  • Kiran brought 1 cup of flour and 12 cup of butter.
    • +
+

 

+
    +
  • Clare brought 114 cups of flour and 34 cup of butter.
    • +
+

 

+

If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of cookies can they make? 

+

 

+

whole batches of cookies

",4,4,,,476732 +PSBBT3N,3,Fill-in-the-blank(s),Numeric,"

Find the answer: 

+

 

+

54 gallons of water fill 56 of a bucket. How many gallons of water fill the entire bucket?

+

 

+

gallons of water

",1 1/2,1 1/2,,,263940 +PSBB5WF,1,Fill-in-the-blank(s),Numeric,"

Lin has two small baking pans, each shaped like a rectangular prism. For each question, explain or show your reasoning.

+

 

+

Lin lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil is 11 14square inches. Its length is 4 12inches. What is the width of the foil?  

+

 

+

inches

",2.5,2.5,,,318942 +PSBBTZP,5,Fill-in-the-blank(s),Numeric,"

A family has a monthly budget of $2,400. How much money is spent on each category?

+

 

+

The rest is put into savings.

+

 

+

$

",240,240,,,263662 +PSBY5V,1,Fill-in-the-blank(s),Numeric,"

At a school, 460 of the students walk to school. 

+

 

+

The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?

+

 

+

students

",92,92,,,119704 +PSBB74F,1,Fill-in-the-blank(s),Numeric,"

Use the two following methods to find the product of 18 and 14, then compare the values obtained.

+

 

+

Calculate numerically.

+

 

+

18×14

+

 

+

 

+

",252,252,,,331934 +PSBB74F,2,Fill-in-the-blank(s),Numeric,"

Here is a rectangle that is 18 units by 14 units. Find its area, in square units by decomposing it. 

+

+

 

+

 

+

square units

",252,252,,,332052 +PSBCPK5,3,Fill-in-the-blank(s),Numeric,"

How many cups of jam are in each jar?

+

 

+

  cups of jam

",1 1/2,1 1/2,,,414757 +PSBCPNT,3,Fill-in-the-blank(s),Numeric,"

How many jars did he fill?

+

 

+

jars of jam

",9,9,,,415185 +PSBCPJC,3,Fill-in-the-blank(s),Numeric,"

Altogether, how many cups of jam are in the jars?  

+

 

+

cups of jam

",9,9,,,414393 +PSBC9BE,2,Fill-in-the-blank(s),Numeric,"

A shopper buys cat food in bags of 3 lbs. Her cat eats 34 lb each week. How many weeks does one bag last?

+

 

+

weeks

",4,4,,,514446 +PRABQPQJ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

10 - 14x = 7

+

 

+

x =

",12,12,,,90428 +PSBBCBH,1,Fill-in-the-blank(s),Numeric,"

A recipe calls for 12 lb of flour for 1 batch. How many batches can be made with 1 lb?

+

 

+

batches

",2,2,,,182148 +PSBBTQT,3,Fill-in-the-blank(s),Numeric,"

Find the answer. If you get stuck, consider drawing a diagram.

+

 

+

How many liters of water fit in the water dispenser?

+

 

+

liters of water

",15/8,15/8,,,261929 +PRABFG25,1,Fill-in-the-blank(s),Numeric,"

What is the side length of a square with area 116 square units?

+

 

+

units

",4-Jan,4-Jan,,,87135 +PSBJQN,3,Fill-in-the-blank(s),Numeric,"

Now solve:  How many minutes does it take to fill a 2-gallon bucket?  

+

 

+

minutes

",6,6,,,45479 +PSBDPDQ,2,Fill-in-the-blank(s),Numeric,"

A stack of 200 file folders is 5.125 inches tall.

+

 

+

Compute the thickness of each file folder.

+

 

+

 inches

",0.025625,0.025625,,,590413 +PSBBT74,2,Fill-in-the-blank(s),Numeric,"

How many groups of 12 pound are in 234 pounds?

+

 

+

 

+

groups of  12 pound

",5 1/2,5 1/2,,,264992 +PSBBCBH,2,Fill-in-the-blank(s),Numeric,"

A recipe calls for 12 lb of flour for 1 batch. How many batches can be made with 34 lb?

+

 

+

batches

",1 1/2,1 1/2,,,182258 +PSBBCBH,3,Fill-in-the-blank(s),Numeric,"

A recipe calls for 12 lb of flour for 1 batch. How many batches can be made with 14 lb?

+

 

+

batches

",2-Jan,2-Jan,,,182395 +PSBEAX,2,Fill-in-the-blank(s),Numeric,"

Use the diagram to answer the question.

+

 

+

How many liters of soap fit into one dispenser?

+

 

+

  liters of soap

+

Write your answer as a fraction.

",3-Feb,3-Feb,,,21767 +PSBBJWZ,1,Fill-in-the-blank(s),Numeric,"

3 tickets to the museum cost $12.75. At this rate, what is the cost of 1 ticket?

+

 

+

$

",4.25,4.25,,,219121 +PSBBJRA,1,Fill-in-the-blank(s),Numeric,"

A group of friends is sharing 212 pounds of berries.  

+

 

+

If each friend received 54of a pound of berries, how many friends are sharing the berries?

+

 

+

friends

",2,2,,,218191 +PSBBJRA,2,Fill-in-the-blank(s),Numeric,"

A group of friends is sharing 212 pounds of berries.  

+

 

+

If 5 friends are sharing the berries, how many pounds of berries does each friend receive?

+

 

+

pounds of berries

",2-Jan,2-Jan,,,218311 +PSBD24,1,Fill-in-the-blank(s),Numeric,"

Elena has two aquariums, each shaped like a rectangular prism. For each question, explain or show your reasoning.

+

 

+

One aquarium has a length of 72 feet, a width of 43 feet, and a height of 32 feet. What is the volume of the aquarium?

+

 

+

cubic feet

",7,7,,,20286 +PRABFFJX,1,Fill-in-the-blank(s),Numeric,"

Find the quotient.

+

31107   

",369,369,,,62644 +PSBBB7F,1,Fill-in-the-blank(s),Numeric,"

You are planning a dinner party with a budget of $50 and a menu that consists of 1 main dish, 2 side dishes, and 1 dessert. There will be 8 guests at your party.

+

 

+

Choose your menu items and decide on the quantities to buy so you stay on budget.

+

 

+

If you choose meat, fish, or poultry for your main dish, plan to buy at least 0.5 pound per person.

+

 

+

The budget is $ per guest.

",6.25,6.25,,,181356 +PSBBE2V,1,Fill-in-the-blank(s),Numeric,"

There is 0.162 liter of water in a 1-liter bottle. How much more water should be put in the bottle so it contains exactly 1 liter? 

+

 

+

liters

",0.838,0.838,,,197603 +PSBBVNT,2,Fill-in-the-blank(s),Numeric,"

Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets.  

+

 

+

What is the exact cost? 

+

 

+

$

",23.75,23.75,,,273109 +PSB66B,1,Fill-in-the-blank(s),Numeric,"

There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.

+

 

+

How many kids own their own instruments?

+

 

+

kids

",18,18,,,153748 +PRABPKZZ,1,Fill-in-the-blank(s),Numeric,"

How many 13inch cubes does it take to fill a box with width 2 23 inches, length 3 13inches, and height 2 13 inches?

+

 

+

  13inch cubes

",560,560,,,320405 +PRABQKWF,1,Fill-in-the-blank(s),Numeric,"

How many 14-inch cubes does it take to fill a box with width 214 inches, length 212 inches, and height 134 inches?  

+

 

+

 14-inch cubes

",630,630,,,21181 +PRABQKS9,1,Fill-in-the-blank(s),Numeric,"

A recipe for cookies calls for 23 of a cup of sugar per batch. Elena used 513 cups of sugar to make multiple batches of cookies. How many batches did she make?

+

 

+

batches

",8,8,,,588744 +PSBBVT3,3,Fill-in-the-blank(s),Numeric,"

What is the exact cost of 3 pound of beef?  $

",13.77,13.77,,,273819 +PSBBVT3,5,Fill-in-the-blank(s),Numeric,"

How much more does 3 pounds of beef cost than 3 pounds of chicken?  $

",4.17,4.17,,,274077 +PSBBVJ9,1,Fill-in-the-blank(s),Numeric,"

A large cheese pizza costs $7.50. Diego has $40 to spend on pizzas. How many large cheese pizzas can he afford? 

+

 

+

large cheese pizzas

",5,5,,,272660 +PSBB5M6,4,Fill-in-the-blank(s),Numeric,"

At which step does the percentage first fall below 1%?

+

 

+

step

",18,18,,,317925 +PSBCPB3,2,Fill-in-the-blank(s),Numeric,"

Calculate how far the hurdles are from one another.   meters

",7.5,7.5,,,412825 +PSBY5V,2,Fill-in-the-blank(s),Numeric,"

At a school, 460 of the students walk to school. 

+

 

+

The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?

+

 

+

students

",23,23,,,119836 +PSBUEM,1,Fill-in-the-blank(s),Numeric,"

Mai walked 18 of a 30-mile walking trail. How many miles did Mai walk?  

+

 

+

miles

",3.75,3.75,,,91787 +PRABFGYU,1,Fill-in-the-blank(s),Numeric,"

Complete the calculation so that the problem shows the correct difference.

+

 

+ + + + + + +
    5-     4.329
+

 

+

5 - = 4.329

",0.671,0.671,,,94160 +PSBB5M6,1,Fill-in-the-blank(s),Numeric,"

To make Sierpinski's triangle,

+
    +
  • Start with an equilateral triangle. This is step 1.
    • +
  • Connect the midpoints of every side, and remove the middle triangle, leaving three smaller triangles. This is step 2.
    • +
  • Do the same to each of the remaining triangles. This is step 3.
    • +
  • Keep repeating this process.
    • +
+

 

+

+

 

+

What percentage of the area of the original triangle is left after step 2?

+

 

+

%

",75,75,,,317639 +PSBB5M6,2,Fill-in-the-blank(s),Numeric,"

What percentage of the area of the original triangle is left after step 3?

+

 

+

%

",56.25,56.25,,,317741 +PSBB5M6,3,Fill-in-the-blank(s),Numeric,"

What percentage of the area of the original triangle is left after step 10?

+

 

+

about %

+

Round your answer to the tenths place.

",7.51,7.51,,,317833 +PSBC5YB,1,Fill-in-the-blank(s),Numeric,"

Tyler uses 7.5 ounces of barbeque sauce from a full bottle. He estimates that he used about 25% of the barbeque sauce in the bottle. About how much barbecue sauce was in the full bottle?  

+

 

+

ounces of barbeque sauce

",30,30,,,496354 +PSBBQXP,2,Fill-in-the-blank(s),Numeric,"

The store bought a pair of shoes for $50 and sold it for $80. What percentage was the markup?

+

 

+

%

",60,60,,,246686 +PSBF4D,1,Fill-in-the-blank(s),Numeric,"

Diego pours 6.8 ounces of water from a full bottle. He estimates that he poured out 20% of the water in the bottle. About how much water was in the full bottle?

+

 

+

  ounces of water

",34,34,,,31188 +PSBF4D,3,Fill-in-the-blank(s),Numeric,"

Diego pours out 25% of the remaining water. About how many ounces did he pour the second time?  

+

 

+

ounces of water

",6.8,6.8,,,31433 +PSBBQRZ,1,Fill-in-the-blank(s),Numeric,"

Lin’s father is paying for a $20 meal. He has a 15%-off coupon for the meal. After the discount, a 7% sales tax is applied.

+

 

+
+

What does Lin’s father pay for the meal? 

+

 

+

$

+
",18.19,18.19,,,245930 +PSBBQXP,1,Fill-in-the-blank(s),Numeric,"

Tyler’s brother works in a shoe store.

+
+

 

+

Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $900 worth of shoes. How much was his commission? 

+

 

+

$

+
",22.5,22.5,,,246376 +PSBU9B,1,Fill-in-the-blank(s),Numeric,"

Kiran’s mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20% as a tip.

+

 

+

What is the total after the discount and tip? 

+

 

+

$

",25.5,25.5,,,97107 +PSBBQN7,1,Fill-in-the-blank(s),Numeric,"

Today, everything at a store is on sale. The store offers a 20% discount off the regular price.

+
+

 

+

The regular price of a T-shirt is $18. What is the discount price? 

+

 

+

$

+
",14.4,14.4,,,244895 +PSBBEZJ,1,Fill-in-the-blank(s),Numeric,"

Lin’s grandmother ordered needles that were 0.3125 inches long to administer her medication, but the pharmacist sent her needles that were 0.6875 inches long. How much longer were these needles than the ones she ordered? 

+

 

+

 

+

inches

",0.375,0.375,,,197306 +PSBCGRS,1,Fill-in-the-blank(s),Numeric,"

This fractal is called a Sierpinski Tetrahedron. A tetrahedron is a polyhedron that has four faces. (The plural of tetrahedron is tetrahedra.)

+

 

+

+

 

+

The small tetrahedra form four medium-sized tetrahedra: blue, red, yellow, and green. The medium-sized tetrahedra form one large tetrahedron.

+

 

+

How many faces does this fractal have?

+

 

+

Be sure to include faces you can't see. Try to find a way to figure this out so that you don't have to count every face.

+

 

+

 

+

faces

",64,64,,,382382 +PSBCGRS,2,Fill-in-the-blank(s),Numeric,"

How many small tetrahedra are in the bottom layer, touching the table?

+

 

+

small tetrahedra

",9,9,,,382485 +PSBCGRS,5,Fill-in-the-blank(s),Numeric,"

How many small tetrahedra would be in the bottom layer?

+

 

+

small tetrahedra

",27,27,,,382737 +PSBEEZ,4,Fill-in-the-blank(s),Numeric,"

A professional runner takes 3 strides between each pair of hurdles. The runner leaves the ground 2.2 meters before the hurdle and returns to the ground 1 meter after the hurdle.

+

 

+

About how long are each of the runner’s strides between the hurdles?

+

 

+

meters

","2.0, 1.98","2.0, 1.98",,,22349 +PRABFE5V,1,Fill-in-the-blank(s),Numeric,"

A pound of blueberries costs $3.98 and a pound of clementines costs $2.49. What is the combined cost of 0.6 pound of blueberries and 1.8 pounds of clementines? Round your answer to the nearest cent.

+

 

+

$

+

 

",6.87,6.87,,,405944 +PSBJFK,1,Fill-in-the-blank(s),Algebraic Expression,"

Each serving of a certain fruit snack contains 90 calories.  Han wants to know how many calories he gets from the fruit snacks. Write an equation that shows the number of calories, c, in terms of the number of servings, n.

+

 

+

c =

+

Use n as your variable.

",90n,90n,,,43771 +PSBCDQN,1,Fill-in-the-blank(s),Numeric,"

29 of the students in a school are in sixth grade.

+

 

+

How many sixth graders are there if the school has 90 students?

+

 

+

 sixth graders

",20,20,,,364872 +PSBCDQN,2,Fill-in-the-blank(s),Numeric,"

How many sixth graders are there if the school has 27 students?

+

 

+

  sixth graders

",6,6,,,365017 +PSBCDQN,3,Fill-in-the-blank(s),Algebraic Expression,"

If the school has x students, write an expression for the number of sixth graders in terms of x.

+

 

+

","2x/9, (2/9)x","2x/9, (2/9)x",,,365152 +PSBCTBM,4,Fill-in-the-blank(s),Numeric,"

What is the largest number of combination bags that Diego can make with no left over? 

+

 

+

combination bags

",16,16,,,436208 +PSBB28B,1,Fill-in-the-blank(s),Numeric,"

Diego is 59.5 inches tall. His brother is 40.125 inches tall. How much taller than his brother is Diego? 

+

 

+

inches

",19.375,19.375,,,304746 +PSBB29K,1,Fill-in-the-blank(s),Numeric,"

A runner has run 1.192 kilometers of a 10-kilometer race. How much farther does he need to run to finish the race? 

+

 

+

kilometers

",8.808,8.808,,,305101 +PSBR9H,1,Fill-in-the-blank(s),Numeric,"

A shipping company is loading cube-shaped crates into a larger cube-shaped container. The smaller cubes have side lengths of 212 feet, and the larger shipping container has side lengths of 10 feet. How many crates will fit in the large shipping container? 

+

 

+

crates

",64,64,,,79361 +PSBCYGB,1,Fill-in-the-blank(s),Numeric,"

A rectangular plot of land is 0.4 kilometer long and 0.07 kilometer wide. What is its area in square kilometers? 

+

 

+

square kilometers

",0.028,0.028,,,465121 +PSBBGX4,1,Fill-in-the-blank(s),Numeric,"

A sports drink bottle contains 16.9 fluid ounces. Andre drank 80% of the bottle. How many fluid ounces did Andre drink? 

+

 

+

ounces

",13.52,13.52,,,208182 +PSBBGPV,2,Fill-in-the-blank(s),Numeric,"

Find the unknown value.

+

 

+

x =

",7,7,,,207052 +PSBBGMJ,2,Fill-in-the-blank(s),Numeric,"

Find the unknown value.

+

 

+

x =

",7,7,,,206599 +PSB4W4,4,Fill-in-the-blank(s),Numeric,"

Find the value of the unknown that makes the equation true.

+

 

+

18 = 3 ⋅ y

+

 

+

y =

",6,6,,,142047 +PSBCC57,2,Fill-in-the-blank(s),Numeric,"

Elena’s dad buys another type of cell phone that also usually sells for $250. He pays 75% of the usual price. How much did he pay?

+

 

+

$

",187.5,187.5,,,361789 +PSB34G,2,Fill-in-the-blank(s),Numeric,"

Find the perimeter of the polygon.

+

 

+

units

",20,20,,,137129 +PSBBFXH,2,Fill-in-the-blank(s),Numeric,"

Find the area of Polygon D in this activity.

+

 

+

square units

",19.5,19.5,,,202997 +PRABFG3F,1,Fill-in-the-blank(s),Numeric,"

What is the edge length of a cube with volume 2764 cubic units?

+

 

+

units

",4-Mar,4-Mar,,,87535 +PSBBYZR,2,Fill-in-the-blank(s),Numeric,"

Choose one equation and solve it.

+

 

+

y =

",2.4,2.4,,,292292 +PSBDW5,2,Fill-in-the-blank(s),Numeric,"

Choose one equation and solve it.

+

 

+

x =kg

",4.65,4.65,,,19879 +PSBBYW,2,Fill-in-the-blank(s),Numeric,"

What area is represented by each square?

+

 

+

 square units

",0.01,0.01,,,8540 +PSBBYW,3,Fill-in-the-blank(s),Numeric,"

What is (0.3) · (0.5)?  

+

 

+

",0.15,0.15,,,8659 +PSBBP6,2,Fill-in-the-blank(s),Numeric,"

Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.

+

 

+

Jada ran how much farther than Noah?  

+

 

+

 miles

",1.977,1.977,,,7207 +PSBH65,1,Fill-in-the-blank(s),Numeric,"

Diego bought 12 mini muffins for $4.20.  At this rate, how much would Diego pay for 4 mini muffins?  

+

 

+

$ 

+

 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
Number of Mini MuffinsPrice in Dollars
124.20
  
  
  
+

 

+

 

",1.4,1.4,,,42395 +PSBH65,2,Fill-in-the-blank(s),Numeric,"

How many mini muffins could Diego buy with $3.00?  If you get stuck, consider using the table.

+

 

+

mini muffins

",8,8,,,42567 +PRABQMBT,1,Fill-in-the-blank(s),Numeric,"

One way to convert from inches to centimeters is to multiply the number of inches by 2.54. How many centimeters are there in 14 inch?  

+

 

+

centimeters

",0.635,0.635,,,354320 +PRABQK7A,1,Fill-in-the-blank(s),Numeric,"

It takes 4.12 gallons of paint to paint a fence. How much paint is needed for 15 of the fence?  

+

 

+

 gallons

",0.824,0.824,,,591069 +PSBD2NU,1,Fill-in-the-blank(s),Numeric,"

Noah has 4 bags of marbles with the same number in each bag. If there are 536 marbles altogether, how many marbles are in each bag?  

+

 

+

marbles in each bag

",134,134,,,655353 +PSBBRG,1,Fill-in-the-blank(s),Numeric,"

One way to compute a 15% tip for a bill is to multiply it by 0.15.

+
 
+
A restaurant bill was $42.40. Calculate the tip.   
+
 
+
$
",6.36,6.36,,,7381 +PSBBP6,1,Fill-in-the-blank(s),Numeric,"

Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.

+

 

+

What is the total running distance of the four runners?  

+

 

+

 miles

",26.563,26.563,,,7096 +PRABQM3T,1,Fill-in-the-blank(s),Numeric,"

For part of a recipe, Jada adds 0.35 milliliters of vanilla extract to 16.4 milliliters of milk. How many milliliters does the mixture contain?  

+

 

+

 millimeters

",16.75,16.75,,,62040 +PRABQMPP,1,Fill-in-the-blank(s),Numeric,"

Andre deposited $24.50 into his bank account each week for 5 weeks. What was the total amount Andre deposited? 

+

 

+

$

",122.5,122.5,,,445524 +PSBBGH2,2,Fill-in-the-blank(s),Numeric,"

Find the value of x.

+

 

+

x = 

",7,7,,,206088 +PSB4W4,2,Fill-in-the-blank(s),Numeric,"

Find the value of the unknown that makes the equation true.

+

 

+

18 = 3 + x 

+

 

+

x =

",15,15,,,141837 +PSBNM4,1,Fill-in-the-blank(s),Numeric,"

One way to compute a 20% discount is to multiply the price by 0.20.

+

 

+

The price of a pair of sneakers is $84.50. Calculate the discount.

+

 

+

$

",16.9,16.9,,,60703 +PRABFFDC,1,Fill-in-the-blank(s),Numeric,"

The daily recommended allowance of vitamin C for a sixth grader is 45 mg. 1 orange has about 75% of the recommended daily allowance of vitamin C. How many milligrams are in 1 orange? If you get stuck, consider using the double number line.

+

 

+

mg

+

 

+

 

+

",33.75,33.75,,,155392 +PRABQMPQ,1,Fill-in-the-blank(s),Numeric,"

Four friends did a job together that paid $85.20. How much should each get if they all get an equal amount? 

+

 

+

$

",21.3,21.3,,,445641 +PRABQMPM,1,Fill-in-the-blank(s),Numeric,"

Noah had $5.25 and Lin had $8.95. How much did they have altogether? 

+

 

+

$

",14.2,14.2,,,445374 +PSBCWXB,1,Fill-in-the-blank(s),Numeric,"

Kiran has 3 containers of blocks with the same number in each container. If there are 852 blocks altogether, how many blocks are in each container?

+

 

+

  blocks

",284,284,,,456745 +PRABQMPN,1,Fill-in-the-blank(s),Numeric,"

Diego had $21.32 and gave $9.50 to Elena. How much did he have left? 

+

 

+

$

",11.82,11.82,,,48374 +PRABFFZJ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2.5t = 10

+

 

+

t =

",4,4,,,74735 +PRABFFZG,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

6 = 12z

+

 

+

z =

",12,12,,,74581 +PRABFFZH,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

314 = 12 + w

+

 

+

w =

",2 3/4,2 3/4,,,61624 +PSBQ32,3,Fill-in-the-blank(s),Numeric,"

Solve the equation. 

+

 

+

x =

",7 1/2,7 1/2,,,73287 +PSBCM9V,2,Fill-in-the-blank(s),Numeric,"

Find the solution for the situation.

+

 

+

y =

",112,112,,,406771 +PSB36Y,2,Fill-in-the-blank(s),Numeric,"

What would be the recycled value of those same cans?

+

 

+

$

",2.1,2.1,,,136814 +PSBBBHE,2,Fill-in-the-blank(s),Numeric,"

After tax, the total is $45.99. What percentage of the subtotal is the total?

+

 

+

%

",109.5,109.5,,,177807 +PSBDEQN,3,Fill-in-the-blank(s),Numeric,"

Blueberries cost $4.00 per pound. 

+

 

+

How many pounds of blueberries can you buy for $13.00?

+

 

+

  pounds of blueberries

",3.25,3.25,,,546982 +PSBZ3C,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation to represent the relationship.

+

 

+

Equation:   y = 

",1/3a,1/3a,,,124698 +PRABETDK,1,Fill-in-the-blank(s),Numeric,"

On a hot day, a football team drank an entire 50-gallon cooler of water and half as much again. How much water did they drink?  

+

 

+

gallons of water

",75,75,,,56172 +PSBBH8,1,Fill-in-the-blank(s),Numeric,"

Noah scored 20 points in a game. Mai's score was 30 points. The mean score for Noah, Mai, and Clare was 40 points. What was Clare's score? 

+

 

+

points

",70,70,,,6006 +PSBWMZ,4,Fill-in-the-blank(s),Numeric,"

If the pattern continues, how many mosquitoes will there be on day 6?

+

 

+

mosquitoes

",64,64,,,105867 +PSBD56Z,2,Fill-in-the-blank(s),Numeric,"

Andre set up a lemonade stand last weekend. It cost him $0.15 to make each cup of lemonade, and he sold each cup for $0.35.

+

 

+

How much money did it cost Andre to make this amount of lemonade?   

+

 

+

$

",4.2,4.2,,,677536 +PSBD56Z,3,Fill-in-the-blank(s),Numeric,"

Andre set up a lemonade stand last weekend. It cost him $0.15 to make each cup of lemonade, and he sold each cup for $0.35.

+

 

+

How much money did Andre make in profit?   

+

 

+

$

",5.6,5.6,,,677544 +PSBCRM3,2,Fill-in-the-blank(s),Numeric,"

Jada makes sparkling juice by mixing 2 cups of sparkling water with every 3 cups of apple juice.

+

 

+

How much apple juice does Jada need if she uses 6 cups of sparkling water?  

+

 

+

cups of apple juice

",9,9,,,426575 +PSBCA4G,1,Fill-in-the-blank(s),Numeric,"

Andre makes green paint by mixing 5 cups of yellow paint with 2 cups of blue paint.

+

 

+

To make the same shade of green, how much yellow paint does Andre need if he uses 8 cups of blue paint?

+

 

+

cups of yellow paint

",20,20,,,349368 +PSBCA4G,2,Fill-in-the-blank(s),Numeric,"

Andre makes green paint by mixing 5 cups of yellow paint with 2 cups of blue paint.

+

 

+

How much blue paint does Andre need if he uses 15 cups of yellow paint?

+

 

+

  cups of blue paint

",6,6,,,349505 +PSBMFR,1,Fill-in-the-blank(s),Numeric,"

37 of the students in a school are in sixth grade.

+

 

+

How many sixth graders are there if the school has 70 students?

+

 

+

 sixth graders

",30,30,,,54317 +PSBC8G,1,Fill-in-the-blank(s),Numeric,"

Jada reads 5 pages every 20 minutes. At this rate, how many pages can she read in 1 hour?

+

 

+

 

+

Use a double number line to find the answer.

+

 

+

 

+

 

+

 

+

+

 

+

 

+

Jada read pages.

",15,15,,,15805 +PSBC6R,1,Fill-in-the-blank(s),Numeric,"

An adult pass at the amusement park costs 1.6 times as much as a child’s pass.  How many dollars does an adult pass cost if a child’s pass costs $5?

+

 

+

 

+

$

+

 

",8,8,,,15120 +PSBJWY,2,Fill-in-the-blank(s),Numeric,"

What is the first quartile (Q1)?  

+

 

+

",5,5,,,46116 +PSBU4E,1,Fill-in-the-blank(s),Algebraic Expression,"

Elena is designing a logo in the shape of a parallelogram. She wants the logo to have an area of 12 square inches. She draws bases of different lengths and tries to compute the height for each.  

+

 

+

Write an equation Elena can use to find the height, h, for each value of the base, b.

+

 

+

h =

+

Use b as your variable.

",12/b,12/b,,,96079 +PRABHAXV,1,Fill-in-the-blank(s),Numeric,"

One morning, the temperature in Phoenix, Arizona was 8∘C and the temperature in Portland, Maine was 12∘C cooler. What was the temperature in Portland?

+

 

+

° Celsius

",-4,-4,,,373578 +PSBQV8,1,Fill-in-the-blank(s),Numeric,"

Two trains are traveling toward each other, on parallel tracks. Train A is moving at a constant speed of 70 miles per hour. Train B is moving at a constant speed of 50 miles per hour. The trains are initially 320 miles apart. How long will it take them to meet? One way to start thinking about this problem is to make a table. Add as many rows as you like.

+

 

+

hours

+

 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
 Train ATrain B
Starting Position0 Miles320 Miles
After 1 Hour70 Miles270 Miles
After 2 Hours  
   
   
+

 

+

 

",2 2/3,2 2/3,,,72169 +PSBQV8,2,Fill-in-the-blank(s),Numeric,"

How long will it take a train traveling at 120 miles per hour to go 320 miles?

+

 

+

hours

",2 2/3,2 2/3,,,72272 +PSBD56S,1,Fill-in-the-blank(s),Numeric,"

At a market, 3.1 pounds of peaches cost $7.72. How much did the peaches cost per pound?  Round your answer to the nearest cent.

+

 

+

 

+

$ per pound

",2.49,2.49,,,677513 +PSBU4E,2,Fill-in-the-blank(s),Numeric,"

Use your equation to find the height of a parallelogram with base 1.5 inches.

+

 

+

inches

",8,8,,,96224 +PSBQA2,2,Fill-in-the-blank(s),Numeric,"

What is the speed of the ship in miles per hour?  

+

 

+

miles per hour

+

 

+

",25,25,,,68783 +PSBQA2,3,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation that relates the time, t, it takes to travel a given distance, d.

+

 

+

d =

+

Use t as your variable.

+

 

+

",25t,25t,,,68963 +PRABFFZF,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

y + 1.8 = 14.7

+

 

+

y =

",12.9,12.9,,,74416 +PRABFGRJ,1,Fill-in-the-blank(s),Numeric,"

A crew has paved 34 of a mile of road. If they have completed 50% of the work, how long is the road they are paving?

+

 

+

miles

",1 1/2,1 1/2,,,113478 +PSBXD5,2,Fill-in-the-blank(s),Numeric,"

Use your equation to find x.

+

 

+

x =

",87.5,87.5,,,110306 +PRABFF3Q,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

 

+

10c = 26

+

 

+

c =

",2.6,2.6,,,223323 +PSBXGX,2,Fill-in-the-blank(s),Numeric,"

Priya has completed 9 exam questions. This is 60% of the questions on the exam. How many questions are on the exam?

+

 

+

questions

",15,15,,,110852 +PSBKFE,2,Fill-in-the-blank(s),Numeric,"

Noah raised $54 to support the animal shelter, which is 60% of his fundraising goal. What is Noah’s fundraising goal?   

+

 

+

$

",90,90,,,48838 +PSBBEXH,2,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

How much does the first bottle hold?  

+

 

+

ounces of water

",10,10,,,196907 +PSBBEZT,1,Fill-in-the-blank(s),Numeric,"

A rectangle has an area of 24 square units and a side length of  234 units. Find the other side length of the rectangle. 

+

 

+

units

+

Express your answer in fraction form.

",8 8/11,8 8/11,,,197182 +PSBBE76,2,Fill-in-the-blank(s),Numeric,"

Tyler's playlist has 36 songs. Noah’s playlist has one quarter as many songs as Tyler's playlist. How many songs are on Noah’s playlist, w?

+

 

+

w = songs

",9,9,,,198805 +PRABFFZE,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2x = 5

+

 

+

x =

",2-May,2-May,,,74258 +PSBCM74,2,Fill-in-the-blank(s),Numeric,"

Find the solution for the situation.

+

 

+

x =

",18,18,,,406364 +PSBBDA4,1,Fill-in-the-blank(s),Algebraic Expression,"

A school paid $31.25 for each calculator.

+

 

+

If the school bought x calculators, how much did they pay?

+

 

+

$

",31.25x,31.25x,,,187657 +PSBZKT,3,Fill-in-the-blank(s),Numeric,"

The area of a rectangle is 14 square units. It has side lengths x and y.  Given the value for x, find y.

+

 

+

x = 76

+

 

+

 

+

y =

",12,12,,,122576 +PSBBE6C,2,Fill-in-the-blank(s),Numeric,"

How far is Lin’s house from school?  

+

 

+

z = meters

",315,315,,,198406 +PSBBKEC,3,Fill-in-the-blank(s),Numeric,"

In a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is red. There are 4 cups of blue paint used in a batch of lilac paint.  

+

 

+

How many cups of lilac paint will this batch yield?  If you get stuck, consider using a tape diagram.

+

 

+

cups of lilac paint

",20,20,,,222018 +PRABFF3N,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

4a = 32

+

 

+

a =

",8,8,,,222907 +PSBBDA4,2,Fill-in-the-blank(s),Numeric,"

The school spent $500 on calculators. How many did the school buy?

+

 

+

calculators

",16,16,,,187859 +PSBXFQ,1,Fill-in-the-blank(s),Numeric,"

A group of 8 friends go to the movies. A bag of popcorn costs $2.99. How much will it cost to get one bag of popcorn for each friend? 

+

 

+

$

",23.92,23.92,,,110609 +PRABFGVG,1,Fill-in-the-blank(s),Numeric,"

You had $50. You spent 10% of the money on clothes, 20% on games, and the rest on books. How much money was spent on books?

+

 

+

$

",35,35,,,199099 +PSBBGPH,1,Fill-in-the-blank(s),Numeric,"

Puppy A weighs 8 pounds, which is about 25% of its adult weight. What will be the adult weight of Puppy A?

+

 

+

pounds

",32,32,,,206730 +PSBBGPH,2,Fill-in-the-blank(s),Numeric,"

Puppy B weighs 8 pounds, which is about 75% of its adult weight. What will be the adult weight of Puppy B?

+

 

+

pounds

",32/3,32/3,,,206901 +PRABHSDM,1,Order / Sort,Ordering,

Place these numbers in order from least to greatest:

,"

6

,

-2.5

,

-3

,

165

,

3.1

,

-38

,

-34

,

14

","

6

,

-2.5

,

-3

,

165

,

3.1

,

-38

,

-34

,

14

",,,191727 +PSBDZ4,4,Fill-in-the-blank(s),Algebraic Expression,"

Use your choice from the second question to write an equation that relates m and d.

+

 

+

d =

+

Use m as your variable.

",.12m,.12m,,,20430 +PRABFH7B,1,Order / Sort,Ordering,"

Put these numbers in order, from least to greatest.

","

-2.7

,

0

,

-1

,

1.3

,

2

","

-2.7

,

0

,

-1

,

1.3

,

2

",,,20763 +PRABGKQU,1,Fill-in-the-blank(s),Numeric,"

How many times larger is the first number in the pair than the second?

+

 

+

710 is times larger than 78.

",49,49,,,21258 +PSBJWY,4,Fill-in-the-blank(s),Numeric,"

What is the interquartile range (IQR)?  

+

",3,3,,,46358 +PSBBEQB,2,Fill-in-the-blank(s),Numeric,"

The whale swims down 300 feet to feed. What is the whale’s elevation now?  

+

 

+

feet

",-300,-300,,,195577 +PRABFFUE,1,Fill-in-the-blank(s),Numeric,"

It was 8 degrees at nightfall. The temperature dropped 10 degrees by midnight. What was the temperature at midnight?

+

 

+

degrees

",-2,-2,,,198077 +PSBPTX,2,Fill-in-the-blank(s),Numeric,"

At noon, the temperature was 5 degrees Celsius. By late afternoon, it has risen 6 degrees Celsius. What was the temperature late in the afternoon?

+

 

+

° Celsius

",11,11,,,66472 +PSBPTX,3,Fill-in-the-blank(s),Numeric,"

The temperature was 8 degrees Celsius at midnight. By dawn, it has dropped 12 degrees Celsius. What was the temperature at dawn?

+

 

+

 

+

° Celsius

",-4,-4,,,66602 +PSBPTX,4,Fill-in-the-blank(s),Numeric,"

Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?

+

 

+

 

+

° Celsius

",-7,-7,,,66748 +PSBBEQB,3,Fill-in-the-blank(s),Numeric,"

The whale swims down 150 more feed. What is the whale’s elevation now?

+

 

+

feet

",-450,-450,,,195675 +PSBBEU9,2,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

How many ounces of water are left in the bottle?  

+

 

+

ounces of water

",6.5,6.5,,,196505 +PSBGBG,4,Fill-in-the-blank(s),Numeric,"

On which day did it occur?

+

 

+

Day

",11,11,,,32600 +PSBGS5,1,Fill-in-the-blank(s),Numeric,"

Some boats were traveling up and down a river. A satellite recorded the movements of several boats. 

+

 

+

A motorboat traveled -3.4 miles per hour for 0.75 hours. How far did it go?

+

 

+

miles

",-2.55,-2.55,,,34746 +PRABMSGW,1,Fill-in-the-blank(s),Numeric,"

A teacher uses 36 centimeters of tape to hang up 9 student projects. At that rate, how much tape would the teacher need to hang up 10 student projects?

+

 

+

centimeters

",40,40,,,37662 +PSBGBG,2,Fill-in-the-blank(s),Numeric,"

On which day did it occur?

+

 

+

Day

",14,14,,,32363 +PRABFKCQ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

1 = 14c

+

 

+

c =

",4,4,,,64410 +PRABFJZQ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

b + 3.3 = 8.9

+

 

+

b =

",5.6,5.6,,,64237 +PRABFKCR,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

512= d + 14

+

 

+

d =

",5 1/4,5 1/4,,,64605 +PSBCG84,1,Fill-in-the-blank(s),Numeric,"

Here are the scores for landing an arrow in the colored regions of the archery target.

+

 

+

 

+ + + + + + + +
+ + + + + + + + + + + + + + + + + + +
Yellow:  10 points
Red:  8 points
Blue:  6 points
Green:  4 points
White:  2 points
+
+

 

+

 

+

Andre shot three arrows and they landed at (-5, 4), (-8, 7) and (1, 6).  What is his total score? 

+

 

+

 

+

points

",14,14,,,385260 +PSBBTPJ,2,Fill-in-the-blank(s),Numeric,"

Lin ran 29 meters in 10 seconds. She ran at a constant speed.  

+

 

+

At this rate, how far can she run in 1 minute?  

+

 

+

meters

",174,174,,,261766 +PSBN47,1,Fill-in-the-blank(s),Algebraic Expression,"

Jada is buying notebooks for school. The cost of each notebook is $1.75.  

+

 

+

Write an equation that shows the cost of Jada’s notebooks, c, in terms of the number of notebooks, n, that she buys.

+

 

+

c =

+

Use n as your variable.

",1.75n,1.75n,,,63146 +PSBBC3,1,Fill-in-the-blank(s),Numeric,"

Three sixth-grade classes raised $25.50, $49.75, and $37.25 for their classroom libraries. They agreed to share the money raised equally. What is each class’s equal share?

+

 

+

$

",37.5,37.5,,,5236 +PSBBA7D,1,Fill-in-the-blank(s),Numeric,"

Square A is a scaled copy of Square B with scale factor 2. If the area of Square A is 10 units2, what is the area of Square B?

+

 

+

units2

",2.5,2.5,,,176093 +PSBBA7D,2,Fill-in-the-blank(s),Numeric,"

Cube A is a scaled copy of Cube B with scale factor 2. If the volume of Cube A is 10 units3, what is the volume of Cube B?

+

 

+

units3

",1.25,1.25,,,176239 +PSBBZFQ,3,Fill-in-the-blank(s),Algebraic Expression,"

A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. There is proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe.

+

 

+

Write the equation for the relationship that has a constant of proportionality less than 1. 

+

 

+

r =

+

Use p as your variable.

",4/6p,4/6p,,,294659 +PSBDMQ,1,Fill-in-the-blank(s),Algebraic Expression,"

Noah’s recipe for sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

+

 

+

Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, t, that he needs to prepare. Write an equation that shows how Noah can find s, the number of liters of soda water, if he knows t.  

+

 

+

s =

+

Use t for your variable.

+

Express your answer in fraction form.

+

 

+

 

",5/9t,5/9t,,,18187 +PSBDMQ,2,Fill-in-the-blank(s),Algebraic Expression,"

Sometimes the school purchases a certain number, j, of liters of orange juice and Noah needs to figure out how much sparkling orange juice he can make. Write an equation that Noah can use to find t if he knows j.

+

 

+

 

+

t =

+

Use j as your variable.

",9/4j,9/4j,,,18301 +PSBDJR,1,Fill-in-the-blank(s),Numeric,"

The set of points are connected to form a line segment. What is the length of the line segment?

+

 

+

A = (3, 5) and B = (3, 6)

+

 

+

units

",1,1,,,17631 +PSBDJR,2,Fill-in-the-blank(s),Numeric,"

The set of points are connected to form a line segment. What is the length of the line segment?

+

 

+

C = (-2, -3) and D = (-2, -6)

+

 

+

units

",3,3,,,17786 +PSBDJR,3,Fill-in-the-blank(s),Numeric,"

The set of points are connected to form a line segment. What is the length of the line segment?

+

 

+

E = (-3, 1) and D = (-3, -1)

+

 

+

units

",2,2,,,17938 +PSBBEYJ,5,Fill-in-the-blank(s),Numeric,"

What is the constant of proportionality?  

",1.6,1.6,,,197156 +PSBDPZ5,1,Fill-in-the-blank(s),Numeric,"

A school wants to raise $2,500 to support its music program.  

+

 

+

If it has met 20% of its goal so far, how much money has it raised?

+

 

+

$

+

 

",500,500,,,593590 +PRABHSCP,1,Order / Sort,Ordering,"

Put these numbers in order, from least to greatest. If you get stuck, consider using the number line.

+

 

+

+



","

-2.1

,

-4.2

,

-1.5

,

-1

,

-0.5

,

3.5

,

4.8

,

0.5

,

-3.5

","

-2.1

,

-4.2

,

-1.5

,

-1

,

-0.5

,

3.5

,

4.8

,

0.5

,

-3.5

",,,5429 +PSBBXFB,1,Fill-in-the-blank(s),Numeric,"

A teacher drew a line segment that was 20 inches long on the blackboard. She asked each of her students to estimate the length of the segment and used their estimates to draw this dot plot.

+

 

+

 

+

+

 

+

 

+

How many students were in the class?  

+

 

+

students

",18,18,,,283170 +PSBBB76,1,Fill-in-the-blank(s),Numeric,"

Ten students each attempted 10 free throws. This list shows how many free throws each student made.

+

 

+

8          5           6          6          4          9          7          6          5          9

+

 

+

What is the median number of free throws made?  

+

 

+

 free throws

",6,6,,,181647 +PSBBB76,2,Fill-in-the-blank(s),Numeric,"

Ten students each attempted 10 free throws. This list shows how many free throws each student made.

+

 

+

8          5           6          6          4          9          7          6          5          9

+

 

+

What is the IQR (interquartile range)?  

+

 

+

 free-throws

",3,3,,,181770 +PSBBSS5,2,Fill-in-the-blank(s),Numeric,"

Ten students took a history quiz. This list shows how many questions each student answered correctly. 

+

 

+ + + + + + + + + + + + + + + +
968105810798
+

 

+

What is the mean?  

+

 

+

questions

",8,8,,,256621 +PSBBSS5,1,Fill-in-the-blank(s),Numeric,"

Ten students took a history quiz. This list shows how many questions each student answered correctly. 

+

 

+ + + + + + + + + + + + + + + +
968105810798
+

 

+

 

+

What is the IQR (interquartile range)?  

+

 

+

questions

",2,2,,,256519 +PSBCC57,1,Fill-in-the-blank(s),Numeric,"

The price of a cell phone is usually $250. Elena’s mom buys one of these cell phones for $150. What percentage of the usual price did she pay?

+

 

+

%

",60,60,,,361669 +PSBC36V,1,Fill-in-the-blank(s),Numeric,"

Andre and Mai leave the post office at the same time. They walk in opposite directions. Andre walks 50 feet, and Mai walks 30 feet. When they stop walking, how far apart are they?

+

 

+

 feet

",80,80,,,486785 +PSB3CK,1,Fill-in-the-blank(s),Numeric,"

A lizard and a snail start out next to each other on a drain pipe. The lizard climbs 10 inches up, and the snail climbs 4 inches down. After they stop climbing, how far apart are they? 

+

 

+

inches

",14,14,,,132573 +PSBCB9S,4,Fill-in-the-blank(s),Numeric,"

What is the distance between these points?

+

 

+

units

",5,5,,,356457 +PSBCBCJ,1,Fill-in-the-blank(s),Numeric,"

Diego wondered how far sixth-grade students could throw a ball. He decided to collect data to find out. He asked 10 friends to throw a ball as far as they could and measured the distance from the starting line to where the ball landed. The data shows the distances he recorded in feet.

+

 

+

 

+ + + + + + + + + + + + + + + +
40764063475749555053
+

 

+

 

+

Find the median of the data set.

+

 

+

feet

",51.5,51.5,,,350537 +PSBDV4,1,Fill-in-the-blank(s),Numeric,"

Lin’s family needs to travel 325 miles to reach her grandmother’s house.  

+

 

+

At 26 miles, what percentage of the trip’s distance have they completed?

+

 

+

%

",8,8,,,19386 +PRABGKQT,1,Fill-in-the-blank(s),Numeric,"

How many times larger is the first number in the pair than the second?

+

 

+

53 is times larger than 52.

",5,5,,,21076 +PRABGKQW,1,Fill-in-the-blank(s),Numeric,"

How many times larger is the first number in the pair than the second?

+

 

+

510 is times larger than 54.

","15,625","15,625",,,21595 +PRABGKQV,1,Fill-in-the-blank(s),Numeric,"

How many times larger is the first number in the pair than the second?

+

 

+

176 is times larger than 174.

",289,289,,,21399 +PSBBMAE,1,Fill-in-the-blank(s),Numeric,"

At the book sale, all books cost less than $5.  

+

 

+

What is the most expensive a book could be?

+

 

+

$

",4.99,4.99,,,227043 +PSBCBCJ,2,Fill-in-the-blank(s),Numeric,"

Find the IQR of the data set.

+

 

+

",10,10,,,350634 +PRABFH7D,1,Fill-in-the-blank(s),Numeric,"

How many times larger is the first number in the pair than the second?

+

 

+

34 is times larger than 33.

",3,3,,,20908 +PSBC968,1,Fill-in-the-blank(s),Numeric,"

For the past 12 school days, Mai has recorded how long her bus rides to school take in minutes. The times she recorded are shown in the table.

+

 

+ + + + + + + + + + + + + + + + + +
986910761298108
+

 

+

Find the mean for Mai’s data. 

+

 

+

minutes

",8.5,8.5,,,519985 +PSBBRUJ,1,Fill-in-the-blank(s),Numeric,"

Last week, the daily low temperatures for a city, in degrees Celsius, were 5, 8, 6, 5, 10, 7, and 1. What was the average low temperature?

+

 

+

 °C

",6,6,,,252066 +PRABFKN2,1,Order / Sort,Ordering,

Order these numbers from least to greatest:

,"

-18

,

-17

,

-18

,

19

,

20

","

-18

,

-17

,

-18

,

19

,

20

",,,6158 +PSBBQP6,1,Fill-in-the-blank(s),Numeric,"

Solve this equation:  3x-5=9x+4.

+

 

+

x=

",-13,-13,,,245814 +PSBX5W,2,Fill-in-the-blank(s),Numeric,"

What is the actual number of kilometers that is represented by 5 centimeters on the map?

+

 

+

  kilometers

",6.25,6.25,,,114712 +PSBYTT,1,Fill-in-the-blank(s),Numeric,"

Mai and Tyler were standing at one corner of a large rectangular field and decided to race to the opposite corner. Since Mai had a bike and Tyler did not, they thought it would be a fairer race if Mai rode along the sidewalk that surrounds the field while Tyler ran the shorter distance directly across the field. The field is 100 meters long and 80 meters wide. Tyler can run at around 5 meters per second, and Mai can ride her bike at around 7.5 meters per second.

+

 

+

+

 

+

A calculator may be necessary to answer the following questions. Round answers to the nearest hundredth.

+

 

+

If you could give the loser of the race a head start, how much time would they need in order for both people to arrive at the same time?

+

 

+

seconds

",1.6,1.6,,,118016 +PSBYTT,2,Fill-in-the-blank(s),Numeric,"

If you could make the winner go slower, how slow would they need to go in order for both people to arrive at the same time?

+

 

+

meters per second

",7.03,7.03,,,118107 +PSBBYGX,1,Fill-in-the-blank(s),Numeric,"

Here is the dot plot showing the travel time, in minutes, of Elena’s bus rides to school.

+

 

+

+

 

+

Find the median travel time. Be prepared to explain your reasoning.

+

 

+

 

+

minutes

",8.5,8.5,,,289171 +PSBCBNU,1,Fill-in-the-blank(s),Numeric,"

Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches.

+

 

+

What is the actual measurement of that side of the courtyard in inches? 

+

 

+

inches

",165,165,,,352275 +PSBCBNU,2,Fill-in-the-blank(s),Numeric,"

Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches.

+

 

+

What is the actual measurement of that side of the courtyard in feet? 

+

 

+

feet

",13.75,13.75,,,352500 +PSBB9,2,Fill-in-the-blank(s),Numeric,"

How many inches is that?

+

 

+

inches

+

 

",205920,205920,,,242 +PSBX5W,1,Fill-in-the-blank(s),Numeric,"

The scale of a map says that 4 cm represents 5 km.

+

 

+

What distance on the map (in centimeters) represents an actual distance of 4 kilometers?

+

 

+

  centimeters

",3.2,3.2,,,114557 +PSBEKA,4,Fill-in-the-blank(s),Numeric,"

Use the equation to predict the fuel efficiency of a car that weighs 100 kilograms.

+

 

+

mpg

+

 

+

Round your answer to the hundredths place.

",40.16,40.16,,,22902 +PSBEKA,5,Fill-in-the-blank(s),Numeric,"

Use the equation to predict the weight of a car that has a fuel efficiency of 22 mpg.

+

 

+

kg

+

 

+

Round your answer to the nearest whole.

",1693,1693,,,23029 +PSBB4BH,1,Fill-in-the-blank(s),Numeric,"

There are 12 inches in 1 foot and 5,280 feet in 1 mile. Elena ran 212 miles.

+

 

+

How many feet is that?

+

 

+

  feet

",13200,13200,,,310779 +PSBB4BH,2,Fill-in-the-blank(s),Numeric,"

How many inches is that?  

+

 

+

inches

",158400,158400,,,310891 +PSBZU8,1,Fill-in-the-blank(s),Numeric,"

A store sells rope by the meter. The equation p = 0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long.

+

 

+

How much does the nylon rope cost per meter?  $

",0.8,0.8,,,122934 +PSBZU8,2,Fill-in-the-blank(s),Numeric,"

A store sells rope by the meter. The equation p = 0.8L represents the price p, in dollars of a piece of nylon rope that is L meters long.

+

 

+

How long is a piece of nylon rope that costs $1.00?  

+

 

+

meters

",1.25,1.25,,,123580 +PSBBGN8,1,Fill-in-the-blank(s),Numeric,"

Here is a histogram that shows some dog weights in pounds.

+

 

+

+

 

+

Each bar includes the left-end value but not the right-end value. For example, the first bar includes dogs that weigh 60 pounds and 68 pounds but not 80 pounds.

+

 

+

 

+

Use the histogram to answer the following questions.

+

How many dogs weigh at least 100 pounds?

+

 

+

dogs

",23,23,,,206643 +PRABFKUK,1,Order / Sort,Ordering,

Order these numbers from greatest to least:

,"

-312

,

0

,

14

,

74

,

4

,

-4

,

-54

","

-312

,

0

,

14

,

74

,

4

,

-4

,

-54

",,,86693 +PSBEWH,3,Fill-in-the-blank(s),Numeric,"

It took Clare 30 minutes to walk around the garden at a constant speed. At what speed was she walking?

+

 

+

 

+

  feet per hour

",16800,16800,,,24870 +PSBEWH,1,Fill-in-the-blank(s),Numeric,"

Here is a map of the Missouri Botanical Garden. Clare walked all the way around the garden.

+

 

+

+

 

+

What is the actual distance around the garden?  

+

 

+

feet

",8400,8400,,,24640 +PRABQP67,1,Order / Sort,Ordering,

Put these numbers in order from least to greatest:

,"

273

,

36

,

643

,

10

,

8

,

163

","

273

,

36

,

643

,

10

,

8

,

163

",,,316129 +PSBBGTE,1,Fill-in-the-blank(s),Numeric,"

Here is Quadrilateral ABCD.

+ + + + + + + +
+

Quadrilateral PQRS is a scaled copy of Quadrilateral ABCD. Point P corresponds to A, Q to B, R to C, and S to D.

+

 

+

If the distance from P to R is 3 units, what is the distance from Q to S?   units

+
",3,3,,,207210 +PSBK3Q,1,Fill-in-the-blank(s),Numeric,"

Your teacher will give you a drawing of the Apollo Lunar Module. It is drawn at a scale of 1 to 50.

+

 

+

The “legs” of the spacecraft are its landing gear. Use the drawing to estimate the actual length of each leg on the sides. Write your answer to the nearest 10 centimeters.

+

 

+

centimeters

",350,350,,,51489 +PSB3YG,6,Fill-in-the-blank(s),Numeric,"

How much will they make if they sell a million tickets?

+

 

+

$

",62200000,62200000,,,135875 +PSBBG4V,4,Fill-in-the-blank(s),Numeric,"

+

What is the distance between B and D?   units

",3,3,,,208594 +PSBBG4V,5,Fill-in-the-blank(s),Numeric,"

 Figure 2 is a scaled copy of Figure 1.

+

+

 

+

What is the scale factor that takes Figure 1 to Figure 2?  

",3,3,,,208921 +PSB3YG,7,Fill-in-the-blank(s),Algebraic Expression,"

How much will they make if they sell x tickets?

+

 

+

$

+

 

+

Use x as your variable.

+

 

",62.2x,62.2x,,,136020 +PSB3YG,8,Fill-in-the-blank(s),Numeric,"

If they make $404,300, how many tickets have they sold?

+

 

+

tickets

",6500,6500,,,136146 +PRABEPJS,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+


5 ·= 15

",3,3,,,109056 +PRABTGS8,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+


4 · = 32

",8,8,,,109387 +PRABTGS9,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+

 

+

6 · = 9

","1 1/2, 3/2, 1.5","1 1/2, 3/2, 1.5",,,109501 +PRABTGTA,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+


12 · = 3

","1/4, 0.25","1/4, 0.25",,,109628 +PRABEQDY,1,Fill-in-the-blank(s),Numeric,"

A model airplane is built at a scale of 1 to 72. If the model plane is 8 inches long, how many feet long is the actual airplane?

+

 

+

  feet

",48,48,,,124091 +PSBBSSH,1,Fill-in-the-blank(s),Numeric,"

These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle?  

+

 

+

square units

+

 

+

",36,36,,,256312 +PSBDYSP,1,Fill-in-the-blank(s),Numeric,"

Water costs $1.25 per bottle. At this rate, what is the cost of 10 bottles?

+

 

+

 $

",12.5,12.5,,,643786 +PSBDYSP,2,Fill-in-the-blank(s),Numeric,"

Water costs $1.25 per bottle. At this rate, what is the cost of 20 bottles? 

+

 

+

$

",25,25,,,644011 +PSBDYSP,3,Fill-in-the-blank(s),Numeric,"

Water costs $1.25 per bottle. At this rate, what is the cost of 50 bottles?

+

 

+

 $

",62.5,62.5,,,644155 +PSBDET5,1,Fill-in-the-blank(s),Numeric,"

An area of 4 square yards is equal to 36 square feet. 10 square yards is equal to how many square feet?  

+

 

+

square feet

",90,90,,,547591 +PSBQ8E,3,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation to represent the relationship between the number of calories, c and the number of servings of granola, s. 

+

 

+

 

+

c =  

",350s,350s,,,74204 +PSB3YG,1,Fill-in-the-blank(s),Numeric,"

A performer expects to sell 5,000 tickets for an upcoming concert. They want to make a total of $311,000 in sales from these tickets.

+

 

+

Assuming that all tickets have the same price, what is the price for one ticket?

+

 

+

$

",62.2,62.2,,,135233 +PSB3YG,2,Fill-in-the-blank(s),Numeric,"

How much will they make if they sell 7,000 tickets?

+

 

+

$

",435400,435400,,,135345 +PSB3YG,3,Fill-in-the-blank(s),Numeric,"

How much will they make if they sell 10,000 tickets?

+

 

+

$

",622000,622000,,,135491 +PSB3YG,4,Fill-in-the-blank(s),Numeric,"

How much will they make if they sell 50,000 tickets?

+

 

+

$

",3110000,3110000,,,135638 +PSB3YG,5,Fill-in-the-blank(s),Numeric,"

How much will they make if they sell 120,000 tickets?

+

 

+

$

",7464000,7464000,,,135753 +PSBDEQN,1,Fill-in-the-blank(s),Numeric,"

Blueberries cost $4.00 per pound. 

+

 

+

How many pounds of blueberries can you buy for $1.00?  

+

 

+

pounds of blueberries

",0.25,0.25,,,546775 +PSBK3Q,5,Fill-in-the-blank(s),Numeric,"

Neil Armstrong was 71 inches tall when he went to the Moon. How tall would he be in this scale drawing?

+

 

+

inches

+

 

+

Round your answer to the tenths.

",1.4,1.4,,,52116 +PRABMPBK,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+

8 ⋅   =  40

",5,5,,,360938 +PRABMPBP,1,Fill-in-the-blank(s),Numeric,"

Complete the equation with a number that makes it true.

+


21 -  =  7

",14,14,,,361546 +PSBBMYV,1,Fill-in-the-blank(s),Numeric,"

A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.  

+

 

+

If the park is shown as a square on the map, each side of which is one foot long, how long is each side of the square park?

+

 

+

 

+

feet

",2400,2400,,,230683 +PSBBMYV,2,Fill-in-the-blank(s),Numeric,"

A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.  

+

 

+

 

+

If a straight path in the park is 900 feet long, how long would the path be when represented on the map?

+

 

+

 

+

  inches

",4.5,4.5,,,231026 +PSBRRZ,1,Fill-in-the-blank(s),Numeric,"

A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing?  

+

 

+

cm

",12.5,12.5,,,76811 +PSBZVR,1,Fill-in-the-blank(s),Numeric,"

Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units.

+

 

+

+

 

+

How many times larger is the area of the scaled copy compared to that of Triangle A?  

+

 

+

times larger

",16,16,,,123304 +PSB3YG,9,Fill-in-the-blank(s),Numeric,"

How many tickets will they have to sell to make $5,000,000?

+

 

+

tickets

",80386,80386,,,136282 +PSBHPP,1,Fill-in-the-blank(s),Numeric,"

Strawberries cost $3.00 per pound. 

+

 

+

How many pounds of strawberries can you buy for $1.00?  

+

 

+

pounds of strawberries

",3-Jan,3-Jan,,,39724 +PSBBZFQ,1,Fill-in-the-blank(s),Algebraic Expression,"

A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. There is proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe.

+

 

+

Write the equation for the relationship that has a constant of proportionality greater than 1. 

+

 

+

p =

+

Use r as your variable.

",6/4r,6/4r,,,294155 +PSBHRT,1,Fill-in-the-blank(s),Numeric,"

Clare made some lemonade by mixing 6 cups of water with 8 tablespoons of lemonade powder.

+

 

+

How many tablespoons of powder per cup of water is that?

+

 

+

  tablespoons of powder per cup of water

",6-Aug,6-Aug,,,40293 +PSBX7W,1,Fill-in-the-blank(s),Numeric,"

Tyler has two different maps of Ohio.

+

 

+
    +
  • The scale on the first map is 1 cm to 10 km. The distance from Cleveland to Cincinnati is 40 cm.
    • +
  • The scale on the second map is 1 cm to 50 km.


    • +
+

What is the distance from Cleveland to Cincinnati on the second map?

+

 

+

  cm

",8,8,,,114882 +PSBHRT,2,Fill-in-the-blank(s),Numeric,"

Clare made some lemonade by mixing 6 cups of water with 8 tablespoons of lemonade powder.

+

 

+

How many cups of water per tablespoon of powder is that?

+

 

+

cups of water per tablespoon of powder

",8-Jun,8-Jun,,,40426 +PSBBBZA,1,Fill-in-the-blank(s),Numeric,"

Clare is cycling at a speed of 12 miles per hour. If she starts at a position chosen as zero, what will her position be after 45 minutes?  

+

 

+

 miles

",9,9,,,179837 +PSBBBZA,2,Fill-in-the-blank(s),Numeric,"

Han is cycling at a speed of -8 miles per hour; if he starts at the same zero point, what will his position be after 45 minutes?

+

 

+

  miles

",-6,-6,,,180087 +PSBBBTV,1,Fill-in-the-blank(s),Numeric,"

A submarine is searching for underwater features. It is accompanied by a small aircraft and an underwater robotic vehicle.

+

 

+

At one time the aircraft is 200 m above the surface, the submarine is 55 m below the surface, and the underwater robotic vehicle is 227 m below the surface. 

+

 

+

What is the difference in height between the submarine and the aircraft?  

+

 

+

m

",255,255,,,179142 +PSBBBZA,3,Fill-in-the-blank(s),Numeric,"

What will the distance between them be after 45 minutes?

+

 

+

 miles

",15,15,,,180403 +PSB36Y,1,Fill-in-the-blank(s),Numeric,"

Aluminum cans can be recycled instead of being thrown in the garbage. The weight of 10 aluminum cans is 0.16 kilograms. The aluminum in 10 cans that are recycled has a value of $0.14.

+

 

+

If a family threw away 2.4 kg of aluminum in a month, how many cans did they throw away?

+

 

+

cans

",150,150,,,136496 +PSBB96V,5,Fill-in-the-blank(s),Numeric,"

How far away from the ticket booth was Tyler after 1 second?

+

 

+

meters

",1.25,1.25,,,343609 +PSBB96V,7,Fill-in-the-blank(s),Numeric,"

What is the constant of proportionality for the relationship between time and distance?

+

 

+

",1.25,1.25,,,343945 +PSBC5SN,1,Fill-in-the-blank(s),Numeric,"

Jada volunteers at an animal shelter that holds picnics to introduce people to animals. For the first picnic, she brought 36 clementines for 16 people, which was the right amount. For the next picnic, there will be 40 people! How many clementines should Jada bring for all those people? (Note: clementines are fruits that are like small oranges.).

+

 

+

clementines

",90,90,,,495575 +PSBU7R,1,Fill-in-the-blank(s),Numeric,"

Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

+

 

+

Noah paid $28 for the jeans after using the coupon. What is the regular price of the jeans? 

+

 

+

$

",40,40,,,96632 +PRABEU34,1,Fill-in-the-blank(s),Numeric,"

A circular running track is 14 mile long. Elena runs on this track, completing each lap in 120 of an hour.

+

 

+
+

What is Elena’s running speed?

+

 

+

  miles per hour

+
",5,5,,,501551 +PSBU7R,2,Fill-in-the-blank(s),Numeric,"

Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

+

 

+

The regular price of a hoodie is $27. What did Noah pay for the hoodie? 

+

 

+

$

",18.9,18.9,,,96761 +PRABJDMR,1,Fill-in-the-blank(s),Numeric,"

The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?

+

 

+

Approximately people

","262000, 262440","262000, 262440",,,318171 +PSBCD55,2,Fill-in-the-blank(s),Numeric,"

If you leave this money in the account, how much will be in your account after 2 years? 

+

 

+

$

",337.08,337.08,,,367651 +PSBDVK,1,Fill-in-the-blank(s),Numeric,"

How many cubic centimeters are there in 1 cubic meter?

+

 

+

cubic centimeters

",1000000,1000000,,,19558 +PSBDZUH,1,Fill-in-the-blank(s),Numeric,"

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.

+

 

+ + + + + + + + + + + + + + + +
cups of white paintcups of red paint
1 
73
+

 

+

 

+

How many cups of red paint should be added to 1 cup of white paint?

+

 

+

cups of red paint

+

Express your answer as a fraction.

",7-Mar,7-Mar,,,650373 +PSBDZUH,2,Fill-in-the-blank(s),Numeric,"

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.

+

 

+ + + + + + + + + + + + + + + +
cups of white paintcups of red paint
1 
73
+

 

+

 

+

What is the constant of proportionality?  

+

 

+

+

Express your answer as a fraction.

",7-Mar,7-Mar,,,650519 +PSBCD55,1,Fill-in-the-blank(s),Numeric,"

If you deposit $300 in an account with a 6% interest rate, how much will be in your account after 1 year? 

+

 

+

$

",318,318,,,367406 +PSB2NP,1,Fill-in-the-blank(s),Numeric,"

Here is a prism with a pentagonal base. The height is 8 cm.

+

 

+

What is the volume of the prism?  

+

 

+

cm3

+

 

+

 

+

",232,232,,,128308 +PRABQWBN,1,Fill-in-the-blank(s),Algebraic Expression,"

A goat (point G) is tied with a 6-foot rope to the corner of a shed. The floor of the shed is a square whose sides are each 3 feet long. The shed is closed and the goat can't go inside. The space all around the shed is flat, grassy, and the goat can't reach any other structures or objects. What is the area over which the goat can roam? 

+
+
+
 
+
+
square feet
+
+

Use pi to represent the  π symbol.

+

For example:

+

32π would be typed as 32pi

+
+
+
",31.5pi,31.5pi,,,56351 +PSB7FG,1,Fill-in-the-blank(s),Numeric,"

A circle’s circumference is approximately 76 cm.

+

 

+

Estimate the radius of the circle.

+

 

+

cm

+

Use  3.14 for π.

+

Round your answer to the nearest whole number.

",12,12,,,155089 +PSBBU6D,3,Fill-in-the-blank(s),Numeric,"

How long does it take the car to travel 26 miles at this speed? 

+

 

+

hours

",5-Feb,5-Feb,,,270281 +PRABESVY,1,Fill-in-the-blank(s),Numeric,"

Jada paints a circular table that has a diameter of 37 inches. What is the area of the table?

+

 

+

inches2  

+

Use 3.14 for π.

+

Round your answer to the nearest whole number.

",1075,1075,,,149544 +PSB7FG,3,Fill-in-the-blank(s),Numeric,"

A circle’s circumference is approximately 76 cm.

+

 

+

Estimate the area of the circle.  

+

 

+

 cm2

+

Use 3.14 for π.

+

Round your answer to the nearest whole number.

","460, 452","460, 452",,,155680 +PSBC7QJ,1,Fill-in-the-blank(s),Numeric,"

A college student takes out a $7,500 loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet):

+

 

+

If the bank charges 3.8% interest each year? 

+

 

+

$

",7785,7785,,,505118 +PSBDNCG,3,Fill-in-the-blank(s),Numeric,"

A certain shade of light blue paint is made by mixing 112 quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint?

+

 

+

quarts of white paint

",13 1/3,13 1/3,,,584537 +PSBBNBQ,1,Fill-in-the-blank(s),Numeric,"

A 200 pound person weighs 33 pounds on the moon.

+

How much did the person's weight decrease?  

+

 

+

 pounds

",167,167,,,232655 +PRABESKP,1,Fill-in-the-blank(s),Numeric,"

A small, test batch of lemonade used 14 cup of sugar added to 1 cup of water and 14 cup of lemon juice. After confirming it tasted good, a larger batch is going to be made with the same ratios using 10 cups of water. How much sugar should be added so that the large batch tastes the same as the test batch?

+

 

+

 

+

cups

",2.5,2.5,,,25209 +PSBBNBQ,2,Fill-in-the-blank(s),Numeric,"

By what percentage did the person's weight decrease?  

+

 

+

%

+

Round your answer to the nearest whole percent. 

",84,84,,,233047 +PSBTDG,2,Fill-in-the-blank(s),Numeric,"

Later, someone wants to use the data to find the amount of water at times before the sensor started. What should the sensor have read at the time -7 minutes?

+

 

+

liters

",120,120,,,86074 +PRABESJV,1,Fill-in-the-blank(s),Numeric,"

Estimate the side length of a square that has a 9 cm long diagonal.

+

 

+

 

+

cm

+

Round your answer to the nearest tenth.

","6.4, 6.3","6.4, 6.3",,,123610 +PSBBU6D,2,Fill-in-the-blank(s),Numeric,"

How many miles does the car travel in 1.5 hours?

+

 

+

miles

",97.5,97.5,,,269923 +PSBBKCS,1,Fill-in-the-blank(s),Numeric,"

A train is traveling at a constant speed and goes 7.5 kilometers in 6 minutes. At that rate:

+

 

+ + + + + + + +
+

How far does the train go in 1 minute?

+

 

+

kilometers

+
",4-May,4-May,,,221573 +PSBBKCS,2,Fill-in-the-blank(s),Numeric,"

How far does the train go in 100 minutes?

+

 

+

kilometers 

",125,125,,,221711 +PSBBVCZ,3,Fill-in-the-blank(s),Numeric,"

Elena has some bottles of water that each holds 17 fluid ounces.

+

 

+

How many bottles does it take to hold 51 fluid ounces of water?  

+

 

+

bottles

",3,3,,,271395 +PSBCGTP,1,Fill-in-the-blank(s),Numeric,"

A cyclist rode 3.75 miles in 0.3 hours. 

+
+

How fast was she going in miles per hour?  

 miles per hour

+
",12.5,12.5,,,382565 +PRABETC7,1,Fill-in-the-blank(s),Numeric,"

A 50-centimeter piece of wire is bent into a circle. What is the area of this circle?

+

 

+

cm2

+

Use 3.14 for π.

+

Round your answer to the nearest whole number. 

",199,199,,,122706 +PSBZAQ,2,Fill-in-the-blank(s),Numeric,"

Crater Lake in Oregon is shaped like a circle with a diameter of about 5.5 miles.

+

 

+

What is the area of the surface of Crater Lake?

+

 

+

square miles

+

Use 3.14 for π.

+

Round to the nearest whole number.

",24,24,,,120578 +PRABETC3,1,Fill-in-the-blank(s),Numeric,"

To make a shade of paint called jasper green, mix 4 quarts of green paint with 23 cups of black paint. How much green paint should be mixed with 4 cups of black paint to make jasper green?  

+

 

+

 

+

quarts

",24,24,,,122274 +PSBCXKJ,2,Fill-in-the-blank(s),Numeric,"

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information.

+

 

+

How much information could be transmitted in 30,000 packets?

+

 

+

bytes

","45,000,000","45,000,000",,,460209 +PSBCXKJ,1,Fill-in-the-blank(s),Numeric,"

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information.

+

 

+

How many packets would be needed to transmit 30,000 bytes of information?

+

 

+

packets

",20,20,,,460042 +PSBBVBE,2,Fill-in-the-blank(s),Numeric,"

The fence around a circular pool is 75 ft long.

+

 

+

Estimate the diameter of the circle: 

+

 

+

feet

+

Use  3.14 for π.

+

Round your answer to the nearest whole number.

",24,24,,,270921 +PSBBVV9,2,Fill-in-the-blank(s),Numeric,"

From the center to the edge of a DVD measures 60 mm.

+

 

+

Estimate the diameter of the circle: 

+

 

+

mm

",120,120,,,274359 +PSBBVSF,2,Fill-in-the-blank(s),Numeric,"

The length of the metal rim around a glass lens is 190 mm.  

+

 

+

Estimate the diameter of the circle:

+

 

+

mm

+

Use  3.14 for π.

+

Round your answer to the nearest whole number.

","60, 61","60, 61",,,273496 +PSBBVV9,3,Fill-in-the-blank(s),Numeric,"

From the center to the edge of a DVD measures 60 mm.

+

 

+

Estimate the circumference of the circle: 

+

 

+

mm

+

Use  3.14 for π.

+

Round your answer to the nearest whole number. 

",377,377,,,274572 +PSBDESP,1,Fill-in-the-blank(s),Numeric,"

Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.

+

 

+

How many tablespoons of cocoa per cup of milk is that?  

+

 

+

tablespoons of cocoa per cup of milk

",4-Jun,4-Jun,,,547291 +PSBRZQ,1,Fill-in-the-blank(s),Numeric,"

At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill.

+

 

+

How much would the sales tax be on a $66 meal? 

+

 

+

$

",5.61,5.61,,,77978 +PRABMR8A,1,Fill-in-the-blank(s),Numeric,"

Jada has 12 library books checked out and Han has 13 less than that. How many books does Han have checked out?  

+

 

+

books

",8,8,,,56590 +PRABPKDE,1,Fill-in-the-blank(s),Algebraic Expression,"

Tyler ate x fruit snacks, and Han ate 34 less than that.  Write an equation to represent the relationship between the number Tyler ate (x) and the number Han ate (y).

+

 

+

 

+

y =

",1/4x,1/4x,,,47104 +PSBDESP,2,Fill-in-the-blank(s),Numeric,"

Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.

+

 

+

How many cups of milk per tablespoon of cocoa is that?  

+

 

+

cups of milk per tablespoon of cocoa

",6-Apr,6-Apr,,,547415 +PRABP94X,1,Fill-in-the-blank(s),Algebraic Expression,"

Mai skated x miles, and Clare skated 35 farther than that.  Write an equation to represent the relationship between distance Mai skated (x) and the distance Clare skated (y).

+

 

+

y =

","8/5x, 8x/5","8/5x, 8x/5",,,47181 +PSBC7JE,2,Fill-in-the-blank(s),Numeric,"

How much money will the store get from the sale of the couch? 

+

 

+

$

",467.77,467.77,,,504695 +PSBDA37,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

8.88 = 4.44(x − 7)

+

 

+

x =

",9,9,,,524787 +PRABESVE,1,Fill-in-the-blank(s),Numeric,"

The radius of the earth is approximately 6,400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere. (The center of the earth is also the center of the equator.) What is the length of the equator?

+

 

+

km

+

Use 3.14 for π.

+

Round your answer to the nearest ten thousand.

",40000,40000,,,102054 +PSBC2YF,1,Fill-in-the-blank(s),Numeric," + + + + + + +
Green sea turtles live most of their lives in the ocean but come ashore to lay their eggs. Some beaches where turtles often come ashore have been made into protected sanctuaries so the eggs will not be disturbed. +

+
+

 

+

One sanctuary had 180 green sea turtles come ashore to lay eggs last year. This year, the number of turtles increased by 10%. How many turtles came ashore to lay eggs in the sanctuary this year?

+

 

+

green sea turtles

",198,198,,,479016 +PSBC2Q7,2,Fill-in-the-blank(s),Numeric,"

What was the price before the discount?

+

 

+

$

",16,16,,,477986 +PSBVWT,1,Fill-in-the-blank(s),Numeric,"

Here are several recipes for sparkling lemonade. For each recipe, describe how many tablespoons of lemonade mix it takes per cup of sparkling water.

+

 

+

 4 tablespoons lemonade mix and 12 cups of sparkling water.

+

 

+

tablespoons lemonade mix per cup of sparkling water

+

Write your answer as a fraction.

",3-Jan,3-Jan,,,100386 +PSBVWT,2,Fill-in-the-blank(s),Numeric,"

Here are several recipes for sparkling lemonade. For each recipe, describe how many tablespoons of lemonade mix it takes per cup of sparkling water.

+

 

+

4 tablespoons of lemonade mix and 6 cups of sparkling water.

+

 

+

tablespoons lemonade mix per cup of sparkling water 

+

Write your answer as a fraction.

",3-Feb,3-Feb,,,100712 +PSBVWT,3,Fill-in-the-blank(s),Numeric,"

Here are several recipes for sparkling lemonade. For each recipe, describe how many tablespoons of lemonade mix it takes per cup of sparkling water.

+

 

+

3 tablespoons of lemonade mix and 5 cups of sparkling water.

+

 

+

tablespoons lemonade mix per cup of sparkling water

+

Write your answer as a fraction.

",5-Mar,5-Mar,,,100983 +PSBB2JV,2,Fill-in-the-blank(s),Numeric,"

A bug was sitting on the tip of the propeller blade when the propeller started to rotate. The bug held on for 5 rotations before flying away. How far did the bug travel before it flew off?

+

 

+

inches

+

 

+

Round to the nearest whole inch.

",754,754,,,301355 +PSBBBHE,3,Fill-in-the-blank(s),Numeric,"

They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?

+

 

+

%

+

Round your answer to the hundredths place.

",16.67,16.67,,,177927 +PSBB2N3,3,Fill-in-the-blank(s),Numeric,"

The track is 9.76 m wide all the way around. What is the distance around the outside of the track?

+

 

+

m

+

Use 3.14 as an approximation for π.

",459.3,459.3,,,301764 +PSBB5M8,1,Fill-in-the-blank(s),Numeric,"
The length of segment AE is 5 centimeters. 
+
 
+
 
+
+
 
+
+

 

+

What is the length of segment CD?

+

 

+

  centimeters

+
",10,10,,,317396 +PSBB2N3,1,Fill-in-the-blank(s),Numeric,"

The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end.

+

 

+

+

 

+

What is the distance around the inside of the track?

+

 

+

m

+

Use 3.14 as an approximation for π.

",398,398,,,301541 +PRABESU5,1,Fill-in-the-blank(s),Numeric,"

The diameter of a bike wheel is 27 inches. If the wheel makes 15 complete rotations, how far does the bike travel?

+

 

+

 

+

inches

+

Round your answer to the nearest whole number. 

",1272,1272,,,318098 +PRABESU8,1,Fill-in-the-blank(s),Numeric,"

Circle A has circumference 223 m. Circle B has a diameter that is 112 times as long as Circle A’s diameter. What is the circumference of Circle B?  

+

 

+

 

+

meters

+

Round to the nearest whole number.

",4,4,,,318855 +PSBBP38,1,Fill-in-the-blank(s),Numeric,"

The wheels on Noah's bike have a circumference of about 5 feet. 

+

 

+

 

+

How far does the bike travel as the wheel makes 15 complete rotations?

+

 

+

feet

",75,75,,,242585 +PSBBP38,2,Fill-in-the-blank(s),Numeric,"

How many times do the wheels rotate if Noah rides 40 feet?  

+

 

+

rotations

",8,8,,,242782 +PSBCTHV,1,Fill-in-the-blank(s),Numeric,"

The circumference of a car wheel is about 65 inches. 

+

 

+

If the car wheel rotates once per second, how far does the car travel in one minute?

+

 

+

inches

",3900,3900,,,437057 +PSBCTHV,2,Fill-in-the-blank(s),Numeric,"

If the car wheel rotates once per second, about how many miles does the car travel in one hour?

+

 

+

+

Round your answer to the nearest tenth of a mile.

+

 

",3.7,3.7,,,437183 +PSBCTHV,4,Fill-in-the-blank(s),Numeric,"

If the car is traveling 65 miles per hour, about how many times per second does the wheel rotate?

+

 

+

times

+

Round your answer to the nearest tenth.

",17.6,17.6,,,437428 +PRABESU6,1,Fill-in-the-blank(s),Numeric,"

The wheels on Kiran's bike are 64 inches in circumference. How many times do the wheels rotate if Kiran rides 300 yards? 

+

 

+

times

+

Round your answer to the nearest whole number.

",169,169,,,318409 +PSBBBKF,2,Fill-in-the-blank(s),Numeric," + + + + + + +
+

Some other person’s sales tax is $1.61. How much was their subtotal?

+

 

+

$

+
","16.95, 16.92, 16.91, 16.90, 16.93, 16.94, 16.96, 16.97, 16.98, 16.99","16.95, 16.92, 16.91, 16.90, 16.93, 16.94, 16.96, 16.97, 16.98, 16.99",,,178224 +PRABPJK5,1,Fill-in-the-blank(s),Numeric,"

Point A is the center of the circle, and the length of CD is 15 centimeters. Find the circumference of this circle.  

+

 

+

+

 

+

 

+

centimeters

+
+
+

Use  3.14 for π.

+
+

Round to the nearest whole number.

+
",47,47,,,156887 +PRABESVN,1,Fill-in-the-blank(s),Numeric,"

Circle A has area 500 in2. The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B.  

+

 

+

 

+

in2

",4500,4500,,,448752 +PRABESVP,1,Fill-in-the-blank(s),Numeric,"

Lin’s bike travels 100 meters when her wheels rotate 55 times. What is the circumference of her wheels?  

+

 

+

meters

+
+

Round your answer to the nearest hundredth place.

+
",1.82,1.82,,,449067 +PRABETPD,1,Fill-in-the-blank(s),Numeric,"

On Monday, the high was 60 degrees Fahrenheit. On Tuesday, the high was 18% more. How much did the high increase from Monday to Tuesday?  

+

 

+

degrees Fahrenheit

",10.8,10.8,,,503044 +PRABETQN,1,Fill-in-the-blank(s),Numeric,"

A watermelon weighs 8,475 grams. A scale measured the weight with an error of 12% under the actual weight. What was the measured weight?

+

 

+

grams

",7458,7458,,,326880 +PSBBU45,1,Fill-in-the-blank(s),Numeric,"

A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter.

+

 

+

A store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.

+

 

+

What is the smallest number of bags the groundskeeper must buy to cover the circular field?  

+

 

+

bags

",4,4,,,270246 +PSBBFAG,1,Fill-in-the-blank(s),Numeric,"

The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m wide all the way around.

+

 

+

+

 

+

What is the area of the running track that goes around the field?

+

 

+

m2

+

Round your answer to the nearest tenth.

+

 

+

 

",4183.6,4183.6,,,199123 +PRABHX6K,1,Fill-in-the-blank(s),Numeric,"

What percentage of the car price is the tax?

+

 

+

%

+

 

+

",25,25,,,15333 +PRABHX6N,1,Fill-in-the-blank(s),Numeric,"

What percentage of the shirt cost is the discount?

+

 

+

%

+

Round your answer to the nearest whole percent.

+

 

+

",33,33,,,15629 +PRABH67F,1,Fill-in-the-blank(s),Numeric,"

Instructions to care for a plant say to water it with 34 cup of water every day. The plant has been getting 25% too much water. How much water has the plant been getting?

+

 

+

cup(s) of water

",15/16,15/16,,,51822 +PSBBU3Q,1,Fill-in-the-blank(s),Numeric,"

This figure is made from a part of a square and a part of a circle. 

+

 

+

+

 

+
+
+
+
+

What is the perimeter of this figure, to the nearest unit?

+

 

+

units

+
+
+
+
",38,38,,,269908 +PSBDRW4,1,Fill-in-the-blank(s),Algebraic Expression,"

The sides of a square have length s.

+

 

+

Write a formula for the perimeter P of the square. 

+

 

+

P =

+

Use s as your variable.

",4s,4s,,,604967 +PSBKW7,1,Fill-in-the-blank(s),Numeric,"

A metal measuring tape expands when the temperature goes above 50°F. For every degree Fahrenheit above 50, its length increases by 0.00064%.

+

 

+

The temperature is 100 degrees Fahrenheit. How much longer is a 30-foot measuring tape than its correct length?

+

 

+

feet

",0.0096,0.0096,,,51480 +PSBKW7,2,Fill-in-the-blank(s),Numeric,"

What is the percent error?

+

 

+

%

",0.032,0.032,,,51614 +PRABETQS,1,Fill-in-the-blank(s),Numeric,"

A student estimated that it would take 3 hours to write a book report, but it actually took her 5 hours. What is the percent error for her estimate?  

+

 

+

%

",40,40,,,359196 +PSBB6QW,3,Fill-in-the-blank(s),Numeric,"

Express the measurement error as a percentage of the actual depth.  

+

 

+

%

+

Round your answer to the nearest hundredths place.

",1.27,1.27,,,324089 +PSBBR5,1,Fill-in-the-blank(s),Numeric,"

Here is a picture that shows one side of a child's wooden block with a semicircle cut out at the bottom.

+

 

+

+

 

+

 

+

Find the area of the side.

+

 

+

 cm2

+

 

+

Use 3.14 for π.

+

Round your answer to the nearest hundredth place.

","30.68, 30.69","30.68, 30.69",,,7411 +PRABETQV,1,Fill-in-the-blank(s),Numeric,"

It took 48 minutes to drive downtown. An app estimated it would be less than that. If the error was 20%, what was the app’s estimate?  

+

 

+

minutes

",38.4,38.4,,,359989 +PRABESV3,1,Fill-in-the-blank(s),Exact Match,"

A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?  

+

 

+

inches2

+

 

+

Use pi to represent the symbol.

+

For example: 32π would be typed as 32pi

",9pi,9pi,,,175501 +PSBDRYP,1,Fill-in-the-blank(s),Numeric,"

Priya measured the perimeter of a square desk and found 248 cm. Noah measured the perimeter of the same desk and found 2,468 mm. 

+

 

+

By how many millimeters do these measurements differ?  

+

 

+

millimeters

",12,12,,,605230 +PSBBQN7,2,Fill-in-the-blank(s),Algebraic Expression,"

If the regular price of an item is x dollars, what is the discounted price in dollars?

+

 

+

$

","x-0.2x, 0.80x, 4/5x","x-0.2x, 0.80x, 4/5x",,,245240 +PSBBUMX,3,Fill-in-the-blank(s),Numeric,"

What was the error, expressed in inches?  

+

 

+

inches

",2,2,,,267646 +PSBBUMX,4,Fill-in-the-blank(s),Numeric,"

What was the error, expressed as a percentage of the actual height?  

+

 

+

%

",4,4,,,267794 +PSBB6QW,1,Fill-in-the-blank(s),Numeric,"

The depth of a lake is 15.8 m.

+

 

+

Jada accurately measured the depth of the lake to the nearest meter. What measurement did Jada get?  

+

 

+

meters

",16,16,,,323501 +PSBB6QW,2,Fill-in-the-blank(s),Numeric,"

By how many meters does the measured depth differ from the actual depth?

+

 

+

meters

",0.2,0.2,,,323812 +PSBRZQ,2,Fill-in-the-blank(s),Numeric,"

At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill.

+

 

+

What is the tax rate for meals in this city?  

+

 

+

%

",8.5,8.5,,,78165 +PSBC6J7,1,Fill-in-the-blank(s),Numeric,"

Here are the prices of some items and the amount of sales tax charged on each in Nevada. 

+

 

+ + + + + + + + + + + + + + + + + + + +
cost of items ($)sales tax ($)
100.46
502.30
50.23
+

 

+

What is the sales tax rate in Nevada?   %

",4.6,4.6,,,499326 +PSBC6J7,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression for the amount of sales tax charged, in dollars, on an item that costs c dollars. 

+

 

+

",0.046c,0.046c,,,499714 +PSBBABF,2,Fill-in-the-blank(s),Numeric,"

If the bike is discounted by 20%, how much will Andre pay (before tax)? 

+

 

+

$

",100,100,,,171421 +PSBY59,2,Fill-in-the-blank(s),Numeric,"

A grocer can buy strawberries for $1.38 per pound.

+

 

+

A strawberry order cost $241.50. How many pounds did the grocer order?  

+

 

+

pounds

",175,175,,,119756 +PSBBGEE,4,Fill-in-the-blank(s),Numeric,"

This car dealership pays the salesperson a bonus for selling the car equal to 6.5% of the sale price. How much commission did the salesperson lose when they decided to off a 10% discount on the price of the car?

+

 

+

$

",102.96,102.96,,,205649 +PSBBGGE,1,Fill-in-the-blank(s),Numeric,"

For each gym membership sold, the gym keeps $42 and the employee who sold it gets $8. What is the commission the employee earned as a percentage of the total cost of the gym membership?

+

 

+

%

",16,16,,,205821 +PSBY88,2,Fill-in-the-blank(s),Numeric,"

How much was the tip as a percentage of the bill?  

+

 

+

%

+

Round your answer to the nearest tenth place.

",18.5,18.5,,,120403 +PSBC36,1,Fill-in-the-blank(s),Numeric,"

To make a Koch snowflake, 

+
    +
  • Start with an equilateral triangle. This is step 1.
    • +
  • Divide each side into 3 equal pieces. Construct a smaller equilateral triangle on the middle third. This is step 2.
    • +
  • Do the same to each of the newly created sides. This is step 3.
    • +
  • Keep repeating this process.
    • +
+

 

+

+

 

+

By what percentage does the perimeter increase at step 2?

+

 

+

%

+

Round your answer to the nearest tenth.

",33.3,33.3,,,14960 +PSBC36,2,Fill-in-the-blank(s),Numeric,"

By what percentage does the perimeter increase at step 3?

+

 

+

%

+

Round your answer to the nearest tenth.

",77.8,77.8,,,15059 +PSBC36,3,Fill-in-the-blank(s),Numeric,"

By what percentage does the perimeter increase at step 10?

+

 

+


%

+

Round your answer to the nearest tenth.

",1675.8,1675.8,,,15138 +PSBBGEE,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

A car dealership pays a wholesale price of $12,000 to purchase a vehicle.

+

 

+

The car dealership wants to make a 32% profit.

+

 

+

By how much will they mark up the price of the vehicle?

+

 

+

$

+
+

 

",3840,3840,,,205281 +PRABHX6R,1,Fill-in-the-blank(s),Numeric,"

The original price of a bicycle was $375. Now it is on sale for $295. What percentage of the original price was the markdown?

+

 

+

%

+

Round your answer to the nearest hundredth.

",21.33,21.33,,,16005 +PRABHX6Q,1,Fill-in-the-blank(s),Numeric,"

The bill for a meal was $33.75. The customer left $40.00. What percentage of the bill was the tip?

+

 

+

%

+

Round your answer to the nearest hundredth.

",18.52,18.52,,,15881 +PRABHX6M,1,Fill-in-the-blank(s),Numeric,"

What percentage of the food cost is the tip?

+

 

+

%

+

 

+

",20,20,,,15492 +PSBYZX,1,Fill-in-the-blank(s),Numeric,"

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds, t, by the equation d = 0.15t.

+

 

+

How fast is it flying?

+

 

+

 

+

  miles per second

",0.15,0.15,,,118275 +PSBYZX,2,Fill-in-the-blank(s),Numeric,"

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds, t, by the equation d = 0.15t.

+

 

+

How far will it travel in 30 seconds?  

+

 

+

 

+

miles

+

Round your answer to the nearest tenths place.

",4.5,4.5,,,118610 +PSBYZX,3,Fill-in-the-blank(s),Numeric,"

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds, t, by the equation d = 0.15t.

+

 

+

How long will it take to go 12.75 miles?

+

 

+

 

+

 seconds

",85,85,,,118986 +PSBY59,1,Fill-in-the-blank(s),Algebraic Expression,"

A grocer can buy strawberries for $1.38 per pound.

+

 

+

Write an equation relating c, the cost, and p, the pounds of strawberries.

+

 

+

c =

",1.38p,1.38p,,,119432 +PRABETDD,1,Fill-in-the-blank(s),Numeric,"

Jada is making circular birthday invitations for her friends. The diameter of the circle is 12 cm. She bought 180 cm of ribbon to glue around the edge of each invitation. How many invitations can she make?  

+

 

+

invitations

+

Use 3.14 for π.

",4,4,,,363499 +PSBS6V,1,Fill-in-the-blank(s),Numeric,"

A soccer field is 120 yards long. Han measures the length of the field using a 30-foot-long tape measure and gets a measurement of 358 feet, 10 inches.

+

 

+

What is the amount of the error?

+

 

+

inches

",14,14,,,84788 +PSBS6V,2,Fill-in-the-blank(s),Numeric,"

Express the error as a percentage of the actual length of the field.

+

 

+

%

",0.32,0.32,,,84918 +PSBB9A8,3,Fill-in-the-blank(s),Numeric,"

Jada measured the height of a plant in a science experiment and finds that, to the nearest 14 of an inch, it is 434 inches.

+

 

+

How large could the percent error in Jada’s measurement be?

+


%

+

Round your answer to the tenths place.

",2.6,2.6,,,338934 +PSBB6V4,2,Fill-in-the-blank(s),Numeric,"

Noah's oven thermometer gives a reading that is 2% greater than the actual temperature.

+

 

+

If the thermometer reading is 76ºF, what is the actual temperature?

+

 

+

ºF

+

Round your answer to the nearest tenths place.

",74.5,74.5,,,324897 +PRABG4Y8,1,Fill-in-the-blank(s),Numeric,"

To be labeled as a jumbo egg, the egg is supposed to weigh 2.5 oz. Priya buys a carton of jumbo eggs and measures one of the eggs as 2.4 oz. What is the percent error?  

+

 

+

%

",4,4,,,87236 +PSBB9A8,2,Fill-in-the-blank(s),Numeric,"

Jada measured the height of a plant in a science experiment and finds that, to the nearest 14 of an inch, it is 434 inches.

+

 

+

What is the smallest the actual height of the plant could be?  

+

 

+

inches

",4 5/8,4 5/8,,,338629 +PSBB9A8,1,Fill-in-the-blank(s),Numeric,"

Jada measured the height of a plant in a science experiment and finds that, to the nearest 14 of an inch, it is 434 inches.

+

 

+

What is the largest the actual height of the plant could be?  

+

 

+

inches

",4 7/8,4 7/8,,,338281 +PRABETQU,1,Fill-in-the-blank(s),Numeric,"

A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, what was the percent error in this measurement?

+

 

+

%

+

Round your answer to the nearest hundredths place. 

",0.19,0.19,,,359617 +PSBCVQQ,1,Fill-in-the-blank(s),Numeric,"

Clare has $150 in her bank account. She buys a bike for $200. What is Clare's account balance now?

+

 

+

 $

",-50,-50,,,449847 +PSBCVQQ,2,Fill-in-the-blank(s),Numeric,"

If Clare earns $75 the next week from delivering newspapers and deposits it in her account, what will her account balance be then? 

+

 

+

$

",25,25,,,450077 +PRABETQW,1,Fill-in-the-blank(s),Numeric,"

A farmer estimated that there were 25 gallons of water left in a tank. If this is an underestimate by 16%, how much water was actually in the tank?  

+

 

+

gallons

+

Round your answer to the tenths place.

",29.8,29.8,,,360293 +PRABHUGE,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

 

+

The price of a shirt is $18.50, but you have a coupon that lowers the price by 20%. What is the price of the shirt after using the coupon?

+

 

+

$

+
+

 

",14.8,14.8,,,100670 +PSBD3S,1,Fill-in-the-blank(s),Numeric,"

Money in a particular savings account increases by about 6% after a year.  

+

 

+

How much money will be in the account after one year if the initial amount is $100?  If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",106,106,,,20026 +PSBD3S,2,Fill-in-the-blank(s),Numeric,"

How much money will be in the account after one year if the initial amount is $50?  If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",53,53,,,20199 +PSBD3S,3,Fill-in-the-blank(s),Numeric,"

How much money will be in the account after one year if the initial amount is $200?  If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",212,212,,,20357 +PSBD3S,4,Fill-in-the-blank(s),Numeric,"

How much money will be in the account after one year if the initial amount is $125?  If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",132.5,132.5,,,20515 +PSBD3S,5,Fill-in-the-blank(s),Algebraic Expression,"

How much money will be in the account after one year if the initial amount is x dollars?  If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

dollars

+

Use x as your variable.

",1.06x,1.06x,,,20669 +PSBEGA,1,Fill-in-the-blank(s),Numeric,"

The gas tank in dad’s car holds 12 gallons. The gas tank in mom’s truck holds 50% more than that. How much gas does the truck’s tank hold? 

+

 

+

gallons

",18,18,,,22470 +PRABH67H,1,Fill-in-the-blank(s),Numeric,"

The crowd at a sporting event is estimated to be 3,000 people. The exact attendance is 2,486 people. What is the percent error?

+

 

+

%.

+

Round to the nearest whole percent.

",21,21,,,52062 +PSBDM9U,1,Fill-in-the-blank(s),Numeric,"

Two students are solving the same problem: At a hardware store, they can cut a length of rope off of a big roll, so you can buy any length you like. The cost for 6 feet of rope is $7.50. How much would you pay for 50 feet of rope, at this rate?

+

 

+

Kiran knows he can solve the problem this way.

+

 

+

+

 

+

What would be Kiran's answer?

+

 

+

$

",62.5,62.5,,,584015 +PSBDNDZ,1,Fill-in-the-blank(s),Numeric,"

Different nerve signals travel at different speeds.

+
    +
  • Pressure and touch signals travel about 250 feet per second.
    • +
  • Dull pain signals travel about 2 feet per second.
    • +
+

 

+

How long does it take a person who is 5.5 feet tall to feel an ant crawling on their foot?

+

 

+

about seconds

",0.022,0.022,,,584854 +PSBDNDZ,2,Fill-in-the-blank(s),Numeric,"

How long does it take a person who is 5.5 feet tall to feel a dull ache in their foot?

+

 

+

about seconds

+

 

+

 

",2.75,2.75,,,584945 +PSBDNCG,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

Tyler swims at a constant speed, 5 meters every 4 seconds. How long does it take him to swim 114 meters?

+

 

+

seconds

+		 + + + + + + + + + + + + + + + +
distance (meters)time (seconds)
54
114 
+
",91.2,91.2,,,584326 +PSBDNCG,2,Fill-in-the-blank(s),Numeric," + + + + + + +
+

A factory produces 3 bottles of sparkling water for every 8 bottles of plain water. How many bottles of sparkling water does the company produce when it produces 600 bottles of plain water?

+

 

+

bottles of sparkling water

+

 

+		 + + + + + + + + + + + + + + + +
number of bottles
of sparkling water		number of bottles
of plain water
  
  
+
",225,225,,,584429 +PSBTHK,1,Fill-in-the-blank(s),Numeric,"

A furniture store pays a wholesale price for a mattress. Then, the store marks up the retail price to 150% of the wholesale price. Later, they put the mattress on sale for 50% off of the retail price. A customer just bought the mattress for sale and paid $1,200.

+

 

+

What was the retail price of the mattress, before the discount?

+

 

+

$

",2400,2400,,,86471 +PSBTDG,1,Fill-in-the-blank(s),Numeric,"

A large aquarium of water is being filled with a hose. Due to a problem, the sensor does not start working until some time into the filling process. The sensor starts its recording at the time zero minutes. The sensor initially detects the tank has 225 liters of water in it.

+

 

+

The hose fills the aquarium at a constant rate of 15 liters per minute. What will the sensor read at the time of 5 minutes?  

+

 

+

 

+

liters

",300,300,,,85726 +PSBBBTV,2,Fill-in-the-blank(s),Numeric,"

What is the difference in height between the underwater robotic vehicle and the submarine?  

+

 

+

m

",172,172,,,179464 +PSBCAUR,1,Fill-in-the-blank(s),Numeric,"

Here is a triangular prism. 

+

 

+

+

 

+

What is the volume of the prism?  

+

 

+

 in3

",288,288,,,348188 +PSBCAUR,2,Fill-in-the-blank(s),Numeric,"

What is the surface area of the prism?

+

 

+

 in2

",336,336,,,348314 +PSBDMGC,1,Fill-in-the-blank(s),Numeric,"

A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays $61 for 8 turkey sandwiches. How much does each turkey sandwich add to the cost of the delivery?

+

 

+

$

",7,7,,,579179 +PRABETM2,1,Fill-in-the-blank(s),Numeric,"

A bakery used 25% more butter this month than last month. If the bakery used 240 kilograms of butter last month, how much did it use this month?  

+

 

+

kilograms

+

Round your answer to the nearest whole number.

",300,300,,,24461 +PRABG4SA,1,Fill-in-the-blank(s),Numeric,"

The number of fish in a lake decreased by 25% between last year and this year. Last year there were 60 fish in the lake. What is the population this year? If you get stuck, consider drawing a diagram.

+

 

+

fish

+

 

",45,45,,,331301 +PSBBRRC,1,Fill-in-the-blank(s),Numeric,"

Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156. 

+

 

+

Find the value of the bond when Tyler's mom purchased it. 

+

 

+

$

",150,150,,,251426 +PRABETNQ,1,Fill-in-the-blank(s),Numeric,"

Elena’s aunt bought her a $150 savings bond when she was born. When Elena is 20 years old, the bond will have earned 105% in interest. How much will the bond be worth when Elena is 20 years old? 

+

 

+

$

",307.5,307.5,,,203873 +PRABETNP,1,Fill-in-the-blank(s),Numeric,"

A pair of designer sneakers was purchased for $120. Since they were purchased, their price has increased by 15%. What is the new price? 

+

 

+

$

",138,138,,,203426 +PRABETN5,1,Fill-in-the-blank(s),Numeric,"

A bakery used 30% more sugar this month than last month. If the bakery used 560 kilograms of sugar last month, how much did it use this month?  

+

 

+

 

+

kilograms

",728,728,,,185005 +PSBFY7,1,Fill-in-the-blank(s),Numeric,"

558 cups of water fill 412 identical water bottles. How many cups fill each bottle?

+

 

+

  cups of water

",4-May,4-May,,,30898 +PSBVBE,1,Fill-in-the-blank(s),Numeric,"

Jada’s sister works in a furniture store.

+

 

+

Jada’s sister earns $15 per hour. The store offers her a raise—a 9% increase per hour. After the raise, how much will Jada’s sister make per hour?

+

 

+

  $

",16.35,16.35,,,97399 +PRABETM3,1,Fill-in-the-blank(s),Numeric,"

Last week, the price of oranges at the farmer's market was $1.75 per pound. This week, the price has decreased by 20%. What is the price of oranges this week? 

+

 

+

$ per pound

",1.4,1.4,,,24777 +PSBESA,3,Fill-in-the-blank(s),Numeric,"

The equation d = 3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.

+

 

+

How far will the snail be from the rock after 9 minutes?  

+

 

+

inches

",27,27,,,24068 +PSBCRQU,1,Fill-in-the-blank(s),Numeric,"

Use long division to express the fraction as a decimal.

+

 

+

925=

+

If your answer is a repeating decimal, type the repeated portion of the decimal only once.

+

 

+

For example:    

+

for 3.66¯ you only type in 3.6               

+

for0.45¯ you only type in 0.45

",0.36,0.36,,,426376 +PSBCRQU,2,Fill-in-the-blank(s),Numeric,"

Use long division to express the fraction as a decimal.

+

 

+

1130=

+

If your answer is a repeating decimal, type the repeated portion of the decimal only once.

+

 

+

For example:    

+

for 3.66¯ you only type in 3.6               

+

for0.45¯ you only type in 0.45

",0.36,0.36,,,426537 +PSBD8C,1,Fill-in-the-blank(s),Numeric,"

The value of a new car decreases by about 15% in the first year. 

+

 

+

How much will a car be worth after one year if its initial value was $1,000? If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",850,850,,,20885 +PSBD8C,2,Fill-in-the-blank(s),Numeric,"

How much will a car be worth after one year if its initial value was $5,000? If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",4250,4250,,,21043 +PSBD8C,3,Fill-in-the-blank(s),Numeric,"

How much will a car be worth after one year if its initial value was $5,020? If you get stuck, consider using diagrams or a table to organize your work.

+

 

+

$

",4267,4267,,,21201 +PRABMSH2,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

c - (-3) = 15

+

 

+

c =

",12,12,,,56136 +PRABMSH3,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

d · (-4) = 32

+

 

+

d =

",-8,-8,,,56457 +PRABMSJQ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

25e + -11 = -86

+

 

+

e =

",-3,-3,,,156087 +PRABESCE,1,Fill-in-the-blank(s),Numeric,"

Han wants to buy a $30 ticket to a game, but the pre-order tickets are sold out. He knows there will be more tickets sold the day of the game, with a markup of 200%. How much should Han expect to pay for the ticket if he buys it the day of the game? 

+

 

+

$

",90,90,,,218838 +PSBC9Y8,1,Order / Sort,Ordering,"

Here is a set of signed numbers: 7, -3, 12, -0.8, 0.8, -110, -2

+

 

+

Order the numbers from least to greatest.

","

-0.8

,

7

,

0.8

,

12

,

-110

,

-2

,

-3

","

-0.8

,

7

,

0.8

,

12

,

-110

,

-2

,

-3

",,,518347 +PSBNQH,1,Fill-in-the-blank(s),Numeric,"

Lin deposited $300 in a savings account that has a 2% interest rate per year. How much is in her account after 1 year? 

+

 

+

$

",306,306,,,61213 +PRABQW3K,1,Fill-in-the-blank(s),Numeric,"

The north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of Earth. The sea floor below the north pole is at an elevation of approximately -2.7 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole?

+

 

+

About miles

",7897,7897,,,11247 +PRABETWD,1,Fill-in-the-blank(s),Numeric,"

A bank charges a service fee of $7.50 per month for a checking account. 

+

 

+

A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?

+

 

+

months

",12,12,,,87614 +PSBBH5N,1,Fill-in-the-blank(s),Numeric,"

A fish is 12 meters below the surface of the ocean. What is its elevation?  

+

 

+

meters

",-12,-12,,,214107 +PSBBH5N,3,Fill-in-the-blank(s),Numeric,"

If the bird is directly above the fish, how far apart are they?

+

 

+

meters

",40,40,,,214762 +PSBBNV9,1,Fill-in-the-blank(s),Numeric,"

When a construction worker is on a platform 10 feet above the ground, we can describe her elevation as +10 feet.

+

 

+

A construction worker digs down to 30 feet below the surface of the ground. What is her elevation?

+

 

+

feet

",-30,-30,,,236452 +PSBBNV9,2,Fill-in-the-blank(s),Numeric,"

The construction worker returns to the surface of the ground. What is her elevation?

+

 

+

  feet

",0,0,,,236567 +PRABMSJX,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

12(c+10) = 24

+

 

+

c =

",-8,-8,,,368501 +PSBDAMA,2,Fill-in-the-blank(s),Numeric,"

The dolphin dives 20 feet below the surface of the ocean. What is its new elevation?  

+

 

+

 feet

",-20,-20,,,522388 +PRABETYP,1,Fill-in-the-blank(s),Numeric,"

On the first math exam, 16 students received an A grade. On the second math exam, 12 students received an A grade. What percentage decrease is that?

+


%

",25,25,,,367429 +PRABETYQ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2(a-3) = 14

+

 

+

a =

",10,10,,,367805 +PRABMSJW,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

 -5(b-1) = 40

+

 

+

b =

",-7,-7,,,368183 +PRABMSJY,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

16(d+6)=11

+

 

+

x =

",60,60,,,368816 +PRABJCT4,1,Fill-in-the-blank(s),Numeric,"

If you run 15 laps per practice, how many practices will it take you to run 30 laps?

+

 

+

practices

",2,2,,,259356 +PRABJCT2,1,Fill-in-the-blank(s),Numeric,"

If you eat 5 grapes per minute for 8 minutes, how many grapes will you eat?

+

 

+

grapes

",40,40,,,259069 +PRABJCT3,1,Fill-in-the-blank(s),Numeric,"

If you hear 9 new songs per day for 3 days, how many new songs will you hear?

+

 

+

new songs

+

 

",27,27,,,259215 +PSBCNJY,1,Fill-in-the-blank(s),Numeric,"

Here are the coordinates of rectangle PLAY: (-11, 20), (-11, -3), (-1, 20), (-1, -3). Find the perimeter of this rectangle. See if you can figure out its side lengths without plotting the points.

+

 

+

units

",66,66,,,407631 +PSBNQH,2,Fill-in-the-blank(s),Numeric,"

Lin deposited $300 in a savings account that has a 2% interest rate per year. How much is in her account after 2 years? 

+

 

+

$

",312.12,312.12,,,61289 +PRABJFRR,1,Fill-in-the-blank(s),Numeric,"

Diego wants to sell his bicycle. It cost $150 when he bought it but has depreciated by 15%. How much should he sell it for?

+

 

+

$

",127.5,127.5,,,62493 +PRABETV9,1,Order / Sort,Ordering,"

The value of x is -14.  Order the expressions from least to greatest.

","

x

,

x - 1

,

-1 ÷ x

,

1 - x

","

x

,

x - 1

,

-1 ÷ x

,

1 - x

",,,62186 +PSBTME,1,Fill-in-the-blank(s),Numeric,"

A restaurant bill is $21. You leave a 15% tip. How much do you pay including the tip? 

+

 

+

$

",24.15,24.15,,,87154 +PSB7MU,2,Fill-in-the-blank(s),Numeric,"

To end the mission DeepSea Challenger made a one-hour ascent to the surface. How many seconds is this?  

+

 

+

seconds

",3600,3600,,,156315 +PSBCUB2,3,Fill-in-the-blank(s),Numeric,"

What is the difference between electricity generated in week 1 and week 2? 

+

 

+

$

",2.61,2.61,,,442008 +PSB7MU,3,Fill-in-the-blank(s),Numeric,"

The ascent can be modeled by a different proportional relationship y=kx. What is the value of k in this case?

+

 

+

k =

+

 

",35814/3600,35814/3600,,,156598 +PSBBCNR,1,Fill-in-the-blank(s),Numeric,"

A utility company charges $0.12 per kilowatt-hour for energy a customer uses. They give a credit of $0.025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don't use themselves.

+

 

+

A customer has a charge of $82.04 and a credit of -$4.10 on this month's bill.

+

 

+

What is the amount due this month?

+

 

+

$

",77.94,77.94,,,184283 +PSBBCNR,3,Fill-in-the-blank(s),Numeric,"

How many kilowatt-hours did they generate that they didn't use themselves?

+

 

+

kilowatt-hours

",164,164,,,184499 +PRABEPM8,1,Fill-in-the-blank(s),Numeric,"

Find the area of a square if its side length is 3.5 cm.

+

 

+

square centimeters

",12.25,12.25,,,424891 +PSB7MU,1,Fill-in-the-blank(s),Numeric,"

In 2012, James Cameron descended to the bottom of Challenger Deep in the Marianas Trench; the deepest point in the ocean. The vessel he rode in was called DeepSea Challenger.

+
+

Challenger Deep is 35,814 feet deep at its lowest point.

+

 

+

DeepSea Challenger’s descent was a change in depth of (-4) feet per second. We can use the equation y=-4x to model this relationship, where y is the depth and xis the time in seconds that have passed. How many seconds does this model suggest it would take for DeepSea Challenger to reach the bottom?

+

 

+

seconds

+
",8953.5,8953.5,,,156040 +PRABTGFE,1,Fill-in-the-blank(s),Numeric,"

Solve.

+

 

+

12 = x · 3

+

 

+

x =

",4,4,,,157516 +PRABTGFF,1,Fill-in-the-blank(s),Numeric,"

Solve.

+

 

+

-12=-3y

+

 

+

y =

",4,4,,,157655 +PRABET5F,1,Fill-in-the-blank(s),Numeric,"

Solve.

+

 

+

25t = 6

+

 

+

t =

",15,15,,,156936 +PSBDA53,1,Fill-in-the-blank(s),Numeric,"

Solve the equation. 

+

 

+

5 y + 25 = -13

+

 

+

y =

",-3,-3,,,525202 +PSBCUB2,2,Fill-in-the-blank(s),Numeric,"

The table shows the value of the electricity they used and the value of the electricity they generated each week for a month. What amount is due for this month?

+

 

+

$

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
 used ($)generated ($)
week 113.45-6.33
week 221.78-8.94
week 318.12-7.70
week 424.05-5.36
+

 

",49.07,49.07,,,441900 +PSBDATV,2,Fill-in-the-blank(s),Numeric,"

Find the distance between C and D.  

+

 

+

 units

",7,7,,,523482 +PSBCUB2,4,Fill-in-the-blank(s),Numeric,"

What is the difference between electricity generated in week 2 and week 3? 

+

 

+

$

",-1.24,-1.24,,,442127 +PRABJCHU,1,Fill-in-the-blank(s),Numeric,"

An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?

+

 

+

miles

",360,360,,,9419 +PSBCQBE,1,Fill-in-the-blank(s),Numeric,"

A family goes to a restaurant. When the bill comes, this is printed at the bottom of it: 

+

 

+ + + + + + +
Gratuity Guide For Your Convenience:
15% would be $4.89
18% would be $5.87
20% would be $6.52
+

 

+

How much was the price of the meal? 

+

 

+

$

",32.6,32.6,,,418897 +PRABQAC3,1,Fill-in-the-blank(s),Numeric,"

Diego and Elena are 2 miles apart and begin walking towards each other. Diego walks at a rate of 3.7 miles per hour and Elena walks 4.3 miles per hour. While they are walking, Elena's dog runs back and forth between the two of them, at a rate of 6 miles per hour. Assuming the dog does not lose any time in turning around, how far has the dog run by the time Diego and Elena reach each other?

+

 

+

miles

",1.5,1.5,,,196520 +PSBCHXB,2,Fill-in-the-blank(s),Numeric,"

Solve the equation to find the number of players on each team.

+

 

+

x = players on each team

",15,15,,,388622 +PSBY8A,2,Fill-in-the-blank(s),Numeric,"

At midnight the temperature is -6°C. At midday the temperature is 9°C. By how much did the temperature rise?  

+

 

+

 °C

",15,15,,,120094 +PSBY8A,1,Fill-in-the-blank(s),Numeric,"

The temperature is -2°C. If the temperature rises by 15°C, what is the new temperature?  

+

 

+

 °C

",13,13,,,119645 +PSBBBW4,1,Fill-in-the-blank(s),Numeric," + + + + + +
+

Mai earns $7 per hour mowing her neighbors' lawns. She also earned $14 for hauling away bags of recyclables for some neighbors.

+

 

+
+ + + + + + + +
+
+
+
+

Priya babysits her neighbor’s children.

+

 

+

The table shows the amount of money m she earns in h hours. 

+

 

+

Priya and Mai have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of work hours.

+
+
+
+		 + + + + + + + + + + + + + + + + + + + +
hm
1$8.40
2$16.80
4$33.60
+
+

 

+

How many hours do they each have to work before they go to the movies?

+

 

+

hours

",10,10,,,180036 +PSBB8E7,1,Fill-in-the-blank(s),Numeric,"

+

 

+

 

+

Here are a cone, a sphere, and a cylinder that all have the same radii and heights.

+

 

+

The radius of the cylinder is 5 units. When necessary, express all answers in terms of π.

+

 

+

What is the height of the cylinder?

+

 

+

units

",10,10,,,333699 +PSBB8E7,4,Fill-in-the-blank(s),Algebraic Expression,"

+

 

+

 

+

Here are a cone, a sphere, and a cylinder that all have the same radii and heights.

+

 

+

The radius of the cylinder is 5 units. When necessary, express all answers in terms of π.

+

 

+

What is the volume of the sphere?

+

 

+

cubic units

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

",500/3pi,500/3pi,,,333981 +PRABTSVH,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.  Be prepared to explain your reasoning.

+

 

+

2x+-3=-23

+

 

+

x=

",-10,-10,,,132093 +PSBBKYY,1,Fill-in-the-blank(s),Numeric,"

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.

+

 

+

How much do you think a bus containing 30 people would be charged?

+

 

+

$

",98,98,,,225175 +PSBBKZ8,2,Fill-in-the-blank(s),Numeric,"

A toaster has 4 slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 10 slices.

+

 

+

If someone makes as many slices of toast as possible in 4 minutes and 40 seconds, how many slices do think they can make?

+

 

+

slices

",32,32,,,225864 +PSBCUB2,1,Fill-in-the-blank(s),Numeric," + + + + + + + + + + +
Han's family got a solar panel. Each month they get a credit to their account for the electricity that is generated by the solar panel. The credit they receive varies based on how sunny it is.
+

Current charges: $83.56

+

Solar Credit: -$6.75

+

Amount due: $76.81

+		 +

Here is their electricity bill from January.

+

 

+

In January they used $83.56 worth of electricity and generated $6.75 worth of electricity.

+
+

 

+

In July they were traveling away from home and only used $19.24 worth of electricity. Their solar panel generated $22.75 worth of electricity. What was their amount due in July?

+

 

+

$

",-3.51,-3.51,,,441780 +PRABTSVE,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.  Be prepared to explain your reasoning.

+

 

+

x+6=4

+

 

+

x=

",-2,-2,,,131796 +PRABTSVF,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.  Be prepared to explain your reasoning.

+

 

+

x--4=-6

+

 

+

x=

",-10,-10,,,131886 +PRABTSVG,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.  Be prepared to explain your reasoning.

+

 

+

2(x-1)=-200

+

 

+

x=

",-99,-99,,,131999 +PSB3EH,2,Fill-in-the-blank(s),Numeric,"

What is the area of the base?

+

 

+

square units

",54,54,,,132812 +PSBCNJY,2,Fill-in-the-blank(s),Numeric,"

 Find the area of this rectangle.  See if you can figure out its side lengths without plotting the points.

+

 

+

square units

",230,230,,,407999 +PSBBCHG,1,Fill-in-the-blank(s),Numeric,"

Here is a diagram and its corresponding equation. Find the solution to the equation.

+

 

+ + + + + + + +
 4x + 17 = 23
+

 

+

x =

",1 1/2,1 1/2,,,183371 +PSBBM79,4,Fill-in-the-blank(s),Numeric,"

Use your expressions to find when Han and Priya meet.

+

 

+

t=hours

",2-Mar,2-Mar,,,232533 +PSBDG45,3,Fill-in-the-blank(s),Numeric,"

A car is traveling at a constant speed. Find the number of miles the car travels in 1 hour at the given rate.

+

 

+

7.5 miles in 14hour 

+

 

+

miles

",30,30,,,558904 +PSBDG45,4,Fill-in-the-blank(s),Numeric,"

A car is traveling at a constant speed. Find the number of miles the car travels in 1 hour at the given rate.

+

 

+

1003 miles in 23hour

+

 

+

miles

",50,50,,,559181 +PSBDG45,5,Fill-in-the-blank(s),Numeric,"

A car is traveling at a constant speed. Find the number of miles the car travels in 1 hour at the given rate.

+

 

+

9712 miles in  32hour

+

 

+

miles

",65,65,,,559523 +PSBB5DC,1,Fill-in-the-blank(s),Numeric,"

Here are the vertices of rectangle FROG: (-2, 5), (-2, 1), (6, 5), (6, 1). Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane.

+

 

+

units

+

 

+

 

",24,24,,,316168 +PRABG42X,1,Fill-in-the-blank(s),Numeric,"

Diego scored 9 points less than Andre in the basketball game. Noah scored twice as many points as Diego.  If Noah scored 10 points, how many points did Andre score?  

+

 

+

points

",14,14,,,186074 +PRABQYEC,1,Fill-in-the-blank(s),Numeric,"

A musician performed at three local fairs. At the first he doubled his money and spent $30. At the second he tripled his money and spent $54. At the third, he quadrupled his money and spent $72. In the end he had $48 left. How much did he have before performing at the fairs?

+

 

+

$

",29,29,,,11331 +PSBCB7,1,Fill-in-the-blank(s),Numeric,"

Priya, Han, and Elena, are members of the running club at school.

+

 

+

Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.

+

 

+

How many miles did Priya run last week?

+

 

+

miles

",43,43,,,10737 +PSBCAG,1,Fill-in-the-blank(s),Numeric,"

A family of 6 is going to the fair. They have a coupon for $1.50 off each ticket. If they pay $46.50 for all their tickets, how much does a ticket cost without the coupon? If you get stuck, consider drawing a diagram or writing an equation.

+

 

+

$

",9.25,9.25,,,10359 +PSBMDX,1,Fill-in-the-blank(s),Numeric,"

To make a Koch snowflake:

+

 

+
    +
  • Start with an equilateral triangle that has side lengths of 1. This is step 1.
    • +
  • Replace the middle third of each line segment with a small equilateral triangle with the middle third of the segment forming the base. This is step 2.
    • +
  • Do the same to each of the line segments. This is step 3.
    • +
  • Keep repeating this process.
    • +
+

 

+

+

 

+

What is the perimeter after step 2?

+

 

+

units

",4,4,,,54233 +PSBMDX,2,Fill-in-the-blank(s),Numeric,"

What is the perimeter after step 3?

+

 

+

units

",5 1/3,5 1/3,,,54349 +PRABTREE,1,Fill-in-the-blank(s),Numeric,"

The running club uses the money they raised to pay for a trip to a canyon. At one point during a run in the canyon, the students are at an elevation of 128 feet. After descending at a rate of 50 feet per minute, they reach an elevation of -472 feet. How long did the descent take?

+

 

+

minutes

",12,12,,,11235 +PRABTREC,1,Fill-in-the-blank(s),Numeric,"

One day last week, 6 teachers joined 57 of the members of the running club in an after-school run. Priya counted a total of 31 people running that day. How many members does the running club have?

+

 

+

members

",35,35,,,11040 +PRABTRED,1,Fill-in-the-blank(s),Numeric,"

Priya and Han plan a fundraiser for the running club. They begin with a balance of -80 because of expenses. In the first hour of the fundraiser they collect equal donations from 9 parents, which brings their balance to -44. How much did each parent give?

+

 

+

$

",4,4,,,11131 +PRABTTCQ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

35=3.5s

+

 

+

s =

",10,10,,,178963 +PRABET6F,1,Fill-in-the-blank(s),Numeric,"

A backpack normally costs $25 but it is on sale for $21. What percentage is the discount?  

+

 %

",16,16,,,235060 +PSBBS2B,1,Fill-in-the-blank(s),Numeric,"

The track team is trying to reduce their time for a relay race. First, they reduce their time by 2.1 minutes. Then they are able to reduce that time by 110. If their final time is 3.96 minutes, what was their beginning time?

+

 

+

minutes

",6.5,6.5,,,257823 +PRABTTCN,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

14q=7

+

 

+

q =

",28,28,,,178686 +PRABTTCR,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

80=30t

+

 

+

t=

",3-Aug,3-Aug,,,179089 +PRABTTCP,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

r+18=24

+

 

+

r =

",6,6,,,178835 +PSBB4YA,1,Fill-in-the-blank(s),Numeric,"

Here are the prices for cheese pizza at a certain pizzeria:

+

 

+ + + + + + + + + + + + + + + + + + + +
pizza sizeprice in dollars
small11.60
medium 
large16.25
+

 

+

You had a coupon that made the price of a large pizza $13.00. For what percent off was the coupon?

+

 

+

%

",20,20,,,313329 +PSBB4YA,2,Fill-in-the-blank(s),Numeric,"

Your friend purchased a medium pizza for $10.31 with a 30% off coupon. What is the price of a medium pizza without a coupon? 

+

 

+

$

",14.73,14.73,,,313685 +PSBMBT,2,Fill-in-the-blank(s),Numeric,"

Use any method to find the value for x that makes the equation true.

+

 

+

x=

",32,32,,,53735 +PRABET9F,1,Fill-in-the-blank(s),Numeric,"

One year ago, Clare was 4 feet 6 inches tall. Now Clare is 4 feet 10 inches tall. By what percentage did Clare’s height increase in the last year?  

+

 

+

%

+
+

Round your answer to the nearest whole number.

+
",7,7,,,468619 +PRABQAC5,1,Fill-in-the-blank(s),Numeric,"

Jada and Diego baked a large batch of cookies.

+

 

+
    +
  • They selected 14of the cookies to give to their teachers.
    • +
  • Next, they threw away one burnt cookie.
    • +
  • They delivered 25of the remaining cookies to a local nursing home.
    • +
  • Next, they gave 3 cookies to some neighborhood kids.
    • +
  • They wrapped up 23of the remaining cookies to save for their friends.

    • +
+

After all this, they had 15 cookies left. How many cookies did they bake?

+

 

+

cookies

",108,108,,,344535 +PSBB9SD,1,Fill-in-the-blank(s),Numeric,"

Solve -x=10

+

 

+

x=

",-10,-10,,,341553 +PSBB9SD,3,Fill-in-the-blank(s),Numeric,"

Solve 2x=-20

+

 

+

x=

",-10,-10,,,341780 +PRABEUAS,1,Fill-in-the-blank(s),Numeric,"

A small staircase is made so that the horizontal piece of each step is 10 inches long and 25 inches wide. Each step is 5 inches above the previous one. What is the surface area of this staircase?

+

 

+

+

 

+

inches2

",2850,2850,,,3195 +PSBGU4,1,Fill-in-the-blank(s),Numeric,"

There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. If the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below.

+

 

+

+

 

+

What is the constant of proportionality in this relationship?

+

 

+

 liters per gram

",5.6,5.6,,,35102 +PSBKVV,1,Fill-in-the-blank(s),Numeric,"

The price of a pair of earrings is $22 but Priya buys them on sale for $13.20.

+

 

+

By how much was the price discounted? 

+

 

+

$  

",8.8,8.8,,,50795 +PSBKVV,2,Fill-in-the-blank(s),Numeric,"

What was the percentage of the discount?  

+

 

+

%

",40,40,,,51164 +PSB3EH,4,Fill-in-the-blank(s),Numeric,"

What is the volume of the prism?

+

 

+

cubic units

",432,432,,,133008 +PRABQYE3,1,Fill-in-the-blank(s),Numeric,"

In a day care group, nine babies are five months old and 12 babies are seven months old. How many full months from now will the average age of the 21 babies first surpass 20 months old?

+

 

+

months

",14,14,,,104742 +PSBBZMJ,1,Fill-in-the-blank(s),Numeric,"

Here is a triangular prism.

+

 

+

+

 

+

What is the volume of the prism, in cubic centimeters?

+

 

+

 cm3

",120,120,,,295905 +PSBBZMJ,2,Fill-in-the-blank(s),Numeric,"

What is the surface area of the prism, in square centimeters?

+

 

+

cm2

",184,184,,,296039 +PSBB86H,2,Fill-in-the-blank(s),Numeric,"

Solve the equation by reasoning about the equation or the hanger. 

+

 

+

x =

",0.2,0.2,,,337756 +PRABEUH3,1,Fill-in-the-blank(s),Numeric,"

A passenger on a ship dropped his camera into the ocean. If it is descending at a rate of -4.2 meters per second, how long (in seconds) until it hits the bottom of the ocean, which is at -1,875 meters?  

+

 

+

seconds

+

Round to the nearest second.

",446,446,,,179693 +PRABEUH5,1,Fill-in-the-blank(s),Numeric,"

Diego has a glue stick with a diameter of 0.7 inches. He sets it down 3.5 inches away from the edge of the table, but it rolls onto the floor. How many rotations did the glue stick make before it fell off of the table?

+

 

+

  rotations

+

Round your answer to the nearest tenth.

",1.6,1.6,,,179995 +PSBKFT,1,Fill-in-the-blank(s),Algebraic Expression,"

+

 

+

The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.

+

 

+

What is the area of the base of the cylinder? Express your answer in terms of π.

+

 

+

 cm2

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",16pi,16pi,,,48656 +PRABKCZ5,1,Fill-in-the-blank(s),Numeric,"

+

 

+

Here is a graph of the relationship between the height and volume of some cylinders that all have the same radius, R. An equation that represents this relationship is V=πR2h (use 3.14 as an approximation for π).

+

 

+

What is the radius of these cylinders?

+

 

+

foot

",1,1,,,140189 +PSBDP7M,1,Fill-in-the-blank(s),Numeric,"

The area of a circular table is 225π in2.

+

 

+

What is the radius of the table?

+

 

+

inches

",15,15,,,594916 +PRABMSHZ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

(-7) + b = (-11)

+

 

+

b =

",-4,-4,,,55829 +PSBPAG,2,Fill-in-the-blank(s),Numeric,"

What is the vertical difference between D and A?

+

 

+

units

",-4,-4,,,64016 +PRABTSVK,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

13(x-10)=-4

+

 

+

x =

",-2,-2,,,308593 +PRABTSVJ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

25 - 3x = 40

+

 

+

x =

",-5,-5,,,308518 +PRABPMA7,1,Fill-in-the-blank(s),Numeric,"

Below is a set of data about temperatures. The range of a set of data is the distance between the lowest and highest value in the set. What is the range of these temperatures?

+

 

+

9°C, -3°C, 22°C, -5°C, 11°C, 15°C

+

 

+

degrees

",27,27,,,279176 +PRABEG67,1,Fill-in-the-blank(s),Numeric,"

A 6 oz paper cup is shaped like a cone with a diameter of 4 inches. How many ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup?

+

 

+

ounces

",18,18,,,116167 +PSBYAA,1,Fill-in-the-blank(s),Numeric,"

A graduated cylinder that is 24 cm tall can hold 1 L of water. What is the radius of the cylinder?  Recall that 1 liter (L) is equal to 1000 milliliters (ml), and that 1 liter (L) is equal to 1,000 cm3.

+

 

+

cm

+

Use 3.14 as an approximation for π.

+

Round your answer to the hundredths place.

",3.64,3.64,,,115049 +PSBBQ3R,2,Fill-in-the-blank(s),Numeric,"

Find the number of problems originally assigned by the teacher. If you get stuck, try drawing a diagram to represent the story.

+

 

+

problems

",5,5,,,247823 +PSBBQZF,2,Fill-in-the-blank(s),Numeric,"

Find the number of problems originally assigned by the teacher.  If you get stuck, try drawing a diagram to represent the story.

+

 

+

problems

",4,4,,,247400 +PRABETX5,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

4a = -28

+

 

+

a =

",-7,-7,,,154770 +PRABTTCM,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

95=p+35

+

 

+

p =

",5-Jun,5-Jun,,,178546 +PSBBK68,2,Fill-in-the-blank(s),Numeric,"

Before filling up the pool, it gets lined with a plastic liner. How much liner is needed for this pool if the liner goes up to 4 feet?  

+

 

+

feet2

",298.3,298.3,,,226452 +PSBBFUZ,2,Fill-in-the-blank(s),Numeric,"
+

The data set shows the number of shells that 12 people collected.

+

 

+

4, 5, 5, 4, 1, 6, 8, 2, 2, 2, 4, 5

+

 

+What is the MAD (mean absolute deviation) of this data?  
+
 
+
+

shells

+
",1.5,1.5,,,202431 +PSBBM6,1,Fill-in-the-blank(s),Numeric,"

Imagine a large, solid cube made out of 64 white snap cubes. Someone spray paints all 6 faces of the large cube blue. After the paint dries, they disassemble the large cube into a pile of 64 snap cubes.

+

 

+

How many of those 64 snap cubes have exactly 2 faces that are blue?

+

 

+

snap cubes

",24,24,,,6562 +PRABEUPZ,1,Fill-in-the-blank(s),Algebraic Expression,"

Clare paid 50% more for her notebook than Priya paid for hers. Priya paid x for her notebook and Clare paid y dollars for hers. Write an equation that represents the relationship between y and x.

+
+

 

+

y =

+

Use x as your variable.

+
","3/2x, 1.5x","3/2x, 1.5x",,,247607 +PRABEUPW,1,Fill-in-the-blank(s),Numeric,"

Two angles are complementary. One has a measure of 19 degrees. What is the measure of the other?  

+

 

+

degrees

",71,71,,,247252 +PSBBQGY,2,Fill-in-the-blank(s),Numeric,"

What is the volume of the other piece not pictured?  

+

 

+

in3

",300,300,,,244865 +PSB7BS,2,Fill-in-the-blank(s),Numeric,"
+

B is the intersection of line AC and line ED. Find the measure of each of the angles.

+
+

 

+

+

 

+

 

+
+

Give the measure of angle ABD.  °

+
",70,70,,,154202 +PSBBG5J,1,Fill-in-the-blank(s),Numeric,"

+

 

+

In a deck of cards, each card measures 6 cm by 9 cm.

+

 

+

When stacked, the deck is 2 cm tall, as shown in the photo. Find the volume of this deck of cards.

+

 

+

cm3

",108,108,,,209528 +PSBBG5J,2,Fill-in-the-blank(s),Numeric,"

+

 

+

Then the cards are fanned out, as shown in the picture. The distance from the rightmost point on the bottom card to the rightmost point on the top card is now 7 cm instead of 2 cm. Find the volume of the new stack.

+

 

+

cm3

",108,108,,,209608 +PSBXCT,1,Fill-in-the-blank(s),Numeric," + + + + + + +
The daycare has two sandboxes that are both prisms with regular hexagons as their bases. The smaller sandbox has a base area of 1,146 in2 and is filled 10 inches deep with sand.
+

 

+

It took 14 bags of sand to fill the small sandbox to this depth. What volume of sand comes in one bag? (Round to the nearest whole cubic inch.)

+

 

+

cubic inches

",819,819,,,109845 +PSBXCT,2,Fill-in-the-blank(s),Numeric,"

The daycare manager wants to add 3 more inches to the depth of the sand in the small sandbox. How many bags of sand will they need to buy?

+

 

+

bags of sand

",5,5,,,109969 +PSBXCT,3,Fill-in-the-blank(s),Numeric,"

The daycare manager also wants to add 3 more inches to the depth of the sand in the large sandbox. The base of the large sandbox is a scaled copy of the base of the small sandbox, with a scale factor of 1.5. How many bags of sand will they need to buy for the large sandbox? 

+

 

+

bags of sand

",10,10,,,110096 +PSB9V9,2,Fill-in-the-blank(s),Numeric,"

Use the equation to find how many days a large bag of dog food will last if it contains 210 cups of food.  

+

 

+

days

",140,140,,,168704 +PSBB2XW,1,Fill-in-the-blank(s),Numeric,"

A runner ran 23 of a 5-kilometer race in 21 minutes. They ran the entire race at a constant speed.

+

 

+

How long did it take to run the entire race?  

+

 

+

 minutes

",31.5,31.5,,,302809 +PSB9V9,1,Fill-in-the-blank(s),Algebraic Expression,"

A small dog gets fed 34 cup of dog food twice a day. Using d for the number of days and f for the amount of food in cups, write an equation relating the variables.

+

 

+

f =

+

Use d as your variable.

",1.5d,1.5d,,,168477 +PRABMSPT,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

32 = 43c + 23

+

 

+

 

+

c =

",8-May,8-May,,,376399 +PRABMSPV,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

11.03 = 8.78 + 0.02e

+

 

+

e =

",112.5,112.5,,,376894 +PSBMFA,1,Fill-in-the-blank(s),Numeric,"

Find the area of the figure. 

+


+

 

+

square units

",31,31,,,54527 +PSBBG36,1,Fill-in-the-blank(s),Numeric,"

Between you and your partner, choose who will use each of these two methods to find the surface area of the prism.

+

 

+
    +
  • Adding the areas of all the faces
    • +
  • Using the perimeter of the base.
    • +
+

 

+

Use your chosen method to calculate the surface area of the prism.

+

 

+

Trade papers with your partner, and check their work. Discuss your thinking. If you disagree, work to reach an agreement.

+

 

+

+

 

+

cm2

",234,234,,,209221 +PRABJWDW,1,Fill-in-the-blank(s),Numeric,"

The other day, you calculated the volume of this heart-shaped box of chocolates.

+

 

+ + + + + + + +
+

The depth of the box is 2 inches. How much cardboard is needed to create the box?

+

 

+

in2

+
",131.2,131.2,,,251994 +PSBBRR7,1,Fill-in-the-blank(s),Numeric,"

A wheelbarrow is being used to carry wet concrete. Here are its dimensions.

+

 

+

+

 

+

What volume of concrete would it take to fill the tray?

+

 

+

cm3

",415800,415800,,,251573 +PSBBRR7,2,Fill-in-the-blank(s),Numeric,"

After dumping the wet concrete, you notice that a thin film is left on the inside of the tray. What is the area of the concrete coating the tray? (Remember, there is no top.)

+

 

+

cm2

",26370,26370,,,251741 +PSBC2DU,2,Fill-in-the-blank(s),Numeric,"

If one bottle of paint covers an area of 40 square feet, how many bottles of paint does Andre need to buy for this project?

+

 

+

bottles

",2,2,,,475938 +PSBDFVZ,1,Fill-in-the-blank(s),Numeric,"

Noah is visiting his aunt in Texas. He wants to buy a belt buckle whose price is $25. He knows that the sales tax in Texas is 6.25%.

+

 

+

How much will the tax be on the belt buckle? 

+

 

+

$

+

Round to the nearest cent.

",1.56,1.56,,,553198 +PRABEURV,1,Fill-in-the-blank(s),Numeric,"

Angle H is half as large as angle J. Angle J is one fourth as large as angle K. Angle K has a measure of 240 degrees. What is the measure of angle H?  

+

 

+

°

",30,30,,,429356 +PSBDFVZ,3,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation that represents the total cost, c, of an item whose price is p.

+

 

+

c =

+

Use p as your variable.

",1.0625p,1.0625p,,,553614 +PSBC2DU,1,Fill-in-the-blank(s),Numeric,"

Andre is preparing for the school play. He needs to paint a cardboard box to look like a dresser. The box is a rectangular prism that measures 5 feet tall, 4 feet long, and 212 feet wide. Andre does not need to paint the bottom of the box.

+

 

+

How much cardboard does Andre need to paint?

+

 

+

square feet

",75,75,,,475820 +PSBXCT,4,Fill-in-the-blank(s),Numeric,"

A lawn and garden store is selling 6 bags of sand for $19.50. How much will they spend to buy all the new sand for both sandboxes?

+

 

+

$

",45.5,45.5,,,110217 +PRABEUAZ,1,Order / Sort,Ordering,

Different events have the following likelihoods. Sort them from least to greatest:

,"

56

,

60%

,

0.37

,

 8 out of 10

,

20%

","

56

,

60%

,

0.37

,

 8 out of 10

,

20%

",,,53108 +PSBJDX,1,Order / Sort,Ordering,"

Your teacher will give you some cards that describe events. Order the events from least likely to most likely.

+

 

+

After ordering the first set of cards, pause here so your teacher can review your work.  Then, your teacher will give you a second set of cards.

","
+
+
+
+

Half of the cards in a deck are red and half are black. Shuffle the cards and select the first card. The chance that the card is red.

+
+
+
+
,
+
+
+
+

The weather report says there is a 20% chance of rain tomorrow. The chance of rain tomorrow.

+
+
+
+
,
+
+
+
+

10% of people are left handed. The chance that a randomly chosen person is left handed.

+
+
+
+
,
+
+
+
+

The offspring of two fruit flies in a science experiment have a 75% chance of having redeyes. The chance that the first fly to hatch has red eyes.

+
+
+
+
","
+
+
+
+

Half of the cards in a deck are red and half are black. Shuffle the cards and select the first card. The chance that the card is red.

+
+
+
+
,
+
+
+
+

The weather report says there is a 20% chance of rain tomorrow. The chance of rain tomorrow.

+
+
+
+
,
+
+
+
+

10% of people are left handed. The chance that a randomly chosen person is left handed.

+
+
+
+
,
+
+
+
+

The offspring of two fruit flies in a science experiment have a 75% chance of having redeyes. The chance that the first fly to hatch has red eyes.

+
+
+
+
",,,43774 +PSBJNA,2,Fill-in-the-blank(s),Numeric,"

 What is the total surface area of the two triangular prisms together?

+

 

+

square inches

",144,144,,,44926 +PSBX7V,1,Fill-in-the-blank(s),Numeric,"

Teachers held a basketball shooting contest. Their goal was to make 60 baskets. For the teacher, determine what percentage of the goal they achieved.

+

 

+

Teacher A made 12 baskets.  

+

 

+

 %

",20,20,,,114644 +PRABEUCA,1,Fill-in-the-blank(s),Numeric,"

Here is a diagram of the base of a bird feeder which is in the shape of a pentagonal prism. Each small square on the grid is 1 square inch. 

+

 

+

The distance between the two bases is 8 inches. What will be the volume of the completed bird feeder? 

+

 

+

cubic inches

+

 

+

",336,336,,,302268 +PRABEUCB,1,Fill-in-the-blank(s),Numeric,"

Find the surface area of the triangular prism.  

+

 

+

square units

+

 

+

",60,60,,,302658 +PSBJNA,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between A and B is 5 inches.

+

 

+

+

What is the surface area of the original rectangular prism?  

+

 

+

square inches

",94,94,,,44592 +PSB2UR,3,Fill-in-the-blank(s),Numeric,"

For which value y is (1, y) on the line you just drew?  

+

 

+

y =

",16-Jan,16-Jan,,,129133 +PRABJ6PF,1,Fill-in-the-blank(s),Numeric,"
Complete the equation with a number that makes the expression on the right side of the equal sign equivalent to the expression on the left side.
+
+

 

+

5x − 2.5 + 6x − 3 = (2x − 1)

+
",5.5,5.5,,,599220 +PSBTFF,1,Fill-in-the-blank(s),Numeric,"

Find the measure of the angles in one column. Your partner will work on the other column. Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.

+

 

+ + + + + + + + + + + + + +
column Acolumn Banswer
P is on line m. Find the value of a.  +

Find the value of b

+

.

+		°
",46,46,,,86278 +PSBTFF,2,Fill-in-the-blank(s),Numeric,"

Find the measure of the angles in one column. Your partner will work on the other column. Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.

+

 

+ + + + + + + + + + + + + +
column Acolumn Banswer
+

 Find the value of a.

+

 

+

+		 +

In right triangle LMN, angles L
and M are complementary.
Find the measure of angle L. 

+

 

+

+		°
",39,39,,,86365 +PSBB5WW,2,Fill-in-the-blank(s),Numeric,"

You might think that the angle between the hour and minute hands at 2:20 is 60 degrees, but it is not! The hour hand has moved beyond the 2. Calculate the angle between the clock hands at 2:20.

+

 

+

°

",50,50,,,319333 +PSBTFF,3,Fill-in-the-blank(s),Numeric,"

Find the measure of the angles in one column. Your partner will work on the other column. Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.

+

 

+ + + + + + + + + + + + + +
column Acolumn Banswer
+

Angle C and angle E are supplementary. Find the measure of angle E.

+

 

+

+		 +

 X is on line WY. Find the value of b.

+

+		°
",51,51,,,86456 +PSBTFF,4,Fill-in-the-blank(s),Numeric,"

Find the measure of the angles in one column. Your partner will work on the other column. Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.

+

 

+ + + + + + + + + + + + + +
column Acolumn Banswer
+

Find the value of c.

+

 

+

+		 +

B is on line FW. Find the measure of angle CBW.

+

 

+

+		°
",48,48,,,86560 +PSBTFF,5,Fill-in-the-blank(s),Numeric,"

Find the measure of the angles in one column. Your partner will work on the other column. Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.

+

 

+ + + + + + + + + + + + + +
column Acolumn Banswer
+

Two angles are complementary. One angle
measures 37 degrees. Find the measure of
the other angle.

+		 +

Two angles are supplementary. One angle
measures 127 degrees. Find the measure of
the other angle.

+		°
",53,53,,,86650 +PSBB5WW,1,Fill-in-the-blank(s),Numeric,"

What is the angle between the hour and minute hands of a clock at 3:00?

+

 

+

°

",90,90,,,319240 +PRABMSPU,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

0.3d + 7.9 = 9.1

+

 

+

d =

",4,4,,,376600 +PRABEUGM,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

17a + 34 = 98

+

 

+

 

+

a =

",21/8,21/8,,,375908 +PRABMSPS,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

23 + 15b = 56

+

 

+

 

+

b =

+

Give your answer in fraction form.

",6-May,6-May,,,376147 +PRABEVDE,1,Fill-in-the-blank(s),Numeric,"

A right rectangular prism has a volume of 30 cubic inches. Its length is 13 inch and its width is 3 feet. What is its height in inches?  

+

 

+

 inches

",2.5,2.5,,,1468 +PRABEU4D,1,Fill-in-the-blank(s),Numeric,"

The figure on the left is a trapezoidal prism. The figure on the right represents its base. Find the volume of this prism.

+

 

+

ft3

+
+

 

+

+
",360,360,,,80588 +PSBBGRZ,1,Fill-in-the-blank(s),Numeric,"

A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? 

+

 

+ + + + + + + +
+
+
    +
  • Breads: Italian, white, wheat
    • +
  • Proteins: Tuna, ham, turkey, beans
    • +
  • Cheese: Provolone, Swiss, American, none
    • +
  • Vegetables: Lettuce, tomatoes, peppers, onions, pickles
    • +
+
+
 
+
+

 

+

different sandwiches

",1200,1200,,,207084 +PSBBGRZ,3,Fill-in-the-blank(s),Numeric,"

Andre knows he wants a sandwich that has ham, lettuce, and tomatoes on it. He doesn’t care about the type of bread or cheese. How many of the different sandwiches would make Andre happy?

+

 

+

sandwiches

",12,12,,,207316 +PSBBGRZ,4,Fill-in-the-blank(s),Numeric,"

If a sandwich is made by randomly choosing each of the options, what is the probability it will be a sandwich that Andre would be happy with?

+

 

+

",12/1200,12/1200,,,207427 +PRABGWJ7,1,Fill-in-the-blank(s),Numeric,"

How many different meals are possible if each meal includes one main course, one side dish, and one drink?

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
main coursesside dishesdrinks
grilled chickensaladmilk
turkey sandwichapplesaucejuice
pasta salad—water
+

 

+

There are different meals. 

",18,18,,,207655 +PSBB6JQ,5,Fill-in-the-blank(s),Numeric,"

How long is OT¯?

+

 

+

units

",5,5,,,322882 +PSBBSTU,1,Fill-in-the-blank(s),Numeric,"

A video game developer wants to know how long it takes people to finish playing their new game. They surveyed a random sample of 13 players and asked how long it took them (in minutes).

+

 

+ + + + + + + + + + + + + + + + + + +
1,2359524571,4861,7591,1485481,0371,8641,2459768661,431
+

 

+

Estimate the median time it will take all players to finish this game.

+

 

+

minutes

",1148,1148,,,256298 +PSBBSTU,2,Fill-in-the-blank(s),Numeric,"

A video game developer wants to know how long it takes people to finish playing their new game. They surveyed a random sample of 13 players and asked how long it took them (in minutes).

+

 

+ + + + + + + + + + + + + + + + + + +
1,2359524571,4861,7591,1485481,0371,8641,2459768661,431
+

 

+

Find the interquartile range for this sample.  

+

 

+

minutes

",549.5,549.5,,,256603 +PSBDBNU,1,Fill-in-the-blank(s),Numeric,"

Ten students each attempted 10 free throws. This list shows how many free throws each student made.

+

 

+
8, 5, 6, 6, 4, 9, 7, 6, 5, 9
+
 
+
What is the median number of free throws made?
+
 
+
free throws
",6,6,,,528652 +PSBBFUZ,1,Fill-in-the-blank(s),Numeric,"

The data set shows the number of shells that 12 people collected.

+

 

+

4, 5, 5, 4, 1, 6, 8, 2, 2, 2, 4, 5

+

 

+

What is the mean number of shells collected?

+

 

+

shells

",4,4,,,202276 +PSBDP7M,2,Fill-in-the-blank(s),Numeric,"

What is the circumference of the table, to the nearest inch?

+

 

+

inches

",94,94,,,595052 +PRABJWEE,1,Fill-in-the-blank(s),Numeric,"

A wood floor is made by laying multiple boards end to end. Each board is measured with a maximum percent error of 5%. What is the maximum percent error for the total length of the floor?

+

 

+

%

",5,5,,,57624 +PSBB6JQ,7,Fill-in-the-blank(s),Numeric,"

What is the measure of angle TOE?

+

 

+

°

+

 

+

",90,90,,,323131 +PSBB6JQ,2,Fill-in-the-blank(s),Numeric,"

What is the measure of angle MON?

+

 

+

°

+

 

+

",30,30,,,322472 +PSBRXQ,2,Fill-in-the-blank(s),Numeric,"

What are the measures of its angles?

+

 

+

degrees

",60,60,,,77888 +PSBB7G7,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2(x+5)=3x+1

+

 

+

x=

",9,9,,,328341 +PSB97X,1,Fill-in-the-blank(s),Numeric,"

Find the measure of angle JGH.   

+

 

+

angle JGH =°

+

 

+

 

+

 

+

+

 

+

 

",150,150,,,170408 +PSBBRCB,2,Fill-in-the-blank(s),Numeric,"

If segment AB measures 2 cm, how long is segment A'B'?

+

 

+

cm

",2,2,,,249173 +PSBBBW4,2,Fill-in-the-blank(s),Numeric,"

How much will each of them have earned?

+

 

+

$

",84,84,,,180127 +PSBYAA,3,Fill-in-the-blank(s),Numeric,"

What is the height of the 250 ml mark? Recall that 1 liter (L) is equal to 1000 milliliters (ml), and that 1 liter (L) is equal to 1,000 cm3. 

+

 

+

cm

",6,6,,,115324 +PSBDP7M,3,Fill-in-the-blank(s),Numeric,"

What is the diameter of the table?

+

 

+

inches

",30,30,,,595192 +PSB2VT,3,Fill-in-the-blank(s),Algebraic Expression,"

Write a second equation whose graph goes through (0,2) so the system has one solution at (4,1).

+

 

+

y=

+

Use x as your variable.

+

 

+

",-0.25x+2,-0.25x+2,,,130008 +PSBB9P,1,Fill-in-the-blank(s),Numeric,"

Find the area of the parallelogram.

+

 

+

A:

+

 

+

+

 

+

Parallelogram A: square units.

+

 

",12,12,,,10254 +PSBUPR,5,Fill-in-the-blank(s),Numeric,"

Use the diagram to find the measure of angle ABE.

+

 

+ + + + + + + +
m∠ABE = ° 
",50,50,,,93262 +PSBBDV8,3,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation that describes the relationship between d and h.

+

 

+

d=

+

Use h as your variable.

",4+3h,4+3h,,,190835 +PSBBDV8,4,Fill-in-the-blank(s),Numeric,"

After how many hours of hiking will they be 16 miles from their car?

+

 

+

hours

",4,4,,,190990 +PSB8PB,1,Fill-in-the-blank(s),Algebraic Expression,"

Students are selling raffle tickets for a school fundraiser. They collect $24 for every 10 raffle tickets they sell.

+

 

+

Suppose M is the amount of money the students collect for selling R raffle tickets. Write an equation that reflects the relationship between M and R.

+

 

+

M =

+

Use R as your variable.

","(12/5)R, 12/5R","(12/5)R, 12/5R",,,161738 +PSBU9K,1,Fill-in-the-blank(s),Numeric,"

Find the area of each parallelogram.

+

 

+

+

 

+

Parallelogram A: square units.

",6,6,,,97111 +PSB6QQ,2,Order / Sort,Ordering,

What is the order of all seven points?

,"

C

,

B'

,

A'

,

D

,

A

,

C'

,

B

","

C

,

B'

,

A'

,

D

,

A

,

C'

,

B

",,,151810 +PSBU7P,3,Fill-in-the-blank(s),Numeric,"

What is the measure of angle DEB?

+

 

+

°

",50,50,,,96780 +PSBC7FK,2,Fill-in-the-blank(s),Numeric,"

What is the measure of angle CBE? 

+

 

+

°

",72,72,,,504078 +PSBC7FK,4,Fill-in-the-blank(s),Exact Match,"

Name a triangle congruent to triangle CBE.

+

 

+

Triangle

","BCA, ACB","BCA, ACB",,,504284 +PRABQPRN,1,Fill-in-the-blank(s),Numeric,"

Lines AC and BD intersect at E.

+

 

+

+

 

+

What is the measure of angle BEC?

+

 

+

°

",108,108,,,504723 +PSBB9P,2,Fill-in-the-blank(s),Numeric,"

Find the area of the parallelogram.

+

 

+

B:

+

 

+

+

 

+

Parallelogram B: square units.

",8,8,,,10364 +PSBBCUH,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

Find the area of the shaded region by summing the areas of the shaded triangles.

+

 

+

units2

+
",64,64,,,185261 +PSBBCUH,2,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region by subtracting the area of the unshaded region from the large triangle.

+

 

+

units2

+

 

+

",66,66,,,185386 +PSBBN9H,1,Fill-in-the-blank(s),Numeric,"

Triangles ABC and DEF are similar.

+

 

+

+

 

+

Find the length of segment DF.

+

 

+

units

",2.68,2.68,,,238499 +PSBBN9H,2,Fill-in-the-blank(s),Numeric,"

Triangles ABC and DEF are similar.

+

 

+

+

 

+

 

+

Find the length of segment EF.  

+

 

+

units

",2.01,2.01,,,238581 +PSBB7K6,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3y−4=6−2y

+

 

+

y=

",2,2,,,328823 +PSBE8E,1,Fill-in-the-blank(s),Numeric,"

Triangles ABC and DEF are similar.

+

 

+

+

 

+


Find the length of segment DE.  

+

 

+

units

",1.2,1.2,,,26752 +PSBE8E,2,Fill-in-the-blank(s),Numeric,"

Triangles ABC and DEF are similar.

+

 

+

+

 

+

 

+

Find the length of segment AC.  

+

 

+

units

",5,5,,,26857 +PSBBYVH,2,Fill-in-the-blank(s),Algebraic Expression,"

Rearrange the equation so b is the independent variable.

+

 

+

r=

+

Use bas your variable.

",5-0.8b,5-0.8b,,,291134 +PSBBYVH,3,Fill-in-the-blank(s),Algebraic Expression,"

Rearrange the equation so r is the independent variable.

+

 

+

b=

+

Use r as your variable.

",6.25-1.25r,6.25-1.25r,,,291282 +PSBFF,3,Fill-in-the-blank(s),Numeric,"

Diego has $11 and begins saving $5 each week toward buying a new phone. At the same time that Diego begins saving, Lin has $60 and begins spending $2 per week on supplies for her art class.

+

 

+

How much money do they have at that time?

+

 

+

$

",46,46,,,682 +PSBBE34,1,Fill-in-the-blank(s),Numeric,"

A shorter style of cup is stacked tall. The graph displays the height of the stack in centimeters for different numbers of cups. How much does each cup after the first add to the height of the stack?

+

 

+ + + + + + + +
centimeters
",0.5,0.5,,,197850 +PSBVNW,1,Fill-in-the-blank(s),Algebraic Expression,"

A cable company charges $70 per month for cable service to existing customers.

+

Find a linear equation representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an existing customer.

+

 

+

 

+

y =

",70x,70x,,,99193 +PSBVNW,2,Fill-in-the-blank(s),Algebraic Expression,"

A cable company charges $70 per month for cable service to existing customers.

+

 

+

For new customers, there is an additional one-time $100 service fee. Repeat the previous problem for new customers.

+

 

+

 

+

y =

+

Use x as your variable.

",70x+100,70x+100,,,99441 +PSB2VT,1,Fill-in-the-blank(s),Algebraic Expression,"

Here is the graph for one equation in a system of equations:

+

 

+

+

 

+

Write a second equation for the system so it has infinitely many solutions.

+

 

+

y=

+

Use x as your variable.

",-0.75x+4,-0.75x+4,,,129599 +PSB2VT,2,Fill-in-the-blank(s),Algebraic Expression,"

Write a second equation whose graph goes through (0,1) so the system has no solutions.

+

 

+

y=

+

Use x as your variable.

+

 

+

",-0.75x+1,-0.75x+1,,,129804 +PSB6SB,1,Fill-in-the-blank(s),Numeric,"

A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings.

+

 

+

How much does an ice cream cost with 4 ounces of toppings?

+

 

+

$

",5,5,,,152004 +PRABECCR,1,Fill-in-the-blank(s),Numeric,"

Tyler reads 215 of a book on Monday, 13 of it on Tuesday, 29 of it on Wednesday, and 34 of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?

+

 

+

pages

",180,180,,,231289 +PSBBAB5,2,Fill-in-the-blank(s),Numeric,"

At a sandwich shop, any sandwich costs $4.50, plus $0.25 for each extra topping.

+

 

+

How much does a sandwich cost with 13 extra toppings?

+

 

+

$

",7.75,7.75,,,171543 +PSBBKP8,1,Fill-in-the-blank(s),Numeric,"

+

 

+

This cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

+

 

+

Find the cylinder's radius.

+

 

+

inches

",2,2,,,223532 +PSBCSCN,2,Fill-in-the-blank(s),Numeric,"

What should her answer have been?

+

 

+

x=

",2-Jan,2-Jan,,,430695 +PSBBY9X,2,Fill-in-the-blank(s),Numeric,"

What is the solution to the equation?

+

 

+

x=

",-1,-1,,,293786 +PRABHSS5,1,Fill-in-the-blank(s),Numeric,"

Solve the equation for x.

+

 

+

-(3x-12)=9x-4 

+

 

+

x=

",3-Apr,3-Apr,,,95029 +PRABHSS4,1,Fill-in-the-blank(s),Numeric,"

Solve the equation for x.

+

 

+

x-4=13(6x-54) 

+

 

+

x=

",14,14,,,94876 +PRABHSS3,1,Fill-in-the-blank(s),Numeric,"

Solve the equation for x.

+

 

+

12+6x3=5-92 

+

 

+

x=

+

 

",-3,-3,,,94737 +PRABEGKV,1,Fill-in-the-blank(s),Algebraic Expression," + + + + + + +
+

The volume of this cone is 36π cubic units.

+

 

+

What is the volume of a cylinder that has the same base area and the same height?

+

 

+

cubic units

+

 

+

Enter your answer in terms of π. Use pi to represent the π symbol. For example: 32π would be typed as 32pi

+
",108pi,108pi,,,89267 +PRABQP4G,1,Fill-in-the-blank(s),Numeric,"

Diego has some money in his bank account before he starts a summer job. He deposits the money from the summer job in his bank account and doesn’t spend any of it. After working 3 hours, he has $71 in the account. After working 12 hours, he has $134 in the account.

+

 

+

How much money does Diego earn per hour?

+

 

+

$ per hour

",7,7,,,41676 +PSBBV9C,1,Fill-in-the-blank(s),Numeric,"

Find the area of each square. Each grid square represents 1 square unit.

+

 

+

Square A:   square units

+

 

+

",17,17,,,276040 +PSBBV9C,2,Fill-in-the-blank(s),Numeric,"

Find the area of each square. Each grid square represents 1 square unit.

+

 

+

Square B:   square units

+

 

+

",20,20,,,276196 +PSBPHS,2,Fill-in-the-blank(s),Numeric,"

Find the side length of square ACEG.

+

 

+

s=units

",10,10,,,65477 +PSBCCUR,1,Fill-in-the-blank(s),Numeric,"

Solve this equation.

+

 

+

12x - 7 = 13(x - 12)

+

 

+

x=

",18,18,,,360109 +PSB26A,3,Fill-in-the-blank(s),Numeric,"

The temperature in degrees Fahrenheit, F, is related to the temperature in degrees Celsius, C, by the equation F=95C+32,

+

 

+

There is one temperature where the degrees Fahrenheit and degrees Celsius are the same, so that C=F. Use the expression from the equation, where F is expressed in terms of C. to solve for this temperature.

+

 

+

C=

",-40,-40,,,131520 +PSBBV9C,3,Fill-in-the-blank(s),Numeric,"

Find the area of each square. Each grid square represents 1 square unit.

+

 

+

Square C:   square units

+

 

+

",13,13,,,276338 +PRABPUKN,1,Fill-in-the-blank(s),Numeric,"

In rectangle ABCD, side AB is 8 centimeters and side BC is 6 centimeters. F is a point on BC and E is a point on AB. The area of triangle DFC is 20 square centimeters, and the area of triangle DEF is 16 square centimeters. What is the area of triangle AED?

+

 

+

square centimeters 

",48/5,48/5,,,19954 +PSBBKZG,1,Fill-in-the-blank(s),Numeric,"

Kiran and his cousin work during the summer for a landscaping company. Kiran's cousin has been working for the company longer, so his pay is 30% more than Kiran's. Last week his cousin worked 27 hours, and Kiran worked 23 hours. Together, they earned $493.85. What is Kiran's hourly pay?

+

 

+

$

",8.5,8.5,,,225403 +PSBBJXR,2,Fill-in-the-blank(s),Numeric,"

What is the perimeter of each of the figures?

+

 

+

units

",72,72,,,219375 +PRABEPF6,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

-4(r + 2) = 4(2 − 2r)

+

 

+

r=

",4,4,,,331070 +PSBBV9C,4,Fill-in-the-blank(s),Numeric,"

Find the area of each square. Each grid square represents 1 square unit.

+

 

+

Square D:   square units

+

 

+

",37,37,,,276480 +PSBJ8E,3,Fill-in-the-blank(s),Numeric,"

The amount of water (in liters) in tank 1 after t minutes is 30t+25. The amount of water (in liters) in tank 2 after t minutes is -20t+1000. Find the time when the amount of water will be equal.

+

 

+

minutes

",19.5,19.5,,,47808 +PRABEC24,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

19(2m − 16) = 13(2m + 4)

+

 

+

m=

",-7,-7,,,330854 +PSBDPNS,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

2k − 3(4 − k) = 3k + 4

+

 

+

k =

",8,8,,,591787 +PSBB7P2,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3(n+2)=9(6−n)

+

 

+

n=

",4,4,,,329327 +PSBDEV,2,Fill-in-the-blank(s),Numeric,"

Complete the equation so that it is true for all values of x.

+

 

+

x-2=-(-x)

",2,2,,,16728 +PSB5TR,1,Fill-in-the-blank(s),Algebraic Expression,"

Write the other side of this equation so it's true for all values of x: 

+

 

+

12(6x−10)−x=

",2x-5,2x-5,,,146938 +PRABEDB7,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

3x − 6 = 4(2 − 3x) − 8x

+

 

+

x=

",14/23,14/23,,,148754 +PRABMTN9,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

12z + 6 = 32(z + 6)

+

 

+

z=

+

 

+

 

",-3,-3,,,148929 +PSBCHU3,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

4x − 5 = 2 − x

+

 

+

x=

",5-Jul,5-Jul,,,388305 +PSBCHZZ,3,Fill-in-the-blank(s),Numeric,"

What is the measure of angle D'?

+

 

+

degrees

+

 

+

",45,45,,,389082 +PSBBM79,1,Fill-in-the-blank(s),Algebraic Expression,"

Priya and Han are biking in the same direction on the same path.

+

 

+

Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after t hours.

+

 

+

+

Use t as your variable.

",16t,16t,,,232017 +PSBBM79,2,Fill-in-the-blank(s),Algebraic Expression,"

Priya started riding a half hour before Han. If Han has been riding for t hours, how long has Priya been riding?

+

 

+

hours

+

Use t as your variable.

",t+1/2,t+1/2,,,232208 +PSBBM79,3,Fill-in-the-blank(s),Algebraic Expression,"

Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for t hours.

+

 

+

+

Use t as your variable.

",12(1/2+t),12(1/2+t),,,232362 +PRABEVTR,1,Fill-in-the-blank(s),Numeric,"
+
+
+

A cylinder has radius 1.6 meters. Its volume is 95 cubic meters. Find its height to the nearest tenth of a meter.

+
+
+
+
+
+

 

+
+
+
+

meters

+
+
+
",11.8,11.8,,,596384 +PSBEV,1,Fill-in-the-blank(s),Numeric,"

A circular field has area 14400π square feet.

+

 

+

What is the radius of the field?

+

 

+

feet

",120,120,,,457 +PSB8P6,2,Fill-in-the-blank(s),Numeric,"

What is the volume of the prism?

+

 

+

+

in3

",28.8,28.8,,,162201 +PSBUA8,1,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder has a radius of 4 cm and a height of 5 cm.

+

 

+

What is the volume of the cylinder?

+

 

+

cm3

+

Enter your answer in terms of π

+

Use pi to represent the π symbol .  For example: 32π would be typed as 32pi

",80pi,80pi,,,90927 +PSBEV,3,Fill-in-the-blank(s),Numeric,"

A circular field has area 14400π square feet.

+

 

+

What is the circumference of the field, to the nearest foot?

+

 

+

feet

",754,754,,,662 +PSBEV,2,Fill-in-the-blank(s),Numeric,"

A circular field has area 14400π square feet.

+

 

+

What is the diameter of the field?

+

 

+

feet

",240,240,,,569 +PRABEAH2,1,Fill-in-the-blank(s),Numeric,"

For what value of x do the expressions 2x+3 and 3x-6 have the same value?

+

 

+

x=

",9,9,,,248217 +PSBBNDD,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3d + 16 = -2(5 − 3d)

+

 

+

d=

",26/3,26/3,,,233384 +PSB6C5,2,Fill-in-the-blank(s),Numeric,"

Solve the equation correctly.

+

 

+

x=

",-36,-36,,,150076 +PSBUA8,2,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder has a radius of 4 cm and a height of 5 cm.

+

 

+

What is the volume of the cylinder when its radius is tripled?

+

 

+

cm3

+

Enter your answer in terms of π

+

Use pi to represent the π symbol .  For example: 32π would be typed as 32pi

",720pi,720pi,,,91074 +PRABEFU6,1,Fill-in-the-blank(s),Numeric,"

A one-quart container of tomato soup is shaped like a rectangular prism. A soup bowl shaped like a hemisphere can hold 8 oz of liquid. How many bowls will the soup container fill? Recall that 1 quart is equivalent to 32 fluid ounces (oz).

+

 

+

bowls

",4,4,,,374418 +PSBKFT,2,Fill-in-the-blank(s),Algebraic Expression,"

+

 

+

The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.

+

 

+

How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of π.

+

 

+

 cm3

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",112pi,112pi,,,48812 +PSBKFT,3,Fill-in-the-blank(s),Numeric,"

Give a decimal approximation of your answer to the previous question using 3.14 to approximate π.

+

 

+

cm3

",351.68,351.68,,,48968 +PSBCBG7,1,Fill-in-the-blank(s),Algebraic Expression,"

A hemisphere fits snugly inside a cylinder with a radius of 6 cm. A cone fits snugly inside the same hemisphere.

+

 

+

What is the volume of the cylinder?

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the  symbol.  For example: 32π would be typed as 32pi

",216pi,216pi,,,351677 +PSBBKP8,2,Fill-in-the-blank(s),Numeric,"

+

 

+

This cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

+

 

+

Find the cylinder's height.

+

 

+

inches

+

 

",3,3,,,223692 +PSBC4Z,1,Fill-in-the-blank(s),Numeric,"

Three cylinders have a volume of 2826 cm3.

+

Cylinder A has a height of 900 cm.

+

Cylinder B has a height of 225 cm.

+

Cylinder C has a height of 100 cm.

+

Find the radius of the cylinder. Use 3.14 as an approximation for π.

+

 

+

Cylinder A has a radius of cm

",1,1,,,14914 +PSBC4Z,2,Fill-in-the-blank(s),Numeric,"

Three cylinders have a volume of 2826 cm3.

+

Cylinder A has a height of 900 cm.

+

Cylinder B has a height of 225 cm.

+

Cylinder C has a height of 100 cm.

+

Find the radius of the cylinder. Use 3.14 as an approximation for π.

+

 

+

Cylinder B has a radius of cm

",2,2,,,15072 +PSBCBQB,5,Fill-in-the-blank(s),Numeric,"

Find the hemisphere’s radius if its diameter is 10003 m.

+

m

",500/3,500/3,,,352921 +PSBT2N,1,Fill-in-the-blank(s),Numeric,"

Diego’s history teacher writes a test for the class with 26 questions. The test is worth 123 points and has two types of questions: multiple choice worth 3 points each, and essays worth 8 points each. How many essay questions are on the test?

+

 

+

essay questions.

",9,9,,,89416 +PSBCBG7,3,Fill-in-the-blank(s),Algebraic Expression,"

Estimate the volume of the hemisphere by calculating the average of the volumes of the cylinder and cone.

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the symbol.  For example: 32π would be typed as 32pi

",144pi,144pi,,,351988 +PSBCBQB,4,Fill-in-the-blank(s),Numeric,"

Find the hemisphere’s radius if its diameter is 6 cm.

+

 

+

cm

",3,3,,,352750 +PSBCBQB,1,Fill-in-the-blank(s),Numeric,"

Find the hemisphere’s diameter if its radius is 6 cm.

+

 

+

cm

",12,12,,,352230 +PSBCBQB,3,Fill-in-the-blank(s),Numeric,"

Find the hemisphere’s diameter if its radius is 9.008 ft.

+

 

+

ft

",18.016,18.016,,,352595 +PSBCBQB,2,Fill-in-the-blank(s),Numeric,"

Find the hemisphere’s diameter if its radius is 10003 m.

+

 

+

m

",2000/3,2000/3,,,352407 +PSBNAB,1,Fill-in-the-blank(s),Algebraic Expression,"

A hemisphere with radius 5 units fits snugly into a cylinder of the same radius and height.

+

 

+

+

 

+

Calculate the volume of the cylinder.

+

 

+

cubic units

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",125pi,125pi,,,58581 +PSBG2Q,1,Fill-in-the-blank(s),Algebraic Expression," + + + + + + +
+

A cone with the same base but a height 3 times taller than the given cylinder exists. What is the volume of the cylinder? Express your answer in terms of π.

+

 

+

cubic units

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

+
",36pi,36pi,,,36511 +PSBE8J,2,Fill-in-the-blank(s),Numeric,"

If the volume of the cone is 120 cm3, what is the volume of the cylinder?

+

 

+

cm3

",360,360,,,26766 +PSBBF4M,1,Fill-in-the-blank(s),Numeric,"

The volume V of a cone with radius r is given by the formula V=13πr2h.

+

 

+

+

 

+

The volume of this cone with height 3 units and radius r is V=64π cubic units. This statement is true:  64π=13πr2·3

+

 

+

What does the radius of this cone have to be? 

+

 

+

units

+

 

",8,8,,,203778 +PRABEPM7,1,Fill-in-the-blank(s),Numeric,"

Find the area of a square if its side length is  0.1 meters.

+

 

+

square meters

",0.01,0.01,,,424722 +PSBE8J,1,Fill-in-the-blank(s),Numeric,"

A cone and cylinder have the same height and their bases are congruent circles.

+ + + + + + + +
+

If the volume of the cylinder is 90 cm3, what is the volume of the cone?

+

 

+

cm3

+
",30,30,,,26678 +PSBFC9,2,Fill-in-the-blank(s),Algebraic Expression,"

How many cubic feet of grain can the entire silo hold?

+

 

+

cubic feet

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

+

 

+

",640pi/3,640pi/3,,,27699 +PRABEGMH,1,Fill-in-the-blank(s),Algebraic Expression,"

The volume of this cylinder is 175π cubic units.

+

 

+

+

 

+

What is the volume of a cone that has the same base area and the same height?

+

 

+

cubic units

+

Enter your answer in terms of π.

+

Use pi to represent the symbol. For example: 32π would be typed as 32pi.

",175/3pi,175/3pi,,,180722 +PRABEPMC,1,Fill-in-the-blank(s),Numeric,"

Write the exact value of the side length, in units, of a square whose area in square units is 36.

+

 

+

units

",6,6,,,423276 +PSB4C3,1,Fill-in-the-blank(s),Algebraic Expression,"

A cone has a radius of 3 units and a height of 4 units.

+

 

+

What is this volume of this cone?

+

 

+

cubic units

+

Enter your answer in terms of π.

+

Use pi to represent the symbol. For example: 32π would be typed as 32pi

",12pi,12pi,,,138360 +PRABQP3Y,1,Fill-in-the-blank(s),Numeric,"

Lin has some money in her bank account before she starts a summer job. She deposits the money from the summer job in her bank account and doesn’t spend any of it. After working 4 hours, she has $85 in the account. After working 15 hours, she has $217 in the account. How much money does Lin earn per hour?

+

 

+

$ per hour

",12,12,,,333185 +PSBBCXS,1,Fill-in-the-blank(s),Algebraic Expression,"

There are many right rectangular prisms with one edge of length 5 units and another edge of length 3 units. Let s represent the length of the third edge and V represent the volume of these prisms.

+

 

+

Write an equation that represents the relationship between V and s.

+

 

+

V=

+

Use s as your variable.

",15s,15s,,,185874 +PSBBCZ3,1,Fill-in-the-blank(s),Algebraic Expression,"

There are many cylinders with radius 5 units. Let h represent the height and V represent the volume of these cylinders.

+

 

+

Write an equation that represents the relationship between V and h. Use 3.14 as an approximation of π.

+

 

+

 V=

+

Use h as your variable.

",78.5h,78.5h,,,186281 +PSBBC6R,4,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation that relates the volume V and height h.

+

 

+

V=

+

Use h as your variable.

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

+

 

+

+

 

",75pih,75pih,,,187219 +PSB6NG,3,Fill-in-the-blank(s),Numeric,"

The radius of Sphere B is double that of Sphere A. How many times greater is the volume of B?

+

 

+

times greater

",8,8,,,151596 +PRABQP26,1,Fill-in-the-blank(s),Algebraic Expression,"

A recipe for salad dressing calls for 13 tablespoon of vinegar for every tablespoon of oil. The equation V=13L gives the amount of vinegar needed (V) in terms of the amount of olive oil used (L). Write another equation describing the recipe, this time giving Lin terms of V. 

+

 

+

 

+

L=

+

Use V as your variable.

","3V, V/(1/3)","3V, V/(1/3)",,,595853 +PSB6NG,2,Fill-in-the-blank(s),Algebraic Expression,"

Sphere A has radius 2 cm. Sphere B has radius 4 cm.

+

 

+

Calculate the volume of Sphere B.

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the π symbol. For example:  32π would be typed as 32pi

",256/3pi,256/3pi,,,151429 +PSB6NG,1,Fill-in-the-blank(s),Algebraic Expression,"

Sphere A has radius 2 cm. Sphere B has radius 4 cm.

+

 

+

Calculate the volume of Sphere A.

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the π symbol. For example:  32π would be typed as 32pi

",32/3pi,32/3pi,,,151258 +PRABEK4Q,1,Fill-in-the-blank(s),Numeric,"

The two triangles are similar. Find x.

+

 

+

x=°

+

 

+

",28,28,,,155904 +PRABEHK6,1,Fill-in-the-blank(s),Numeric,"

A farmer has a water tank for cows in the shape of a cylinder with radius of 7 ft and a height of 3 ft. The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity. What is the volume of the tank be when the sensor turns on?

+

 

+

cubic feet

+

Use 3.14 as an approximation for π.

+

Round your answer the nearest whole number.

",92,92,,,165493 +PSBUA8,3,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder has a radius of 4 cm and a height of 5 cm.

+

 

+

What is the volume of the cylinder when its radius is halved?

+

 

+

cm3

+

Enter your answer in terms of π

+

Use pi to represent the π symbol .  For example: 32π would be typed as 32pi

",20pi,20pi,,,91237 +PSBBB3X,3,Fill-in-the-blank(s),Numeric,"

Based on the model, how many points per game would you expect a player who attempts 4.5 free throws per game to have? Round your answer to the nearest tenth of a point per game.

+

 

+

points per game

+

 

+

",20.2,20.2,,,180839 +PSBDP9E,2,Fill-in-the-blank(s),Numeric,"

What is the perimeter of the rectangle?

+

 

+

cm

+

 

+

",22,22,,,595520 +PSBT2V,3,Fill-in-the-blank(s),Numeric,"

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200.

+

 

+

If the car spends no time going 35 miles per hour, how long would the trip take? 

+

 

+

hour(s)

+

Round your answer to the hundredths place.

",3.64,3.64,,,89478 +PSBMK9,1,Fill-in-the-blank(s),Numeric,"

Find a value of x that makes the equation true:

+

 

+
-(-2x + 1) = 9 − 14x
+
 
+
x=
",8-May,8-May,,,55154 +PRABEQAV,1,Fill-in-the-blank(s),Numeric,"
+
+
+

a and b represent the length of a leg of a right triangle, and c represents the length of its hypotenuse. Find the missing length, given the other two lengths.

+

 

+

a=12, b=5, c=?

+

 

+

c=

+
+
+
+
+
 
+
",13,13,,,7859 +PRABQP47,1,Fill-in-the-blank(s),Numeric,"

A cone and cylinder have the same height and their bases are congruent circles. If the volume of the cylinder is 120 in3, what is the volume of the cone?

+

 

+
+

in3

+
",40,40,,,674266 +PRABEVSZ,1,Fill-in-the-blank(s),Algebraic Expression,"

There are 16 cups in a gallon. The equation c=16g gives the number of cups in terms of the number of gallons. Write another equation for this situation, giving the number of gallons in terms of the number of cups: 

+

 

+

g = 

+

Use c as your variable.

",1/16c,1/16c,,,1195 +PSBS5V,1,Fill-in-the-blank(s),Algebraic Expression,"

Here is the graph for one equation in a system of equations.

+

 

+

+

 

+

Write a second equation for the system so it has infinitely many solutions.

+

 

+

y=

+

Use x as your variable.

",3/2x-3,3/2x-3,,,84315 +PSBB6QU,1,Fill-in-the-blank(s),Numeric,"

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn’t touch the money in her account, she can find the amount she’ll have the next year by multiplying her current amount by 1.03.

+

 

+

How much money will Clare have in her account after 1 year?

+

 

+

$

",164.8,164.8,,,323397 +PSBBZQT,3,Fill-in-the-blank(s),Numeric,"

The high temperature this Sunday is expected to be 5 degrees warmer than the high temperature this Saturday. Using the line c=2t-89, how many more cups of lemonade should Lin expect to sell on Sunday than Saturday? 

+

 

+

more cups of lemonade

",10,10,,,296579 +PSBRR9,2,Fill-in-the-blank(s),Numeric,"

The deli owner found that the line s=-t+120 is a good fit for the data. Use this equation to predict how many bowls of soup they might sell on a day when the high temperature is 32 degrees.

+

 

+

bowls of soup

",88,88,,,76861 +PSBRR9,3,Fill-in-the-blank(s),Numeric,"

The high temperature this Saturday is expected to be 10 degrees colder than the high temperature this Friday. Using the line s=-t+120, how many more bowls of soup should the deli expect to sell on Saturday than Friday? 

+

 

+

more bowls of soup

",10,10,,,76975 +PSB3FD,1,Fill-in-the-blank(s),Numeric,"

In many schools, students have the choice between taking art, music, or some other elective.

+

 

+

At Euclid Middle School, there are 200 students in the 8th grade. 40 students are taking art. What percentage of 8th graders at Euclid Middle School are taking art?

+

 

+

%

",20,20,,,132871 +PSB3FD,3,Fill-in-the-blank(s),Numeric,"

At Newton Middle School, there are 320 students in the 8th grade. 54 are taking music. What percentage of 8th graders at Newton Middle School are taking music?

+

 

+

%

",16.875,16.875,,,133098 +PSBB6QU,2,Fill-in-the-blank(s),Numeric,"

How much money will Clare have in her account after 2 years?

+

 

+

$

",169.74,169.74,,,323576 +PSBB6QU,3,Fill-in-the-blank(s),Numeric,"

How much money will Clare have in her account after 5 years?

+

 

+

$

",185.48,185.48,,,323787 +PRABEQ5G,1,Fill-in-the-blank(s),Numeric,"

Find the value of the variable, to the nearest tenth.

+

 

+

+

 

+

x≈

",7.1,7.1,,,162344 +PRABEPM5,1,Fill-in-the-blank(s),Numeric,"

Find the area of a square if its side length is 37 units.

+

 

+

square unit

",Sep-49,Sep-49,,,424393 +PSBBRT8,1,Order / Sort,Ordering,"

Let a, b, c, d, e, and f be positive numbers.

+

 

+

Given these equations, arrange a, b, c, d, e, and f from least to greatest.

","

b3 = 8

,

f3 = 7

,

d3 = 9

,

e2 = 8

,

a2 = 9

,

c2 = 10

","

b3 = 8

,

f3 = 7

,

d3 = 9

,

e2 = 8

,

a2 = 9

,

c2 = 10

",,,252048 +PRABEQMW,1,Fill-in-the-blank(s),Numeric,"

Find the distance between the pair of points. If you get stuck, try plotting the points on graph paper.

+

 

+

X=(5,0) and Y=(-4,0)

+

 

+

units

",9,9,,,332409 +PRABEQME,1,Fill-in-the-blank(s),Numeric,"

What is the side length of a cube with a volume of  1,000 cubic centimeters?

+

 

+

centimeters

",10,10,,,330781 +PRABEQMC,1,Fill-in-the-blank(s),Numeric,"

What is the volume of a cube with a side length of  113 feet?

+

 

+

cubic feet

",11,11,,,330485 +PRABEQMB,1,Fill-in-the-blank(s),Numeric,"

What is the volume of a cube with a side length of 4 centimeters?

+

 

+

cubic centimeters

",64,64,,,330320 +PRABEQMF,1,Fill-in-the-blank(s),Algebraic Expression,"

What is the side length of a cube with a volume of 23 cubic inches?

+

 

+

inches

+

Type your answer in the following format:

+

cbrt(7) for 7 or 12cbrt(7) for127 

",cbrt(23),cbrt(23),,,330959 +PRABEQ7Q,1,Fill-in-the-blank(s),Numeric,"

Find the value of the variable, to the nearest tenth.

+

 

+

+

 

+

f≈

+
 
",5.4,5.4,,,162490 +PRABEQ44,1,Order / Sort,Ordering,

Order the following values from least to greatest:

,"

5303

,

192

,

121

,

273

,

π

,

48

","

5303

,

192

,

121

,

273

,

π

,

48

",,,162174 +PRABEPDG,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

-2(3x-4)=4(x+3)+6

+

 

+

x= 

",-1,-1,,,155341 +PRABMT57,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

12z+4-6=-2z+8

+

 

+

z=

",24/5,24/5,,,155556 +PSBPHS,1,Fill-in-the-blank(s),Numeric,"

Find the area of square ACEG.

+

 

+

A=square units

+

 

+

",100,100,,,65337 +PRABEQCF,1,Fill-in-the-blank(s),Numeric,"

A man is trying to zombie-proof his house. He wants to cut a length of wood that will brace a door against a wall. The wall is 4 feet away from the door, and he wants the brace to rest 2 feet up the door. About how long should he cut the brace?

+

 

+

+

 

+

feet

+

Round your answer to the nearest tenth. 

",4.5,4.5,,,487312 +PSBBSR,4,Fill-in-the-blank(s),Numeric,"

If the volume of each prism is 60 units3 what would be the height of prism C?

+

 

+

 

+

units

",5,5,,,7407 +PSBYWG,1,Fill-in-the-blank(s),Numeric,"

Find the distances between the three points shown.

+

 

+

+

 

+

The distance between (-14,9)  and (-14,-3) is   units.

",12,12,,,118249 +PSBYWG,2,Fill-in-the-blank(s),Numeric,"

The distance between (16,-3)  and (-14,-3) is   units.

",30,30,,,118376 +PSBYWG,3,Fill-in-the-blank(s),Algebraic Expression,"

The distance between (-14,9)  and (16,-3) is   units.

+

 

+

Type your answer in the following format: sqrt(7) for 7 or 12sqrt(7) for 127.

",sqrt(1044),sqrt(1044),,,118522 +PRABEQ7R,1,Fill-in-the-blank(s),Numeric,"

Find the value of the variable, to the nearest tenth.

+

 

+

+

 

+

d≈

",15.1,15.1,,,162661 +PSBBWD2,3,Fill-in-the-blank(s),Numeric,"

Find the length of a side of a square if its area is 0.49 square units.

+

 

+

units

",0.7,0.7,,,277038 +PRABEQ4F,1,Fill-in-the-blank(s),Numeric,"

Find the positive solution to m3=8. If the solution is irrational, write the solution using square root or cube root notation.

+

 

+

m=

+

If needed, type your answer in the following format:

+

sqrt(7) for 73v or 12sqrt(7) for 1273 

",2,2,,,161664 +PRABEQ4G,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Find the positive solution to c3=343. If the solution is irrational, write the solution using square root or cube root notation.

+

 

+

c=

+

If needed, type your answer in the following format:

+

sqrt(7) for 73v or 12sqrt(7) for 1273 

+

 

+
+
+
+
+
 
+
",7,7,,,161838 +PRABMQEV,1,Fill-in-the-blank(s),Numeric,"

Take a 3-4-5 right triangle, add on the squares of the side lengths, and form a hexagon by connecting vertices of the squares as in the image. What is the area of this hexagon?

+

 

+

+

 

+

square units

",110,110,,,354090 +PRABESJE,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Find the positive solution to y3=1. If the solution is irrational, write the solution using square root or cube root notation.

+

 

+

y=

+
+
+
",1,1,,,356901 +PRABESJF,1,Fill-in-the-blank(s),Numeric,"

Find the positive solution to w2=36. If the solution is irrational, write the solution using square root or cube root notation.

+

 

+

w=

",6,6,,,357082 +PRABESJD,1,Fill-in-the-blank(s),Numeric,"

Find the positive solution to z2=1. If the solution is irrational, write the solution using square root or cube root notation.

+

 

+

z=

",1,1,,,356718 +PRABESJG,1,Fill-in-the-blank(s),Numeric,"

Find the positive solution to h3=64. If the solution is irrational, write the solution using square root or cube root notation.

+

 

+

h=

",4,4,,,357261 +PSBCBY8,1,Fill-in-the-blank(s),Numeric,"

Here is a right square pyramid.

+

 

+

+

 

+

What is the measurement of the slant height l of the triangular face of the pyramid? If you get stuck, use a cross section of the pyramid.

+

 

+

units

",17,17,,,354627 +PRABEPMZ,1,Fill-in-the-blank(s),Numeric,"

Write the exact value of the side length, in units, of a square whose area in square units is 0.0001.

+

 

+

units

",0.01,0.01,,,423932 +PRABMECE,1,Fill-in-the-blank(s),Algebraic Expression," + + + + + + +
+

A farmer has a grassy patch of land enclosed by a fence in the shape of a square with a side length of 4 meters. To make it a suitable home for some animals, the farmer would like to carve out a smaller square to be filled with water, as in the figure.

+


What should the side length of the smaller square be so that half of the area is grass and half is water?

+

 

+

meters

+

 

+

Type your answer in the following format:

+

sqrt(7) for 7 or 12sqrt(7) for 7.

+
",sqrt(8),sqrt(8),,,307803 +PRABEPMD,1,Fill-in-the-blank(s),Algebraic Expression,"

Write the exact value of the side length, in units, of a square whose area in square units is 37.

+

 

+

units

+

If needed type your answer in the following format:

+

sqrt(7) for 7 or 12sqrt(7) for 127 

+

 

",sqrt(37),sqrt(37),,,423450 +PRABPT5M,1,Fill-in-the-blank(s),Numeric," + + + + + + +
+

One vertex of the equilateral triangle is in the center of the square, and one vertex of the square is in the center of the equilateral triangle. What is x?

+

 

+

x=°

+
",105,105,,,94804 +PRABEPN8,1,Fill-in-the-blank(s),Numeric,"

The high school is hosting an event for seniors but will also allow some juniors to attend. The principal approved the event for 200 students and decided the number of juniors should be 25% of the number of seniors.  How many juniors will be allowed to attend?  If you get stuck, try writing two equations that each represent the number of juniors and seniors at the event.

+

 

+

juniors

",40,40,,,146750 +PSBBSR,3,Fill-in-the-blank(s),Numeric,"

If the volume of each prism is 60 units3 what would be the height of prism B?

+

 

+

units

",10,10,,,7280 +PSBDCHG,2,Fill-in-the-blank(s),Numeric,"

Based on the model, how many points will a player have if he has 30 assists?

+

 

+

points

+

 

+

",46.2,46.2,,,533341 +PSBKZ4,1,Fill-in-the-blank(s),Numeric,"

A right triangle has sides of length 3, 4, and x.

+

 

+

Find x if it is the hypotenuse.

+

 

+

x=

",5,5,,,52069 +PSBCBU,2,Fill-in-the-blank(s),Algebraic Expression,"

a2=

+

 

+

Use the ^ symbol to represent an exponent.

+

For example: 52 should be typed as 5^2

+

 

",c^2-b^2,c^2-b^2,,,10564 +PSBCBU,3,Fill-in-the-blank(s),Algebraic Expression,"

b2=

+

 

+

Use the ^ symbol to represent an exponent.

+

For example: 52 should be typed as 5^2

+

 

",c^2-a^2,c^2-a^2,,,10729 +PRABP56U,1,Fill-in-the-blank(s),Numeric,"

The spiral in the figure is made by starting with a right triangle with both legs measuring one unit each. Then a second right triangle is built with one leg measuring one unit, and the other leg being the hypotenuse of the first triangle. A third right triangle is built on the second triangle’s hypotenuse, again with the other leg measuring one unit, and so on.

+

 

+

+

 

+

Find the length, x, of the hypotenuse of the last triangle constructed in the figure.

+

 

+

x=

",4,4,,,223006 +PRABKB2P,1,Fill-in-the-blank(s),Algebraic Expression,"

Find c.

+

 

+

+

 

+

c=units

+

 

+

Type your answer in the following format: sqrt(7) for 7 or 12sqrt(7) for 127. 

",sqrt(50),sqrt(50),,,222369 +PRABMCJQ,1,Fill-in-the-blank(s),Algebraic Expression,"

A right triangle has sides of length 2.4 cm and 6.5 cm. What is the length of the hypotenuse?

+

 

+

cm

+

 

+

Type your answer in the following format: sqrt(7) for 7 or 12sqrt(7) for 127. 

",sqrt(48.01),sqrt(48.01),,,222626 +PRABMCJP,1,Fill-in-the-blank(s),Algebraic Expression,"

Find b.

+

 

+

+

 

+

b= units

+

 

+
+
+
Type your answer in the following format: sqrt(7) for 7 or 12sqrt(7) for 127. 
+
+
",sqrt(18),sqrt(18),,,222494 +PRABMCJR,1,Fill-in-the-blank(s),Algebraic Expression,"

A right triangle has a side of length 14 and a hypotenuse of length 13.  What is the length of the other side?

+

 

+

units

+

 

+

Type your answer in the following format: sqrt(7) for 7 or 12sqrt(7) for 127. 

",sqrt(7/144),sqrt(7/144),,,222741 +PRABMCJS,1,Fill-in-the-blank(s),Numeric," + + + + + +
+
+

Find the value of x in the figure.

+

 

+

x=units

+
+
+

",3,3,,,222860 +PSBJU5,1,Fill-in-the-blank(s),Algebraic Expression,"

Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 17 cm long and the cup is 15 cm tall. How much water can the cup hold?

+

 

+

(The surface area of a cylinder is 2πr2+2πrh The volume of a cylinder is πr2h.)

+

 

+

+

 

+

cm3

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",240pi,240pi,,,46033 +PRABQP48,1,Fill-in-the-blank(s),Numeric,"

How long is the segment from -5, 2 to -5, -8?

+

 

+

units

",10,10,,,37999 +PSBBSR,2,Fill-in-the-blank(s),Numeric,"

If the volume of each prism is 60 units3 what would be the height of prism A?

+

 

+

 

+

units

",7.5,7.5,,,7158 +PSBBSR,5,Fill-in-the-blank(s),Numeric,"

If the volume of each prism is 60 units3 what would be the height of prism D?

+

 

+

 

+

units

",12,12,,,7514 +PRABEVX6,1,Fill-in-the-blank(s),Algebraic Expression,"

Find the length of the segment that joins the points (-5, 4) and (6, -3).

+

 

+

+

 

+

units

+

Type your answer in the following format: sqrt(7) for.7.

+

 

",sqrt(170),sqrt(170),,,46660 +PSBB6QT,2,Fill-in-the-blank(s),Numeric,"

What about whole numbers starting with 1 and ending with 1,000?

+

 

+

whole numbers

",31,31,,,324258 +PRABGZF3,1,Fill-in-the-blank(s),Numeric,"

A cube has side length of 4 cm. What is its volume?

+

 

+

cubic cm

",64,64,,,48585 +PSBX8G,3,Fill-in-the-blank(s),Numeric Expression,"

Write an expression for the surface area, in square units.

+

 

+

 

+

square units 

",6*17^2,6*17^2,,,115025 +PRABGZF5,1,Fill-in-the-blank(s),Algebraic Expression,"

A cube has side length of s units. What is its volume?  

+

 

+

cubic units

",sss,sss,,,48967 +PSBX8G,4,Fill-in-the-blank(s),Numeric Expression,"

Write an expression for the volume, in cubic units.

+

 

+

cubic inches

+

 

",17^3,17^3,,,115150 +PSBBUYK,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

The distance across a sink drain is 3.8 cm.  

+

 

+

","

circumference

,

diameter

,

radius

",

diameter

,,,268814 +PSBTWZ,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region(s) of the figure.

+

+

 

+

 

+

cm2

",15,15,,,88950 +PSBBVFW,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

The distance from the tip of a slice of pizza to the crust is 7 in.

+

 

+

","

circumference

,

radius

,

diameter

",

radius

,,,271552 +PSBBVBE,3,Fill-in-the-blank(s),Numeric,"

The fence around a circular pool is 75 ft long.

+

 

+

Estimate the radius of the circle: 

+

 

+

feet

",12,12,,,271219 +PSBBVFW,2,Fill-in-the-blank(s),Numeric,"

The distance from the tip of a slice of pizza to the crust is 7 in.

+

 

+

Estimate the diameter of the circle: 

+

 

+

inches

",14,14,,,271772 +PSBBVK9,2,Fill-in-the-blank(s),Numeric,"

Breaking a cookie in half creates a straight side 10 cm long.

+

 

+

Estimate the radius of the circle: 

+

 

+

cm

",5,5,,,272544 +PSBBVK9,3,Fill-in-the-blank(s),Numeric,"

Breaking a cookie in half creates a straight side 10 cm long.

+

 

+

Estimate the circumference of the circle: 

+

 

+

cm

+

Use 3.14 for π.  

+

Round your answer to the nearest whole number.

",31,31,,,272853 +PSBBVSF,3,Fill-in-the-blank(s),Numeric,"

The length of the metal rim around a glass lens is 190 mm.  

+

 

+

Estimate the radius of the circle: 

+

 

+

mm

+

Round your answer to the nearest whole number.

",30,30,,,273737 +PSBBUSX,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

The length of the minute hand on a clock is 5 in.  

+

 

+

+

 

","

diameter

,

circumference

,

radius

",

radius

,,,267963 +PSBBVBE,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

The fence around a circular pool is 75 ft long.

+

 

+

","

radius

,

circumference

,

diameter

",

circumference

,,,270634 +PSBBVK9,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

Breaking a cookie in half creates a straight side 10 cm long.

+

 

+

","

radius

,

diameter

,

circumference

",

diameter

,,,272370 +PSBBVV9,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

From the center to the edge of a DVD measures 60 mm.

+

 

+

 

","

diameter

,

circumference

,

radius

",

radius

,,,274114 +PSBBUYK,2,Fill-in-the-blank(s),Numeric,"

The distance across a sink drain is 3.8 cm.  

+

 

+

Estimate the radius of the circle:

+

 

+

  cm

",1.9,1.9,,,269095 +PSBBVSF,1,Fill-in-the-blank(s),Drop Down,"

Identify the measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

+

 

+

The length of the metal rim around a glass lens is 190 mm.  

+

 

+

+

 

","

Radius

,

Circumference

,

Diameter

",

Circumference

,,,273221 +PRABQBHC,1,Fill-in-the-blank(s),Numeric,"

Your teacher will give you 1 square and some small, medium, and large right triangles. The area of the square is 1 square unit.

+

 

+

 

+

Find a way to use all of the pieces to compose a single large square. What is the area of this large square?

+

 

+

 

+

square units

",8,8,,,54202 +PSBG9Y,1,Fill-in-the-blank(s),Numeric,"

A librarian is curious about the habits of the library's patrons. He records the type of item that the first 10 patrons check out from the library.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
patronitem type
1fiction book
2non-fiction book
3fiction book
4fiction book
5audiobook
6non-fiction book
7DVD
8non-fiction book
9fiction book
10DVD
+

 

+

Based on the information from these patrons, estimate the probability that the next patron will check out a fiction book?

+

 

+

",10-Apr,10-Apr,,,37467 +PSBC77E,3,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

30 ÷ 12

+

 

+

","2.50, 2.5","2.50, 2.5",,,508286 +PSBBSR,1,Order / Sort,Ordering,"

There are 4 different prisms that all have the same volume. Here is what the base of each prism looks like.

+

 

+

+

 

+

Order the prisms from shortest to tallest.

","

,

,

,

","

,

,

,

",,,6946 +PSBBQKA,2,Fill-in-the-blank(s),Numeric,"

The volume of both of these trapezoidal prisms is 24 cubic units. Their heights are 6 and 8 units, as labeled. What is the area of a trapezoidal base of the prism with a height of 8 units?  

+

 

+

units2

+

 

+

",3,3,,,245152 +PSBBAK8,4,Fill-in-the-blank(s),Algebraic Expression,"

For diameter and circumference of a circle, what is the constant of proportionality?

+

 

+

 

+

Use pi to represent the symbol

+

For example:

+

32π would be typed as 32pi

+

 

+

","pi, 1/pi, 1/(pi)","pi, 1/pi, 1/(pi)",,,172894 +PSBBPPB,1,Fill-in-the-blank(s),Numeric,"

Noah drew a scaled copy of Polygon P and labeled it Polygon Q.  

+

+

 

+

If the area of Polygon P is 5 square units, what scale factor did Noah apply to Polygon P to create Polygon Q?

+

 

+

",3,3,,,240434 +PSBDBS6,1,Fill-in-the-blank(s),Numeric,"

This dot plot shows the number of coins in 10 students’ pockets.

+

 

+
+
 
+

What is the mean of this data?  

+

 

+

 coins

",3,3,,,529389 +PSBDBS6,3,Fill-in-the-blank(s),Numeric,"

This dot plot shows the number of coins in 10 students’ pockets.

+

 

+
+

 

+

What is the MAD (mean absolute deviation) of this data?  

+

 

+

 coins

",2.2,2.2,,,529581 +PSBCCG,2,Fill-in-the-blank(s),Numeric,"

The scale of a map says that 3 cm represents 5 km.

+

 

+

What actual distance is represented by 15 cm on the map?

+

 

+

kilometers

",25,25,,,10844 +PSBKZ4,2,Fill-in-the-blank(s),Algebraic Expression,"

A right triangle has sides of length 3, 4, and x.

+

 

+

Find x if it is one of the legs.

+

 

+

x=

+

 

+

Type your answer in the following format: sqrt(5) for 7

",sqrt(7) ,sqrt(7) ,,,52189 +PSBNYP,1,Fill-in-the-blank(s),Numeric,"

Here are two triangles.

+

 

+

+

 

+

What is the scale factor from triangle ABC to triangle A'B'C' ?

+

 

+

","1 1/3, 4/3","1 1/3, 4/3",,,62717 +PSB33P,2,Fill-in-the-blank(s),Algebraic Expression,"

Here are two line segments with lengths e and f. 

+

 

+

+

 

+

 

+

What is the length of f?

+

 

+

units

+

Type your answer in the following format: sqrt(7) for 7

",sqrt(18),sqrt(18),,,136831 +PSB33P,1,Fill-in-the-blank(s),Algebraic Expression,"

Here are two line segments with lengths e and f. 

+

 

+

+

 

+

 What is the length of e?

+

 

+

units

+

Type your answer in the following format: sqrt(7) for 7

",sqrt(17),sqrt(17),,,136694 +PSBBX35,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Last month, there were 4 sunny days for every rainy day. If there were 30 days in the month, how many days were rainy? If you get stuck, consider using a tape diagram.

+

 

+

days

+
+
+
",6,6,,,286756 +PSBCC,2,Fill-in-the-blank(s),Numeric,"

Given the equation y = ‐3x + 2.5:

+

 

+

When x is -1.5, what value of y makes the equation true?

+
 
+

 

+

y =

",7,7,,,207 +PRABMSG3,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression. If the answer is not a whole number, write your answer as a fraction.

+

 

+

-24 · -76

+

 

+

",28,28,,,38268 +PSBBX6F,1,Fill-in-the-blank(s),Numeric,"

Noah entered a 100-mile bike race. He knows he can ride 32 miles in 160 minutes. At this rate, how long will it take him to finish the race? Use each table to find the answer.

+

 

+

minutes

+

 

+ + + + + + + +
+ + + + + + + + + + + + + + + + + + + +
 Distance (miles)Elapsed Time (minutes)
32160
1 
100 
+		 + + + + + + + + + + + + + + + + + + + + + + + +
Distance (miles)Elapsed Time (minutes)
32160
96 
4 
100 
+
+

 

",500,500,,,287230 +PRABFFFD,1,Fill-in-the-blank(s),Numeric,"

Andre is planting saplings (baby trees). It takes him 30 minutes to plant 3 saplings. If each sapling takes the same amount of time to plant, how long will it take Andre to plant 14 saplings? If you get stuck, consider using the table.

+

 

+

minutes

+

 

+ + + + + + + + + + + + + + + + + + + +
Number of SaplingsTime in Minutes
330
1 
4 
",140,140,,,406068 +PSBRSJ,1,Fill-in-the-blank(s),Numeric,"

Two horses start a race at the same time. Horse A gallops at a steady rate of 32 feet per second and Horse B gallops at a steady rate of 28 feet per second. After 5 seconds, how much farther will Horse A have traveled? 

+

 

+

feet

",20,20,,,76912 +PSBCAT8,1,Fill-in-the-blank(s),Numeric,"

A kangaroo hops 2 kilometers in 3 minutes. At this rate:

+

 

+

How long does it take the kangaroo to travel 5 kilometers?  

+

 

+

minutes

",7.5,7.5,,,347954 +PSBCAT8,2,Fill-in-the-blank(s),Numeric,"

A kangaroo hops 2 kilometers in 3 minutes. At this rate:

+

 

+

How far does the kangaroo travel in 2 minutes?

+

 

+

kilometers

",3-Apr,3-Apr,,,348162 +PSB2Z9,1,Fill-in-the-blank(s),Numeric,"

For the following equation, find y when x = -3.

+

 

+

y = 6x + 8

+

 

+

y =

",-10,-10,,,130584 +PSBQ8E,1,Fill-in-the-blank(s),Numeric,"

Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories.

+

 

+

If she eats 2 servings of granola, how many calories does she eat?  

+

 

+

calories

",700,700,,,73890 +PSBQ8E,2,Fill-in-the-blank(s),Numeric,"

If she wants to eat 175 calories of granola, how many servings should she eat?  

+

 

+

servings

",2-Jan,2-Jan,,,74049 +PSBB9N5,2,Fill-in-the-blank(s),Numeric,"

Imagine you scale Triangle B by a scale factor of 12 to get Triangle C. How many times bigger will the side lengths of Triangle C be when compared with Triangle A?

+

 

+

",4-Jan,4-Jan,,,341117 +PSBB9N5,1,Fill-in-the-blank(s),Numeric,"

Triangle B is a scaled copy of Triangle A with scale factor 12.

+

 

+

How many times bigger are the side lengths of Triangle B when compared with Triangle A?

+

 

+

",2-Jan,2-Jan,,,341023 +PRABEPVY,1,Fill-in-the-blank(s),Numeric,"

Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. What is the perimeter of Quadrilateral B?

+

 

+

",12,12,,,4480 +PSB5FH,2,Fill-in-the-blank(s),Algebraic Expression,"

The table below represents a proportional relationship.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
dC
26.28
39.42
515.7
1031.4
+

 

+

Write an equation that represents the relationship.

+

 

+

Equation: C =

","3.14*d, 3.14d","3.14*d, 3.14d",,,144928 +PSBZF4,1,Order / Sort,Ordering,"

A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. (There are about 1.1 yards in a meter, and 2.54 cm in an inch.) 

","

1 inch to 1 meter

,

1 inch to 1 yard

,

1 inch to 1 foot

","

1 inch to 1 meter

,

1 inch to 1 yard

,

1 inch to 1 foot

",,,121497 +PSBFH9,1,Fill-in-the-blank(s),Numeric,"

These triangles are scaled copies of each other.

+

 

+

+

 

+

The area of the second triangle is how many times larger than the area of the first?

+

 

+

The area of Triangle G is times larger than the area of Triangle F.

",4,4,,,26892 +PSBBVCZ,1,Fill-in-the-blank(s),Algebraic Expression,"

Elena has some bottles of water that each holds 17 fluid ounces.

+

 

+

Write an equation that relates the number of bottles of water (b) to the total volume of water (w) in fluid ounces.

+

 

+

w =

+

Use b as your variable

",17b,17b,,,270760 +PSBEK6,6,Fill-in-the-blank(s),Numeric,"

What is the y-coordinate of your graph when the x-coordinate is 1?

+

 

+

(1, )

","5/8, 2/5, 5/4","5/8, 2/5, 5/4",,,22967 +PSBD4P2,1,Fill-in-the-blank(s),Numeric,"

Each small square in the grid represents 1 square unit. Find the area of the figure in square units.  

+

 

+

+

 

+

square units

",8,8,,,668703 +PSBB5M8,3,Fill-in-the-blank(s),Algebraic Expression,"
The length of segment AE is 5 centimeters. 
+
 
+
 
+
+
 
+
+

 

+

Name a segment that has the same length as segment AB.

+
+

 

+

segment

","DA, FA, CA, AE, AG, AB","DA, FA, CA, AE, AG, AB",,,317851 +PSBB5M8,2,Fill-in-the-blank(s),Numeric,"
The length of segment AE is 5 centimeters. 
+
 
+
 
+
+
 
+
+

 

+
+

What is the length of segment AB?

+

 

+

  centimeters

",5,5,,,317673 +PRABESVU,1,Fill-in-the-blank(s),Numeric,"

Priya drew a circle whose circumference is 25 cm. Clare drew a circle whose diameter is 3 times the diameter of Priya's circle. What is the circumference of Clare's circle?

+

 

+

cm

+

Use 3.14 for π .

+

Round to the nearest whole number.

",75,75,,,449437 +PRABESVA,1,Fill-in-the-blank(s),Numeric,"

Find the area of the polygon.

+

 

+

+

 

+

  cm2

",20,20,,,37379 +PSB7FG,2,Fill-in-the-blank(s),Numeric,"

A circle’s circumference is approximately 76 cm.

+

 

+

Estimate the diameter of the circle.  

+

 

+

cm

+

Use  3.14 for π.

+

Round your answer to the nearest whole number.

",24,24,,,155429 +PSBUPR,3,Fill-in-the-blank(s),Numeric,"

Use the diagram to find the measure of angle EBD.

+ + + + + + + +
m∠EBD = ° 
",130,130,,,92939 +PSBCQU6,3,Fill-in-the-blank(s),Numeric,"

Multiply. Express your answer as a decimal.

+

 

+

(0.3) · 60

+

 

+

",18,18,,,422084 +PRABQP66,1,Fill-in-the-blank(s),Exact Match,"

What is the decimal expansion of 169?

+

 

+

+

 

+

If your answer is a repeating decimal, type the repeated portion of the decimal only once. 

+

For example: for 3.66 you only type in 3.6 for 0.4545 you only type in 0.45

+

 

",1.7,1.7,,,316024 +PSBCQU6,1,Fill-in-the-blank(s),Exact Match,"

Multiply. Express your answer as a decimal.

+

 

+

12 · 13

+

 

+

","6.50, 6.5","6.50, 6.5",,,421838 +PSBRYP,2,Fill-in-the-blank(s),Numeric,"

A farm lets you pick 3 pints of raspberries for $12.00.

+

 

+

How many pints do you get per dollar?

+

 

+

pints

",12-Mar,12-Mar,,,77688 +PRABHHJ5,1,Fill-in-the-blank(s),Exact Fraction,"

Find the quotient. Write your answer as a fraction or a mixed number.

+

 

+

812÷11

+

 

+

",17/22,17/22,,,81470 +PSBB33G,2,Fill-in-the-blank(s),Exact Fraction,"

Here is line segment DE and its image D′E′ under a dilation.

+

 

+

+

What is the scale factor of the dilation?

+

 

+

",4-Jan,4-Jan,,,309708 +PSBB2KM,1,Fill-in-the-blank(s),Numeric,"

Triangle ABC is a scaled copy of triangle DEF. Side AB measures 12 cm and is the longest side of ABC. Side DE measures 8 cm and is the longest side of DEF.

+

 

+

Triangle ABC is a scaled copy of triangle DEF with what scale factor?

+

 

+

",1.5,1.5,,,301201 +PSB6SB,3,Fill-in-the-blank(s),Numeric,"

A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings.

+

 

+

If Elena’s ice cream cost $1.50 more than Jada’s ice cream, how much more did Elena’s toppings weigh?

+

 

+

ounces of toppings

",3,3,,,152206 +PSB25J,2,Fill-in-the-blank(s),Numeric,"

Now find x when y = 2.

+

 

+

y = 23x

+

 

+

x =

",3,3,,,131367 +PSB282,1,Fill-in-the-blank(s),Numeric,"

For the following equation, find y when x = -3.

+

 

+

y = -x + 5

+

 

+

y =

",8,8,,,131672 +PRABD8HX,1,Fill-in-the-blank(s),Algebraic Expression,"

Write an equation for the line that passes through (2, 5) and (6, 7).

+

 

+

y =

+

Use x as your variable.

",0.5x+4,0.5x+4,,,18591 +PSB6SB,2,Fill-in-the-blank(s),Numeric,"

A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings.

+

 

+

How much does an ice cream cost with 11 ounces of toppings?

+

 

+

$

",8.5,8.5,,,152091 +PSBBAB5,3,Fill-in-the-blank(s),Numeric,"

At a sandwich shop, any sandwich costs $4.50, plus $0.25 for each extra topping.

+

 

+

If Andre’s sandwich cost $2.00 more than Clare’s sandwich, how many more toppings did Andre add to his sandwich?

+

 

+

more toppings

",8,8,,,171630 +PSB64G,2,Fill-in-the-blank(s),Numeric,"

Here is the base of a prism.

+

 

+

+

 

+

 

+

If the height of the prism is 5 cm, what is its volume?  

+

 

+

cm3

",180,180,,,152894 +PSBXC8,1,Fill-in-the-blank(s),Algebraic Expression,"

The graph shows the height in inches, h, of a bamboo plant t months after it has been planted.

+

 

+ + + + + + + +
+

Write an equation that describes the relationship between h and t.

+

 

+

h =

+

Use t as your variable.

+
",3t+12,3t+12,,,109764 +PSB25J,1,Fill-in-the-blank(s),Numeric,"

For the following equation, find y when x = -3.

+

 

+

y = 23x

+

 

+

y =

",-2,-2,,,131134 +PSB282,2,Fill-in-the-blank(s),Numeric,"

Now find x when y = 2.

+

 

+

y = -x + 5

+
 
+

 

+

x =

",3,3,,,131899 +PSB3EU,2,Fill-in-the-blank(s),Numeric,"

Now find x when y = 2.

+

 

+

y = 1.5x + 11

+

 

+

x =

",-6,-6,,,132932 +PSB64G,5,Fill-in-the-blank(s),Numeric,"

Here is the base of a prism.

+

 

+

+

 

+

 

+

When the height doubled, what was the percent increase for the surface area?

+

 

+

%

+

Round the percent to the nearest tenths place.

",67.6,67.6,,,153479 +PRABFAHC,1,Fill-in-the-blank(s),Numeric,"

Clare is paid $90 for 5 hours of work. At this rate, how many seconds does it take for her to earn 25 cents?

+

 

+

seconds

",50,50,,,147205 +PSBUE2,3,Fill-in-the-blank(s),Numeric,"

Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

+

 

+

If someone uses 400 liters of orange juice, how much soda water would they need?

+

 

+

liters of soda water

",500,500,,,91811 +PSBUE2,2,Fill-in-the-blank(s),Numeric,"

Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

+

 

+

If someone mixes 36 liters of orange juice and 45 liters of soda water, how many batches would they make?

+

 

+

batches

",9,9,,,91684 +PRABE9GW,1,Fill-in-the-blank(s),Numeric,"

Elena has 80 unit cubes. What is the volume of the largest cube she can build with them?

+

 

+

cubic units

",64,64,,,601993 +PSBUE2,4,Fill-in-the-blank(s),Numeric,"

Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

+

 

+

If someone uses 455 liters of soda water, how much orange juice would they need?

+

 

+

liters of orange juice

",364,364,,,91913 +PSB64G,1,Fill-in-the-blank(s),Numeric,"

Here is the base of a prism.

+

 

+

+

 

+

If the height of the prism is 5 cm, what is its surface area?

+

 

+

 cm2

",222,222,,,152711 +PSBB6QT,1,Fill-in-the-blank(s),Numeric,"

Recall that a perfect square is a number of objects that can be arranged into a square. For example, 9 is a perfect square because 9 objects can be arranged into 3 rows of 3. 16 is also a perfect square, because 16 objects can be arranged into 4 rows of 4. In contrast, 12 is not a perfect square because you can’t arrange 12 objects into a square.

+

 

+

How many whole numbers starting with 1 and ending with 100 are perfect squares?

+

 

+

whole numbers

",10,10,,,324197 +PSBC8AZ,1,Fill-in-the-blank(s),Exact Match,"

Multiply. Express your answer as a decimal.

+

 

+
+
+
+
+

12 · 15

+
+
+
+
+

 

+

","7.50, 7.5","7.50, 7.5",,,508616 +PSBCEMX,5,Fill-in-the-blank(s),Numeric,"

How much yellow water should be used for 11 ml of blue water?

+

 

+

ml of yellow water

+

 

+

",33,33,,,370357 +PSBCQR6,1,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

5 ÷ 2

+

 

+

","2.50, 2.5","2.50, 2.5",,,421173 +PSBCEMX,6,Fill-in-the-blank(s),Numeric,"

How much yellow water should be used for 8 ml of blue water?

+

 

+

ml of yellow water

+

 

+

",24,24,,,370431 +PSBC77E,1,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+
+
+
+
+

5 ÷ 4

+
+
+
+
+

 

+

",1.25,1.25,,,508017 +PSBC8AZ,3,Fill-in-the-blank(s),Exact Match,"

Multiply. Express your answer as a decimal.

+

 

+

(0.2) · 60

+

 

+

","12.0, 12","12.0, 12",,,508887 +PSBCEMX,3,Fill-in-the-blank(s),Numeric,"

How much yellow water should be used for 1 ml of blue water? 

+

 

+

ml of yellow water

+

 

+

",3,3,,,370138 +PRABPFQW,1,Fill-in-the-blank(s),Numeric,"

A square with side of 10 units overlaps a square with side of 8 units in such a way that its corner B is placed exactly at the center of the smaller square. As a result of the overlapping, the two sides of the large square intersect the two sides of the small square exactly at points C and E, as shown. The length of CD is 6 units.

+

 

+

+

 

+

What is the area of the overlapping region CDEB?

+

 

+

square units

",16,16,,,372037 +PSBC77E,4,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

12 ÷ 30

+

 

+

",".4, 0.4",".4, 0.4",,,508402 +PSBC8AZ,2,Fill-in-the-blank(s),Exact Match,"

Multiply. Express your answer as a decimal.

+

 

+

34 · 200

+

 

+

","150.0, 150","150.0, 150",,,508769 +PSBRYP,3,Fill-in-the-blank(s),Numeric,"

A farm lets you pick 3 pints of raspberries for $12.00.

+

 

+

At this rate, how many pints can you afford for $20.00?

+

 

+

pints

",5,5,,,77847 +PSBDG4M,3,Fill-in-the-blank(s),Numeric,"

Lin runs 5 laps around a track in 6 minutes.

+

 

+

If Lin runs 21 laps at the same rate, how long does it take her?

+

 

+

  minutes

",25.2,25.2,,,559654 +PSBC8AZ,4,Fill-in-the-blank(s),Exact Match,"

Multiply. Express your answer as a decimal.

+

 

+

(0.75) · 20

+

 

+

","15, 15.0","15, 15.0",,,509009 +PSBCQR6,4,Fill-in-the-blank(s),Exact Match,"

Divide. Express your answer as a decimal.

+

 

+

4 ÷ 50

+

 

+

",".08, 0.08",".08, 0.08",,,421588 +PSBCRQ,3,Fill-in-the-blank(s),Numeric,"

A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost $12. How much will the caterer pay for the pasta there?

+

 

+

$

",31.5,31.5,,,12985 +PSBDG4M,2,Fill-in-the-blank(s),Numeric,"

Lin runs 5 laps around a track in 6 minutes.

+

 

+

How many laps per minute is that?  

+

 

+

 laps per minute

",6-May,6-May,,,559546 +PRABG3FJ,1,Fill-in-the-blank(s),Numeric," + + + + + + + + + +
+

A window-washing crew can finish 15 windows in 18 minutes.

+

 

+

If this crew was assigned to wash all the windows on the outside of the Burj Khalifa, how long will the crew be washing at this rate?

+

 

+

minutes

+
 
","29,217.60","29,217.60",,,354136 +PSBRYP,4,Fill-in-the-blank(s),Numeric,"

A farm lets you pick 3 pints of raspberries for $12.00.

+

 

+

At this rate, how much will 8 pints of raspberries cost?

+

 

+

$

",32,32,,,78012 +PSBW43,1,Fill-in-the-blank(s),Numeric,"

For the situation, find the unit rates.

+

 

+

Tyler paid $16 for 4 raffle tickets.

+

 

+ + + + + + + + + + + +
+

a. What is the price per ticket?

+		 +

$per ticket

+
+

b. How many tickets is that per dollar? 

+		 +

ticket per dollar

+
+

 

","0.25, 4","0.25, 4",,,108670 +PRABHUQ4,1,Fill-in-the-blank(s),Numeric,"

Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98.
 
How many sets of two or more consecutive positive integers can be added to obtain a sum of 100?

+

 

+

sets

",2,2,,,17667 +PSBBCRJ,2,Fill-in-the-blank(s),Numeric,"

If x is 6, what is y?

+

 

+

y =

",9,9,,,184908 +PSBDEV,1,Fill-in-the-blank(s),Numeric,"

Complete the equation so that it is true for all values of x.

+

 

+

3x=6=3(x+)

",2,2,,,16591 +PRABHN3R,1,Fill-in-the-blank(s),Exact Fraction,"

Find the value of k so that the line passing through the pair of points has the given slope.

+

 

+

 (-152, 316) and (-1322, k), slope = 0

+

 

+

",16-Mar,16-Mar,,,166028 +PSBBJXR,1,Fill-in-the-blank(s),Numeric,"

The triangle and the square have equal perimeters.

+

 

+

+

 

+
+

Find the value of x.

+

 

+

x=

+
",16,16,,,219253 +PSBDEV,3,Fill-in-the-blank(s),Algebraic Expression,"

Complete the equation so that it is true for all values of x.

+

 

+

15x-105=-2

+

Use x as your variable.

",3x,3x,,,16856 +PSB2BT,2,Fill-in-the-blank(s),Numeric,"

For what number of cups will the two stacks have the same height?

+

 

+

cups

",0,0,,,126461 +PSBCG4K,2,Fill-in-the-blank(s),Numeric,"

How many solutions does this system of equations have?

+

 

+

+

 

+

",0,0,,,384509 +PRABMTPA,1,Fill-in-the-blank(s),Numeric,"

Solve the equation and check your solution.

+

 

+

9 − 7w = 8w + 8

+

 

+

w=

",15-Jan,15-Jan,,,149101 +PRABP8NM,1,Fill-in-the-blank(s),Numeric,"

 

+

+

""""football / soccer ball"""" by Tobbi. Public Domain.

+

 

+

A soccer ball is a polyhedron with 12 black pentagonal faces and 20 white hexagonal faces. How many edges in total are on this polyhedron?

+

 

+

edges

+

 

",90,90,,,139860 +PSB26A,2,Fill-in-the-blank(s),Numeric,"

The temperature in degrees Fahrenheit, F, is related to the temperature in degrees Celsius, C, by the equation F=95C+32,

+

 

+

In parts of Alaska, the temperatures can reach -60 degrees Fahrenheit. How many degrees Celsius is this?

+

 

+

degrees Celsius

",-51 1/9,-51 1/9,,,131293 +PSBWDG,3,Fill-in-the-blank(s),Numeric,"

Here is an equation: 15(x-3)5=3(2x-3)

+

 

+

Check your solution.

+

 

+

x=

",0,0,,,104135 +PSBCC,3,Fill-in-the-blank(s),Numeric,"

Given the equation y = ‐3x + 2.5:

+

 

+

When y is 8.5, what value of x makes the equation true?

+
 
+

 

+

y =

",-2,-2,,,312 +PSBB96V,2,Fill-in-the-blank(s),Numeric,"

The table representing Tyler's walk shows other values of time and distance. Complete the table.

+

 

+ + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
time
(seconds)		distance
(meters)
00
2025
3037.5
4050
1
+
+

 

",1.25,1.25,,,343125 +PSB7JA,1,Fill-in-the-blank(s),Numeric,"

The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is.

+
+

 

+

In one rotation of the carousel, how much farther does Mai travel than Kiran?

+

 

+

feet farther

+

Use 3.14 for π.

+

Round your answer to the tenths place.

+
","50.3, 50.2","50.3, 50.2",,,155994 +PSBCE8P,3,Fill-in-the-blank(s),Algebraic Expression,"

Three cylinders have a height of 8 cm.

+

Cylinder 1 has a radius of 1 cm.

+

Cylinder 2 has a radius of 2 cm.

+

Cylinder 3 has a radius of 3 cm.

+

Find the volume of each cylinder.

+

 

+

Cylinder 3 has a volume of  cm3

+

 

+

Enter your answer in terms of π.

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

",72pi,72pi,,,374368 +PSBCE8P,2,Fill-in-the-blank(s),Algebraic Expression,"

Three cylinders have a height of 8 cm.

+

Cylinder 1 has a radius of 1 cm.

+

Cylinder 2 has a radius of 2 cm.

+

Cylinder 3 has a radius of 3 cm.

+

Find the volume of each cylinder.

+

 

+

Cylinder 2 has a volume of  cm3

+

 

+

Enter your answer in terms of π.

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

",32pi,32pi,,,374220 +PSBCE8P,1,Fill-in-the-blank(s),Algebraic Expression,"

Three cylinders have a height of 8 cm.

+

Cylinder 1 has a radius of 1 cm.

+

Cylinder 2 has a radius of 2 cm.

+

Cylinder 3 has a radius of 3 cm.

+

Find the volume of each cylinder.

+

 

+

Cylinder 1 has a volume of  cm3

+

 

+

Enter your answer in terms of π.

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

",8pi,8pi,,,374058 +PSBTE8,2,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder and cone have the same height and radius. The height of each is 5 cm, and the radius is 2 cm. Calculate the volume of the cone.

+

 

+

  cm3

+

Enter your answer in terms of π. Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",20pi/3,20pi/3,,,86515 +PSBB8E7,2,Fill-in-the-blank(s),Algebraic Expression,"

+

 

+

 

+

Here are a cone, a sphere, and a cylinder that all have the same radii and heights.

+

 

+

The radius of the cylinder is 5 units. When necessary, express all answers in terms of π.

+

What is the volume of the cylinder?

+

 

+

cubic units

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

",250pi,250pi,,,333800 +PSBX6P,3,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder has a radius of 3 cm and a height of 5 cm.

+

 

+

What is the volume of the cylinder when its height is halved?

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the symbol. For example: 32π would be typed as 32pi

",45/2pi,45/2pi,,,114806 +PSBBHR6,1,Fill-in-the-blank(s),Numeric,"

+

The volume of this sphere with radius r is V=288π.

+

 

+

This statement is true:  288π=43r3π.

+

 

+

What is the value of r for this sphere?

+

 

+

units

+

 

",6,6,,,212876 +PSBDG45,1,Fill-in-the-blank(s),Numeric,"

A car is traveling at a constant speed. Find the number of miles the car travels in 1 hour at the given rate.

+

 

+

 135 miles in 3 hours

+

 

+

miles

",45,45,,,558351 +PSBB8E7,3,Fill-in-the-blank(s),Algebraic Expression,"

+

 

+

 

+

Here are a cone, a sphere, and a cylinder that all have the same radii and heights.

+

 

+

The radius of the cylinder is 5 units. When necessary, express all answers in terms of π.

+

 

+

What is the volume of the cone?

+

 

+

cubic units

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi.

",250/3pi,250/3pi,,,333895 +PSB89M,1,Fill-in-the-blank(s),Numeric,"

A coin-operated bouncy ball dispenser has a large glass sphere that holds many spherical balls. The large glass sphere has a radius of 9 inches. Each bouncy ball has radius of 1 inch and sits inside the dispenser.

+

 

+

If there are 243 bouncy balls in the large glass sphere, what proportion of the large glass sphere’s volume is taken up by bouncy balls? 

+

 

+

+

Give your answer as a fraction.

",3-Jan,3-Jan,,,164833 +PSBT2V,2,Fill-in-the-blank(s),Numeric,"

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200.

+

 

+

If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?

+

 

+

hour(s)

",1,1,,,89270 +PSBT2V,1,Fill-in-the-blank(s),Numeric,"

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200.

+

 

+

If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?

+

 

+

hour(s)

+

Round your answer to the hundredths place.

",2.05,2.05,,,89069 +PSBJS4,6,Fill-in-the-blank(s),Numeric,"

The graph shows the temperature between noon and midnight in one day in a certain city.

+

 

+

+

 

+

 

+

When the input of the function is 8, what is the output?

+

 

+

",57,57,,,45704 +PSBX6P,2,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder has a radius of 3 cm and a height of 5 cm.

+

 

+

What is the volume of the cylinder when its height is tripled?

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the symbol. For example: 32π would be typed as 32pi

",135pi,135pi,,,114637 +PSBX6P,1,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder has a radius of 3 cm and a height of 5 cm.

+

 

+

What is the volume of the cylinder?

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the symbol. For example: 32π would be typed as 32pi

",45pi,45pi,,,114450 +PSBBC6R,3,Fill-in-the-blank(s),Numeric,"

Use the labeled point to find the radius of these cones.  Use 3.14 as an approximation for π.

+

 

+

units

+

 

+

",15,15,,,187127 +PRABP7YW,1,Fill-in-the-blank(s),Numeric,"

A thirsty crow wants to raise the level of water in a cylindrical container so that it can reach the water with its beak.

+

 

+
    +
  • The container has diameter of 2 inches and a height of 9 inches.
    • +
  • The water level is currently at 6 inches.
    • +
  • The crow can reach the water if it is 1 inch from the top of the container.
    • +
+

 

+

In order to raise the water level, the crow puts spherical pebbles in the container. If the pebbles are approximately 12 in diameter, what is the fewest number of pebbles the crow needs to drop into the container in order to reach the water?

+

 

+

",97,97,,,213558 +PSBTE8,1,Fill-in-the-blank(s),Algebraic Expression,"

A cylinder and cone have the same height and radius. The height of each is 5 cm, and the radius is 2 cm. Calculate the volume of the cylinder.

+

 

+

 cm3

+

Enter your answer in terms of π. Use pi to represent the π symbol. For example: 32π would be typed as 32pi

",20pi,20pi,,,86322 +PSBCBG7,2,Fill-in-the-blank(s),Algebraic Expression,"

A hemisphere fits snugly inside a cylinder with a radius of 6 cm. A cone fits snugly inside the same hemisphere.

+

 

+

What is the volume of the cone?

+

 

+

 cm3

+

Enter your answer in terms of π.

+

Use pi to represent the symbol.  For example: 32π would be typed as 32pi

",72pi,72pi,,,351813 +PRABEAZ4,1,Fill-in-the-blank(s),Numeric,"

Solve the system of equations:  y=7x+10y=-4x-23

+

 

+

(,)

","-11, -3","-11, -3",,,14761 +PSBFC9,1,Fill-in-the-blank(s),Algebraic Expression," + + + + + + +
+

A grain silo has a cone shaped spout on the bottom in order to regulate the flow of grain out of the silo. The diameter of the silo is 8 feet. The height of the cylindrical part of the silo above the cone spout is 12 feet while the height of the entire silo is 16 feet.

+

 

+

How many cubic feet of grain are held in the cone spout of the silo?

+

 

+

cubic feet

+

 

+

Use pi to represent the π symbol. For example: 32π would be typed as 32pi

+
",64/3pi,64/3pi,,,27604 +PSBB73F,3,Fill-in-the-blank(s),Numeric,"

A line contains the points (-1, 4) and (5, -3).

+

 

+

Calculate the slope of the line.

+

 

+

",-1.166666667,-1.166666667,,,332048 +PSB64G,3,Fill-in-the-blank(s),Numeric,"

Here is the base of a prism.

+

 

+

+

 

+

 

+

If the height of the prism is 10 cm, what is its surface area?  

+

 

+

cm2

",372,372,,,153106 +PSBFXP,1,Fill-in-the-blank(s),Numeric,"

Elena is feeding her neighbor’s dogs. Each dog gets 23 cup of dog food, and she uses 313 cups of food. How many dogs does her neighbor have?  

+

 

+

 dogs

",5,5,,,30601 +PSBC6AU,1,Fill-in-the-blank(s),Numeric,"

Solve the problem below.

+

 

+

What is 150% of 26?

+

 

+

",39,39,,,498428 +PSBU7R,3,Fill-in-the-blank(s),Algebraic Expression,"

Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

+

 

+

If the regular price of an item is x dollars, what is the discounted price in dollars?  

+

 

+

","7/10x, x-0.03x, 0.70x","7/10x, x-0.03x, 0.70x",,,96895 +PSBEKA,1,Fill-in-the-blank(s),Numeric,"

The scatter plot shows the weight and fuel efficiency data used in an earlier lesson along with a linear model represented by the equation y=-0.0114x+41.3021.

+

 

+

+

 

+

What is the value of the slope?  

+

 

+

",-0.0114,-0.0114,,,22573 +PSBRKJ,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

‐3x − 5 = 16

+

 

+

x =

",-7,-7,,,75928 +PSBRPF,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

-4(y − 2) = 12

+

 

+

y =

",-1,-1,,,76294 +PSBBNC8,1,Fill-in-the-blank(s),Algebraic Expression,"

A cone has a volume V, radius r, and a height of 12 cm.

+

 

+

A cone has the same height and 13 of the radius of the original cone. Write an expression for its volume.

+

 

+

",V/9,V/9,,,233319 +PRABETPT,1,Fill-in-the-blank(s),Numeric,"

A car dealership pays $8,350 for a car. They mark up the price by 17.4% to get the retail price. What is the retail price of the car at this dealership? 

+

 

+

$

",9802.9,9802.9,,,509509 +PRABG4ZE,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Find the sum.

+

 

+
+
+
+

-240 + 370 =

",130,130,,,153749 +PRABG4ZD,1,Fill-in-the-blank(s),Numeric,"
+
+
+

Find the sum.

+
+
+
+
 
+

56+(-56)

+

 

+

",0,0,,,405832 +PSBDTTH,3,Fill-in-the-blank(s),Numeric,"

Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
daychange
Monday+2,000
Tuesday-125
Wednesday-127
Thursday+1,719
Friday-356
Saturday-782
Sunday0
+

 

+

How many cups do you think were used on Thursday?  

+

 

+

cups

",281,281,,,615367 +PSBDTTH,2,Fill-in-the-blank(s),Numeric,"

Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
daychange
Monday+2,000
Tuesday-125
Wednesday-127
Thursday+1,719
Friday-356
Saturday-782
Sunday0
+

 

+

Assume the starting amount of coffee cups is 0. How many paper cups are left at the end of the week?

+


paper cups

",2329,2329,,,615225 +PSBDG45,2,Fill-in-the-blank(s),Numeric,"

A car is traveling at a constant speed. Find the number of miles the car travels in 1 hour at the given rate.

+

 

+

22 miles in 12hour

+

 

+

  miles

",44,44,,,558648 +PSB64G,4,Fill-in-the-blank(s),Numeric,"

Here is the base of a prism.

+

 

+

+

 

+

 

+

If the height of the prism is 10 cm, what is its volume?  

+

 

+

cm3

",360,360,,,153291 +PRABEURW,1,Fill-in-the-blank(s),Numeric,"

The Colorado state flag consists of three horizontal stripes of equal height. The side lengths of the flag are in the ratio 2 : 3.  The diameter of the gold-colored disk is equal to the height of the center stripe. What percentage of the flag is gold?  

+

 

+

%

+

Round to the nearest hundredth of a percent.

+

 

+

","5.81, 5.82","5.81, 5.82",,,429590 +PSBB8DR,2,Fill-in-the-blank(s),Numeric Expression,"

Write an expression to represent this situation.

+

 

+

“On Tuesday at lunchtime, it was 29°C. By sunset, the temperature had dropped to 16°C.”

+

 

+

","29+(-13), 29-13, 29+-13","29+(-13), 29-13, 29+-13",,,333811 +PRABESGG,1,Fill-in-the-blank(s),Numeric,"

Add.

+
+
+
+
+

14.7 + 28.9

+
+
+
+
+

 

+

",43.6,43.6,,,585630 +PRABTTED,1,Fill-in-the-blank(s),Numeric,"

Solve the equation below.

+

 

+

p + 12 = 17

+

 

+

",5,5,,,194530 +PSBCNU9,1,Fill-in-the-blank(s),Numeric,"

It costs $3.45 to buy 34 foot of electrical wire. How much would it cost to purchase 712 feet of wire? 

+

 

+

$

",34.5,34.5,,,409731 +PRABTSUR,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

-57 · 75 =

",-1,-1,,,278775 +PSBY88,1,Fill-in-the-blank(s),Numeric,"

A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77.

+

 

+

How much was the tip in dollars? 

+

 

+

$

",7.77,7.77,,,120069 +PSBTHK,2,Fill-in-the-blank(s),Numeric,"

A furniture store pays a wholesale price for a mattress. Then, the store marks up the retail price to 150% of the wholesale price. Later, they put the mattress on sale for 50% off of the retail price. A customer just bought the mattress for sale and paid $1,200.

+

 

+

What was the wholesale price, before the markup? 

+

 

+

$

","1,600","1,600",,,86791 +PRABETQH,1,Fill-in-the-blank(s),Numeric,"

The price of gold is often reported per ounce. At the end of 2005, this price was $513. At the end of 2015, it was $1,060. By what percentage did the price per ounce of gold increase?  

+

 

+

%

+

Round your answer to the nearest whole percent.

",107,107,,,121257 +PSBBGEE,3,Fill-in-the-blank(s),Numeric,"

During a special sales event, the dealership offers a 10% discount off of the retail price.

+

 

+

After the discount, how much will a customer pay for this vehicle?

+

 

+

$

",14256,14256,,,205498 +PRABET32,1,Fill-in-the-blank(s),Numeric,"

The baby giraffe weighed 132 pounds at birth. He gained weight at a steady rate for the first 7 months until his weight reached 538 pounds. How much did he gain each month?  

+

 

+

 pounds

",58,58,,,389120 +PRABTSUS,1,Fill-in-the-blank(s),Numeric,"

Find the product. 

+

 

+

-239 · 39 =

",-2,-2,,,278908 +PRABETXM,1,Fill-in-the-blank(s),Numeric,"

A school ordered 3 large boxes of board markers. After giving 15 markers to each of 3 teachers, there were 90 markers left. The diagram represents the situation. How many markers were originally in each box?   

+

 

+

+

 

+

markers

",45,45,,,118504 +PRABMSH5,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(-7.3) • (5)

+

 

+

",-36.5,-36.5,,,65010 +PRABETR6,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(100) • (-0.09)

+

 

+

",-9,-9,,,64437 +PSBBBKF,1,Fill-in-the-blank(s),Numeric,"

The tax rate at this restaurant is 9.5%

+

 

+ + + + + + + +
+

Another person’s subtotal is $24.95. How much will their sales tax be?

+

 

+

$

+

Round your answer to the hundredths place.

+
",2.37,2.37,,,178110 +PRABMSH4,1,Fill-in-the-blank(s),Numeric,"

Find the product.

+

 

+

(-7) • (-1.1)

+

 

+

",7.7,7.7,,,64758 +PRABTSUQ,1,Fill-in-the-blank(s),Numeric Expression,"

Find the product. 

+

 

+

23 · -45

+
 
+

 

+

",-0.533333333,-0.533333333,,,278653 +PSBCUKN,3,Fill-in-the-blank(s),Numeric,"

Use the new diagram to find a correct value for x.

+

 

+

",17,17,,,443136 +PRABQPQK,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

3(x + 8) = 21

+

 

+

x =

",-1,-1,,,90560 +PSBCUKN,1,Fill-in-the-blank(s),Numeric,"

Clare drew this diagram to match the equation 2x + 16 = 50 , but she got the wrong solution as a result of using this diagram. 

+

 

+

+

 

+

What value for x can be found using the diagram?

+

 

+

",32,32,,,442685 +PSBBQEE,2,Fill-in-the-blank(s),Algebraic Expression,"

""Pick a number, add -2, and multiply by 5.""

+

 

+

What would be a correct expression for this number puzzle?

+

 

+

",5(x-2),5(x-2),,,244242 +PSBED4,1,Fill-in-the-blank(s),Exact Match,"

Write the expression with fewer terms. 

+

 

+

10x − 3y + 2x

+

 

+

","-3y+12x, 12x-3y","-3y+12x, 12x-3y",,,22093 +PSBBGEE,2,Fill-in-the-blank(s),Numeric," + + + + + +
+

A car dealership pays a wholesale price of $12,000 to purchase a vehicle.

+

 

+

The car dealership wants to make a 32% profit.

+
+

 

+

After the markup, what is the retail price of the vehicle?

+

 

+

$

",15840,15840,,,205401 +PSBBKYY,2,Fill-in-the-blank(s),Numeric,"

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.

+

 

+

If a bus is charged $122, how many people do you think it contains?

+

 

+

people

",38,38,,,225359 +PRABG428,1,Fill-in-the-blank(s),Algebraic Expression,"

Use the distributive property to write an expression that is equivalent to 5(-2x − 3). If you get stuck, use the boxes to help organize your work.

+

 

+

+

+

 

+

 

",-10x-15,-10x-15,,,147088 +PSBCRQU,3,Fill-in-the-blank(s),Numeric,"

Use long division to express the fraction as a decimal.

+

 

+

411=

+

If your answer is a repeating decimal, type the repeated portion of the decimal only once.

+

 

+

For example:    

+

for 3.66¯ you only type in 3.6               

+

for0.45¯ you only type in 0.45

",0.36,0.36,,,426703 +PSBBBKT,3,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

12 · -54

+

 

+

",-15,-15,,,177979 +PSBDGUS,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area?   

+

 

+

 

+

+

 

+

square centimeters

",48,48,,,558257 +PRABEUC6,1,Fill-in-the-blank(s),Numeric,"

In this figure, angles R and S are complementary. Find the measure of angle S.

+

 

+

+

 

+

m∠S = °

",28,28,,,168990 +PSBZAQ,1,Fill-in-the-blank(s),Numeric,"

Crater Lake in Oregon is shaped like a circle with a diameter of about 5.5 miles.

+

 

+

How far is it around the perimeter of Crater Lake?

+

 

+

miles

+

Use 3.14 for π.

+

Round to the nearest whole number.

",17,17,,,120203 +PSBXTM,5,Fill-in-the-blank(s),Numeric,"

Calculate the value of the expression below.

+

 

+

(-18)(-3)

+

 

+

",6,6,,,112931 +PSBNQS,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression below.

+

 

+

-22 + 5

+
 
+

 

+

",-17,-17,,,60187 +PSBBCDJ,1,Fill-in-the-blank(s),Numeric,"

22% of 65 is 14.3. What is 22.6% of 65?

+

 

+

+

Round your answer to the nearest hundredths place.

",14.69,14.69,,,182437 +PSBXTM,3,Fill-in-the-blank(s),Numeric,"

Calculate the value of the expression below.

+

 

+

-183

+

 

+

",-6,-6,,,112644 +PSBBBKT,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

-12· 13

+

 

+

",-4,-4,,,177403 +PSBBBKT,4,Fill-in-the-blank(s),Numeric,"

Evaluate the expression:

+

 

+

-12 · -54

+

 

+

",15,15,,,178227 +PRABETRZ,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression. If the answer is not a whole number, write your answer as a fraction.

+

 

+

-4 · -6

+

 

+

",24,24,,,37975 +PRABMSG4,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression. If the answer is not a whole number, write your answer as a fraction.

+

 

+

4 ÷ -6

+

 

+

",-0.666666667,-0.666666667,,,38524 +PSB27H,2,Fill-in-the-blank(s),Numeric,"

The departure from the average is the difference between the actual amount of rain and the average amount of rain for a given month. The historical average for rainfall in Albuquerque, NM for June, July, and August is shown in the table.

+

 

+ + + + + + + + + + + + + +
JuneJulyAugust
0.671.51.57
+

 

+

 

+

The departure from the average rainfall last July was -0.36 inches. How much rain fell last July?

+

 

+

inches

",1.14,1.14,,,131027 +PSB27H,3,Fill-in-the-blank(s),Numeric,"

The departure from the average is the difference between the actual amount of rain and the average amount of rain for a given month. The historical average for rainfall in Albuquerque, NM for June, July, and August is shown in the table.

+

 

+ + + + + + + + + + + + + +
JuneJulyAugust
0.671.51.57
+

 

+

 

+

How much rain would have to fall in August so that the total amount of rain equals the average rainfall for these three months?

+

 

+

inches

",2.43,2.43,,,131322 +PRABETNX,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+

 

+

14 · (-12)

+

 

+

",-3,-3,,,408499 +PRABMSES,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+

 

+

-13 · 39

+

 

+

",-13,-13,,,25486 +PSB27H,4,Fill-in-the-blank(s),Numeric,"

The departure from the average is the difference between the actual amount of rain and the average amount of rain for a given month. The historical average for rainfall in Albuquerque, NM for June, July, and August is shown in the table.

+

 

+ + + + + + + + + + + + + +
JuneJulyAugust
0.671.51.57
+

 

+

 

+

What would the departure from the average be in August in that situation?

+

 

+

inches

",0.86,0.86,,,131590 +PSB27H,1,Fill-in-the-blank(s),Numeric,"

The departure from the average is the difference between the actual amount of rain and the average amount of rain for a given month. The historical average for rainfall in Albuquerque, NM for June, July, and August is shown in the table.

+

 

+ + + + + + + + + + + + + +
JuneJulyAugust
0.671.51.57
+

 

+

Last June only 0.17 inches of rain fell all month. What is the difference between the average rainfall and the actual rainfall for last June?

+

 

+

inches

",0.5,0.5,,,130668 +PRABMSET,1,Fill-in-the-blank(s),Numeric,"

Find the value of the expression.

+

 

+

-45 · (-75)

+

 

+

 

+

",60,60,,,25718 +PSBBEYJ,1,Fill-in-the-blank(s),Numeric,"

Mai is filling her fish tank. Water flows into the tank at a constant rate. How many gallons of water will be in the fish tank after 3 minutes?

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
time (minutes)water (gallons)
0.50.8
1 
3
 40
+

 

",4.8,4.8,,,196523 +PSBBEYJ,3,Fill-in-the-blank(s),Numeric,"

How long will it take to fill the tank with 40 gallons of water? 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
time (minutes)water (gallons)
0.50.8
1 
3 
40
",25,25,,,196819 +PSB8S3,2,Fill-in-the-blank(s),Algebraic Expression,"

Write an expression equivalent to ‐4(x + 3) - 12x + 5 that only has two terms.

+

 

+

",-16x - 7,-16x - 7,,,162630 +PSBBVHN,2,Fill-in-the-blank(s),Numeric,"

Elena is 56 inches tall. 

+

 

+

What is her height in meters?  

+

 

+

meters

+

Round your answer to two decimal places.

",1.42,1.42,,,272435 +PRABEUGX,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

(8.5) · (-3) = a

+

 

+

a =

",-25.5,-25.5,,,55569 +PRABFCGD,1,Order / Sort,Ordering,"

Order from greatest to least:

+

 

+
    +
  • 55% of 180
    • +
  • 300% of 26
    • +
  • 12% of 700
    • +
","300% of 26, 12% of 700, 55% of 180","300% of 26, 12% of 700, 55% of 180",,,229674 +PSBBMGT,2,Fill-in-the-blank(s),Numeric,"

Last Sunday 1,575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under.

+

 

+

Find the number of teenagers that visited the park.

+

 

+

teenagers

",252,252,,,228285 +PRABFK9Q,1,Fill-in-the-blank(s),Numeric,"

The box plot displays the data on the response times of 100 mice to seeing a flash of light. How many mice are represented by the rectangle between 0.5 and 1 second?

+

 

+

mice

+

 

+

",50,50,,,55325 +PRABMSS4,1,Fill-in-the-blank(s),Numeric,"

Edge lengths are given in units. Find the surface area in square units.

+

 

+

 square units

+

 

+

",300,300,,,156599 +PSBBQGY,1,Fill-in-the-blank(s),Numeric,"

A rectangular prism with dimensions 5 inches by 13 inches by 10 inches was cut to leave a piece as shown in the image.

+

 

+

+

 

+

What is the volume of this piece?  

+

 

+

 in3

",350,350,,,244645 +PSB7BS,3,Fill-in-the-blank(s),Numeric,"
+

B is the intersection of line AC and line ED. Find the measure of each of the angles.

+
+

 

+

+

 

+

 

+
+

Give the measure of angle EBC.  °

+
",70,70,,,154426 +PRABFF38,1,Fill-in-the-blank(s),Numeric,"

Solve the equation.

+

 

+

 

+

26 = 100d

+

 

+

d =

",0.26,0.26,,,223535 +PSBCQFB,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded triangle.

+

 

+

+

 

+

square units

",18,18,,,419590 +PSB7BS,1,Fill-in-the-blank(s),Numeric,"

B is the intersection of line AC and line ED. Find the measure of each of the angles.

+
+

 

+

+

 

+

Give the measure of angle ABF.  °

+
",130,130,,,153940 +PSB7BS,4,Fill-in-the-blank(s),Numeric,"
+

B is the intersection of line AC and line ED. Find the measure of each of the angles.

+
+

 

+

+

 

+

 

+
+

Give the measure of angle FBC.  °

+
",50,50,,,154657 +PSB7BS,5,Fill-in-the-blank(s),Numeric,"
+

B is the intersection of line AC and line ED. Find the measure of each of the angles.

+
+

 

+

+

 

+

 

+
+

Give the measure of angle DBG.  °

+
",45,45,,,154915 +PSBBGSD,1,Fill-in-the-blank(s),Numeric,"

Find the surface area of this prism.  

+

 

+

cm2

+

 

+

 

+

",270,270,,,207279 +PRABEDYA,1,Fill-in-the-blank(s),Numeric,"

Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?

+

 

+

months

",25,25,,,233780 +PSBCDTH,1,Fill-in-the-blank(s),Numeric,"

A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many unique triangles can be drawn that fit that description?  

+

 

+

unique triangle(s)

",1,1,,,365643 +PRABE6XY,1,Fill-in-the-blank(s),Numeric,"

Find the surface area of this triangular prism. All measurements are in meters.

+

 

+

 

+

+

 

+

 

+

square meters

",4.8,4.8,,,248279 +PRABMTPT,1,Fill-in-the-blank(s),Numeric,"

For what value of x do the expressions 23x + 2 and 43x - 6 have the same value? 

+

 

+

x =

",12,12,,,234184 +PRABFCA2,1,Fill-in-the-blank(s),Numeric,"

There is a 10% off sale on laptop computers. If someone saves $35 on a laptop, what was its original cost? If you get stuck, consider using the table.

+
+
+
+

 

+
+
$
+
 
+
+ + + + + + + + + + + + + + + + + +
Savings (dollars)Percentage
3510
?100
+
+
+
",350,350,,,240555 +PSBBUYK,3,Fill-in-the-blank(s),Numeric,"

The distance across a sink drain is 3.8 cm.  

+

 

+

Estimate the circumference of the circle: 

+

 

+

 cm

+

 

+

Use  3.14 for π. 

+

Round your answer to the nearest whole number.

",12,12,,,269382 +PRABFCBV,1,Fill-in-the-blank(s),Numeric,"

Lin and Andre start walking toward each other at the same time from opposite ends of 22-mile walking trail. Lin walks at a speed of 2.5 miles per hour. Andre walks at a speed of 3 miles per hour.

+

 

+

Here is a table showing the distances traveled and how far apart Lin and Andre were over time. Use the table to find how much time passes before they meet.

+

 

+

hours

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Elapsed Time (hour)Lin’s Distance (miles)Andre’s Distance (miles)Distance Apart (miles)
00022
12.5316.5
    
    
   0
",4,4,,,240818 +PRABEEXH,1,Fill-in-the-blank(s),Algebraic Expression,"

The point where the graphs of two equations intersect has y-coordinate 2. One equation is y = -3x + 5. Find the other equation if its graph has a slope of 1.

+

 

+

y =

+

Use x as your variable.

",x+1,x+1,,,1867 +PRABTGFN,1,Fill-in-the-blank(s),Numeric,"

Evaluate the expression if x is 25, y is -4, and z is -0.2.

+

 

+

y · x

+

 

+

",-1.6,-1.6,,,158903 +PRABQACZ,1,Fill-in-the-blank(s),Numeric,"

Here is a rough map of a neighborhood.

+

 

+

+

 

+

There are 4 mail routes during the week.

+

 

+
    +
  • On Monday, the mail truck follows the route A-B-E-F-G-H-A, which is 14 miles long.
    • +
  • On Tuesday, the mail truck follows the route B-C-D-E-F-G-B, which is 22 miles long.
    • +
  • On Wednesday, the truck follows the route A-B-C-D-E-F-G-H-A, which is 24 miles long.
    • +
  • On Thursday, the mail truck follows the route B-E-F-G-B.
    • +
+

 

+

How long is the route on Thursdays?

+

 

+

miles

",12,12,,,308662 +PSBBUSX,3,Fill-in-the-blank(s),Numeric,"

The length of the minute hand on a clock is 5 in.  

+

 

+

Estimate the circumference of the circle:

+

 

+

inches

+

Use 3.14 for π.

",31.4,31.4,,,268435 +PSBBUSX,2,Fill-in-the-blank(s),Numeric,"

The length of the minute hand on a clock is 5 in.  

+

 

+

Estimate the diameter of the circle: 

+

 

+

inches

",10,10,,,268157 +PRABESTV,1,Fill-in-the-blank(s),Numeric,"

A half circle is joined to an equilateral triangle with side lengths of 12 units. What is the perimeter of the resulting shape?

+

 

+

units

+

Use 3.14 for π. 

+

Round your answer to the nearest hundredth. 

+

 

+

",42.84,42.84,,,275547 +PRABERU7,1,Fill-in-the-blank(s),Numeric,"

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is t = 1500d. How long will it take the airplane to travel 800 miles?

+

 

+

hours

+

Round your answer to the nearest tenths place.

",1.6,1.6,,,42964 +PRABESVC,1,Fill-in-the-blank(s),Numeric,"

Jada’s bike wheels have a diameter of 20 inches. How far does she travel if the wheels rotate 37 times?  

+

 

+

inches

+

Use 3.14 for π.

+

Round your answer to the nearest whole number.

","2324, 2325","2324, 2325",,,101757 +PSBDR2D,1,Fill-in-the-blank(s),Numeric,"

Each small square in the graph paper represents 1 square unit. Find the area of the given figure in square units.

+

 

+

 

+

+

 

+

square units

",22,22,,,605478 +PSBB2R3,1,Fill-in-the-blank(s),Numeric,"

Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.

+

 

+

+

 

+

Find the perimeter of the wire picture frame. 

+

 

+

inches

+

Round to the nearest tenth.

",62.8,62.8,,,302084 +PRABEUMW,1,Fill-in-the-blank(s),Exact Match,"

A cube is cut into two pieces by a single slice that passes through points A, B, and C. What shape is the cross section?

+

 

+

+

+

 

+

 

+

 

","Rectangle, rectangle","Rectangle, rectangle",,,114275 +PRABESV5,1,Fill-in-the-blank(s),Numeric,"

The face of a clock has a circumference of 63 in. What is the area of the face of the clock?

+

 

+

 in2

+

 

+
+

Use 3.14 for π.

+

Round your answer to the nearest whole number.

+
","316, 314","316, 314",,,176149 +PRABG4R4,1,Fill-in-the-blank(s),Numeric,"

The side lengths of the state flag of Colorado are in the ratio 2 : 3. If a flag is 12 feet long, what is its height? 

+

 

+

feet

+

 

+

 

+

",8,8,,,114159 +PRABEVDF,1,Fill-in-the-blank(s),Numeric,"

What is the area of this trapezoid?   

+

 

+

+

 

+

square units

",204,204,,,1630 +PRABG43G,1,Fill-in-the-blank(s),Numeric,"

Point F is on line CD. Find the measure of angle CFE.

+

+

 

+

m∠CFE = °

",28,28,,,351554 +PSBB6KJ,3,Fill-in-the-blank(s),Exact Match,"

Esta es una recta numérica con algunos puntos marcados.

+

 

+

+

 

+

 

+

Escribe el número C como un decimal.

+

 

+

",2.25,2.25,,,323486 +PSBB6KJ,1,Fill-in-the-blank(s),Exact Match,"

Esta es una recta numérica con algunos puntos marcados.

+

 

+

+

 

+

 

+

Escribe el número B como un decimal.

+

 

+

","1.50, 1.5","1.50, 1.5",,,323318 +PSBZ28,1,Fill-in-the-blank(s),Numeric,"

A box is shaped like an octagonal prism. Here is what the base of the prism looks like.

+

+

 

+

If the height of the box is 7 inches, what is the volume of the box?  

+

 

+

inches3

",287,287,,,124486 +PSBZ28,3,Fill-in-the-blank(s),Numeric,"

A box is shaped like an octagonal prism. Here is what the base of the prism looks like.

+

+

 

+

If the volume of the box is 123 in3, what is the height of the box?  

+

 

+

inches

",3,3,,,124819 +PSBBMNM,4,Fill-in-the-blank(s),Numeric,"

Compute the volume of the prism when d = 12.

+

 

+

cubic units

+

 

+

",1,1,,,229303 +PSBBMNM,3,Fill-in-the-blank(s),Numeric,"

Compute the volume of the prism when d = 2.

+

 

+

cubic units

+

 

+

",16,16,,,229143 +PSBBBHE,1,Fill-in-the-blank(s),Numeric,"

Jada has a meal in a restaurant. She adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00.

+

 

+ + + + + + + +
+

When the check comes, it says they also need to pay $3.99 in sales tax. What percentage of the subtotal is the sales tax?

+

 

+

%

+
",9.5,9.5,,,177693 +PSBFF,2,Fill-in-the-blank(s),Numeric,"

Diego has $11 and begins saving $5 each week toward buying a new phone. At the same time that Diego begins saving, Lin has $60 and begins spending $2 per week on supplies for her art class. 

+

 

+

After how many weeks will Diego and Lin have the same amount of money?

+

 

+

After weeks

+

 

+

 

",7,7,,,503 +PSBYMT,2,Fill-in-the-blank(s),Numeric,"

The second H-shaped polygon is a scaled copy of the first.

+

 

+

+

 

+

What scale factor takes the original polygon to its smaller copy?

+

 

+

",4-Jan,4-Jan,,,116350 +PSBCP64,2,Fill-in-the-blank(s),Numeric,"

For the triangle, a base and its corresponding height are labeled.

+

Find the area of the triangle.

+

 

+

+

 

+

square units

",16,16,,,418012 +PSB6A4,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region. 

+

 

+

+

 

+

cm2

",28,28,,,149451 +PSBBAK8,3,Fill-in-the-blank(s),Algebraic Expression,"

For radius and circumference of a circle, what is the constant of proportionality?

+

 

+

 

+

Use pi to represent the symbol

+

For example:

+

32π would be typed as 32pi

+

 

+

","2pi, 1/(2pi)","2pi, 1/(2pi)",,,172629 +PSBBYA9,3,Fill-in-the-blank(s),Numeric,"

A cashier worked an 8-hour day, and earned $58.00. The double number line shows the amount she earned for working different numbers of hours.

+

 

+

 

+

+

 

+

 

+

How much does the cashier earn if she works 3 hours? 

+

 

+

$

",21.75,21.75,,,287949 +PRABFAGF,1,Fill-in-the-blank(s),Numeric,"

The olive trees in an orchard produce 3,000 pounds of olives a year. It takes 20 pounds of olives to make 3 liters of olive oil.

+

 

+

How many liters of olive oil can this orchard produce in a year? If you get stuck, consider using the table.

+

 

+

liters

+

 

+ + + + + + + + + + + + + + + + + + + +
Olives (pounds)Olive Oil (liters)
203
100 
3,000 
",450,450,,,284919 +PSBBDRK,1,Fill-in-the-blank(s),Numeric,"

Here is a diagram and its corresponding equation. Find the solution to the equation.

+

 

+ + + + + + + +
4(x + 7) = 38 
+

 

+

x =

",2 1/2,2 1/2,,,190220 +PSBGWX,1,Fill-in-the-blank(s),Numeric,"

One inch is around 21120 centimeters.

+

 

+

+

 

+

How many centimeters long is 3 inches?  

+

 

+

centimeters

",7 13/20,7 13/20,,,35549 +PSBDHRQ,1,Fill-in-the-blank(s),Numeric,"

Use the tape diagram to answer the question: How many 25s are in 112?

+

 

+

25s are in 112

+

 

+

 

+

",3 3/4,3 3/4,,,563384 +PSBBYW,1,Fill-in-the-blank(s),Numeric,"

You can use a rectangle to represent (0.3) · (0.5).

+

+

What must the side length of each square represent for the rectangle to correctly represent (0.3) · (0.5)? 

+

 

+

units

",0.1,0.1,,,8390 +PRABFEMT,1,Fill-in-the-blank(s),Numeric,"

The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of milk has 25% of the recommended daily allowance of calcium. How many milligrams of calcium are in a cup of milk? If you get stuck, consider using the double number line.

+

 

+

milligrams

+

 

+

 

+

",300,300,,,210383 +PSBCBAC,2,Fill-in-the-blank(s),Numeric,"

Find the weight of one circle. 

+

 

+

w =units

+

 

+

",6 1/4,6 1/4,,,350665 +PRABEUP2,1,Fill-in-the-blank(s),Numeric,"

You find a crystal in the shape of a prism. Find the volume of the crystal.

+

 

+

  mm3

+

 

+

The point B is directly underneath point E, and the following lengths are known:

+ + + + + + + +
+
    +
  • From A to B: 2 mm
    • +
  • From B to C: 3 mm
    • +
  • From A to F: 6 mm
    • +
  • From B to E: 10 mm
    • +
  • From C to D: 7 mm
    • +
  • From A to G: 4 mm
    • +
+

 

+
+

 

",166,166,,,246416 +PSB64G,6,Fill-in-the-blank(s),Numeric,"

Here is the base of a prism.

+

 

+

+

 

+

 

+

When the height doubled, what was the percent increase for the volume?  

+

 

+

%

",100,100,,,153688 +PRABET92,1,Fill-in-the-blank(s),Numeric,"

Here is a square and some regular octagons.

+

 

+

In this pattern, all of the angles inside the octagons have the same measure. The shape in the center is a square. Find the measure of one of the angles inside one of the octagons.  

+
+

 

+

+

 

+
+

degrees

",135,135,,,130937 +PRABEUGH,1,Fill-in-the-blank(s),Numeric,"

Segments AB, EF, and CD intersect at point C, and angle ACD is a right angle. Find the value of g.

+

 

+

+

 

+

m∠g = °

",37,37,,,188665 +PRABQPRC,1,Fill-in-the-blank(s),Numeric,"

What is the area of this trapezoid? 

+

 

+

+

 

+

units2

",312,312,,,12774 +PSBB6KJ,2,Fill-in-the-blank(s),"Exact Fraction, Exact Match","

Esta es una recta numérica con algunos puntos marcados.

+

 

+

+

 

+

 

+

Escribe el número en C de dos maneras diferentes: como fracción y como decimal.

+

 

+ + + + + + + +
+

fracción:  

+

+		 +

decimal:

+

 

+
","2.25, 2 1/4, 9/4","2.25, 2 1/4, 9/4",,,323395 +PSBEB6,1,Fill-in-the-blank(s),Numeric,"

A group of students was asked, “How many children are in your family?” The responses are displayed in the dot plot.

+

 

+

+

 

+

 

+

How many students responded to the questions?

+

 

+

students

",20,20,,,21754 +PSBJWY,1,Fill-in-the-blank(s),Numeric,"

In a word game, 1 letter is worth 1 point. This dot plot shows the scores for 20 common words.

+

 

+

+

 

+

What is the median score?  

+

 

+

points

+

 

+

 

",6.5,6.5,,,46015 +PSBCR72,1,Fill-in-the-blank(s),Numeric,"

The two triangles displayed are scaled copies of one another. 

+

 

+

+

 

+

Find the scale factor. 

+

 

+

","4/3, 3/4","4/3, 3/4",,,429837 +PRABFGYV,1,Fill-in-the-blank(s),Numeric,"

Complete the calculation so that the problem shows the correct difference.

+

 

+ + + + + + +
    1-     0.015
+

 

+

1 - = 0.015

",0.985,0.985,,,94291 +PRABESV4,1,Fill-in-the-blank(s),Algebraic Expression,"

Find the area of the shaded region. Express your answer in terms of π.   

+

 

+

+

 

+

 

+

in2

+

 

+

Use pi to represent π.

+

For example: 32π would be typed as 32pi

",540 - 65.25pi,540 - 65.25pi,,,175875 +PSBBU3Q,2,Fill-in-the-blank(s),Numeric,"

This figure is made from a part of a square and a part of a circle. 

+

 

+

+

 

+
+
+
+
+

 

+
+
+
+
+

What is the area of this figure, to the nearest square unit?  

+

 

+

square units

",95,95,,,270027 +PSBF6A,2,Fill-in-the-blank(s),Numeric,"

Now solve the problem.

+

 

+

56 is what percent of 70?  

+

 

+

%

+

 

+

",80,80,,,31856 +PSBB72,1,Fill-in-the-blank(s),Numeric,"

Lines AC and BD intersect at E.

+ + + + + + + +
+

What is the measure of angle BEC?

+

 

+

°

+
",120,120,,,9804 +PSBCHZZ,1,Fill-in-the-blank(s),Numeric,"

In the picture triangle A'B'C' is an image of triangle ABC after a rotation. The center of rotation is E.

+

+

 

+

 

+

What is the length of side AB? 

+

 

+

units

",9,9,,,388718 +PSBU7P,1,Fill-in-the-blank(s),Numeric,"

Lines AB and CD intersect at E.

+

 

+ + + + + + + +
+

What is the measure of angle AED?

+

 

+

°

+
",130,130,,,96584 +PSBBEUD,1,Fill-in-the-blank(s),Numeric,"

Noah is planning his birthday party. Here is a tree showing all of the possible themes, locations, and days of the week that Noah is considering.

+

 

+

How many themes is Noah considering?

+

 

+

themes

+

",3,3,,,194307 +PSBUPR,1,Fill-in-the-blank(s),Numeric,"

Use the diagram to find the measure of angle ABC.

+ + + + + + + +
m∠ABC = ° 
",130,130,,,92551 +PSBBDV8,1,Fill-in-the-blank(s),Numeric,"

A group of hikers park their car at a trail head and walk into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car after h hours of hiking.

+

 

+

+

 

+

How far is the campsite from their car?

+

 

+

miles

",4,4,,,190411 +PSBQ8P,1,Multiple Choice (select 1),Multiple Choice,"

Elena and Han are discussing how to write the repeating decimal  as a fraction. Hans says that  equals . ""I calculated  because the decimal begins repeating after 3 digits. Then I subtracted to get . Then I multiplied by 100 to get rid of the decimal: . And finally, I divided to get ."" Elena says that  equals . ""I calculated  because one digit repeats. Then I subtracted to get . Then I did what Han did to get  and .

+

 

+

Do you agree with either of them?

",,,Han is correct || Elena is correct || Both are correct || Neither is correct,Both are correct,74236 +PRABQM8U,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,"Given a box plot, it is always possible to calculate the mean of the data. || Given a box plot, it is always possible to calculate the median of the data. || Given a box plot, it is always possible to construct a corresponding dot plot. || Given a dot plot, it is always possible to construct a corresponding box plot. || Given a histogram, it is always possible to construct a corresponding box plot.","Given a box plot, it is always possible to calculate the median of the data. || Given a dot plot, it is always possible to construct a corresponding box plot.",193572 +PSBCC5E,3,Multiple Choice (select 1),Multiple Choice,"

Which data set has the smaller MAD? 

+

 

+

",,,South Africa || Australia,Australia,361422 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681 +PSBB73F,1,Multiple Choice (select 1),Multiple Choice,"

A line contains the points (-1, 4) and (5, -3).

+

 

+

Without doing any calculations, determine whether the slope of this line is positive or negative.

",,,Positive || Negative,Negative,331866 +PRABPVSV,1,Multiple Choice (select 1),Multiple Choice,"

Which equation matches the hanger diagram?

+

 

",,,"

 x ⋅ x = 1 ⋅ 1 ⋅ 1 ⋅ 1 ⋅ 1 

||

x = 25

||

x + 3 = 5

||

2x = 5

",

2x = 5

,367186 +PSBCW9S,1,Multiple Choice (select 1),Multiple Choice,"
+
+
+

Determine if the following is true or false.

+

 

+

l-5l > 3

+
+
+
",,1,True || False,TRUE,458552 +PRABQMW2,1,Multiple Choice (select all),Check All That Apply,"

Diego’s dog weighs more than 10 kilograms and less than 15 kilograms.

+

Select all the inequalities that must be true if w is the weight of Diego’s dog in kilograms.

+

 

",,,w > 10 || w < 10 || w > 11 || w < 11 || w > 15 || w < 15,w > 10 || w < 15,410688 +PSBJS4,5,Multiple Choice (select 1),Multiple Choice,"

The graph shows the temperature between noon and midnight in one day in a certain city.

+

 

+

+

 

+

 

+

Does this graph show that the temperature is a function of time, or is time a function of temperature?

",,,Temperature is a function of time || Time is a function of temperature,Temperature is a function of time,45592 +PSBVBV,1,Multiple Choice (select 1),Multiple Choice,"

Jada and Noah wanted to find the total volume of a cube and a rectangular prism. They know the prism's volume is 20 cubic units, and they know the cube has side lengths of 10 units. Jada says the total volume is 27,000 cubic units. Noah says it is 1,020 cubic units. Here is how each of them reasoned:

+

 

+

 

+ + + + + + + + + + + +
+

Jada's Method:

+		 +

Noah's Method:

+
+

20 + 10³

+

30³

+

27,000

+		 +

20 + 10³

+

20 + 1,000

+

1,020

+ 
+

 

+

 

+

Do you agree with either of them?

",,,Agree with both || Agree with Jada || Agree with Noah || Disagree with both,Agree with Noah,97579 +PSBEUG,5,Multiple Choice (select 1),Multiple Choice,"

On the second graph, which point shows Andre’s consumption and which shows Jada’s consumption?

",,,"The rightmost point shows Andre's consumption, the leftmost point shows Jada's consumption || The rightmost point shows Jada's consumption, the leftmost point shows Andre's consumption","The rightmost point shows Jada's consumption, the leftmost point shows Andre's consumption",24277 +PRABJGFX,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions equivalent to . 

",,,1. 2⋅(x+3) || 2. (x+3)2 || 3. 2⋅x+2⋅3  || 4. 2⋅x+3 || 5. (2⋅x)+3  || 6. (2+x)3,1. 2⋅(x+3) || 2. (x+3)2 || 3. 2⋅x+2⋅3 ,109572 +PSB2UH,2,Multiple Choice (select 1),Multiple Choice,

Is 100 a solution of 10 − 0.035d > 4?

,,,Yes || No,Yes,129703 +PSBBWDP,1,Multiple Choice (select 1),Multiple Choice,"

Decide which calculation shows the correct way to find 0.3 - 0.006. 

",,,"

+

 

||

+

 

||

+

 

||

","

",277053 +PSBR54,1,Multiple Choice (select 1),Multiple Choice,"

Jada and Elena learned that 8% of students have asthma. They want to know the probability that in a team of 4 students, at least one of them has asthma. To simulate this, they put 25 slips of paper in a bag. Two of the slips say “asthma.” Next, they take four papers out of the bag and record whether at least one of them says “asthma.” They repeat this process 15 times.

+

 

+
    +
  • +

    Jada says they could improve the accuracy of their simulation by using 100 slips of paper and marking 8 of them.

    +
    • +
+

 

+
    +
  • +

    Elena says they could improve the accuracy of their simulation by conducting 30 trials instead of 15.

    +
    • +
+

 

+

Do you agree with either of them?

",,,I agree with Elena || I agree with Jada || I agree with both of them || I agree with neither of them,I agree with Elena,78469 +PSBB6PY,3,Multiple Choice (select 1),Multiple Choice,"

",,,< || = || >,>,323873 +PSBB6HD,1,Multiple Choice (select 1),Multiple Choice,"

Una cinta tiene 30 pulgadas de longitud. Debes cortarla en varios trozos, todos de la misma longitud.

+

 

+

¿Puedes cortar la cinta en trozos de 4 pulgadas?

",,,Sí || No,No,322962 +PRABEQDX,1,Multiple Choice (select all),Check All That Apply,

Which scales are equivalent to 1 inch to 1 foot? Select all that apply.

,,,"

1 to 12 

||

112 to 1 

||

100 to 12 

||

5 to 60 

||

36 to 3 

||

9 to 108 

","

1 to 12 

||

112 to 1 

||

5 to 60 

||

9 to 108 

",123653 +PSBDG6F,1,Multiple Choice (select 1),Multiple Choice,"

Which weighs more: a watermelon that weighs 7.5 kilograms or a baby that weighs 12 pounds?

+

 

+

Note: 1 pound is about 0.45 kilograms.

",,,a watermelon that weighs 7.5 kilograms || a baby that weighs 12 pounds,a watermelon that weighs 7.5 kilograms,559856 +PRABEBM6,1,Multiple Choice (select all),Check All That Apply,"

The solution to a system of equations is (6, -3). Choose two equations that might make up the system.

",,,

y = -3x + 6

|| y = 2x - 9 || y = -5x + 27 || y = 2x - 15 || y = -4x + 27,y = -5x + 27 || y = 2x - 15,91020 +PRABQP6S,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 78.

",,,"

7-2·710

||

(73)5

||

(73)47-4

||

(74)-2

||

767-2

","

7-2·710

||

767-2

",552296 +PSBR6F,1,Multiple Choice (select 1),Multiple Choice,

A stack of books is 72 inches tall. Each book is 2 inches thick. Which expression tells us how many books are in the stack? 

,,,72 ⋅ 2 || 72 − 2 || 2 ÷ 72 || 72 ÷ 2,72 ÷ 2,78941 +PSBDA,1,Multiple Choice (select 1),Multiple Choice,"

For the following pair of shapes, decide whether or not they are congruent. 

+

 

+

",,,"Yes, they are congruent || No, they are not congruent","No, they are not congruent",336 +PRABQKVG,1,Multiple Choice (select 1),Multiple Choice,"

Kiran has used 45 of the pieces in his jigsaw puzzle. He has used 120 pieces. How many pieces are in the whole puzzle?

",,150,96 || 125 || 150 || 216,150,518730 +PRABFFDV,1,Multiple Choice (select all),Check All That Apply,"

Which expression has the same value as (0.06) · (0.154)?   Select all that apply.

",,,"

6 · 1100 · 154 · 11,000

||

6 · 154 · 1100,000

||

6 · (0.1) · 154 · (0.01)

||

6 · 154 · (0.00001)

||

0.00924

","

6 · 1100 · 154 · 11,000

||

6 · 154 · 1100,000

||

6 · 154 · (0.00001)

||

0.00924

",8563 +PSB32P,1,Multiple Choice (select 1),Multiple Choice,"

Decide if the responses will produce numerical data or categorical data.

+

 

+

How did you get to school this morning?

",,,Categorical || Numerical,Categorical,136547 +PSBBMWY,1,Multiple Choice (select all),Check All That Apply,

Select all the quadrilaterals that you think can be decomposed into two identical triangles using only one line.

,,,"

||

||

||

||

||

","

||

||

||

",230682 +PSBC296,3,Multiple Choice (select 1),Multiple Choice,

Is the line y=x a good fit for the data?

,,,Yes || No,Yes,480902 +PRABQMT7,1,Multiple Choice (select all),Check All That Apply,"

Given that x is -4, select all the true statements.

+

 

+

+

 

",,,Point A is at |6| || Point B is at -x || Point C is at |-2.5| || Point D is at |3| || Point E is at |x| || Point F is at -|6|,Point C is at |-2.5| || Point D is at |3| || Point E is at |x|,49529 +PRABQPMU,1,Multiple Choice (select all),Check All That Apply,"

Select all the situations that can be represented by the tape diagram.

+

 

+

",,,"Noah walked a family’s dog 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $6 at the end of the month. Noah earned $106 from dog walking. || A family of 5 drove to a soccer game. They paid $6 for parking, and all of their tickets were the same price. They paid $106 in total. || 5 bags of coins each contain 6 nickels and the same number of pennies. Altogether, the bags contain 106 coins. || Kiran is baking 5 batches of muffins. Each batch needs the same amount of sugar in the muffins, and each batch needs six extra teaspoons of sugar for the topping. Kiran uses 106 total teaspoons of sugar. || Priya buys 5 cases of water, each with the same number of bottles. The store clerk gives her an extra 6 bottles before she leaves. She leaves with a total of 106 bottles.","5 bags of coins each contain 6 nickels and the same number of pennies. Altogether, the bags contain 106 coins. || Kiran is baking 5 batches of muffins. Each batch needs the same amount of sugar in the muffins, and each batch needs six extra teaspoons of sugar for the topping. Kiran uses 106 total teaspoons of sugar.",90188 +PSB7YF,1,Multiple Choice (select 1),Multiple Choice,"

There are 2 mixtures of light purple paint.

+

 

+
    +
  • Mixture A is made with 5 cups of purple paint and 2 cups of white paint.
    • +
  • Mixture B is made with 15 cups of purple paint and 8 cups of white paint.
    • +
+

 

+

Which mixture is a lighter shade of purple?

",,,Mixture A || Mixture B,Mixture B,158226 +PSB724,5,Multiple Choice (select 1),Multiple Choice,"

Overall, which group of students—sixth- or seventh-grade—sent more text messages?

",,,Sixth-grade students || Seventh-grade students || Neither,Neither,158855 +PRABFKN9,1,Multiple Choice (select all),Check All That Apply,

Here are descriptions of data sets. Select all descriptions of data sets that could be graphed as dot plots.

,,,

Class size for the classes at an elementary school

||

Colors of cars in a parking lot

||

Favorite sport of each student in a sixth-grade class

||

Birth weights for the babies born during October at a hospital

||

Number of goals scored in each of 20 games played by a school soccer team

,

Class size for the classes at an elementary school

||

Birth weights for the babies born during October at a hospital

||

Number of goals scored in each of 20 games played by a school soccer team

,285834 +PRABQPKU,1,Multiple Choice (select all),Check All That Apply,"

Select all expressions that are equivalent to -4(x + 2) - 2x + 4.

",,,-6x - 4 || -4x + 2 - 2x + 4 || -10x || -4x + -8 - 2x + 4 || -4x - 2x - 8 + 4,-6x - 4 || -4x + -8 - 2x + 4 || -4x - 2x - 8 + 4,163965 +PRABEU62,1,Multiple Choice (select all),Check All That Apply,

Select all the statements that are true for any value of x.

,,,"

7x + (2x + 7) = 9x + 7

||

7x + (2x - 1) = 9x + 1

||

12x + 3 - 12x = 3

||

5x - (8 - 6x) = -x - 8

||

0.4x - (0.2x + 8) = 0.2x - 8

||

6x - (2x - 4) = 4x + 4

","

7x + (2x + 7) = 9x + 7

||

12x + 3 - 12x = 3

||

0.4x - (0.2x + 8) = 0.2x - 8

||

6x - (2x - 4) = 4x + 4

",277314 +PSBXP5,1,Multiple Choice (select 1),Multiple Choice,"

A large fish tank is filled with table tennis balls with numbers written on them. Jada chooses 10 table tennis balls from the tank and writes down their numbers.

+ + + + + + + + + + + + + + + +
1351324153
+

 

+

 A second tank is filled with golf balls with numbers written on them. Jada chooses 10 golf balls from the tank and writes down their numbers.

+ + + + + + + + + + + + + + + +
1452622148
+

 

+

To win a prize, Jada must get a a ball with an even number. Should she try to win the prize using the tank of table tennis balls or the tank of golf balls? 

",,,tank of table tennis balls || tank of golf balls,tank of golf balls,111989 +PSBEQY,2,Multiple Choice (select 1),Multiple Choice,"

The mean age for the population is 35 years. If Elena picks a new sample of size 10 from this population, should she expect her sample mean to be within 1 year of the population mean?

",,,Yes || No,No,23659 +PRABEVAH,1,Multiple Choice (select all),Check All That Apply,"

A heron is perched in a tree 50 feet above sea level. Directly below the heron, a pelican is flying 17 feet above sea level. Directly below the birds is a trout, swimming 23 feet below sea level.

+

 

+

Select all the true statements.

",,,The difference in height between the pelican and the heron is -33 feet. || The difference in height between the pelican and the heron is 33 feet. || The distance between the heights of the pelican and heron is -33 feet. || The difference in height between the pelican and the trout is -40 feet. || The difference in height between the pelican and the trout is 40 feet. || The distance between the heights of the pelican and the trout is 40 feet.,The difference in height between the pelican and the heron is -33 feet. || The difference in height between the pelican and the trout is 40 feet. || The distance between the heights of the pelican and the trout is 40 feet.,114294 +PSBBMT9,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

",,0,True || False,FALSE,230244 +PSBH8S,10,Multiple Choice (select 1),Multiple Choice,"

Spinning this spinner will result in yellow.

+

 

+

",,,impossible || unlikely || equally likely as not || likely || certain,impossible,42864 +PRABEPN5,1,Multiple Choice (select 1),Multiple Choice,"

A square has vertices (0,0), (5,2), (3,7), and (-2,5). Which of these statements is true?

",,,The square’s side length is 5. || The square’s side length is between 5 and 6. || The square’s side length is between 6 and 7. || The square’s side length is 7.,The square’s side length is between 5 and 6.,146523 +PSBX69,9,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

There is no solution for the equation for line ℓ that has y=0.

",,0,True || False,FALSE,114103 +PSBS2E,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

9 · 9 · 3 = 35

+
 
",,1,True || False,TRUE,83709 +PRABFGVX,1,Multiple Choice (select all),Check All That Apply,"

Choose the expressions that do not represent the total area of the rectangle. Select all that apply.

+

 

+

",,,5t + 4t || t + 5 + 4 || 9t || 4 · 5 · t || t(5 + 4),t + 5 + 4 || 4 · 5 · t,189623 +PSBGTE,1,Multiple Choice (select 1),Multiple Choice,"

Here are two triangles.

+

+

Is Triangle B a rotation of Triangle A?

+
 
",,,Yes || No,No,35246 +PRABQN9B,1,Multiple Choice (select all),Check All That Apply,

Select all expressions whose value is negative.

,,,"

‐154

||

15‐4

||

‐15‐4

||

‐8  · 34

||

(‐8) ·‐34

","

‐154

||

15‐4

||

‐8  · 34

",24305 +PRABMTN8,1,Multiple Choice (select 1),Multiple Choice,"

For the equation, decide if it is always true or never true.

+

 

+

3(x − 5) = 2(x − 5) + x

",,,Always True || Never True,Never True,148466 +PRABQNYY,1,Multiple Choice (select all),Check All That Apply,"

The shape is composed of squares and quarter circles. Select all the expressions that represent its perimeter.

+

",,,42 + 14π || 7 + 7 + 7 + 7 + 7 + 7 + 3.5π + 3.5 π + 3.5π + 3.5π || 91 + 14π || 147 + 49π || 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7,42 + 14π || 7 + 7 + 7 + 7 + 7 + 7 + 3.5π + 3.5 π + 3.5π + 3.5π,27039 +PSBZP8,3,Multiple Choice (select 1),Multiple Choice,

Did the bakery owner receive more or spend more money on May 5? 

,,,

Receive More Money

||

Spend More Money

,

Receive More Money

,123053 +PRABE57G,1,Multiple Choice (select 1),Multiple Choice,"

What is the surface area of this rectangular prism?

+

 

+

",,,16 square units || 32 square units || 48 square units || 64 square units,64 square units,273669 +PSBPP,1,Multiple Choice (select 1),Multiple Choice,"

When asked to draw a triangle with two 45º angles and a side length of 8 cm, Diego drew this triangle.

+

 

+

+

 

+

Do you agree with Diego’s answer?

",,,Yes || No,Yes,1442 +PRABETYD,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that match the diagram.

+

 

+

",,,"

x + 5 = 18

||

18 ÷ 3 = x + 5

||

3(x + 5) = 18

||

x + 5 = 13 · 18

||

3x + 5 = 18

","

18 ÷ 3 = x + 5

||

3(x + 5) = 18

||

x + 5 = 13 · 18

",156494 +PRABFJXB,1,Multiple Choice (select 1),Multiple Choice,"

One night, it is  24°C warmer in Tucson than it was in Minneapolis. If the temperatures in Tucson and Minneapolis are opposites, what is the temperature in Tucson?

",,,"

-24°C

||

-12°C

||

12°C

||

24°C

","

12°C

",39966 +PSB5HF,1,Multiple Choice (select 1),Multiple Choice,"

A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same?

",,,Yes || No,Yes,145212 +PRABQPTZ,1,Multiple Choice (select 1),Multiple Choice,"

For two weeks, the highest temperature each day was recorded in four different cities. Lines l, m, n, and p are graphs of the temperature over time in Lubbock, Memphis, New Orleans, and Phoenix.

+

 

+

+


Which statement is true?

",,,"The high temperature in Lubbock increased as time passed. || The high temperature in Memphis decreased steadily. || Initially, the high temperature was warmer in Phoenix than in Memphis. || The high temperature in Phoenix rose faster than the temperature in NewOrleans.",The high temperature in Memphis decreased steadily.,79163 +PRABQMB3,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations represented by this tape diagram.

+

",,,3.9 + ? = 8.6 || 8.6 + 3.9= ? || 8.6 = ? + 3.9 || 8.6 - 3.9 = ? || ? - 3.9 = 8.6,3.9 + ? = 8.6 || 8.6 = ? + 3.9 || 8.6 - 3.9 = ?,427819 +PRABQKJE,1,Multiple Choice (select all),Check All That Apply,"

Select all the true statements.

+

 

+

+

 

",,,The ratio of triangles to squares is 2 to 6. || The ratio of squares to smiley faces is 2 : 4. || The ratio of smiley faces to triangles is 4 to 2. || There are three triangles for every square. || There are two smiley faces for every square. || There are two triangles for every smiley face.,The ratio of squares to smiley faces is 2 : 4. || There are three triangles for every square. || There are two smiley faces for every square.,2196 +PSBCRM2,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the inequality statement is true or false. 

+

 

+

3 > -8

",,1,True || False,TRUE,426543 +PSBCM2F,1,Multiple Choice (select 1),Multiple Choice,"

Which has a greater value: 7.4 − 0.0022 or 7.39 − 0.0012? 

",,,7.4 − 0.0022 || 7.39 − 0.0012,7.4 − 0.0022,405351 +PRABE9UJ,1,Multiple Choice (select all),Check All That Apply,

Diego estimates that there will need to be 3 pizzas for every 7 kids at his party. Select all the statements that express this ratio.

,,,

The ratio of kids to pizzas is 7 : 3.

|| The ratio of pizzas to kids is 3 to 7. ||

The ratio of kids to pizzas is 3 : 7.

|| The ratio of pizzas to kids is 7 to 3. || For every 7 kids there need to be 3 pizzas.,

The ratio of kids to pizzas is 7 : 3.

|| The ratio of pizzas to kids is 3 to 7. || For every 7 kids there need to be 3 pizzas.,83745 +PSBX69,15,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

There is a point whose coordinates make the equations of all three lines true.

",,0,True || False,FALSE,114797 +PSBBWBK,1,Multiple Choice (select 1),Multiple Choice,"

A student said we cannot subtract 1.97 from 20 because 1.97 has two decimal digits and 20 has none.

+

 

+

Do you agree with his statement? 

",,,Agree || Disagree,Disagree,276696 +PSBN6A,1,Multiple Choice (select 1),Multiple Choice,"

The x-axis represents the number of hours before or after noon, and the y-axis represents the temperature in degrees Celsius.

+

 

+

+

 

+

At 9 a.m., it was below freezing. In what quadrant would this point be plotted? 

",,,Quadrant I || Quadrant II || Quadrant III || Quadrant IV,Quadrant III,63054 +PRABFK39,1,Multiple Choice (select 1),Multiple Choice,"

Here is a dot plot that shows the ages of teachers at a school.

+

 

+
+
+
+
+

Which of these statements is true of the data set shown in the dot plot?

+

 

+

+
+
+
+
",,,The mean is less than the median. || The mean is approximately equal to the median. || The mean is greater than the median. || The mean cannot be determined.,The mean is greater than the median.,188655 +PSBTTV,2,Multiple Choice (select 1),Multiple Choice,

There are 10 people on the team. Do they save money if they buy an extra shirt?

,,,Yes || No,Yes,87609 +PSBB2ZW,1,Multiple Choice (select 1),Multiple Choice,"

When asked to draw a quadrilateral with all four sides measuring 5 cm, Jada drew a square.

+

+


Do you agree with Jada’s answer?

",,,Yes || No,Yes,303405 +PRABECYV,1,Multiple Choice (select all),Check All That Apply,"

Which of the changes would keep the hanger in balance?

+

 

+

Select all that apply.

+

 

+

+

 

+

 

",,,"
+

Adding two circles on the left and a square on the right

+
||

Adding 2 triangles to each side

||

Adding two circles on the right and a square on the left

||

Adding a circle on the left and a square on the right

||

Adding a triangle on the left and a square on the right

","
+

Adding two circles on the left and a square on the right

+
||

Adding 2 triangles to each side

||

Adding two circles on the right and a square on the left

",498517 +PSBJXX,1,Multiple Choice (select 1),Multiple Choice,"

Which square—large, medium, or small—covers more of the plane?

+

 

+

",,,

large

||

medium

||

small

,

large

,46209 +PRABQMBQ,1,Multiple Choice (select 1),Multiple Choice,

A woodworker wants to cut a board that is 8.225 feet long into 5 equal-length pieces. How long will each of the cut boards be?

,,,0.1645 feet || 1.645 feet || 4.1125 feet || 41.125 feet,1.645 feet,278232 +PRABQJS9,1,Multiple Choice (select all),Check All That Apply,

Select all the triangles that have an area of 45 square units.

,,,"

||

||

||

||

","

||

",383830 +PRABPG8F,1,Multiple Choice (select 1),Multiple Choice,

Suppose you have a pint of grape juice and a pint of milk. You pour 1 tablespoon of the grape juice into the milk and mix it up. Then you pour 1 tablespoon of this mixture back into the grape juice. Which liquid is more contaminated?

,,,Milk || Grape Juice,Milk,350776 +PSB5Y4,1,Multiple Choice (select 1),Multiple Choice,"

A rectangular solid has a square base with side length l, height 8, and volume V. Is the relationship between l and V a proportional relationship?

",,,Yes || No,No,147904 +PRABQPRY,1,Multiple Choice (select all),Check All That Apply,"

Select all the points that are 5 units away from (6, 2). 

",,,"(1, 2) || (6, 5) || (11, 7) || (30, 10) || (6, -3) || (11, 2)","(1, 2) || (6, -3) || (11, 2)",1910 +PRABQP43,1,Multiple Choice (select 1),Multiple Choice,"

Which is closest to the difference in the volume of the two cylinders? 

+

 

+ + + + + + + +
",,,"

15,795 cm³

|| 2,534 cm³ || 806 cm³ || 512 cm³",806 cm³,674243 +PSBCKT6,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of numbers below, select the number that is greater.

",,,"

42 · 107

||

8.5 · 108

","

8.5 · 108

",399091 +PRABFG2Q,1,Multiple Choice (select all),Check All That Apply,"
+

Select all expressions that are equal to 3 · 3 · 3 · 3 · 3.

+
",,,"

3 · 5

||

35

||

34 · 3

||

5 · 3

||

53

","

35

||

34 · 3

",86722 +PSBHYF,1,Multiple Choice (select 1),Multiple Choice,"

To decompose a quadrilateral into two identical shapes, Clare drew a dashed line as shown in the diagram.

+

 

+

+

 

+
She said the that two resulting shapes have the same area. Do you agree?
",,,Yes || No,Yes,41185 +PSBBREW,1,Multiple Choice (select 1),Multiple Choice,"

Tyler said this net cannot be a net for a square prism because not all the faces are square.
 

+

Do you agree with Tyler's statement?

+

",,,Yes || No,No,249682 +PSB7HB,1,Multiple Choice (select 1),Multiple Choice,

Which of the following graphs could represent the volume of water in a cylinder as a function of its height?

,,,"

 

||

||

","

 

",155954 +PRABERFN,1,Multiple Choice (select 1),Multiple Choice,"

Which scale is equivalent to 1 cm to 1 km?

+
 
",,,"1 to 1,000 || 10,000 to 1 || 1 to 100,000 || 100,000 to 1 || 1 to 1,000,000","1 to 100,000",146478 +PRABQK7Z,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that represent the total area of the rectangle.

+

",,,"

15c + 15

||

 15 · c + 15 · 15

||

15(c + 15)

||

3c

||

15c + 3

","

 15 · c + 15 · 15

||

15(c + 15)

||

15c + 3

",56749 +PRABPMNH,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that have the same value. 

,,,

24

||

26

||

28

||

43

||

82

||

88

,

26

||

43

||

82

,427433 +PRABE5HQ,1,Multiple Choice (select all),Check All That Apply,

Select all parallelograms that have a correct height labeled for the given base.

,,,"

||

||

||

","

||

||

",375655 +PRABQM98,1,Multiple Choice (select all),Check All That Apply,"

Quadrilateral ABCD is a scaled copy of quadrilateral EFGH. Select all of the true statements.

+

 

+

",,,Segment BC is half the length of segment EF. || Segment CD is half the length of segment GH. || The measure of angle ADC is equal to the measure of angle EHG. || The length of segment AB is 3 units. || The area of ABCD is half the area of EFGH.,Segment CD is half the length of segment GH. || The measure of angle ADC is equal to the measure of angle EHG. || The length of segment AB is 3 units.,12006 +PRABFEYB,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equal to .

",,,"30 || 3,000 || 1,000 × 3 || 10 × 3 || 10 × 10 × 10 || 100 ||

1,000

","10 × 10 × 10 ||

1,000

",104252 +PRABQMB4,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations represented by this tape diagram.

+

 

+

",,,4 + 3 = ? || 3 + 3 + 3 + 3 = ? || ? = 4 · 3 || ? = 3 · 3 · 3 · 3 || 4 ÷ 3= ? || 4 = ? ÷ 3,3 + 3 + 3 + 3 = ? || ? = 4 · 3 || 4 = ? ÷ 3,427946 +PSBYUC,5,Multiple Choice (select 1),Multiple Choice,"

At which time period, 8:05–8:09 or 8:25–8:29, was there a greater change to the number of bottles in the machine? 

",,,"8:05-8:09 || 8:25-8:29 || Both, same amount of change to the number of bottles","Both, same amount of change to the number of bottles",117977 +PRABEUF6,1,Multiple Choice (select all),Check All That Apply,"

Select all the inequalities that have the same solutions as -4x<20. 

",,,-x < 5 || 4x > -20 || 4x < -20 || x < -5 || x > 5 || x > -5,-x < 5 || 4x > -20 || x > -5,110803 +PRABFS5R,1,Multiple Choice (select all),Check All That Apply,"

Select the unit from the list that you would use to measure the object.

+

 

+

The length of the border between the United States and Canada

",,,centimeters || cups || feet || gallons || grams || inches || kilograms || kilometers || liters || meters || miles || milliliters || millimeters || ounces || pounds || quarts || tons || yards,kilometers || miles,174042 +PRABETPU,1,Multiple Choice (select 1),Multiple Choice,"

A store has a 20% off sale on pants. With this discount, the price of one pair of pants before tax is $15.20. What was the original price of the pants?

",,,$3.04 || $12.16 || $18.24 || $19.00,$19.00 ,509942 +PRABQKNX,1,Multiple Choice (select 1),Multiple Choice,"

A mixture of purple paint contains 6 teaspoons of red paint and 15 teaspoons of blue paint. To make the same shade of purple paint using 35 teaspoons of blue paint, how much red paint would you need? Use the double number line diagram to help if needed.

+
",,,12 teaspoons || 14 teaspoons || 18 teaspoons || 26 teaspoons,14 teaspoons,115193 +PSBB5SU,1,Multiple Choice (select 1),Multiple Choice,"

Andre draws this tape diagram for :

+

+


Andre says that because there are 4 groups of  and  left. Do you agree with Andre?

",,,Agree || Disagree,Disagree,318653 +PRABQMFM,1,Multiple Choice (select 1),Multiple Choice,

Which expression is equal to 73?

,,,"

7 · 7 · 7

||

21

||

37

||

10

",

7 · 7 · 7

,350322 +PSBBZA9,1,Multiple Choice (select 1),Multiple Choice,"

The students in art class are designing a stained-glass window to hang in the school entryway. The window will be 3 feet tall and 4 feet wide. Here is their design.

+

 

+

+

 

+

They have raised $100 for the project. The colored glass costs $5 per square foot and the clear glass costs $2 per square foot. The material they need to join the pieces of glass together costs 10 cents per foot and the frame around the window costs $4 per foot.

+

 

+

A local community member sees the school’s stained glass window and really likes the design. They ask the students to create a larger copy of the window using a scale factor of 3. Would $450 be enough to buy the materials for the larger window?

",,,Yes || No,No,294072 +PSBEQM,1,Multiple Choice (select all),Check All That Apply,"

Select all of the parallelograms.

+

 

+

",,,A || B || C || D || E,B || C,23769 +PSBNHS,1,Multiple Choice (select 1),Multiple Choice,"

A brownie recipe calls for 1 cup of sugar and 12 cup of flour to make one batch of brownies.  To make multiple batches, the equation f = 12s where f is the number of cups of flour and s is the number of cups of sugar represents the relationship. Which graph also represents the relationship? 

",,,"

+

 

||

+

 

||

","

+

 

",60015 +PSBDHVR,1,Multiple Choice (select 1),Multiple Choice,"

At a farmer’s market, two vendors sell fresh milk. One vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. Which is the better deal? 

",,,2 liters for $3.80 || 1.5 liters for $2.70,1.5 liters for $2.70,564260 +PRABG6MX,1,Multiple Choice (select 1),Multiple Choice,"

Clare’s recipe for banana bread won’t fit in her favorite pan. The pan is inches by 11 inches by 2 inches. The batter fills the pan to the very top, and when baking, the batter spills over the sides. To avoid spills, there should be about an inch between the top of the batter and the rim of the pan.

+

 

+

Clare has another pan that is 9 inches by 9 inches by inches. If she uses this pan, will the batter spill over during baking? 

",,,Yes || No,Yes,167762 +PRABFKET,1,Multiple Choice (select all),Check All That Apply,

Here are some bank transactions from a bank account last week. Which transactions represent negative values?

,,,Monday: $650 paycheck deposited || Tuesday: $40 withdrawal from the ATM at the gas pump || Wednesday: $20 credit for returned merchandise || Thursday: $125 deducted for cell phone charges || Friday: $45 check written to pay for book order || Saturday: $80 withdrawal for weekend spending money || Sunday: $10 cash-back reward deposited from a credit card company,Tuesday: $40 withdrawal from the ATM at the gas pump || Thursday: $125 deducted for cell phone charges || Friday: $45 check written to pay for book order || Saturday: $80 withdrawal for weekend spending money,63725 +PRABEU65,1,Multiple Choice (select all),Check All That Apply,"

Suppose you are interested in learning about how much time seventh grade students at your school spend outdoors on a typical school day.

+

 

+

Select all the samples that are a part of the population you are interested in.

",,,The 20 students in a seventh grade math class. || The first 20 students to arrive at school on a particular day. || The seventh grade students participating in a science fair put on by the four middle schools in a school district. || The 10 seventh graders on the school soccer team. || The students on the school debate team.,The 20 students in a seventh grade math class. || The 10 seventh graders on the school soccer team.,100451 +PRABEVCW,1,Multiple Choice (select 1),Multiple Choice,"

Which number line shows all the values of x that make the inequality -3x + 1 < 7 true?

+

 

+

+
 
",,,"

A

||

B

||

C

||

D

","

D

",189992 +PSBBME6,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

24 = 2 ⋅ 4

",,0,True || False,FALSE,228008 +PRABEUKM,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that match the tape diagram.

+

 

+

",,,35 = 8 + x + x + x + x + x + x || 35 = 8 + 6x || 6 + 8x = 35 || 6x + 8 = 35 || 6x + 8x = 35x || 35 − 8 = 6x,35 = 8 + x + x + x + x + x + x || 35 = 8 + 6x || 6x + 8 = 35 || 35 − 8 = 6x,274694 +PSB5BQ,1,Multiple Choice (select 1),Multiple Choice,"

In one version of trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes?

",,,Yes || No,Yes,143888 +PSBH8S,5,Multiple Choice (select 1),Multiple Choice,

No one in your class will be late to class next week.

,,,impossible || unlikely || equally likely as not || likely || certain,impossible || unlikely || equally likely as not || likely || certain,42389 +PRABESCX,1,Multiple Choice (select all),Check All That Apply,"

Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2.

+

 

+

Select all of the following that are side lengths of Quadrilateral B.

",,,5 || 6 || 7 || 8 || 9,6 || 8,247183 +PSBBWKR,1,Multiple Choice (select 1),Multiple Choice,"

The school store sells pencils for $0.30 each, hats for $14.50 each, and binders for $3.20 each. Elena would like to buy 3 pencils, a hat, and 2 binders. She estimated that the cost will be less than $20.

+

 

+

Do you agree with her estimate? 

",,,Agree || Disagree,Disagree,277881 +PSBEUG,1,Multiple Choice (select 1),Multiple Choice,"

Andre and Jada were in a hot dog eating contest. Andre ate 10 hot dogs in 3 minutes. Jada ate 12 hot dogs in 5 minutes.

+

 

+

Here are two different graphs that both represent this situation.

+

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

 

+

On the first graph, which point shows Andre’s consumption, and which shows Jada’s consumption?

",,,"The rightmost point shows Andre's consumption, the leftmost point shows Jada's consumption || The rightmost point shows Jada's consumption, the leftmost point shows Andre's consumption","The rightmost point shows Jada's consumption, the leftmost point shows Andre's consumption",23819 +PSBDADV,1,Multiple Choice (select 1),Multiple Choice,"

Diego said that the answer to the question “How many groups of 56 are in 1?” is 65   or 115. Do you agree with his statement?

",,,Agree || Disagree,Agree,521139 +PRABFFX7,1,Multiple Choice (select all),Check All That Apply,"

A cube has a side length of 8 inches.

+

 

+

Select all the values that represent the cube’s volume in cubic inches.

",,,8² || 8³ || 6 · 8² || 6 · 8 || 8 · 8 · 8,8³ || 8 · 8 · 8,558716 +PSBTS,1,Multiple Choice (select 1),Multiple Choice,"

A company tests two new products to make sure they last for more than a year.

+

 

+
    +
  • Product 1 had 950 out of 1,000 test items last for more than a year.
    • +
  • Product 2 had 150 out of 200 last for more than a year.
    • +
+

 

+

If you had to choose one of these two products to use for more than a year, which one is more likely to last?

",,,Product 1 || Product 2,Product 1,1805 +PRABJGVV,1,Multiple Choice (select all),Check All That Apply,"

An item costs x dollars and then a 20% discount is applied. Select all the expressions that could represent the price of the item after the discount. 

",,,"

20100x

||

x-20100x

||

(1-0.20)x

||

100-20100x

||

0.80x

||

(100-20)x

","

x-20100x

||

(1-0.20)x

||

100-20100x

||

0.80x

",137922 +PSBBT4K,4,Multiple Choice (select 1),Multiple Choice,"

The equation c = 2.95g shows how much it costs to buy gas at a gas station on a certain day. In the equation, c represents the cost in dollars, and g represents how many gallons of gas were purchased.

+

 

+

Jada’s mom remarks, “You can get about a third of a gallon of gas for a dollar.” Is she correct?

",,,Yes || No,Yes,263961 +PRABEVS9,1,Multiple Choice (select all),Check All That Apply,"

A rectangle has length x and width y.

+

 

+

+

 

+
+

Select all the statements that must be true. 

+
",,,The perimeter is x + y. || The perimeter is xy. || The perimeter is 2(x + y). || The perimeter is 2xy. || The perimeter is 2x + 2y. || The area is x + y. || The area is xy. || The area is 2xy.,The perimeter is 2(x + y). || The perimeter is 2x + 2y. || The area is xy.,1366 +PSBBSW7,2,Multiple Choice (select 1),Multiple Choice,"

Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students.

+

 

+
    +
  • The mean height for Han's sample is 59 inches.
    • +
  • The mean height for Priya's sample is 61 inches.
    • +
+

 

+

Are the population means different?

",,,Yes || No,No,257090 +PRABFMAH,1,Multiple Choice (select all),Check All That Apply,"

Pineapples were packed in three large crates. For each crate, the weight of every pineapple in the crate was recorded. Here are three box plots that summarize the weights in each crate.

+

 

+

+

 

+

Select all of the statements that are true, according to the box plots.

",,,A. The weights of the pineapples in Crate 1 were the most variable. || B. The heaviest pineapple was in Crate 1. || C. The lightest pineapple was in Crate 1. || D. Crate 3 had the greatest median weight and the greatest IQR. || E. More than half the pineapples in Crate 1 and Crate 3 were heavier than the heaviest pineapple in Crate 2.,A. The weights of the pineapples in Crate 1 were the most variable. || B. The heaviest pineapple was in Crate 1. || E. More than half the pineapples in Crate 1 and Crate 3 were heavier than the heaviest pineapple in Crate 2.,80061 +PRABEUF9,1,Multiple Choice (select all),Check All That Apply,"

Select all expressions that are equivalent to 5x − 15 − 20x + 10.

",,,"

5x - (15 + 20x) + 10

||

5x + -15 + -20x + 10

||

5(x - 3 - 4x + 2)

||

-5 (-x + 3 + 4x + -2)

||

-15x - 5

||

-5(3x + 1)

||

-15x - 13

",

5x - (15 + 20x) + 10

||

5x + -15 + -20x + 10

||

5(x - 3 - 4x + 2)

||

-5 (-x + 3 + 4x + -2)

||

-15x - 5

||

-5(3x + 1)

,43371 +PRABQMBJ,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are greater than 3.

,,,1.67 + 1.4 || 2.97 + 0.004 || 3.017 - 0.05 || 4.5 - 1.47 || 5.503 - 2.52,1.67 + 1.4 || 4.5 - 1.47,8476 +PSBCNNT,1,Multiple Choice (select 1),Multiple Choice,"

The equation S = 50 + 45w represents the savings S, after w weeks working and depositing money into a savings account at the bank.

+

 

+

Is there a proportional relationship between S and w?

",,,Yes || No,No,408662 +PSBBMXK,4,Multiple Choice (select 1),Multiple Choice,"

For this sample, the mean absolute deviation is 19.6, and the interquartile range is 15. Which of these values is associated with the measure of center that you chose?

",,,Mean absolute deviation (MAD) || Interquartile range (IQR),Interquartile range (IQR),230845 +PSBBRED,2,Multiple Choice (select 1),Multiple Choice,

Is the height of the candle a function of time?

,,,Yes || No,Yes,249681 +PSBBZMW,3,Multiple Choice (select 1),Multiple Choice,

Now compare the volumes of these boxes in cubic centimeters. Which box will hold the most 1-centimeter cubes? 

,,,"Box A || Box B || Box C || Boxes A,B,C fits the same number of 1-centimeter cubes",Box C,295992 +PRABE57Z,1,Multiple Choice (select all),Check All That Apply,

Select all the polyhedra.

,,,"

||

||

||

||

","

||

||

",250066 +PSBH8S,1,Multiple Choice (select 1),Multiple Choice,"

Label each event with one of these options:

+

impossible,   unlikely,   equally likely as not,   likely,   certain

+

 

+

You will win grand prize in a raffle if you purchased 2 out of the 100 tickets.

",,,impossible || unlikely || equally likely as not || likely || certain,unlikely,41980 +PSBX69,11,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

The coordinates of point H are solutions to the equation for line ℓ.

",,1,True || False,TRUE,114342 +PRABPUBW,1,Multiple Choice (select 1),Multiple Choice,

All of these sequences of transformations would return a shape to its original position except?

,,,"Translate 3 units up, then 3 units down. ||

Reflect over line p, then reflect over line p again.

|| Translate 1 unit to the right, then 4 units to the left, then 3 units to the right. ||

Rotate 120° counterclockwise around center C, then rotate 220° counterclockwise around center C again.

","

Rotate 120° counterclockwise around center C, then rotate 220° counterclockwise around center C again.

",40538 +PSBB3M4,1,Multiple Choice (select 1),Multiple Choice,"

A student got 16 out of 21 questions correct on a quiz. Use mental estimation to answer these questions.

+

 

+

Did the student answer less than or more than 80% of the questions correctly?

",,,Less than 80% || More than 80%,Less than 80%,307360 +PRABFKZ5,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that represent the total area of the large rectangle.

+

 

+

",,,"

5(x + y)

||

5 + xy

||

5x + 5y

||

2(5 + x + y)

||

5xy

","

5(x + y)

||

5x + 5y

",6876 +PRABQPSC,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.​

,,,Dilations always increase the length of line segments. || Dilations take perpendicular lines to perpendicular lines. || Dilations of an angle are congruent to the original angle. || Dilations increase the measure of angles. || Dilations of a triangle are congruent to the original triangle. || Dilations of a triangle are similar to the original triangle.,Dilations take perpendicular lines to perpendicular lines. || Dilations of an angle are congruent to the original angle. || Dilations of a triangle are similar to the original triangle.,239691 +PRABETDC,1,Multiple Choice (select all),Check All That Apply,

Select all ratios that are equivalent to 4 : 5.

,,,2 : 2.5 || 2 : 3 || 3 : 3.75 || 7 : 8 || 8 : 10 || 14 : 27.5,2 : 2.5 || 3 : 3.75 || 8 : 10,363127 +PRABEVKU,1,Multiple Choice (select all),Check All That Apply,

Select all the tables that could represent proportional relationships.

,,," + + + + + + + + + + + + + + + + + + +
xy
23
57.5
1015
|| + + + + + + + + + + + + + + + + + + +
xy
00
37
614
|| + + + + + + + + + + + + + + + + + + +
xy
02
24
46
"," + + + + + + + + + + + + + + + + + + +
xy
23
57.5
1015
|| + + + + + + + + + + + + + + + + + + +
xy
00
37
614
",152397 +PSBUC9,7,Multiple Choice (select 1),Multiple Choice,"

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

+

 

+

Will all three students complete a sign at the same time?

",,,Yes || No,No,91453 +PRABEU32,1,Multiple Choice (select 1),Multiple Choice,"

Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm.

+

 

+
+

Which of these is closest to the percent error for Diego’s measurement?

+
",,,4.3% || 4.5% || 95.7% || 104.5%,4.30%,247727 +PRABQPKS,1,Multiple Choice (select 1),Multiple Choice,"

Tyler has run 15 miles this month. For the rest of the month, he plans to run the same number of miles each day. There are 12 days left in the month. Before the end of the month, Tyler needs to run at least 35 miles to meet his goal.

+

 

+

Which of these inequalities describes this situation, where m is the number of miles Tyler runs each day to meet his goal?

",,,

12m - 15 ≥ 35

||

12m - 15 ≤ 35

||

35 ≥ 15 + 12m

||

35 ≤ 15 + 12m

,

35 ≤ 15 + 12m

,163692 +PSBCM74,1,Multiple Choice (select all),Check All That Apply,"

Select all of the equations that describe the situation. If you get stuck, draw a diagram.

+

 

+

 

+

Clare has 8 fewer books than Mai. If Mai has 26 books, how many books does Clare have?

",,,

26 − x = 8

||

x = 26 + 8

||

x + 8 = 26

||

26 − 8 = x

,

26 − x = 8

||

x + 8 = 26

||

26 − 8 = x

,406161 +PSBBFAV,2,Multiple Choice (select 1),Multiple Choice,"

How do you travel to school on most days? Choose one.

+

 

+
 
",,,Walk || Bike || Scooter or Skateboard || Car || School Bus || Public Transport || Other,Walk || Bike || Scooter or Skateboard || Car || School Bus || Public Transport || Other,198387 +PSBBK6,2,Multiple Choice (select 1),Multiple Choice,"

Is 23 < 34, or is 34 < 23?

",,,"

 

+

23 < 34

+

 

||

 

+

34 < 23

+

 

","

 

+

23 < 34

+

 

",6476 +PSB5RF,1,Multiple Choice (select 1),Multiple Choice,"

Mai says that the equation 2x + 2 = x + 1 has no solution because the left hand side is double the right hand side. Do you agree with Mai?

",,,Yes || No,No,146473 +PSBMSN,1,Multiple Choice (select 1),Multiple Choice,"

Jada poured 3.7 liters of water into a partially-filled bucket. The bucket then contained 15.3 liters.

+

 

+

Which diagram (A, B, or C) represents this situation?

",,,"

||

||

","

",55944 +PSBBZ52,3,Multiple Choice (select 1),Multiple Choice,"

If the comic book authors give the new hero the ability to fly, will that please most of the readers?

",,,Yes || No,No,298561 +PSB962,1,Multiple Choice (select 1),Multiple Choice,"

Jada wants to know if there is a meaningful difference in the mean number of friends on social media for teens and adults. She looks at the friend count for the 10 most popular of her friends and the friend count for 10 of her parents’ friends. She then computes the mean and MAD of each sample and determines there is a meaningful difference.

+

 

+

Jada’s dad later tells her he thinks she has not come to the right conclusion. Jada checks her calculations and everything is right. Do you agree with her dad?

",,,Yes || No,Yes,170227 +PSBCBXY,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the quantity can be represented by a positive number or by a negative number. 

+

 

+

The aquarium leaked 2 gallons of water.

",,,positive || negative,negative,354353 +PSBBD5P,3,Multiple Choice (select 1),Multiple Choice,"

Noah says that 24 ·32 = 66. Tyler says that 24 ·42 = 162.

+

 

+

Do you agree with Tyler?

",,,Yes || No,Yes,192377 +PSBC47,1,Multiple Choice (select 1),Multiple Choice,"

 

+

+

The actual length of Walls A, C, and D are 2.5 m, 4 m, and 3.75 m, respectively.

+

 

+

If Noah wanted to draw another floor plan on which Wall C was 20 cm, would 1 cm to 5 m be the right scale to use?

",,,Yes || No,No,15259 +PRABFF3K,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 3.150.45.

",,,"

(3.15) · (0.45)

||

(3.15) ÷ (0.45)

||

(3.15) · 10.45

||

(3.15) ÷ 45100

||

(3.15) · 10045

||

0.453.15

","

(3.15) ÷ (0.45)

||

(3.15) · 10.45

||

(3.15) ÷ 45100

||

(3.15) · 10045

",222661 +PRABFGVZ,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 4b.

",,,"

b + b + b + b

||

b + 4

||

2b + 2b

||

b · b · b · b

||

b ÷ 14

","

b + b + b + b

||

2b + 2b

||

b ÷ 14

",189763 +PRABFS44,1,Multiple Choice (select all),Check All That Apply,"

Select the unit from the list that you would use to measure the object.

+

 

+

The weight or mass of a pencil

",,,centimeters || cups || feet || gallons || grams || inches || kilograms || kilometers || liters || meters || miles || milliliters || millimeters || ounces || pounds || quarts || tons || yards,grams || ounces,172779 +PSBX7,6,Multiple Choice (select 1),Multiple Choice,

Can -8 be a solution to n in this context? 

,,,Yes || No,No,2951 +PSBZYY,1,Multiple Choice (select 1),Multiple Choice,"

Here is a scatter plot that shows weights and fuel efficiencies of 20 different types of cars.

+

If a car weighs 1,750 kg, would you expect its fuel efficiency to be closer to 22 mpg or to 28 mpg?

",,,22 mpg || 28 mpg,22 mpg,124523 +PRABQP6D,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equal to .

",,,"7,610 ÷ 50 || 762 ÷ 6 || 76.1 ÷ 0.05 || 7.61 ÷ 0.5 || 0.761 ÷ 0.005","7,610 ÷ 50 || 0.761 ÷ 0.005",505841 +PRABUZ7Y,1,Multiple Choice (select 1),Multiple Choice,"

A standard number cube has the numbers 1 through 6 on its faces. 

+

 

+

A standard number cube is rolled. What is the probability of rolling a number less than or equal to 2?

",,,"

16

||

26

||

36

||

46

","

26

",349910 +PSBBE7Q,6,Multiple Choice (select 1),Multiple Choice,"

Which is faster, light through ice or light through diamond?

",,,Light through ice || Light through diamond,Light through ice,198635 +PSBQCW,1,Multiple Choice (select 1),Multiple Choice,"

Here are two calculations of 0.2 + 0.05.

+

 

+ + + + + + + +
     0 . 2+  0 . 0 5     0 . 2 5     0 . 2+  0 . 0 5     0 . 0 7
+

 

+

Which one is correct?

",,,"

     0 . 2+  0 . 0 5     0 . 2 5

||

     0 . 2+  0 . 0 5     0 . 0 7

","

     0 . 2+  0 . 0 5     0 . 2 5

",69196 +PSBBZQC,1,Multiple Choice (select 1),Multiple Choice,"

 Is the statement true or false?

+

 

+

45100·72=4572·100

",,0,True || False,FALSE,296344 +PSBB47J,1,Multiple Choice (select 1),Multiple Choice,"

Clare has a -liter bottle full of water. A cone-shaped paper cup has diameter 10 cm and slant height 13 cm as shown. Can she pour all the water into one paper cup, or will it overflow?

+

 

+

(The volume of a cone is  and  liter = 500 cubic centimeters.)

+

 

+

",,,She can pour all the water into one paper cup. || The paper cup will overflow.,The paper cup will overflow.,315454 +PSBBCDY,6,Multiple Choice (select 1),Multiple Choice,"

Can Jada use these data displays to find the exact mean?

+

 

+

",,,yes || no,no,182704 +PSBDHBJ,1,Multiple Choice (select 1),Multiple Choice,"

The equation F = 95C + 32 relates temperature measured in degrees Celsius, C, to degrees Fahrenheit, F.

+

 

+

Is the relationship between C and F proportional?

",,,Yes || No,No,560745 +PRABEVSX,1,Multiple Choice (select all),Check All That Apply,"

Jada is three years older than twice her brother’s age.

+

 

+

Select all the equations that correctly represent the relationship between Jada’s age j and her brother’s age b.

",,,"

j=2b+3

||

j=2(b+3)

||

j=b2-3

||

b=2j+3

||

b=j-32

||

b=j2-3

","

j=2b+3

||

b=j-32

",162424 +PRABUZ7Z,1,Multiple Choice (select all),Check All That Apply,

Select all the events that have a probability of 0.

,,,"Choosing a red block from a bag with 9 white blocks and 1 red block. || Rolling a 6, three times in a row, on a standard number cube. || Rolling a 7 on a standard number cube. || Opening a 400-page book to exactly page 231. || Opening a 400-page book a page number greater than 450.",Rolling a 7 on a standard number cube. || Opening a 400-page book a page number greater than 450.,349992 +PSB9XX,1,Multiple Choice (select 1),Multiple Choice,"

For the pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not.

+

 

+

 

+

Triangle G: 121, ___, ___; Triangle H: 70, ___, ___

",,,similar || not similar,not similar,168820 +PSBBMUY,2,Multiple Choice (select 1),Multiple Choice,"

Driving at a constant speed of 70 mph, will it be possible to make this trip in 3 hours?

",,,Yes || No,No,230204 +PRABEVJY,1,Multiple Choice (select 1),Multiple Choice,"

Which of these points is closest to the point (7, 1)?

",,,"(4, 1) || (7, -1) || (7, 4) || (11, 1)","(7, -1)",3724 +PSBCWRE,1,Multiple Choice (select 1),Multiple Choice,"

This diagram shows two small squares and three rectangles each composed of 10 small squares.

+

+

 

+

Priya says that this diagram can represent 320. Do you agree with Priya?

",,,yes || no,yes,455397 +PSB5S8,1,Multiple Choice (select 1),Multiple Choice,"

If two rectangles have the same perimeter, do they have to be congruent?

",,,Yes || No,No,146791 +PRABEPR3,1,Multiple Choice (select all),Check All That Apply,"

Select all the irrational numbers in the list.

+
 
+
23, -12345, 14, 64, 91, -99, -100
",,,"

23

||

-12345

||

14

||

64

||

91

||

-99

||

-100

","

14

||

-99

",15689 +PRABEVSQ,1,Multiple Choice (select all),Check All That Apply,"

Select all the lines that have a slope of 

+

 

+

",,,A || B || C || D || E,A || E,239904 +PRABQN9C,1,Multiple Choice (select 1),Multiple Choice,"

A sunken ship is resting at 3,000 feet below sea level. Directly above the ship, a whale is swimming 1,960 feet below sea level. Directly above the ship and the whale is a plane flying at 8,500 feet above sea level.

+

 

+

Select the true statement.

",,,"The distance between the heights of the whale and the plane is -10,460 feet. || The difference in height between the whale and the plane is 10,460 feet. || The difference in height between the whale and the ship is -1,040 feet. || The distance between the heights of the whale and the ship is 1,040 feet.","The distance between the heights of the whale and the ship is 1,040 feet.",24438 +PRABQP58,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 6-10.

",,,"

6-5·62

||

1625

||

6-52

||

6-367

||

65·6-368

","

1625

||

6-52

||

6-367

",263664 +PSB5BQ,1,Multiple Choice (select 1),Multiple Choice,"

In one version of trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes?

",,,Yes || No,Yes,143888 +PRABQMA7,1,Multiple Choice (select all),Check All That Apply,"

Diego drew this line plot showing the width, in inches, of all the bolts in a storage bin. Select all the true statements.

+

 

+

",,,"

There are 12 bolts in the storage bin.

||

The widest bolt is 78 inches wide.

||

Half of the bolts are less than 12 inch wide.

||

None of the bolts is exactly 28 inches wide.

||

None of the bolts is exactly 68 inches wide.

||

The difference between the maximum and minimum width of the bolts is 1 inch.

","

There are 12 bolts in the storage bin.

||

None of the bolts is exactly 68 inches wide.

||

The difference between the maximum and minimum width of the bolts is 1 inch.

",256500 +PRABQM3S,1,Multiple Choice (select all),Check All That Apply,"

Mai’s backpack weighs 9 pounds. Han’s backpack weighs 8.3 pounds. Priya’s backpack weighs 7.75 pounds, and Kiran’s backpack weighs 6.125 pounds. Select all the true statements.

",,,Han’s backpack is 2.175 pounds heavier than Kiran’s. || Mai’s backpack is 2.25 pounds heavier than Priya’s. || Han’s backpack is 16.05 pounds heavier than Priya’s. || Kiran’s backpack and Han’s backpack together weigh 14.3125 pounds. || The backpacks weigh 31.175 pounds together.,Han’s backpack is 2.175 pounds heavier than Kiran’s. || The backpacks weigh 31.175 pounds together.,61905 +PRABQKS6,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are greater than 1.

,,,"

5 ÷ 910

||

35 ÷ 6

||

45 ÷ 37

||

235 ÷ 135

||

125 ÷ 135

","

5 ÷ 910

||

45 ÷ 37

||

235 ÷ 135

",588511 +PRABQMWG,1,Multiple Choice (select all),Check All That Apply,"

Select all the numbers that point A could reasonably represent on this number line.

+

 

+

",,,0.65 || 1.3 || 1.5 || 1.6 || 1.65,1.6 || 1.65,488652 +PSBBZ52,2,Multiple Choice (select 1),Multiple Choice,

Are most of the sample proportions within 0.1 of your estimate for the population proportion?

,,,Yes || No,Yes,298486 +PRABEVC7,1,Multiple Choice (select 1),Multiple Choice,

How many degrees are there in a right angle?

,,90,60 || 90 || 180 || 360,90,115085 +PSBFMC,2,Multiple Choice (select 1),Multiple Choice,

Jada says that she found three different ways to complete the first question correctly. Do you think this is possible? 

,,,Yes - It is possible || No - It is not possible,Yes - It is possible,28640 +PRABQJSQ,1,Multiple Choice (select all),Check All That Apply,"

Select all the line segments that appear to be parallel to a.

+

 

+

",,,

segment a

||

segment b

||

segment c

||

segment d

||

segment e

||

segment f

,

segment d

||

segment e

,104004 +PSBJDF,1,Multiple Choice (select 1),Multiple Choice,"

Han has a number cube that he suspects is not so standard.

+

 

+
    +
  • Han rolls the cube 100 times, and it lands on a six 40 times.
    • +
  • Kiran rolls the cube 50 times, and it lands on a six 21 times.
    • +
  • Lin rolls the cube 30 times, and it lands on a six 11 times.
    • +
+

 

+
+
+
+

Based on these results, is there evidence to help prove that this cube is not a standard number cube?

+
+
+
",,,Yes || No,Yes,43700 +PSB96F,8,Multiple Choice (select 1),Multiple Choice,"

+

Which model does a better job of predicting the price of a used car from its year?

",,,Model A || Model B,Model A,170383 +PRABJKPQ,1,Multiple Choice (select all),Check All That Apply,

Select all expressions that are equal to 8 − 12 − (6 + 4).

,,,

8 - 6 - 12 + 4

||

8 - 12 - 6 - 4

||

8 - 12 + (6 + 4)

||

8 - 12 - 6 + 4

||

8 - 4 - 12 - 6

,

8 - 12 - 6 - 4

||

8 - 4 - 12 - 6

,214651 +PSBTXU,7,Multiple Choice (select 1),Multiple Choice,"

A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is the statement true or false? 

+

 

+

 Time is a function of speed.

",,1,True || False,TRUE,88965 +PRABE55W,1,Multiple Choice (select all),Check All That Apply,

Select all the polygons.

,,,"

||

||

||

||

||

","

||

",243115 +PSBPP,2,Multiple Choice (select 1),Multiple Choice,

Is there a different triangle Diego could have drawn that would answer the question? 

,,,Yes || No,Yes,1606 +PSBCBAF,1,Multiple Choice (select 1),Multiple Choice,"

A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches.

+

 

+

Is the baseball’s volume greater than, less than, or equal to 2.93 cubic inches?

",,,greater than 2.9³ || less than 2.9³ || equal to 2.9³,less than 2.9³,350639 +PRABFENA,1,Multiple Choice (select all),Check All That Apply,

Which figure is a triangular prism? Select all that apply.

,,,"

||

||

||

||

","

||

||

",36768 +PRABFBN2,1,Multiple Choice (select 1),Multiple Choice,

A large soup pot holds 20 quarts. What could be its volume in liters?

,,,

7.57

||

19

||

21

||

75.7

,

19

,14371 +PRABQPJ6,1,Multiple Choice (select 1),Multiple Choice,"

This hanger is in balance. There are two labeled weights of 4 grams and 12 grams. The three circles each have the same weight. What is the weight of each circle, in grams? 

+

 

+

",,,"

38

||

1

||

83

||

8

","

83

",308146 +PSBDAN7,1,Multiple Choice (select 1),Multiple Choice,"

Kiran says that -2<-5. Do you agree with Kiran?

",,,Agree || Disagree,Disagree,522597 +PRABFGZR,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are equivalent to 64.

,,,

26

||

28

||

43

||

82

||

164

||

322

,

26

||

43

||

82

,297160 +PSBCRRZ,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the inequality statement is true or false. 

+

 

+

-12.5 > -12

",,0,True || False,FALSE,427265 +PSBBJTA,1,Multiple Choice (select 1),Multiple Choice,"

25 kilogram of soil fills 13 of a container. Can 1 kilogram of soil fit in the container?

",,,Yes || No,Yes,218537 +PSBKEB,1,Multiple Choice (select 1),Multiple Choice,"

Figure B is the image of Figure A when reflected across line ℓ. Are Figure A and Figure B congruent?

+

 

+

+
 
",,,Yes || No,Yes,48569 +PSBBTFY,1,Multiple Choice (select 1),Multiple Choice,"

Which skateboarder is faster: Jada, who travels 2 miles in 12 minutes at a constant speed, or Clare, who travels 2 miles in 10 minutes at a constant speed?

",,,"Jada, who travels 2 miles in 12 minutes at a constant speed || Clare, who travels 2 miles in 10 minutes at a constant speed","Clare, who travels 2 miles in 10 minutes at a constant speed",260638 +PSBCU6,2,Multiple Choice (select 1),Multiple Choice,"

Ten people can dig five holes in three hours. If n people digging at the same rate dig m holes in d hours:

+

 

+

Is n proportional to d when m = 5?

",,,Yes || No,No,13854 +PRABE9ZA,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that represents the pints of red and yellow paint in a mixture.

+

 

+

+

 

+

Select all statements that accurately describe the diagram.

",,,"The ratio of yellow paint to red paint is 2 to 6. || For every 3 pints of red paint, there is 1 pint of yellow paint. || For every pint of yellow paint, there are 3 pints of red paint. || For every pint of yellow paint there are 6 pints of red paint. ||

The ratio of red to yellow paint is 6 : 2

","The ratio of yellow paint to red paint is 2 to 6. || For every 3 pints of red paint, there is 1 pint of yellow paint. || For every pint of yellow paint, there are 3 pints of red paint. ||

The ratio of red to yellow paint is 6 : 2

",39085 +PSBDFK7,1,Multiple Choice (select 1),Multiple Choice,"

Here are the approximate populations of three cities in the United States, expressed in scientific notation: San Jose: ; Washington: ; Atlanta: 

+


Lin says that about  more people live in San Jose than in Atlanta. Do you agree with her?

",,,Yes || No,Yes,551634 +PRABEVSP,1,Multiple Choice (select 1),Multiple Choice,"

Which pair of triangles must​ be similar?

+
 
",,,Triangles 1 and 2 each have a 35º angle. || Triangles 3 and 4 are both isosceles. They each have a 40º angle. || Triangle 5 has a 30º angle and a 90º angle. Triangle 6 has a 30º angle and a 70º angle. || Triangle 7 has a 50º angle and a 25º angle. Triangle 8 has a 50º angle and a 105º angle.,Triangle 7 has a 50º angle and a 25º angle. Triangle 8 has a 50º angle and a 105º angle.,239815 +PSBURX,2,Multiple Choice (select 1),Multiple Choice,

Is there more than one point R that works for part a?

,,,Yes || No || Not enough information,No,93881 +PRABQKWC,1,Multiple Choice (select 1),Multiple Choice,"

Which statement shows correct reasoning for finding 12 ÷ 38?

",,,"

Multiply 12 by 8, then divide by 3.

||

Multiply 12 by 3, then divide by 8.

||

Multiply 3 by 8, then divide by 12.

||

Multiply 12 by 18, then multiply by 3.

","

Multiply 12 by 8, then divide by 3.

",21032 +PRABFK3V,1,Multiple Choice (select 1),Multiple Choice,"

The dot plots show the amounts of time that ten U.S. students and ten Australian students took to get to school. Which statement is true about the MAD of the Australian data set?

+

 

+

",,,It is significantly less than the MAD of the U.S. data set. || It is exactly equal to the MAD of the U.S. data set. || It is approximately equal to the MAD of the U.S. data set. || It is significantly greater than the MAD of the U.S. data set.,It is significantly greater than the MAD of the U.S. data set.,363244 +PRABQMW3,1,Multiple Choice (select all),Check All That Apply,

Select all the numbers that are common multiples of 4 and 6.

,,,1 || 2 || 10 || 12 || 24 || 40 || 60,12 || 24 || 60,410833 +PRABQJQT,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that give the area of the figure in square units.

+

",,,7 x 5 || (7 + 5) x (5 + 2) || (7 x 3) + (5 x 2) || 7 x 5 x 5 x 2 x 2 x 3 || (7 x 5) - (2 x 2),(7 x 3) + (5 x 2) || (7 x 5) - (2 x 2),543878 +PSBDSKY,1,Multiple Choice (select 1),Multiple Choice,"

A ribbon is 24 inches long. You need to cut it into pieces so that all the pieces are the same length.

+

 

+

Can you cut the ribbon into 5-inch pieces?

",,,Yes || No,No,608636 +PSBBAQY,1,Multiple Choice (select 1),Multiple Choice,"

Which is a better deal, 5 tickets for $12.50 or 8 tickets for $20.16? 

",,,5 tickets for $12.50 || 8 tickets for $20.16,5 tickets for $12.50,173472 +PRABQPRM,1,Multiple Choice (select all),Check All That Apply,"

Select all the true statements.

+
 
",,,Two rhombuses with the same side lengths are always congruent. || Two squares with the same side lengths are always congruent. || Two quadrilaterals with the same side lengths are always congruent. || Two rectangles with the same side lengths are always congruent. || Two parallelograms with the same side lengths are always congruent.,Two squares with the same side lengths are always congruent. || Two rectangles with the same side lengths are always congruent.,504583 +PRABFERD,1,Multiple Choice (select 1),Multiple Choice,

Mai had $14.50. She spent $4.35 at the snack bar and $5.25 at the arcade. What is the exact amount of money Mai has left?

,,,

$9.60

||

$10.60

||

$4.90

||

$5.90

,

$4.90

,274984 +PSBX69,3,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

The coordinates of the point G make both the equation for line m and the equation for line n true.

+

 

",,1,True || False,TRUE,113306 +PRABQK7R,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations represented by this tape diagram.

+

 

+

",,,6 + 6 + 6 + 6 + 6 = ? || 5 + 6 = ? || ? = 6 · 5 || ? = 6 · 6 · 6 · 6 · 6 || ? ÷ 5 = 6 || 5 = ? ÷ 6,6 + 6 + 6 + 6 + 6 = ? || ? = 6 · 5 || ? ÷ 5 = 6 || 5 = ? ÷ 6,299836 +PRABQPJB,1,Multiple Choice (select all),Check All That Apply,"

Select all the triangles that can be rotated to match up with Triangle 1.

+

 

+

",,,"

||

||

||

","

||

",11215 +PSBZX3,1,Multiple Choice (select 1),Multiple Choice,"

Choose the inequality that best matches the given situation.

+

 

+

The Chemistry Club is experimenting with different mixtures of water with a certain chemical (sodium polyacrylate) to make fake snow.
To make each mixture, the students start with some amount of water, and then add 17 of that amount of the chemical, and then 9 more grams of the chemical. The chemical is expensive, so there can’t be more than a certain number of grams of the chemical in any one mixture.

",,,"

17x+9≤26.25

||

9x+17≤26.25

||

26.25x+9≤17

||

17x+26.25≤9

","

17x+9≤26.25

",124358 +PRABQN7F,1,Multiple Choice (select 1),Multiple Choice,"

It takes Diego 124 of an hour to complete a lap on a circular bike track. The track is 13 mile long. What is Diego’s bike speed?

",,,"

18 mile per hour

||

18 hours per mile

||

8 miles per hour

||

8 hours per mile

",

8 miles per hour

,75212 +PSB5PB,1,Multiple Choice (select 1),Multiple Choice,"

Here are some line segments.

+

 

+

+

 

+

Which segment is a dilation of BC using A as the center of dilation and a scale factor of 23?

+
 
",,,ED || GJ || FH,FH,145792 +PSBVKV,1,Multiple Choice (select 1),Multiple Choice,

Which shaded region is larger?

,,,"

||

","

",99309 +PSBCN7,1,Multiple Choice (select 1),Multiple Choice,"

Priya, Jada, Han, and Diego are playing a game. They stand in a circle in this order and take turns playing a game.

+

Priya says, SAFE. Jada, standing to Priya's left, says, OUT and leaves the circle. Han is next: he says, SAFE. Then Diego says, OUT and leaves the circle. At this point, only Priya and Han are left. They continue to alternate. Priya says, SAFE. Han says, OUT and leaves the circle. Priya is the only person left, so she is the winner. Priya says, “I knew I’d be the only one left, since I went first.”

+

Record this game on paper a few times with different numbers of players. Does the person who starts always win?

",,,Yes || No,No,12541 +PRABEVTP,1,Multiple Choice (select 1),Multiple Choice,"

A sphere has radius 2.7 centimeters.

+

 

+

+

 

+

What is its volume, to the nearest cubic centimeter?

",,82,23 || 26  || 62 || 82,82,297864 +PRABQMBS,1,Multiple Choice (select 1),Multiple Choice,"

Which is closest to the quotient ?

",,,"1,000 || 10,000 || 100,000 || 1,000,000","1,000,000",278455 +PSBEUH,1,Multiple Choice (select all),Check All That Apply,"

Here is a circle with center H and some line segments and curves joining points on the circle.

+

 

+

Identify examples of diameter.

+

+

 

",,,AE || AH || BH || BF || CE || DG || DH || EH || FH || GH,AE || DG,23899 +PRABP75T,1,Multiple Choice (select all),Check All That Apply,"

Salt and sugar give two distinctly different tastes, one salty and the other sweet. In a mixture of salt and sugar, it is possible for the mixture to be salty, sweet or both. Will any of these mixtures taste exactly the same?

",,,"Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture B: 1.5 cups water, 3 teaspoons salt, 0.2 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar || None of these mixtures taste the same.","Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar",48435 +PSBB6YN,2,Multiple Choice (select 1),Multiple Choice,"

Based on the dot plots, which estimate is more likely to be accurate? 

",,,Sample 1 || Sample 2,Sample 1,325378 +PSB3HJ,1,Multiple Choice (select 1),Multiple Choice,"

True or false:

The points (6, 13), (21, 33), and (99, 137) all lie on the same line. The equation of the line is y = 43x + 5. 

",,1,True || False,TRUE,133257 +PRABQPSK,1,Multiple Choice (select 1),Multiple Choice,"

Select the true statement.

+
 
",,,Dilations of an angle must be congruent to the original angle. || Dilations of a triangle must be congruent to the original triangle. || Dilations of a segment must be congruent to the original segment. || Dilations of a circle must be congruent to the original circle.,Dilations of an angle must be congruent to the original angle.,28184 +PSBD3T,1,Multiple Choice (select all),Check All That Apply,"

It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let w be the number of gallons of water in the cooler after t minutes.

+

 

+

Which of the following equations represent the relationship between w and t? Select all that apply.

",,,w = 1.6t || w = 0.625t || t = 1.6w || t = 0.625w,w = 1.6t || t = 0.625w,19877 +PSBB6PY,4,Multiple Choice (select 1),Multiple Choice,"

",,,< || = || >,<,323959 +PSBB93N,1,Multiple Choice (select 1),Multiple Choice,"

Jada says: “If you multiply a number by 0.001, the decimal point of the number moves three places to the left.”

+

 

+

Do you agree with her statement?

",,,I agree || I disagree,I agree,343445 +PSB6EU,1,Multiple Choice (select 1),Multiple Choice,"

A cylinder can be constructed from a piece of paper by curling it so that you can glue together two opposite edges (the dashed edges in the figure).

+

 

+

+

If you wanted to increase the volume inside the resulting cylinder, would it make more sense to double x, y , or does it not matter?

",,,Double x || Double y || It does not matter,Double x,150182 +PSBBFSQ,2,Multiple Choice (select 1),Multiple Choice,

Which student’s scores show greater variability?

,,,Student A || Student B,Student B,201945 +PRABQMXJ,1,Multiple Choice (select 1),Multiple Choice,"

There are 9 children in a class who take the bus to school, and there are 15 total children in the class. What percentage of the children take the bus to school?

",,,90% || 60% || 9% || 0.6%,60%,4091 +PRABFMAG,1,Multiple Choice (select all),Check All That Apply,"

Here is a box plot that summarizes data for the time, in minutes, that a fire department took to respond to 100 emergency calls. 

+

+

 

+

Select all the statements that are true, according to the box plot.

",,,

Most of the response times were under 13 minutes.

||

Fewer than 30 of the response times were over 13 minutes.

||

More than half of the response times were 11 minutes or greater.

||

There were more response times that were greater than 13 minutes than those that were less than 9 minutes.

||

About 75% of the response times were 13 minutes or less.

,

Most of the response times were under 13 minutes.

||

Fewer than 30 of the response times were over 13 minutes.

||

About 75% of the response times were 13 minutes or less.

,65288 +PSBNT9,1,Multiple Choice (select all),Check All That Apply,

Which graphs could not represent a proportional relationship?

,,,"

||

||

||

","

||

",61559 +PRABQTPR,1,Multiple Choice (select all),Check All That Apply,"

The shape is composed of three squares and two semicircles. Select all the expressions that correctly calculate the perimeter of the shape.

+

 

+

+

 

",,,40 + 20π || 80 + 20π || 120 + 20π || 300 + 100π || 10 + 10 + 10π + 10 + 10 + 10π,40 + 20π || 10 + 10 + 10π + 10 + 10 + 10π,270690 +PRABE6XR,1,Multiple Choice (select all),Check All That Apply,"

Prism A and Prism B are rectangular prisms.

+
    +
  • Prism A is 3 inches by 2 inches by 1 inch.
    • +
  • Prism B is 1 inch by 1 inch by 6 inches.
    • +
+

 

+

Select all statements that are true about the two prisms.

",,,They have the same volume || They have the same number of faces || More inch cubes can be packed into Prism A than into Prism B || The two prisms have the same surface area || The surface area of Prism B is greater than that of Prism A,They have the same volume || They have the same number of faces || The surface area of Prism B is greater than that of Prism A,248037 +PSBBYDD,1,Multiple Choice (select 1),Multiple Choice,"

A grocery store sells bags of oranges in two different sizes.

+

 

+
    +
  • The 3-pound bags of oranges cost $4.
    • +
  • The 8-pound bags of oranges for $9.
    • +
+

 

+

Which oranges cost less per pound?

",,,

The 8-pound bags

||

The 3-pound bags

,

The 8-pound bags

,288360 +PRABQPTJ,1,Multiple Choice (select 1),Multiple Choice,

Which of these points is closest to the y-axis?

,,,"(-6, 0) || (-2, 12) || (4, 2) || (5, 1)","(-2, 12)",3634 +PSBCBCJ,5,Multiple Choice (select 1),Multiple Choice,

Were the distances in the second data set more variable or less variable compared to those in the first round? 

,,,

More Variable

||

Less Variable

,

Less Variable

,351005 +PSBBB8S,1,Multiple Choice (select 1),Multiple Choice,

One rectangle measures 2 units by 7 units. A second rectangle measures 11 units by 37 units. Are these two figures scaled versions of each other?

,,,Yes || No,No,181638 +PSBDC9D,1,Multiple Choice (select 1),Multiple Choice,"

Sports drinks use sodium (better known as salt) to help people replenish electrolytes. Here are the nutrition labels of two sports drinks.

+

 

+

+

 

+

Which of these drinks is saltier?

",,,Drink A || Drink B,Drink A,537832 +PSBVHJ,1,Multiple Choice (select 1),Multiple Choice,"

A scientist wants to know if there is a meaningful difference between two groups of gels that grow bacteria. He randomly selects five gels from each group, and counts the number of bacteria spots on each gel:

+

 

+

Group A: 9, 12, 13, 14, 17

+

Group B: 6, 5, 8, 13, 8

+

 

+

Is there a meaningful difference between the two groups?

",,,Yes || No,Yes,98828 +PSBS9K,1,Multiple Choice (select 1),Multiple Choice,"

28 students travel on a field trip. They bring a van that can seat 12 students. Elena and Kiran’s teacher asks parents to drive cars that seat 3 children each to transport the rest of the students.

+

 

+

Elena wonders if she should use the inequality  or  to figure out how many cars are needed. Kiran doesn’t think it matters in this case. Do you agree with Kiran?

",,,Yes || No,Yes,85212 +PSBBR99,3,Multiple Choice (select 1),Multiple Choice,

Is there an association between the country’s budget and their spending in these areas? 

,,,Yes || No,Yes,254278 +PRABE3GZ,1,Multiple Choice (select all),Check All That Apply,"

Select all segments that could represent a corresponding height if the side m is the base.

+

 

+

+

 

+

 

",,,

e

||

f

||

g

||

h

||

j

||

k

||

n

,

e

||

f

||

j

||

k

,504115 +PSB6H3,1,Multiple Choice (select 1),Multiple Choice,"

Two plots of land have very different shapes. Noah said that both plots of land have the same area. Do you agree with Noah?

+

 

+

",,,Yes || No,Yes,150868 +PRABEUQ8,1,Multiple Choice (select 1),Multiple Choice,"

Each set of three numbers represents the lengths, in units, of the sides of a triangle. Which set can not be used to make a triangle?

",,,"7, 6, 14 || 4, 4, 4 || 6, 6, 2 || 7, 8, 13","7, 6, 14",130499 +PRABQPTY,1,Multiple Choice (select all),Check All That Apply,"

Select all the points that are on the graph of the line 2x + 4y = 20.

",,,"(0, 5) || (0, 10) || (1, 2) || (1, 4) || (5, 0) || (10, 0)","(0, 5) || (10, 0)",79065 +PRABFG35,1,Multiple Choice (select all),Check All That Apply,"

Lin says, “I took the number 8, and then multiplied it by the square of 3.” Select all expressions that equal Lin’s answer.

",,,8 ⋅ 3² || (8 · 3)² || 8 · 2³ || 3² · 8 || 24² || 72,8 ⋅ 3² || 3² · 8 || 72,46101 +PSBBFAV,11,Multiple Choice (select 1),Multiple Choice,"

If you could meet one of these celebrities, who would you choose?

+

 

+
 
",,,A city or state leader || A champion athlete || A movie star || A musical artist || A best-selling author,A city or state leader || A champion athlete || A movie star || A musical artist || A best-selling author,199218 +PRABQTFC,1,Multiple Choice (select 1),Multiple Choice,"

A map of Utah is shown. Which area is closest to the area of Utah?

+

 

+

",,,"1,240 square miles || 87,150 square miles || 94,500 square miles || 119,000 square miles","87,150 square miles",606133 +PSBNVZ,1,Multiple Choice (select 1),Multiple Choice,"

Lin wants to know if flipping a quarter really does have a probability of 12 of landing heads up, so she flips a quarter 10 times. It lands heads up 3 times and tails up 7 times. Has she proven that the probability is not 12?

",,,Yes || No,No,61911 +PSBBG5E,1,Multiple Choice (select 1),Multiple Choice,"

Noah is growing three different types of trees. He is keeping track of the height of each tree over time.

+

 

+
    +
  • This equation represents the height (in feet) of the first tree over months. h = 3.5m

    • +
+ + + + + + + + + + + +
The second tree’s information is in the table: This graph shows how long, in months, it takes the third tree to grow h feet.
+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
time (months)height of tree (feet)
25
410
512.5
820
+
+

Which tree is growing the slowest?

",,,First tree || Second tree || Third tree,Third tree,209506 +PSB9FG,1,Multiple Choice (select 1),Multiple Choice,"

Lin and Noah are packing small cubes into a cube with an edge length of inches. Lin is using cubes with an edge length of inch, and Noah is using cubes with an edge length of inch.

+

 

+

Who would need more cubes to fill the -inch cube? Be prepared to explain your reasoning.

",,,Lin || Noah,Noah,165863 +PSB3SQ,2,Multiple Choice (select 1),Multiple Choice,"

Place the decimal point in the appropriate location in the quotient:

+

 

+

+
 
",,6,0.608571 || 6.08571 || 60.8571 || 608.571 || 6085.71 || 60857.1,6.08571,134923 +PRABETY5,1,Multiple Choice (select all),Check All That Apply,"

Select all expressions that represent a correct solution to the equation 6(x+4)=20.

",,,"

(20 − 4) ÷ 6

||

1620 - 4

||

20 − 6 − 4

||

20 ÷ 6 − 4

||

1620 - 24

||

(20 − 24) ÷ 6

","

20 ÷ 6 − 4

||

1620 - 24

||

(20 − 24) ÷ 6

",369393 +PSBBBFB,1,Multiple Choice (select 1),Multiple Choice,"

Are these two triangles identical?

+

 

+
+
+

+
+
",,,Yes || No,No,177311 +PSBCVBZ,1,Multiple Choice (select 1),Multiple Choice,"

Andre ran 2 kilometers in 15 minutes, and Jada ran 3 kilometers in 20 minutes. Both ran at a constant speed.

+

 

+

Did they run at the same speed?

",,,Yes || No,No,447809 +PSBB27S,1,Multiple Choice (select 1),Multiple Choice,"

In a certain city in France, they gain 2 minutes of daylight each day after the spring equinox (usually in March), but after the autumnal equinox (usually in September) they lose 2 minutes of daylight each day.

+

 

+

Which of the graphs is most likely to represent the graph of daylight for the month after the spring equinox?

",,,"

||

||

||

","

",304444 +PRABQKRY,1,Multiple Choice (select 1),Multiple Choice,

Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip? 

,,,24.5 miles || 50 miles || 59.5 miles || 200 miles,50 miles,560450 +PSBBACU,5,Multiple Choice (select 1),Multiple Choice,"
+

On which item did she spend the most amount of money? 

+
",,,doughnuts || straws || hot dogs || pizza || apples || french fries,pizza,171657 +PRABFS48,1,Multiple Choice (select all),Check All That Apply,"

Select the unit from the list that you would use to measure the object.

+

 

+

The length of a fingernail clipping

",,,centimeters || cups || feet || gallons || grams || inches || kilograms || kilometers || liters || meters || miles || milliliters || millimeters || ounces || pounds || quarts || tons || yards,millimeters,173266 +PSBNEN,3,Multiple Choice (select 1),Multiple Choice,"

Lin and Diego travel in cars on the highway at constant speeds. Decide who was traveling faster.

+

 

+

After stopping for lunch, they travel at different speeds. To travel the next 60 miles, it takes Lin 65 minutes and it takes Diego 70 minutes.

",,,Lin || Diego,Lin,59398 +PSBBS47,1,Multiple Choice (select all),Check All That Apply,"

Here are three fractions: 34, 56, 68. Two of these fractions are equivalent to each other. Which two?

",,,"

34

||

56

||

68

","

34

||

68

",258570 +PSB9FG,2,Multiple Choice (select 1),Multiple Choice,"

If Lin and Noah use their small cubes to find the volume of the -inch cube, would they get the same value?

",,,Yes || No,Yes,166007 +PSBVEV,1,Multiple Choice (select 1),Multiple Choice,"

Two classes of students took an exam.

+

 

+

Here is a list of the scores in Class A:

+

 

+

65, 70, 70, 80, 80, 85, 85, 85, 90, 90, 100

+

 

+

Here is a box plot that shows the scores in Class B:

+

 

+
+
 
+
 
+
 
+
Which class had better overall results on the exam?
",,,Class A || Class B,Class A,98217 +PSBBHTM,1,Multiple Choice (select all),Check All That Apply,"

+

A cylinder with diameter 3 centimeters and height 8 centimeters is filled with water. Decide which figures described here, if any, could hold all of the water from the cylinder. 

",,,"1. Cone with a height of 8 centimeters and a radius of 3 centimeters. || 2. Cylinder with a diameter of 6 centimeters and height of 2 centimeters. || 3. Rectangular prism with a length of 3 centimeters, width of 4 centimeters, and height of 8 centimeters. || 4. Sphere with a radius of 2 centimeters.","1. Cone with a height of 8 centimeters and a radius of 3 centimeters. || 2. Cylinder with a diameter of 6 centimeters and height of 2 centimeters. || 3. Rectangular prism with a length of 3 centimeters, width of 4 centimeters, and height of 8 centimeters.",213135 +PRABJKA9,1,Multiple Choice (select all),Check All That Apply,

Select all of the statements that are true. Be prepared to explain your reasoning.

,,,1. 4 - 2(3 + 7) = 4 - 2 · 3 - 2 · 7 || 2. 4 - 2(3 + 7) = 4 + -2 · 3 + -2 · 7 || 3. 4 - 2(3 + 7) = 4 - 2 · 3 + 2 · 7 || 4. 4 - 2(3 + 7) = 4 - (2 · 3 + 2 · 7),1. 4 - 2(3 + 7) = 4 - 2 · 3 - 2 · 7 || 2. 4 - 2(3 + 7) = 4 + -2 · 3 + -2 · 7 || 4. 4 - 2(3 + 7) = 4 - (2 · 3 + 2 · 7),537870 +PSBV9Y,7,Multiple Choice (select 1),Multiple Choice,

Could a dot plot be used to represent Kiran’s data? 

,,,Yes || No,No,103419 +PSBSY3,1,Multiple Choice (select 1),Multiple Choice,"

Which is larger: the number of meters across the Milky Way, or the number of cells in all humans? 

+
+

 

+

Some useful information:

+
    +
  • The Milky Way is about 100,000 light years across.
    • +
  • There are about 37 trillion cells in a human body.
    • +
  • One light year is about 1016 meters.
    • +
  • The world population is about 7 billion.
    • +
+
",,,The number of meters across the Milky Way || The number of cells in all humans,The number of cells in all humans,83409 +PRABQP5V,1,Multiple Choice (select 1),Multiple Choice,"

Which is closest to the product 19,898·0.002?

",,40,"4,000 || 400 || 40 || 4",40,156504 +PSBGHR,4,Multiple Choice (select 1),Multiple Choice,"

Based on your scatter plot, do taller students in your class tend to have bigger hands? 

",,,yes || no,yes,33514 +PRABDYEC,1,Multiple Choice (select 1),Multiple Choice,"

The point (-4, 1) is rotated 180 degrees counterclockwise using center (-3, 0). What are the coordinates of the image?

",,,"

(-5, -2)

||

(-4, -1)

||

(-2, -1)

||

(4, -1)

","

(-2, -1)

",274206 +PSBDVUA,1,Multiple Choice (select all),Check All That Apply,"

Select all pairs of lines that appear to be perpendicular.

+

 

+

",,,m and p || m and r || m and s || m and t || p and r || p and s || p and t || r and s || r and t || s and t,p and s || p and t,627401 +PRABJJPE,1,Multiple Choice (select all),Check All That Apply,"

The stage manager of the school musical is trying to figure out how many sandwiches he can order with the $83 he collected from the cast and crew. Sandwiches cost $5.99 each, so he lets x represent the number of sandwiches he will order and writes 5.99x ≤ 83. He solves this to 2 decimal places, getting x ≤ 13.86.

+

Which of these are valid statements about this situation? (Select all that apply.)

",,,1. He can call the sandwich shop and order exactly 13.86 sandwiches. || 2. He can round up and order 14 sandwiches. || 3. He can order 12 sandwiches. || 4. He can order 9.5 sandwiches. || 5. He can order 2 sandwiches. || 6. He can order -4 sandwiches.,3. He can order 12 sandwiches. || 4. He can order 9.5 sandwiches. || 5. He can order 2 sandwiches.,104597 +PRABFFG7,1,Multiple Choice (select 1),Multiple Choice,"
+

Which of the polygons has the greatest area?

+
",,,

A rectangle that is 3.25 inches wide and 6.1 inches long.

||

A square with side length of 4.6 inches.

||

A parallelogram with a base of 5.875 inches and a height of 3.5 inches.

||

A triangle with a base of 7.18 inches and a height of 5.4 inches.

,

A square with side length of 4.6 inches.

,215152 +PRABQUFF,1,Multiple Choice (select 1),Multiple Choice,"
Below is a dot plot showing how much time customers spent in a store, rounded to the nearest five minutes.
+
 
+
+
 
+
Which of the following is a representative sample of this population?
",,,"

||

||

||

","

",99239 +PSBNB9,1,Multiple Choice (select 1),Multiple Choice,

Here are some expressions. All but one of them equals 16. Find the one that is not equal to 16.

,,,"

23 · 2

||

42

||

252

||

82

","

82

",59107 +PRABQP59,1,Multiple Choice (select 1),Multiple Choice,"

About 3.9×107 people live in California. About 1.3×106 people live in Maine. About how many more people live in California than live in Maine?

",,,"

2.6×106

||

2.6×107

||

3.77×106

||

3.77 ×107

","

3.77 ×107

",263739 +PSB6EU,3,Multiple Choice (select 1),Multiple Choice,"

If you wanted to increase the surface area of the resulting cylinder, would it make more sense to double x, y, or does it not matter?

",,,Double x || Double y || It does not matter,Double x,150288 +PSBCB3Y,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the quantity can be represented by a positive number or by a negative number. 

+

 

+

Kiran gave a gift of $10.

",,,positive || negative,negative,355221 +PRABQM5R,1,Multiple Choice (select all),Check All That Apply,"

The dot plot shows the number of hours 20 sixth grade students spent studying in a week.

+

 

+

+

 

+

 

+

Select all true statements about the data used to build the dot plot.

",,,The difference between the most hours and the least hours spent studying was 6 hours. || The mean amount of study time was 5 hours. || Nine students studied for at least 4 hours. || Most students studied less than 4 hours. || Only 1% of the students studied more than 6 hours.,The difference between the most hours and the least hours spent studying was 6 hours. || Nine students studied for at least 4 hours. || Most students studied less than 4 hours.,150918 +PRABEDDX,1,Multiple Choice (select 1),Multiple Choice,"

Using the data in the scatter plot, what can you tell about the slope of a good model?

+

 

+

",,,The slope is positive. || The slope is zero. || The slope is negative. || There is no association.,The slope is negative.,68821 +PSB2SG,3,Multiple Choice (select 1),Multiple Choice,

Can you put copies of an equilateral triangle together to form a right angle? 

,,,Yes || No,No,129121 +PRABFFJY,1,Multiple Choice (select 1),Multiple Choice,

One ounce of a yogurt contains of 1.2 grams of sugar. How many grams of sugar are in 14.25 ounces of yogurt?

,,,

0.171 grams

||

1.71 grams

||

17.1 grams

||

171 grams

,

17.1 grams

,204910 +PSBBBHZ,1,Multiple Choice (select 1),Multiple Choice,"

Are these triangles identical?

+

 

+
+
+

+
+
",,,Yes || No,No,177761 +PSBJS4,4,Multiple Choice (select 1),Multiple Choice,"

The graph shows the temperature between noon and midnight in one day in a certain city.

+

 

+

+

 

+

 

+

Did the temperature change more between 1:00 p.m. and 3:00 p.m. or between 3:00 p.m. and 5:00 p.m.?

",,,Between 1:00 p.m. and 3:00 p.m. || Between 3:00 p.m. and 5:00 p.m.,Between 1:00 p.m. and 3:00 p.m.,45497 +PRABEURH,1,Multiple Choice (select 1),Multiple Choice,"

Use a protractor to try to draw each triangle.

+

 

+

Which of these triangles is impossible to draw?

",,,Triangle 1: A triangle where one angle measures 20 degrees and another angle measures 45 degrees. || Triangle 2: A triangle where one angle measures 120 degrees and another angle measures 50 degrees. || Triangle 3: A triangle where one angle measures 90 degrees and another angle measures 100 degrees.,Triangle 3: A triangle where one angle measures 90 degrees and another angle measures 100 degrees.,107995 +PRABEB54,1,Multiple Choice (select all),Check All That Apply,

Select all the representations that are appropriate for comparing exam score to number of hours of sleep the night before the exam.

,,,Histogram || Scatter plot || Dot plot || Table || Box plot,Scatter plot || Table,327381 +PRABPUGM,1,Multiple Choice (select 1),Multiple Choice," + + + + + + +
+

Here is a balanced hanger diagram:

+

 

+

A circle has a mass of 3 grams and a square has a mass of 2 grams. Which is the mass of a triangle?

+
",,,"

95 grams

||

113 grams

||

3 grams

||

7 grams

",

3 grams

,360720 +PRABPUCY,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,Two squares with the same length sides are always congruent. || Two rectangles with the same length sides are always congruent. || Two rhombuses with the same length sides are always congruent. || Two parallelograms with the same length sides are always congruent. || Two quadrilaterals with the same side lengths are always congruent.,Two squares with the same length sides are always congruent. || Two rectangles with the same length sides are always congruent.,544776 +PRABEPNA,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 10-6.

",,,"

11,000,000

||

‐11,000,000

||

1106

||

108 · 10-2

||

1106

||

110 · 10 · 10 · 10 · 10 · 10

","

11,000,000

||

1106

||

1106

||

110 · 10 · 10 · 10 · 10 · 10

",425079 +PRABTVKH,1,Multiple Choice (select 1),Multiple Choice,

La familia de Lin ha completado el 60% de un viaje. Ellos han viajado 30 millas. ¿Qué tan largo es todo el viaje?

,,,50 millas || 48 millas || 30 millas || 18 millas,50 millas,320133 +PSBDZX2,2,Multiple Choice (select all),Check All That Apply,"

Identify all pairs of perpendicular lines in the diagram.

+

 

+

",,,g and i || f and j || f and i || j and i || h and g || h and f || h and j || h and i || g and f || g and j,h and g || h and f,651370 +PSBBUSP,1,Multiple Choice (select 1),Multiple Choice,"

A class measured the radius and circumference of various circular objects. The results are plotted on the graph.

+

 

+
+
+
+
+
+
 
+
Does there appear to be a proportional relationship between the radius and circumference of a circle?
+
+
+
+
",,,Yes || No,Yes,268402 +PRABQMAT,1,Multiple Choice (select all),Check All That Apply,"

Select all statements that show correct reasoning for finding 15÷29.

",,,"

Multiply 15 by 2, then divide by 9.

||

Multiply 15 by 9, then divide by 2.

||

Multiply 15 by 19, then multiply by 2.

||

Multiply 15 by 9, then multiply by 12.

","

Multiply 15 by 9, then divide by 2.

||

Multiply 15 by 9, then multiply by 12.

",319778 +PRABFGRQ,1,Multiple Choice (select 1),Multiple Choice,"

Which of these is a solution to the equation 18 = 25 · x?

+

 

",,,"

 

+

240

+

 

||

 

+

516

+

 

||

 

+

1140

+

 

||

 

+

1740

+

 

","

 

+

516

+

 

",113676 +PSBFC,1,Multiple Choice (select 1),Multiple Choice,"

For the following pair of shapes, decide whether or not they are congruent. 

+

 

+

",,,"Yes, they are congruent || No, they are not congruent","Yes, they are congruent",577 +PSBWRH,1,Multiple Choice (select 1),Multiple Choice,"

 The graph shows how much snow fell after a certain amount of time measured in hours.

+

 

+

+

 

+

Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell?

",,,Yes || No,No,106336 +PSBBCQT,3,Multiple Choice (select 1),Multiple Choice,

Does it appear in your equation?

,,,Yes || No,Yes || No,184505 +PSBS86,1,Multiple Choice (select all),Check All That Apply,"

+

 

+

Which of these rectangles have the same area as Rectangle R but different perimeter?

",,,Rectangle A. || Rectangle B. || Rectangle C. || Rectangle D. || Rectangle E. || Rectangle F.,Rectangle B. || Rectangle C.,85020 +PRABQNYZ,1,Multiple Choice (select all),Check All That Apply,"

Select all true statements.

+

 

+

+
 
",,,Circle A has a circumference of π. || Circle B has a circumference of π. || Circle B has an area of π. || Circle C has an area of π. || π is the constant of proportionality relating the radius of a circle to its circumference. || π is the constant of proportionality relating the diameter of a circle to its circumference.,Circle A has a circumference of π. || Circle B has an area of π. || π is the constant of proportionality relating the diameter of a circle to its circumference.,27175 +PRABG5Z5,1,Multiple Choice (select all),Check All That Apply,

Select all the equations that can be used to answer the question: “How many rhombuses are in a trapezoid?”

,,,"

23 ÷ ? = 1

||

1 ÷ 23 = ?

||

? ÷ 23 = 1

||

? · 23 = 1

||

1 · 23 = ?

","

1 ÷ 23 = ?

||

? · 23 = 1

",46664 +PRABEVAG,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,"

2.3 + (-2.3) is equal to zero.

||

(-3.7) + (-4.1) is positive.

||

-2.6 - -124 is positive.

||

52 + -2.5 is negative.

||

72 - (-100) is negative.

","

2.3 + (-2.3) is equal to zero.

||

-2.6 - -124 is positive.

",69320 +PRABQPCJ,1,Multiple Choice (select all),Check All That Apply,

Select all the equations that are true when x is -6.

,,,"

18 = x + x + x

||

4 = x + 10

||

‐12 = 2x

||

9 - x = 3

||

x2 = ‐3

||

‐18 = x ·‐3

","

4 = x + 10

||

‐12 = 2x

||

x2 = ‐3

",179454 +PSBB8W,6,Multiple Choice (select all),Check All That Apply,"

A city has a higher elevation than Coachella, CA.

+

 

+

Select all numbers that could represent the city’s elevation.

",,,-11 feet || -35 feet || 4 feet || -8 feet || 0 feet,-11 feet || 4 feet || -8 feet || 0 feet,10141 +PSBTXU,1,Multiple Choice (select 1),Multiple Choice,"

A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is the statement true or false? 

+

 

+

Speed is a function of time.

",,1,True || False,TRUE,87902 +PSBBCW4,1,Multiple Choice (select 1),Multiple Choice,"

Elena said, “I think this line is a good fit because half of the points are on one side of the line and half of the points are on the other side.” Do you agree?

+

+
 
",,,Yes || No,No,185871 +PRABE57H,1,Multiple Choice (select 1),Multiple Choice,"

Which description can represent the surface area of this trunk?

+

 

+

",,,The number of square inches that cover the top of the trunk. || The number of square feet that cover all the outside faces of the trunk. || The number of square inches of horizontal surface inside the trunk. || The number of cubic feet that can be packed inside the trunk.,The number of square feet that cover all the outside faces of the trunk.,273879 +PRABEG3A,1,Multiple Choice (select 1),Multiple Choice,"

The points (2,4) and (6,7) lie on a line. What is the slope of the line?

",,,"

2

||

1

||

43

||

34

","

34

",325132 +PSBS7T,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

41 = 4 · 1

",,1,True || False,TRUE,84944 +PSBCDCF,1,Multiple Choice (select 1),Multiple Choice,"

Adult elephant seals generally weigh about 5,500 pounds. If you weighed 5 elephant seals, would you expect each seal to weigh exactly 5,500 pounds?

",,,Yes || No,No,362897 +PSBBQJ,1,Multiple Choice (select 1),Multiple Choice,"

Predict if the mean is greater than, less than, or approximately equal to the median.

+

 

+

Backpack weights of 55 sixth-grade students

+

",,,Greater than || Less than || Equal to,Greater than,7018 +PRABESYD,1,Multiple Choice (select all),Check All That Apply,"

Select all stories that the tape diagram can represent.

+

 

+
",,,"There are 87 children and 39 adults at a show. The seating in the theater is split into 4 equal sections. || There are 87 first graders in after-care. After 39 students are picked up, the teacher puts the remaining students into 4 groups for an activity. || Lin buys a pack of 87 pencils. She gives 39 to her teacher and shared the remaining pencils between herself and 3 friends. || Andre buys 4 packs of paper clips with 39 paper clips in each. Then he gives 87 paper clips to his teacher. || Diego’s family spends $87 on 4 tickets to the fair and a $39 dinner.","There are 87 first graders in after-care. After 39 students are picked up, the teacher puts the remaining students into 4 groups for an activity. || Lin buys a pack of 87 pencils. She gives 39 to her teacher and shared the remaining pencils between herself and 3 friends. || Diego’s family spends $87 on 4 tickets to the fair and a $39 dinner.",55274 +PRABQM9A,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements. 

,,,"

Given a dot plot, it is always possible to construct a corresponding histogram.

||

Given a dot plot, it is always possible to calculate the mean of the data.

||

Given a box plot, it is always possible to calculate the IQR of the data.

||

Given a histogram, it is always possible to calculate the mean of the data.

||

Given a histogram, it is always possible to calculate the median of the data.

","

Given a dot plot, it is always possible to construct a corresponding histogram.

||

Given a dot plot, it is always possible to calculate the mean of the data.

||

Given a box plot, it is always possible to calculate the IQR of the data.

",591536 +PSBWMQ,3,Multiple Choice (select 1),Multiple Choice,

Whose estimate is more accurate?

,,,Tyler's || Kiran's,Kiran's,105511 +PRABESMB,1,Multiple Choice (select all),Check All That Apply,"

In football, the team that has the ball has four chances to gain at least ten yards. If they don't gain at least ten yards, the other team gets the ball. Positive numbers represent a gain and negative numbers represent a loss. Select all of the sequences of four plays that result in the team getting to keep the ball.

+

 

",,,"8, -3, 4, 21 || 30, -7, -8, -12 || 2, 16, -5, -3 || 5, -2, 20, -1 || 20, -3, -13, 2","8, -3, 4, 21 || 2, 16, -5, -3 || 5, -2, 20, -1",67623 +PSBBC4S,1,Multiple Choice (select 1),Multiple Choice,"

Is the area of the shaded rectangle 6(2−m) or 6(m−2)?

+

 

+

",,,6(2 - m) || 6(m - 2),6(m - 2),186704 +PRABFKNR,1,Multiple Choice (select all),Check All That Apply,

Here is a list of questions about the students and teachers at a school. Select all the questions that are statistical questions.

,,,

What is the most popular lunch choice?

||

What school do these students attend?

||

How many math teachers are in the school?

||

What is a common age for the teachers at the school?

||

About how many hours of sleep do students generally get on a school night?

||

How do students usually travel from home to school?

,

What is the most popular lunch choice?

||

What is a common age for the teachers at the school?

||

About how many hours of sleep do students generally get on a school night?

||

How do students usually travel from home to school?

,262608 +PRABQKVF,1,Multiple Choice (select 1),Multiple Choice,

Which expression is less than 1?

,,,"

4 ÷ 23

||

34 ÷ 23

||

148 ÷ 158

||

248 ÷ 158

","

148 ÷ 158

",518589 +PSBB2TW,3,Multiple Choice (select 1),Multiple Choice,"

For the inequality, decide whether the solution is represented by x < 4.5 or x > 4.5.

+

 

+

-2(x + 3.2) < -15.4

",,,x < 4.5 || x > 4.5,x > 4.5,302522 +PRABQK7P,1,Multiple Choice (select all),Check All That Apply,"

Without computing, select all of the expressions that have the same value as 74·(29+56).

",,,74 • 29 + 56 || 74 + (29 + 56) || 74 + (56 • 29) || (74 • 29) + (74 • 56) || (56 + 29) • 74,(74 • 29) + (74 • 56) || (56 + 29) • 74,299546 +PSBS57,1,Multiple Choice (select 1),Multiple Choice,"

Here is a scatter plot that shows the years when some used cars were made and their prices in 2016, together with the graph of a linear model for the relationship between year and price.

+

+


Is the slope positive or negative?

",,,Positive || Negative,Positive,84521 +PRABG2WD,1,Multiple Choice (select 1),Multiple Choice,"

True or false?

+

 

+

15 · 45 = 455

",,1,True || False,TRUE,348598 +PRABQKSF,1,Multiple Choice (select all),Check All That Apply,"

Select all the fractions that are greater than 12.

",,,"

35

||

713

||

715

||

107

||

100200

||

10002001

","

35

||

713

||

107

",133202 +PSBN2F,1,Multiple Choice (select all),Check All That Apply,

Which of the following changes would you represent using a negative number? 

,,,

A loss of 4 points

||

A gain of 50 yards

||

A loss of $10

||

An elevation above sea level

,

A loss of 4 points

||

A loss of $10

,62772 +PSBBMV2,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

82 = 43

",,1,True || False,TRUE,230550 +PSBEMQ,1,Multiple Choice (select 1),Multiple Choice,"

Noah thinks the answers to these two questions will be the same. Do you agree with him?

+

 

+
    +
  • This year, a herd of bison had a 10% increase in population. If there were 550 bison in the herd last year, how many are in the herd this year?
    • +
+

 

+
    +
  • This year, another herd of bison had a 10% decrease in population. If there are 550 bison in the herd this year, how many bison were there last year?
    • +
",,,Yes || No,No,23144 +PSBBZ52,7,Multiple Choice (select 1),Multiple Choice,

Should the authors of either of these series give their new hero the ability to fly?

,,,Beyond Human || Mysterious Planets,Beyond Human,298906 +PSBBCY4,1,Multiple Choice (select 1),Multiple Choice,"

Noah said, “I think this line is a good fit because it passes through the leftmost point and the rightmost point.” Do you agree?

+

+
 
",,,Yes || No,No,186153 +PRABQKJF,1,Multiple Choice (select all),Check All That Apply,

Select all the ratios that are equivalent to 9 : 6.

,,,6 : 9 || 3 : 2 || 13 : 10 || 5 : 2 || 18 : 12,3 : 2 || 18 : 12,2319 +PRABEDC7,1,Multiple Choice (select all),Check All That Apply,"

Here is a scatter plot:

+

 

+

+

 

+

Select all the following that describe the association in the scatter plot:

",,,Linear association || Non-linear association || Positive association || Negative association || No association,Linear association || Positive association,233989 +PSB5PB,2,Multiple Choice (select 1),Multiple Choice,"

Here are some line segments.

+

 

+

+

 

+

 

+

Which segment is a dilation of BC using A as the center of dilation and a scale factor of 32?

",,,ED || GJ || FH,GJ,145971 +PSBCQHC,1,Multiple Choice (select 1),Multiple Choice,"

A baseball team sells snacks at their games to raise money. At their last game, they made 78 as much money as they made at their first game.

+

 

+

 

+

Did they make more money at their first or last game?

+

 

",,,First game || Last game,Last game,420156 +PSBCNC3,1,Multiple Choice (select all),Check All That Apply,"

Select all of the equations that describe the situation. If you get stuck, draw a diagram.

+

 

+

 

+

Kiran scored 223 more points in a computer game than Tyler. If Kiran scored 409 points, how many points did Tyler score?

",,,

223 = 409 − z

||

409 − 223 = z

||

409 + 223 = z

||

409 = 223 + z

,

223 = 409 − z

||

409 − 223 = z

||

409 = 223 + z

,406962 +PSBH8S,9,Multiple Choice (select 1),Multiple Choice,"

Spinning this spinner will result in green.

+

 

+

",,,impossible || unlikely || equally likely as not || likely || certain,equally likely as not,42766 +PSB3HE,1,Multiple Choice (select 1),Multiple Choice,"

A cube has side length 10 inches. Jada says the surface area of the cube is 600 in2, and Noah says the surface area of the cube is 3,600 in2. Here is how each of them reasoned:

+ + + + + + + +
+

Jada’s Method:

+

6 ⋅ 102
6 ⋅ 100
600

+		 +

Noah’s Method:

+

6 ⋅ 102
602
3,600

+
+

 

+
+
+

Do you agree with either of them?

+
+
",,,Agree with Jada || Agree with Noah,Agree with Jada,133477 +PRABEURT,1,Multiple Choice (select all),Check All That Apply,

Select all the situations where knowing the volume of an object would be more useful than knowing its surface area.

,,,Determining the amount of paint needed to paint a barn. || Determining the monetary value of a piece of gold jewelry. || Filling an aquarium with buckets of water. || Deciding how much wrapping paper a gift will need. || Packing a box with watermelons for shipping. || Charging a company for ad space on your race car. || Measuring the amount of gasoline left in the tank of a tractor.,Determining the monetary value of a piece of gold jewelry. || Filling an aquarium with buckets of water. || Packing a box with watermelons for shipping. || Measuring the amount of gasoline left in the tank of a tractor.,156797 +PRABTV8G,1,Multiple Choice (select all),Check All That Apply,"

Selecciona todos los números que el punto podría representar en esta recta numérica.

+

+

 

",,,2.5 || 2.25 || 2.2 || 2.0 || 1.2,2.25 || 2.2,325103 +PSB36P,1,Multiple Choice (select 1),Multiple Choice,"

Decide if the responses will produce numerical data or categorical data.

+

 

+

What is the last thing you ate or drank?

",,,Categorical || Numerical,Categorical,137297 +PSBC9HN,1,Multiple Choice (select 1),Multiple Choice,"

Noah and his friends are going to an amusement park. The total cost of admission for 8 students is $100, and all students share the cost equally. Noah brought $13 for his ticket.

+

 

+

Did he bring enough money to get into the park?

",,,Yes || No,Yes,515874 +PSBB6MU,1,Multiple Choice (select all),Check All That Apply,"

The number line shows values of x that make the inequality x > 1 true.

+

 

+

+

 

+

Select all the values of x from this list that will make the inequality x > 1 true. 

",,,3 || -3 || 1 || 700 || 1.05,3 || 700 || 1.05,323597 +PSBFD,3,Multiple Choice (select 1),Multiple Choice,"

Jada drank 2 liters of water yesterday. Andre drank 14 times as much water as Jada. Lin drank three times as much water as Andre.

+

 

+

 

+

Did Lin drink more or less water than Jada drank?

",,,More || Less,Less,648 +PRABQM9B,1,Multiple Choice (select 1),Multiple Choice,"

Here is a dot plot of a data set. 

+

 

+

 

+

Which statement is true about the mean of the data set?

",,,The mean is less than 8. || The mean is equal to 8. || The mean is greater than 8. || There is not enough information to determine the mean.,The mean is less than 8.,591659 +PRABE55W,1,Multiple Choice (select all),Check All That Apply,

Select all the polygons.

,,,"

||

||

||

||

||

","

||

",243115 +PRABEH47,1,Multiple Choice (select 1),Multiple Choice,"

Elena noticed that, nine years ago, her cousin Katie was twice as old as Elena was then. Then Elena said, “In four years, I’ll be as old as Katie is now!” If Elena is currently e years old and Katie is k years old, which system of equations matches the story?

",,,"

k-9=2ee+4=k

||

2k=e-9e=k+4

||

k=2e-9e+4=k+4

||

k-9=2(e-9)e+4=k

","

k-9=2(e-9)e+4=k

",105121 +PRABG4ZK,1,Multiple Choice (select all),Check All That Apply,"

Select all of the choices that are equal to (-5)-(-12).

",,,

-7

||

7

||

The difference between -5 and -12.

||

The difference between -12 and -5.

||

(-5) + 12

||

(-5) + (-12)

,

7

||

The difference between -5 and -12.

||

(-5) + 12

,162021 +PSBCWKM,1,Multiple Choice (select 1),Multiple Choice,"
+
+
+
+ + + + + + + +
+

 

+		 
+

 

+
+
+
+
+

Sails come in many shapes and sizes. The sail on the right is a triangle. Is it a right triangle?

",,,Yes || No,No,454526 +PSBBK3R,2,Multiple Choice (select 1),Multiple Choice,

Are there more numbers that have this property?

,,,Yes || No,Yes,226116 +PSBGHR,6,Multiple Choice (select 1),Multiple Choice,"

Based on your scatter plot, is hand span a linear function of height? 

",,,yes || no,no,33779 +PRABEGJC,1,Multiple Choice (select 1),Multiple Choice,"

Two paper drink cups are shaped like cones. The small cone can hold 6 oz of water. The large cone is 43 the height and 43 the diameter of the small cone. Which of these could be the amount of water the large cone holds?

",,,8 cm || 14 oz || 4.5 oz || 14 cm,14 oz,50592 +PSBCS3Z,1,Multiple Choice (select 1),Multiple Choice,"

Han says that you can wrap a 5-foot rope around a wheel with a 2-foot diameter because 52 is less than pi. Do you agree with Han?

",,,Yes || No,No,434672 +PRABQPTT,1,Multiple Choice (select 1),Multiple Choice,"

Which expression is equivalent to 6(2y-5)?

",,,12y - 5 || 5 - 12y || 12y - 30 || 30 - 12y,12y - 30,35781 +PSBRC,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of shapes, decide whether or not Shape A is congruent to Shape B. 

+

 

+

 

",,,"Yes, they are congruent || No, they are not congruent","Yes, they are congruent",1864 +PRABQN9D,1,Multiple Choice (select all),Check All That Apply,"

Let x = -56 and y = 43.

+

 

+

 

+

+

 

+

 

+

Select all the expressions that have a positive value.

",,,"

x · y

||

yx

||

xy

||

x + y

||

x - y

||

y - x

",

x + y

||

y - x

,24564 +PRABQMBC,1,Multiple Choice (select 1),Multiple Choice,"

Which estimate is closest to the actual value of (2.99548)⋅(1.8342)?

",,5,4.8 || 5.5 || 6.2 || 8.3,5.5,8234 +PRABEP2C,1,Multiple Choice (select all),Check All That Apply,"

m, p, and z represent the lengths of the three sides of this right triangle.

+

 

+

Select all the equations that represent the relationship between m, p, and z.

+

",,,m² + p² = z² || m² = p² + z² || m² = z² + p² || p² + m² = z² || z² + p² = m² || p² + z² = m²,m² = p² + z² || m² = z² + p² || z² + p² = m² || p² + z² = m²,9217 +PRABQP6F,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 34·32.

",,,"

36

||

38

||

93

||

96

||

98

","

36

||

93

",506037 +PSB4BS,1,Multiple Choice (select 1),Multiple Choice,"

Which of the following is the correct value of (0.22) · (0.4)? 

",,,

8.8

||

0.88

||

0.088

||

0.0088

,

0.088

,138228 +PRABHK6E,1,Multiple Choice (select 1),Multiple Choice,"

Which is larger, 52 or 33?

",,,

5²

|| 3³,3³,141384 +PSB2G7,1,Multiple Choice (select 1),Multiple Choice,"

Four different stores posted ads about special sales on 15-oz cans of baked beans.

+

 

+

Which store is offering the best deal?

+

 

+
 
",,,8 for $6 || 10 for $10 || 2 for $3 || $0.80 each,8 for $6,127489 +PSBB6PY,5,Multiple Choice (select 1),Multiple Choice,"

",,,< || = || >,<,324036 +PRABKDUG,1,Multiple Choice (select 1),Multiple Choice,"

State whether the following is in scientific notation.

+

 

+

5.23 x 108

",,,Already in scientific notation || Not in scientific notation,Already in scientific notation,258045 +PRABHGR2,1,Multiple Choice (select all),Check All That Apply,"

All of these triangles are congruent. Sometimes we can take one figure to another with a translation. Choose the triangles that are images of triangle ABC under a translation.

+

 

",,,A. || B. || C. || D. || E. || F. || G. || H.,B. || F. || H.,3160 +PRABEVHS,1,Multiple Choice (select all),Check All That Apply,"

Lin wants to know if students in elementary school generally spend more time playing outdoors than students in middle school. She selects a random sample of size 20 from each population of students and asks them how many hours they played outdoors last week. Suppose that the MAD for each of her samples is about 3 hours.

+

 

+

Select all pairs of sample means for which Lin could conclude there is a meaningful difference between the two populations

",,,"Elementary school: 12 hours, middle school: 10 hours || Elementary school: 14 hours, middle school: 9 hours || Elementary school: 13 hours, middle school: 6 hours || Elementary school: 13 hours, middle school: 10 hours || Elementary school: 7 hours, middle school: 15 hours","Elementary school: 13 hours, middle school: 6 hours || Elementary school: 7 hours, middle school: 15 hours",9612 +PRABQK69,1,Multiple Choice (select 1),Multiple Choice,"

Which is closest to the quotient 5,278 ÷ 0.05?

",,,"1,000,000 || 100,000 || 10,000 || 1,000","100,000",590968 +PRABQPHA,1,Multiple Choice (select all),Check All That Apply,"

Select all the triangles that can be rotated to match up with Triangle 1.

+

 

+

",,,"

||

||

||

","

||

",98785 +PSBFEK,1,Multiple Choice (select 1),Multiple Choice,

Mai and Priya were on scooters. Mai traveled 15 meters in 6 seconds. Priya travels 22 meters in 10 seconds. Who was moving faster?

,,,Mai || Priya,Mai,27697 +PSBTXU,3,Multiple Choice (select 1),Multiple Choice,"

A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is the statement true or false? 

+

 

+

Time is a function of distance.

",,0,True || False,FALSE,88255 +PRABQNAA,1,Multiple Choice (select 1),Multiple Choice,"

A scale drawing of a rectangular parking lot is 6 inches long and 5 inches wide. The actual parking is 240 feet long. What is the area of the actual parking lot, in square feet?

+

 

+

",,,"48,000 || 1,200 || 200 || 30","48,000",12289 +PRABQJRF,1,Multiple Choice (select all),Check All That Apply,

Select all triangles that appear to be a right triangle.

,,,"

||

||

||

||

||

","

||

||

",544510 +PSB9VC,1,Multiple Choice (select 1),Multiple Choice,"

For the pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not.

+

 

+

 

+

Triangle E: 63, 45, ___; Triangle F: 14, 71, ___

",,,similar || not similar,not similar,168353 +PSBT77,3,Multiple Choice (select 1),Multiple Choice,"

Based on this data, would you expect 1956 to have closer to 50,000 cases or closer to 100,000 cases?

",,,"Closer to 50,000 cases || Closer to 100,000 cases","Closer to 50,000 cases",90685 +PSBDT5,1,Multiple Choice (select 1),Multiple Choice,"

A plant measured x inches tall last week and 8 inches tall this week.

+

 

+

Select the expression that represents the number of inches the plant grew this week.

+
 
",,,x - 8 || 8 - x,8 - x,19255 +PRABQMAS,1,Multiple Choice (select all),Check All That Apply,"

Select all equations that represent this question:

+

 

+

Priya is stacking building blocks to make a tower. She takes a break when the tower is 212 feet tall, which is 58 of the height of the tower she wants to build. How tall is the tower when finished?

",,,"

58 · ? = 212

||

58 ÷ 212 = ?

||

212 · ? = 58

||

212 · 58 = ?

||

212 · 85 = ?

||

212 ÷ 58 = ?

","

58 · ? = 212

||

212 · 85 = ?

||

212 ÷ 58 = ?

",319658 +PSBBCB2,1,Multiple Choice (select 1),Multiple Choice,"

Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, a, to the number of ant legs l. Elena writes a = 6 · l and Andre writes l = 16· a. Do you agree with either of the equations?

",,,Andre is correct || Elena is correct || Both are correct || Neither are correct,Neither are correct,182080 +PSB65U,1,Multiple Choice (select 1),Multiple Choice,"

State whether you agree with the statement below. 

+

 

+

A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of -10 meters.

",,,Agree || Disagree,Disagree,153861 +PSBBC95,5,Multiple Choice (select 1),Multiple Choice,

Decide whether the two groups are very different or not.

,,,Yes || No,Yes,187772 +PRABFGWF,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 16x + 36.

",,,"

16(x + 20)

||

x(16 + 36)

||

4(4x + 9)

||

2(8x + 18)

||

2(8x + 36)

","

4(4x + 9)

||

2(8x + 18)

",35632 +PSBBB4U,3,Multiple Choice (select 1),Multiple Choice,"

Could she have bought 1 pretzel, 1 drink, and 5 bags of popcorn?

",,,Yes || No,No,181066 +PSBBRY5,1,Multiple Choice (select 1),Multiple Choice,"

Can you decompose this triangle and rearrange its parts to form a rectangle?

+

 

+
+

+
",,,Yes. || No.,Yes.,253000 +PSBBNG,3,Multiple Choice (select all),Check All That Apply,"

Which measure of center - the mean or the median - better describes a typical value for this distribution?

+

 

+

",,,Mean || Median,Mean || Median,6843 +PSBSC7,2,Multiple Choice (select all),Check All That Apply,"

Select all the values that are solutions to :

",,,3 || -3 || 4 || -4 || 4.001 || -4.001,3 || -3 || 4 || -4 || -4.001,80087 +PSBS3F,1,Multiple Choice (select 1),Multiple Choice,"

Noah and Lin both solved the equation 14a = 2(a − 3).

+

 

+
+
+
+
+ + + + + + + + + + + +
+

Noah's solution:

+		 +

Lin's solution: 

+
14a=2(a-3)14a=2a-612a=-6    a= -1214a=2(a-3)7a=a-36a=-3  a=-12  
+

 

+

Do you agree with either of them? 

+
+
+
+
",,,Noah's Solution || Lin's Solution || Both Solutions || Neither Solutions,Both Solutions,83813 +PSBCBAP,3,Multiple Choice (select 1),Multiple Choice,"

Here is a picture of an older version of the flag of Great Britain. There is a rigid transformation that takes Triangle 1 to Triangle 2, another that takes Triangle 1 to Triangle 3, and another that takes Triangle 1 to Triangle 4.

+

 

+

+

 

+

Do all eight triangles in the flag have the same area? 

",,,Yes || No || Not enough information,No,350622 +PRABEVCX,1,Multiple Choice (select all),Check All That Apply,"

Select all expressions that are equivalent to 6x + 1 − (3x − 1).

",,,6x + 1 - 3x - 1 || 6x + -3x + 1 + 1 || 3x + 2 || 6x - 3x + 1 - 1 || 6x + 1 + -3x - -1,6x + -3x + 1 + 1 || 3x + 2 || 6x + 1 + -3x - -1,190106 +PSBJTV,1,Multiple Choice (select 1),Multiple Choice,"

Jada explains how she finds 15⋅23:

+

 

+

“I know that ten 23's is 230, so five 23's will be half of 230, which is 115.

+

15 is 10 plus 5, so 15 · 23 is 230 plus 115, which is 345.""

+

 

+

Do you agree with Jada?

",,,Yes || No,Yes,45675 +PSB38Y,1,Multiple Choice (select 1),Multiple Choice,"

Decide if the responses will produce numerical data or categorical data.

+

 

+

How many minutes did it take you to get ready this morning - from waking up to leaving for school?

",,,Categorical || Numerical,Numerical,137690 +PSBDJFQ,2,Multiple Choice (select 1),Multiple Choice,

Is there a different triangle Noah could draw that would answer the question? 

,,,Yes || No,Yes,567463 +PRABQKWA,1,Multiple Choice (select 1),Multiple Choice,"

Priya ran 112 miles today, and Tyler ran 334 miles. How many times the length of Priya’s run was Tyler’s run?

",,,"

458 times as far

||

94 times as far

||

52 times as far

||

25 times as far

","

52 times as far

",20788 +PSBBBKX,1,Multiple Choice (select 1),Multiple Choice,"
    +
  • Circle A has a diameter of approximately 20 inches and an area of approximately 300 in2.

    • +
  • Circle B has a diameter of approximately 60 inches.
    • +
+

 

+

Which of these could be the area of Circle B? 

",,,"About 100 in² || About 300 in² || About 900 in² || About 2,700 in²","About 2,700 in²",178083 +PSB6BE,1,Multiple Choice (select all),Check All That Apply,"

m, n, a, b, and c all represent positive integers. Consider these two equations: 

+

 

+

m = a + b + c      n = abc

+

 

+

Which of these statements are true? Select all that apply.

",,,"If a is tripled, m is tripled. || If a, b, and c are all tripled, then m is tripled. || If a is tripled, n is tripled. || If a, b, and c are all tripled, then n is tripled.","If a, b, and c are all tripled, then m is tripled. || If a is tripled, n is tripled.",149599 +PSBC8XC,4,Multiple Choice (select 1),Multiple Choice,

Is d proportional to n?

,,,Yes || No,Yes,511978 +PRABEVHJ,1,Multiple Choice (select all),Check All That Apply,"

Select all the numbers that represent point A.

+

 

+

",,,"

0.25

||

0.5

||

0.75

||

12

||

34

||

1216

","

0.75

||

34

||

1216

",5125 +PSBDXP,1,Multiple Choice (select 1),Multiple Choice,"

Lin draws this tape diagram for :

+

 

+

 

+

+

 

+

 

+

Lin says that  because there are 5 groups of  and  left. Do you agree with Lin?

+

 

",,,Agree || Disagree,Disagree,20000 +PSBYH6,1,Multiple Choice (select 1),Multiple Choice,"

Which estimate is closest to the actual value of the expression? 

+

 

+

",,5,4 || 4.5 || 5,5,116435 +PRABFS47,1,Multiple Choice (select all),Check All That Apply,"

Select the unit from the list that you would use to measure the object.

+

 

+

The length of a hippopotamus

",,,centimeters || cups || feet || gallons || grams || inches || kilograms || kilometers || liters || meters || miles || milliliters || millimeters || ounces || pounds || quarts || tons || yards,feet || meters || yards,173140 +PSBUSE,1,Multiple Choice (select 1),Multiple Choice,"

Here is an equation, and the steps Clare wrote to solve it:

+

 

+

14x-2x+3=3(5x+9)        12x+3=3(5x+9)      3(4x+1)=3(5x+9)           4x+1=5x+9                   1=x+9               -8=x

+

 

+

Here is the same equation, and the steps Lin wrote to solve it:

+

 

+

14x−2x+3=3(5x+9)         12x+3=3(5x+9)         12x+3=15x+27                12x=15x+24               -3x=24                    x=-8

+

 

+

Are both of their solutions correct?

",,,Yes || No,Yes,93475 +PRABFEH4,1,Multiple Choice (select all),Check All That Apply,"
+

A television screen has length 1612 inches, width w inches, and area 462 square inches. Select all the equations that represent the relationship of the side lengths and area of the television.

+
",,,"

w · 462 = 1612

||

1612 · w = 462

||

462 ÷ 1612 = w

||

462 ÷ w = 1612

||

1612 · 462 = w

","

1612 · w = 462

||

462 ÷ 1612 = w

||

462 ÷ w = 1612

",243888 +PSBB3KR,1,Multiple Choice (select 1),Multiple Choice,"

Jada y Noah querían hallar el volumen total de un cubo y un prisma rectangular. Ellos saben que el volumen del prisma es 20 unidades cúbicas y también que el cubo tiene longitudes de lado de 10 unidades.

+

 

+

Jada dice que el volumen total es 27,000 unidades cúbicas. Noah dice que es 1,020 unidades cúbicas. Así fue como cada uno razonó:

+

 

+ + + + + + + + + + + +
+

Método de Jada

+		 +

Método de Noah

+
+

20 + 10³

+

30³

+

27,000

+		 +

20 + 10³

+

20 + 1,000

+

1,020

+ 
+

 

+

¿Estás de acuerdo con alguno de los dos?

",,,Acuerdo con ambos || Acuerdo con Jada || Acuerdo con Noah || Acuerdo con ninguno,Acuerdo con Noah,307185 +PSBBUBF,1,Multiple Choice (select 1),Multiple Choice,"

Students are conducting a class experiment to see if there is a meaningful difference between two groups of plants that have begun to sprout leaves. The teacher randomly selects 8 plants from each group and counts the number of leaves on each plant.

+


Group A: 2, 2, 3, 3, 5, 5, 5, 7

+

Group B: 10, 9, 7, 8, 10, 12, 14, 10

+

 

+


Is there a meaningful difference between the two groups?

",,,yes || no,yes,265806 +PRABQKNP,1,Multiple Choice (select all),Check All That Apply,

Select all the ratios that are equivalent to 8 : 6.

,,,

4 : 3

||

6 : 8

||

16 : 12

||

10 : 8

||

7 : 5

,

4 : 3

||

16 : 12

,115064 +PSBU7J,1,Multiple Choice (select 1),Multiple Choice,"

A restaurant is offering 2 specials: 10 burritos for $12, or 6 burritos for $7.50. Noah needs 60 burritos for his party. Should he buy 6 orders of the 10-burrito special or 10 orders of the 6-burrito special? 

",,,10 burritos for $12 || 6 burritos for $7.50,10 burritos for $12,96695 +PRABQN7D,1,Multiple Choice (select 1),Multiple Choice,"

Clare has a recipe for yellow cake. She uses 913 cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c cakes using f cups of flour.

+

 

+

Which of these equations represent the relationship between c and f?

",,,"

c = 163f

||

c = 316f

||

c = 37f

||

c = 73f

","

c = 37f

",97850 +PRABEAY2,1,Multiple Choice (select all),Check All That Apply,"

Here is an equation that represents a function: 72x+12y=60.

+

 

+

Select all the different equations that describe the same function:

",,,"

120y+720x=600

||

y=5-6x

||

2y+12x=10

||

y=5+6x

||

x=56-y6

||

7x+2y=6

||

x=56+y6

","

120y+720x=600

||

y=5-6x

||

2y+12x=10

||

x=56-y6

",292178 +PSBCKRX,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of numbers below, select the number that is greater.

",,,"

2 · 106 

||

7.839 · 106 

","

7.839 · 106 

",398730 +PSB2J,1,Multiple Choice (select 1),Multiple Choice,"

Is Figure B a scaled copy of Figure A?

+

 

+

",,,Yes || No,No,3378 +PRABPUH8,1,Multiple Choice (select 1),Multiple Choice,"

Noah gathered data at his school among 7th and 8th graders to see if there was an association between grade level and handedness. This table and graph show his data, but the number of right-handed 8th graders is missing.

+ + + + + + + +
+ + + + + + + + + + + + + + + + + + +
 left-handedright-handed
7th grade1172
8th grade24 
+
+

 

+

Noah found there was no evidence of an association between grade level and handedness. Which of these could be the number of right-handed 8th graders?

",,157,33 || 85 || 107 || 157,157,636346 +PRABE5HU,1,Multiple Choice (select 1),Multiple Choice,"

If the side that is 6 units long is the base of this parallelogram, what is its corresponding height?

+

 

+

",,,6 units || 4.8 units || 4 units || 5 units,4 units,375982 +PRABFGWH,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 12z.

",,,"

z + z

||

z ÷ 2

||

z · z

||

14z + 14z

||

2z

","

z ÷ 2

||

14z + 14z

",541977 +PRABQM3R,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are greater than 5.

,,,4.88 + 0.009 || 3.76 + 1.3 || 5.012 - 0.04 || 7.702 - 2.71 || 6.5 - 1.49,3.76 + 1.3 || 6.5 - 1.49,61764 +PRABEVRV,1,Multiple Choice (select 1),Multiple Choice,"

Which of these expressions is equivalent to -2(x-5) ?

",,,-2x − 5 || -2x + 5 || -2x + 10 || -2x − 10,-2x + 10,53138 +PRABD877,1,Multiple Choice (select all),Check All That Apply,

Select all equations that have graphs with the same y-intercept.

,,,"

y=3x-8

||

y=3x-9

||

y=3x+8

||

y=5x-8

||

y=2x-8

||

y=13x-8

","

y=3x-8

||

y=5x-8

||

y=2x-8

||

y=13x-8

",17046 +PSB3J,2,Multiple Choice (select 1),Multiple Choice,"

Which day had the least number of people?

+

 

+

",,,Day 1 || Day 2 || Day 3,Day 1,3501 +PSBZT4,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the table could represent a proportional relationship.

+

 

+

The number of wheels on a group of buses.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
number of busesnumber of wheelswheels per bus
530 
848 
1060 
1590 
",,,"

Yes, it is proportional

||

No, it is not proportional

","

Yes, it is proportional

",123317 +PRABG3XQ,1,Multiple Choice (select 1),Multiple Choice,"

Is the value of the expression closer to 12, 1, or 112?

+

 

+

9 ÷ 20

+

 

",,,"

12

||

1

||

112

","

12

",128010 +PRABMTN5,1,Multiple Choice (select 1),Multiple Choice,"

For the equation, decide if it is always true or never true.

+

 

+

x + 12 = x − 12

",,,Always True || Never True,Never True,147962 +PRABFFDM,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that represent the hanger.

+

 

+

",,,"

x + x + x = 1 + 1 + 1 + 1 + 1 + 1

||

x · x · x = 6

||

3x = 6

||

x + 3 = 6

||

x · x · x = 1 · 1 · 1 · 1 · 1 · 1

","

x + x + x = 1 + 1 + 1 + 1 + 1 + 1

||

3x = 6

",123623 +PSBCBZ4,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the quantity can be represented by a positive number or by a negative number. 

+

 

+

Andre received a gift of $10.

",,,positive || negative,positive,354803 +PRABFEZG,1,Multiple Choice (select 1),Multiple Choice,

Which parallelogram has an area of 60 square units?

,,,"

||

||

||

","

",433197 +PRABE3HF,1,Multiple Choice (select 1),Multiple Choice,"

Two copies of this triangle are used to compose a parallelogram.

+

 

+

Which parallelogram cannot be a result of the composition? If you get stuck, consider using tracing paper.

+

 

+

",,,"

||

||

||

","

",42371 +PSBBMH,1,Multiple Choice (select all),Check All That Apply,"

The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.

+

 

+

+

 

+

Which lines are images of line f under a translation?

",,,g || h || i || j,h || i,6467 +PSBCMM5,1,Multiple Choice (select 1),Multiple Choice,"

Jada collects data about the number of letters people get in the mail each week. The population distribution is shown in the dot plot.

+

 

+

+

 

+

Which of the following dot plots are likely to represent the means from samples of size 10 from this population?

",,,"

||

","

",403293 +PSBEUH,3,Multiple Choice (select all),Check All That Apply,"

Here is a circle with center H and some line segments and curves joining points on the circle.

+

 

+

Identify examples of radius.

+

+

 

",,,AE || AH || BH || BF || CE || DG || DH || EH || FH || GH,AH || DH || EH || GH,24350 +PSBFD,1,Multiple Choice (select 1),Multiple Choice,"

Jada drank 2 liters of water yesterday. Andre drank 14 times as much water as Jada. Lin drank three times as much water as Andre.

+

 

+

 

+

Did Andre drink more or less water than Jada?

",,,More || Less,Less,438 +PRABQP5M,1,Multiple Choice (select all),Check All That Apply,

Select all the numbers that are greater than 1.

,,,"

23

||

0.63

||

75

||

57

||

132

||

322

","

23

||

75

||

322

",337576 +PSBBPHJ,1,Multiple Choice (select 1),Multiple Choice,"

Diego has 75% of $10. Noah has 25% of $30. Diego thinks he has more money than Noah, but Noah thinks they have an equal amount of money. Who is right?

",,,Diego || Noah,Noah,239810 +PRABQP24,1,Multiple Choice (select all),Check All That Apply,"

A rectangular prism has length l, width w, and height h. Select all the statements that must be true. 

+

",,,

The volume is (lwh)².

||

The volume is 2(lwh).

||

The volume is (lwh).

||

The surface area is 2(lwh).

||

The surface area is 2(lw) + 2(wh) + 2(lh).

||

The surface area is 2(lw) · 2(wh) · 2(lh).

,

The volume is (lwh).

||

The surface area is 2(lw) + 2(wh) + 2(lh).

,674301 +PSBBSPP,1,Multiple Choice (select 1),Multiple Choice,"

A random sample of 15 items were selected.

+

 

+

 

+

For this data set, is the mean or median a better measure of center?

",,,mean || median,median,255819 +PSBCC9B,1,Multiple Choice (select 1),Multiple Choice,"

Jada thinks the perimeter of this rectangle can be represented with the expression a+a+b+b. Andre thinks it can be represented with 2a+2b.

+

 

+

+

 

+
+
+
+
+

Do you agree with either, both, or neither of them?

+
+
+
+
",,,Jada || Andre || Both || Neither,Both,362327 +PSBC8XC,9,Multiple Choice (select 1),Multiple Choice,

Is r proportional to n?

,,,Yes || No,No,512430 +PRABD5BR,1,Multiple Choice (select all),Check All That Apply,"

A rectangle has length 6 and height 4.

+

Which of these would tell you that quadrilateral ABCD is definitely not similar to this rectangle? Select all that apply.

",,,"AB = BC || m∠ABC = 105° || AB = 8 || BC = 8 || BC=2·AB || 2·AB=3·BC","AB = BC || m∠ABC = 105° || BC=2·AB",237321 +PRABFFX5,1,Multiple Choice (select 1),Multiple Choice,"

Polyhedron P is a cube with a corner removed and relocated to the top of P. Polyhedron Q is a cube. How do their surface areas compare?

+

 

+

",,,P’s surface area is less than Q’s surface area. || P’s surface area is equal to Q’s surface area. || P’s surface area is greater than Q’s surface area. || There is not enough information given to compare their surface areas.,P’s surface area is greater than Q’s surface area.,55545 +PRABEUP5,1,Multiple Choice (select all),Check All That Apply,"

Select all equations that represent a relationship between angles in the figure.

+
+

 

+

+
",,,90 − 30 = b || 30 + b = a + c || a + c + 30 + b = 180 || a = 30 || a = c = 30 || 90 + a + c = 180,90 − 30 = b || 30 + b = a + c || a + c + 30 + b = 180 || 90 + a + c = 180,246605 +PRABQMBF,1,Multiple Choice (select all),Check All That Apply,"

This line plot shows the amount of time, in seconds, that it took 20 sixth graders to run a 50-meter dash.

+

+

 

+

 

+

Select all the true statements.

",,,The fastest time was 7.0 seconds. || No runner recorded a time of 7.2 seconds. || The fastest 5 students’ total time was 36.3 seconds. || Exactly half of the students were faster than 7.7 seconds. || The difference between the fastest and slowest times was 0.9 seconds.,No runner recorded a time of 7.2 seconds. || The fastest 5 students’ total time was 36.3 seconds. || The difference between the fastest and slowest times was 0.9 seconds.,256627 +PRABER4B,1,Multiple Choice (select all),Check All That Apply,

Which of these scales are equivalent to 3 cm to 4 km? Select all that apply. Recall that 1 inch is 2.54 centimeters.

,,,

0.75 cm to 1 km

||

1 cm to 12 km

||

6 mm to 2 km

||

0.3 mm to 40 m

||

1 in to 7.62 km

,

0.75 cm to 1 km

||

0.3 mm to 40 m

,257011 +PRABKDVC,1,Multiple Choice (select 1),Multiple Choice,

The Pythagorean Theorem is:

,,,True for all triangles || True for all right triangles || True for some right triangles || Never true,True for all right triangles,196678 +PSBRZZ,1,Multiple Choice (select 1),Multiple Choice,"

A rare and delicate plant will only produce flowers from 10% of the seeds planted. To see if it is worth planting 5 seeds to see any flowers, the situation is going to be simulated. Which of the following options is the best simulation?

",,,"

Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds each and wait 6 months for the plants to grow and count the fraction of groups that produce flowers.

||

Roll a standard number cube 5 times. Each time a 6 appears, it represents a plant producing flowers. Repeat this process 30 times and count the fraction of times at least one number 6 appears.

||

Have a computer produce 5 random digits (0 through 9). If a 9 appears in the list of digits, it represents a plant producing flowers. Repeat this process 300 times and count the fraction of times at least one number 9 appears.

||

Create a spinner with 10 equal sections and mark one of them “flowers.” Spin the spinner 5 times to represent the 5 seeds. Repeat this process 30 times and count the fraction of times that at least 1 “flower” was spun.

","

Have a computer produce 5 random digits (0 through 9). If a 9 appears in the list of digits, it represents a plant producing flowers. Repeat this process 300 times and count the fraction of times at least one number 9 appears.

",77989 +PSBBA4W,1,Multiple Choice (select 1),Multiple Choice,"

Triangle ABC is dilated using D as the center of dilation with scale factor 2. 

+

+

The image is triangle A'B'C'. Clare says the two triangles are congruent, because their angle measures are the same. Do you agree? 

",,,Yes || No,No,175643 +PSBCWSX,2,Multiple Choice (select all),Check All That Apply,

Select all the fractions that are equal to 0.082.

,,,"

820100

||

8201000

||

821000

||

82010

||

8210

||

82100

","

821000

",455995 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681 +PRABQKZG,1,Multiple Choice (select all),Check All That Apply,"

Rectangle A is 10 times as long as Rectangle B.

+

+

If Rectangle A is 50 units long, select all the ways to find the length of Rectangle B.

",,,"

Multiply 50 by 10.

||

Divide 50 by 10.

||

Multiply 50 by 110.

||

Divide 50 by 110.

||

Multiply 10 by 50.

||

Divide 10 by 50.

","

Divide 50 by 10.

||

Multiply 50 by 110.

",457262 +PSBBE7Q,4,Multiple Choice (select 1),Multiple Choice,

There is one speed that you cannot plot on the bottom number line. Which is it?

,,,space || water || copper wire (electricity) || diamond || ice || olive oil,diamond,198440 +PRABTVKK,1,Multiple Choice (select 1),Multiple Choice,"

En una clase de 15 niños, 9 de ellos toman el bus a la escuela. ¿Qué porcentaje de los niños de la clase toman el bus a la escuela?

",,,90% || 60% || 9% || 0.6%,60%,320333 +PSBCTT,1,Multiple Choice (select 1),Multiple Choice,"

Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.

+

If she continues to read at the same rate, will she be able to complete this book in under 1 hour?

",,,Yes || No,No,13384 +PSBBA2A,1,Multiple Choice (select all),Check All That Apply,

Select all numbers that are solutions to the inequality k > 5.

,,,4 || 5 || 6 || 5.2 || 5.01 || 0.5,6 || 5.2 || 5.01,175247 +PSBBEGX,1,Multiple Choice (select all),Check All That Apply,

Select all numbers that are solutions to the inequality w < 1.

,,,5 || -5 || 0 || 0.9 || -1.3,-5 || 0 || 0.9 || -1.3,194547 +PSBBTU4,1,Multiple Choice (select 1),Multiple Choice,"

Mini muffins cost $3.00 per dozen.

+

 

+
    +
  • Andre says, “I have $2.00, so I can afford 8 muffins.”

    • +
  • Elena says, “I want to get 16 muffins, so I’ll need to pay $4.00.""
    • +
+

 

+

Do you agree with either of them?

",,,I agree with Andre || I agree with Elena || I agree with both || I don't agree with either,I agree with both,262715 +PSBR45,1,Multiple Choice (select 1),Multiple Choice,

Andre types 208 words in 4 minutes. Noah types 342 words in 6 minutes. Who types faster?

,,,Andre || Noah,Noah,78634 +PSBBHQ2,2,Multiple Choice (select 1),Multiple Choice,

Did more cubic inches or cubic centimeters fit in the cardboard box?

,,,cubic inch || cubic centimeter,cubic centimeter,212653 +PSB6J5,1,Multiple Choice (select all),Check All That Apply,"

Here are three fractions: 23, 45, 69. Two of these fractions are equivalent to each other. Which two?  

",,,"

23

||

45

||

69

","

23

||

69

",151128 +PRABQJVF,1,Multiple Choice (select 1),Multiple Choice,"

Polyhedron P is a cube with a corner removed and relocated to the top of P. Polyhedron Q is a cube with the same size base as Polyhedron P. How do their surface areas compare?

+

 

+

",,,Q’s surface area is less than P’s surface area. || Q’s surface area is equal to P’s surface area. || Q’s surface area is greater than P’s surface area. || There is not enough information given to compare their surface areas.,Q’s surface area is less than P’s surface area.,502927 +PSBC2H,1,Multiple Choice (select 1),Multiple Choice,"

The graph shows the temperature between noon and midnight in City A on a certain day.

+

 

+

+

 

+

The table shows the temperature, T, in degrees Fahrenheit, for h hours after noon, in City B.

+

 

+ + + + + + + + + + + + + + + + + + + + + +
h123456
T827875625859
+

 

+

Which city was warmer at 4:00 p.m.?

",,,City A || City B || Neither city,City B,14567 +PRABET5V,1,Multiple Choice (select all),Check All That Apply,

Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)

,,,1 in to 1 mi || 1 cm to 1 km || 1 in to 10 mi || 1 ft to 100 mi || 1 cm to 200 km || 1 in to 100 mi || 1 cm to 1000 km,1 cm to 200 km || 1 in to 100 mi,386124 +PRABETDM,1,Multiple Choice (select all),Check All That Apply,"

If x represents a positive number, select all expressions whose value is greater than x.

",,,"

1 - 14x

||

1 + 14x

||

78x

||

98x

","

1 + 14x

||

98x

",56910 +PRABD4SY,1,Multiple Choice (select 1),Multiple Choice,"

Which of these four figures are congruent to this figure?

+

 

+

",,,"

||

||

||

","

",241939 +PSBCDYX,1,Multiple Choice (select 1),Multiple Choice,"

Mai poured 2.6 liters of water into a partially filled pitcher. The pitcher then contained 10.4 liters. 

+

 

+

Which diagram represents this situation?

",,,"

||

||

","

",366543 +PRABEUGV,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to -36x + 54y − 90.

",,,"

-9 (4x - 6y - 10)

||

-18 (2x - 3y +5)

||

-6 (6x +9y -15)

||

18 (-2x +3y -5)

||

-2 (18x - 27y +45)

||

2 (-18x +54y - 90)

","

-18 (2x - 3y +5)

||

18 (-2x +3y -5)

||

-2 (18x - 27y +45)

",303522 +PRABQPK5,1,Multiple Choice (select 1),Multiple Choice,

Which of these sequences of transformations would return a shape to its original position?

,,,"Translate 5 units right, then 5 units down. || Translate 3 units down, then 2 units up, and then 1 unit down. || Rotate 120° counterclockwise around center C, then rotate 240° clockwise around C again. || Reflect over line l, then reflect over line l again.","Reflect over line l, then reflect over line l again.",275670 +PRABQPT2,1,Multiple Choice (select all),Check All That Apply,"

Jada earns twice as much money per hour as Diego. Diego earns twice as much money per hour as Lin.

+

 

+

Select all the graphs that could represent how much Jada, Diego, and Lin earn for different amounts of time worked.

",,,"

||

||

||

||

","

||

",79256 +PSBX69,13,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

There are exactly two solutions of the equation for line ℓ.

",,0,True || False,FALSE,114584 +PSBE3P,3,Multiple Choice (select 1),Multiple Choice,"

A class measured the radius r, circumference C, and area A of various circular objects. The results are recorded in this table.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
r(cm)C(cm)A(cm2)
42550
531.578.5
850201
1275452
+

 

+

 

+

Does the equation A = 12 · r  · C describe the relationships in the table?

",,,Yes || No,Yes,25874 +PSBGXA,1,Multiple Choice (select 1),Multiple Choice,

The side lengths of Triangle B are all 5 more than the side lengths of Triangle A. Can Triangle B be a scaled copy of Triangle A?

,,,Yes || No,Yes,36042 +PSBB9D3,1,Multiple Choice (select 1),Multiple Choice,"

The reading on a car’s speedometer has 1.6% maximum error. The speed limit on a road is 65 mph.

+

 

+

The speedometer reads 64 mph. Is it possible that the car is going over the speed limit?

",,,Yes || No,Yes,339221 +PSBB52F,1,Multiple Choice (select 1),Multiple Choice,"

Is 312 cups more or less than 1 liter? (Note: 1 cup ≈ 236.6 milliliters)

",,,More || Less,Less,319813 +PSBBSQ,1,Multiple Choice (select 1),Multiple Choice,"

Predict if the mean is greater than, less than, or approximately equal to the median.

+

 

+

Ages of 30 people at a family dinner party

+

",,,Greater than || Less than || Equal to,Less than,7452 +PRABEUA5,1,Multiple Choice (select all),Check All That Apply,

Select all the situations where knowing the surface area of an object would be more useful than knowing its volume.

,,,Placing an order for tiles to replace the roof of a house. || Estimating how long it will take to clean the windows of a greenhouse. || Deciding whether leftover soup will fit in a container. || Estimating how long it will take to fill a swimming pool with a garden hose. || Calculating how much paper is needed to manufacture candy bar wrappers. || Buying fabric to sew a couch cover. || Deciding whether one muffin pan is enough to bake a muffin recipe.,Placing an order for tiles to replace the roof of a house. || Estimating how long it will take to clean the windows of a greenhouse. || Calculating how much paper is needed to manufacture candy bar wrappers. || Buying fabric to sew a couch cover.,53711 +PSBDKZF,1,Multiple Choice (select 1),Multiple Choice,"

The school orchestra sells snacks at their concerts to raise money. At the spring concert, they made 98 as much money as they made at their fall concert.

+

 

+

Did they make more money at the spring or the fall concert?

",,,Spring concert || Fall concert,Spring concert,576826 +PRABD5B8,1,Multiple Choice (select all),Check All That Apply,"

Select all the points that are on the line through (0,5) and (2,8).

+

 

",,,"

(4,11)

||

(5,10)

||

(6,14)

||

(30,50)

||

(40,60)

","

(4,11)

||

(6,14)

||

(30,50)

",146496 +PRABE52Q,1,Multiple Choice (select all),Check All That Apply,"

Andre drew a line connecting two opposite corners of a parallelogram. Select all true statements about the triangles created by the line Andre drew.

+

 

+

",,,"

Each triangle has two sides that are 3 units long.

||

Each triangle has a side that is the same length as the diagonal line.

||

Each triangle has one side that is 3 units long.

||

When one triangle is placed on top of the other and their sides are aligned, we will see that one triangle is larger than the other.

||

The two triangles have the same area as each other.

",

Each triangle has a side that is the same length as the diagonal line.

||

Each triangle has one side that is 3 units long.

||

The two triangles have the same area as each other.

,421017 +PRABHAFY,1,Multiple Choice (select 1),Multiple Choice,"

The students in art class are designing a stained-glass window to hang in the school entryway. The window will be 3 feet tall and 4 feet wide. Here is their design.

+

 

+

+

 

+

They have raised $100 for the project. The colored glass costs $5 per square foot and the clear glass costs $2 per square foot. The material they need to join the pieces of glass together costs 10 cents per foot and the frame around the window costs $4 per foot.

+

 

+
Do they have enough money to cover the cost of making the window?
",,,Yes || No,Yes,294382 +PRABETNR,1,Multiple Choice (select all),Check All That Apply,"

In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and t is the number of points that Tyler scored, which equations are correct? Select all that apply.

",,,

c = 1.5t

||

c = t + 0.5

||

c = t + 0.5t

||

c = t + 50

||

c = (1 + 0.5)t

,

c = 1.5t

||

c = t + 0.5t

||

c = (1 + 0.5)t

,204231 +PRABQKS7,1,Multiple Choice (select 1),Multiple Choice,"

Jada has read 35 of a book. She has read 75 pages so far. How many pages are in the whole book?

+

 

",,,45 pages || 105 pages || 120 pages || 125 pages,125 pages,588631 +PRABG427,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are equivalent to 4 − x.

,,,x − 4 || 4 + -x || -x + 4 || -4 + x || 4 + x,4 + -x || -x + 4,146878 +PSBFNZ,1,Multiple Choice (select all),Check All That Apply,"

Select all quadrilaterals that are scaled copies of the unlabeled rectangle. 

+

 

+

",,,"

+

 

||

+

 

||

+

 

||

+

 

||

+

 

||

+

 

||

+

 

||

+

 

","

+

 

||

+

 

||

+

 

||

+

 

",28656 +PSBD3T,5,Multiple Choice (select 1),Multiple Choice,

Was the cooler filling faster before or after Priya changed the rate of water flow?

,,,Before || After,Before,20510 +PSBWQA,1,Multiple Choice (select 1),Multiple Choice,"

The science teacher gives daily homework. For a random sample of days throughout the year, the median number of problems is 5 and the IQR is 2. The Spanish teacher also gives daily homework. For a random sample of days throughout the year, the median number of problems is 10 and the IQR is 1. If you estimate the median number of science homework problems to be 5 and the median number of Spanish problems to be 10, which is more likely to be accurate?

",,,Science || Spanish,Spanish,106008 +PRABKCT3,1,Multiple Choice (select 1),Multiple Choice,"

The table shows the area of a square for specific side lengths.

+

 

+ + + + + + + + + + + + + + + + + +
side length (inches)0.5123
area (square inches)0.25149
+

 

+

The area A of a circle with radius r is given by the equation A=π·r2 .

+

Is the area of a square with side length 2 inches greater than or less than the area of a circle with radius 1.2 inches?

",,,Greater than || Less than,Less than,269076 +PSBB39,1,Multiple Choice (select 1),Multiple Choice,"

Let’s look at a square and a rhombus.

+

+

Priya says, “These polygons are similar because their side lengths are all the same.” Clare says, “These polygons are not similar because the angles are different.” Do you agree with either Priya or Clare?

",,,Priya || Clare || Neither,Clare,9287 +PRABQP57,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 4×106.

",,,"

2×1082×10-2

||

40×105

||

406

||

400,000

||

1.2×1093×102

","

2×1082×10-2

||

40×105

||

1.2×1093×102

",263567 +PRABQWBZ,1,Multiple Choice (select all),Check All That Apply,"

Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?

",,,Traveling a billion meters in 5 seconds || Traveling a meter in 2.5 nanoseconds. (A nanosecond is a billionth of a second.) || Traveling a parsec in a year. (A parsec is about 3.26 light years and a light year is the distance light can travel in a year.),Traveling a billion meters in 5 seconds,222861 +PSBBT89,2,Multiple Choice (select 1),Multiple Choice,

Which class had less variability in the amount of time spent on homework?

,,,Class A || Class B,Class B,265301 +PRABFK4C,1,Multiple Choice (select all),Check All That Apply,"

The dot plots show how much time, in minutes, students in a class took to complete each of five different tasks.  Select all the dot plots of tasks for which the mean time is approximately equal to the median time.

+

 

+

 

",,,"

+

                                        Time in Minutes

||

+

                                        Time in Minutes

||

+

                                           Time in Minutes

||

+

                                            Time in Minutes

||

+

                                            Time in Minutes

","

+

                                        Time in Minutes

||

+

                                           Time in Minutes

",188925 +PRABET72,1,Multiple Choice (select all),Check All That Apply,"

Select all the stories that can be represented by the diagram.

+

 

+

+

 

",,,"Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history. || Lin spends $3 on 7 markers and a $1 pen. || Diego spends $1 on 7 stickers and 3 marbles. || Noah shares 7 grapes with 3 friends. He eats 1 and gives each friend the same number of grapes. || Elena spends $7 on 3 notebooks and a $1 pen.","Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history. || Noah shares 7 grapes with 3 friends. He eats 1 and gives each friend the same number of grapes. || Elena spends $7 on 3 notebooks and a $1 pen.",314711 +PSBYTD,1,Multiple Choice (select 1),Multiple Choice,"

A student said, “To find the value of 109.2÷6, I can divide 1,092 by 60.”

+

 

+

Do you agree with this statement? 

",,,Yes || No,Yes,117735 +PSBJDY,1,Multiple Choice (select 1),Multiple Choice,"

Jada, Diego, and Elena each use the same spinner that has four (not necessarily equal sized) sections marked A, B, C, and D.

+
    +
  • +

    Jada says, ""The probability of spinning B is 0.3 because I spun 10 times, and it landed on B 3 times.""

    +
    • +
  • +

    Diego says, ""The probability of spinning B is 20% because I spun 5 times, and it landed on B once.""

    +
    • +
  • +

    Elena says, ""The probability of spinning B is 27 because I spun 7 times, and it landed on B twice.""

    +
    • +
+

 

+

Based on their methods, which probability estimate do you think is the most accurate?

",,,Jada's || Diego's || Elena's,Jada's,43505 +PRABQPS4,1,Multiple Choice (select 1),Multiple Choice,"

Here is a dot plot showing how many books are read by each student per month.

+

 

+

+

 

+

Which of these is a representative sample of the population?

",,,"

||

||

||

","

",258429 +PSBBCDY,2,Multiple Choice (select 1),Multiple Choice,"

Is the mean or the median a more appropriate measure of center for this data set?

+

 

+

",,,mean || median,median,182285 +PRABQM8V,1,Multiple Choice (select 1),Multiple Choice,"

Here’s a dot plot of a data set.

+

 

+

+

 

+

 

+

Which statement is true about the mean of the data set?

",,,The mean is less than 5. || The mean is equal to 5. || The mean is greater than 5. || There is not enough information to determine the mean.,The mean is equal to 5.,193691 +PSBCB6T,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the quantity can be represented by a positive number or by a negative number. 

+

 

+

A climber descended 550 feet.

",,,

Positive

||

Negative

,

Negative

,355654 +PSBYP4,1,Multiple Choice (select 1),Multiple Choice,"

Which estimate is closest to the actual value of the expression? 

+

 

+

",,13,13 || 13.25 || 13.5,13,117298 +PSBBJRE,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 16x − 12 − 24x + 4. 

+

 

",,,4 + 16x − 12(1 + 2x) || 40x − 16 || 16x − 24x − 4 + 12 || -8x − 8 || 10(1.6x - 1.2 - 2.4x + 4),4 + 16x − 12(1 + 2x) || -8x − 8,218163 +PSBNNV,1,Multiple Choice (select 1),Multiple Choice,

Are two squares with the same side lengths scaled copies of one another?

,,,Yes || No,Yes,60631 +PRABP9VA,1,Multiple Choice (select all),Check All That Apply,"

Elena mixed 2 cups of white paint with 6 tablespoons of blue paint.

+

 

+
+
+
+
+

Here is a diagram that represents this situation.

+

 

+

+

 

+

Select all the statements that correctly describe this situation. 

+
+
+
+
",,,"

The ratio of cups of white paint to tablespoons of blue paint is 2 : 6.

|| For every cup of white paint, there are 2 tablespoons of blue paint. || There is 1 cup of white paint for every 3 tablespoons of blue paint. || There are 3 tablespoons of blue paint for every cup of white paint. || For each tablespoon of blue paint, there are 3 cups of white paint. || For every 6 tablespoons of blue paint, there are 2 cups of white paint. || The ratio of tablespoons of blue paint to cups of white paint is 6 to 2.","

The ratio of cups of white paint to tablespoons of blue paint is 2 : 6.

|| There is 1 cup of white paint for every 3 tablespoons of blue paint. || There are 3 tablespoons of blue paint for every cup of white paint. || For every 6 tablespoons of blue paint, there are 2 cups of white paint. || The ratio of tablespoons of blue paint to cups of white paint is 6 to 2.",54134 +PSBXZW,3,Multiple Choice (select 1),Multiple Choice,

Is the price of the phone this month the same as it was two months ago?

,,,No || Yes,No,113830 +PRABQMT5,1,Multiple Choice (select 1),Multiple Choice,"

These four numbers are plotted on a number line:  -45, 12, 18, -34

+

 

+

Which is the correct ordering on the number line, from left to right?

",,,"

12, 18, -34, -45

||

-45, -34, 12, 18

||

-34, -45, 18, 12

||

-45, -34, 18, 12

","

-45, -34, 18, 12

",49246 +PSBTHR,1,Multiple Choice (select 1),Multiple Choice,"

Are any of these numbers a solution to the equation ? 

+
    +
  • 1
    • +
+

 

+
    +
    • +
+

 

+
    +
    • +
+

 

+
    +
    • +
",,,Yes || No,No,86904 +PSBCBF7,1,Multiple Choice (select 1),Multiple Choice,"

Which group of blocks is the bluest?

+

 

+

+
 
",,,A || B || C || D || E,A || D,351684 +PRABFGU9,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that represent the area of the large, outer rectangle.

+

 

+

",,,5(2 + 4) || 5 · 2 + 4 || 5 · 2 + 5 · 4 || 5 · 2 · 4 || 5 + 2 + 4 || 5 · 6,5(2 + 4) || 5 · 2 + 5 · 4 || 5 · 6,113030 +PSB5Z9,1,Multiple Choice (select 1),Multiple Choice,"

A small company is selling a new board game, and they need to know how many to produce in the future.

+

 

+

After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand games; and after 36 months, they sold 15 thousand games.

+

 

+

Could this information be reasonably estimated using a single linear model?

+

 

",,,Yes || No,Yes,148105 +PRABEU3Y,1,Multiple Choice (select 1),Multiple Choice,"

Priya has a recipe for banana bread. She uses 712 cups of flour to make 3 loaves of banana bread.

+

 

+
+

Andre will follow the same recipe. He will make b loaves of banana bread using f cups of flour.

+

 

+

Which of these equations represents the relationship between b and f?

+
",,,"

b=29f

||

b=25f

||

b=52f

||

b=92f

","

b=25f

",247330 +PRABERVX,1,Multiple Choice (select all),Check All That Apply,"

On a map of Chicago, 1 cm represents 100 m. Select all statements that express the same scale.

",,,5 cm on the map represents 50 m in Chicago || 1 mm on the map represents 10 m in Chicago || 1 km in Chicago is represented by 10 cm on the map || 100 cm in Chicago is represented by 1 m on the map.,1 mm on the map represents 10 m in Chicago || 1 km in Chicago is represented by 10 cm on the map,160506 +PSB3AD,1,Multiple Choice (select 1),Multiple Choice,"

A line contains the points (-3, -2) and (7, 2).

+

 

+

Without doing any calculations, determine whether the slope of this line is positive or negative.

+
 
",,,positive || negative,positive,132090 +PRABFKYU,1,Multiple Choice (select all),Check All That Apply,"

A preschool teacher is rearranging four boxes of playing blocks so that each box contains an equal number of blocks. Currently Box 1 has 32 blocks, Box 2 has 18, Box 3 has 41, and Box 4 has 9.

+

 

+

Select all the ways he could make each box have the same number of blocks.

",,,"

Remove all the blocks and make four equal piles of 25, then put each pile in one of the boxes.

||

Remove 7 blocks from Box 1 and place them in Box 2.

||

Remove 21 blocks from Box 3 and place them in Box 4.

||

Remove 7 blocks from Box 1 and place them in Box 2, and remove 21 blocks from Box 3 and place them in Box 4.

||

Remove 7 blocks from Box 1 and place them in Box 2, and remove 16 blocks from Box 3 and place them in Box 4.

","

Remove all the blocks and make four equal piles of 25, then put each pile in one of the boxes.

||

Remove 7 blocks from Box 1 and place them in Box 2, and remove 16 blocks from Box 3 and place them in Box 4.

",6735 +PSB873,1,Multiple Choice (select 1),Multiple Choice,"

After buying the supplies, you start painting the east wall. It takes you 96 minutes to put two coats of paint on that wall (not including a lunch break between the two coats).

+

 

+

Your friend stops by to see how you are doing and comments that you are 25% finished with the painting. Are they correct?

",,,"

Yes,  your friend is correct.

||

No,  your friend is not correct.

","

No,  your friend is not correct.

",164620 +PSBBK4C,1,Multiple Choice (select 1),Multiple Choice,

Decide which story can be represented by the system of equations y = x + 6 and x + y = 100.

,,,"

Diego’s teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.

||

Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.

","

Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.

",225929 +PSBDDKB,1,Multiple Choice (select 1),Multiple Choice,"

This is a dot plot of the scores on a video game for a population of 50 teenagers.

+

+

 

+

The three dot plots together are the scores of teenagers in three samples from this population. Which of the three samples is most representative of the population?

",,,"

||

||

","

",539841 +PSBCKP4,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of numbers below, select the number that is greater.

",,,"

17·108   

||

4·108

","

17·108   

",398365 +PRABQPQX,1,Multiple Choice (select 1),Multiple Choice,

What is a 90° angle called? 

,,,acute || obtuse || right || straight,right,12623 +PRABQK67,1,Multiple Choice (select 1),Multiple Choice,

A runner is preparing for a marathon that is cut into 5 equal sections. The marathon is 42.195 kilometers long. How long is each section of the marathon?

,,,210.975 km || 21.0975 km || 8.439 km || 0.8439 km,8.439 km,590738 +PRABQP64,1,Multiple Choice (select 1),Multiple Choice,"

What is the length of the line segment?

+

 

+

",,,"

8

||

128

||

16

||

260

","

128

",315827 +PRABQNER,1,Multiple Choice (select 1),Multiple Choice,"

A map of Utah is shown. Which area is closest to the area of Utah in square kilometers?

+

 

+

",,,"274,963 || 244,905 || 225,808 || 1,997","225,808",444018 +PSBH8S,2,Multiple Choice (select 1),Multiple Choice,

You will wait less than 10 minutes before ordering at a fast food restaurant.

,,,impossible || unlikely || equally likely as not || likely || certain,likely,42091 +PRABHRJQ,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are solutions to 5 = 23x.

",,,"

 

+

5 · 23

+

 

||

 

+

523

+

 

||

 

+

5 ÷ 23

+

 

||

 

+

152

+

 

||

 

+

103

+

 

","

 

+

523

+

 

||

 

+

5 ÷ 23

+

 

||

 

+

152

+

 

",21566 +PSB4AR,2,Multiple Choice (select all),Check All That Apply,"

In the graphed function, which values of x give an output of 0?

+

 

+

",,,0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14,0 || 5 || 10,138133 +PSBH8S,6,Multiple Choice (select 1),Multiple Choice,

The next baby born at a hospital will be a boy.

,,,impossible || unlikely || equally likely as not || likely || certain,equally likely as not,42491 +PSBCNJG,1,Multiple Choice (select 1),Multiple Choice,"

The two lines represent the distance, over time, that two cars are traveling. Which car is traveling faster?

+

",,,Car A || Car B,Car B,408074 +PRABQN7E,1,Multiple Choice (select 1),Multiple Choice,"

A graduated cylinder actually contains 7.5 milliliters of water. When Han measures the volume of the water inside the graduated cylinder, his measurement is 7 milliliters. Which of these is closest to the percent error for Han’s measurement?

",,,107.1% || 93.3% || 7.1% || 6.7%,6.70%,97961 +PSBGXA,1,Multiple Choice (select 1),Multiple Choice,

The side lengths of Triangle B are all 5 more than the side lengths of Triangle A. Can Triangle B be a scaled copy of Triangle A?

,,,Yes || No,Yes,36042 +PSBBYZR,1,Multiple Choice (select all),Check All That Apply,"

For the situation, select all the equations that represent it.

+

 

+

Apples cost $1.60 per pound at the farmer’s market. They cost 1.5 times as much at the grocery store. How much do the apples cost per pound at the grocery store?

",,,"

y = (1.5) · (1.60)

||

y = 1.60 ÷ 1.5

||

(1.5)y = 1.60

||

y1.5 = 1.60

","

y = (1.5) · (1.60)

||

y1.5 = 1.60

",292175 +PSBWXS,1,Multiple Choice (select all),Check All That Apply,"

Here is a figure that looks like the letter A, along with several other figures. Which figures are scaled copies of the original A? 

+

 

+

",,,Figure 1 || Figure 2 || Figure 3 || Figure 4,Figure 2 || Figure 4,107252 +PSBBCDY,4,Multiple Choice (select 1),Multiple Choice,"

Can Jada use these data displays to find the exact median?

+

 

+

",,,yes || no,yes,182483 +PSBWPH,1,Multiple Choice (select 1),Multiple Choice,"

The graph shows the height of a plant after a certain amount of time measured in days.

+

 

+

+

 

+

Do you think that there may be a proportional relationship between the number of days and the height of the plant?

",,,Yes || No,Yes,105953 +PSB67U,1,Multiple Choice (select 1),Multiple Choice,"

State whether you agree with the statement below. 

+

 

+

A city that has an elevation of -17 meters is closer to sea level than a city that has an elevation of -40 meters.

",,,Agree || Disagree,Agree,154138 +PRABER4Y,1,Multiple Choice (select 1),Multiple Choice,"
+

Kiran and Mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. Kiran says that if the the field were twice as long and twice as wide, then it would be twice the distance to the far corner. Mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths.

+

 

+

Do you agree with either of them?

+
",,,

I agree with Kiran.

||

I agree with Mai.

||

I agree with both.

||

I agree with neither.

,

I agree with Kiran.

,347917 +PSBCG3,1,Multiple Choice (select 1),Multiple Choice,"

Clare says, “This classroom is 11 meters long. A meter is longer than a yard, so if I measure the length of this classroom in yards, I will get less than 11 yards.”

+

 

+

Do you agree with Clare?

",,,Yes || No,No,11608 +PRABQPRF,1,Multiple Choice (select 1),Multiple Choice,

Which of these describes a unique polygon?

,,,"A quadrilateral with 4 right angles || A triangle with angles 30°, 80°, and 70° || A triangle with side lengths 7 cm and 8 cm and a 70° angle || A triangle with each side length 5 inches",A triangle with each side length 5 inches,558308 +PRABQPS3,1,Multiple Choice (select all),Check All That Apply,"

Elena would like to know the average speed that people drive on her street. She tracks the speed of 30 random cars that drive through with a speedometer. The mean of Elena’s sample is 30 miles per hour, and the MAD (mean absolute deviation) is 3.

+


Select all the true statements.

",,,Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars. || The median speed of the sample must be between 25 and 35 miles per hour. || Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour. || The mean speed of these 30 cars is likely to be the same as the mean speed of a second sample of 30 cars. || The mean speed of these random 30 cars is likely to be the same as the mean of all cars that drive in a residential area.,Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars. || Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.,266053 +PRABG424,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the solution is represented by x < 2.5 or x > 2.5.

+

 

+

-25 > -5(x + 2.5)

+
 
",,,x < 2.5 || x > 2.5,x > 2.5,237641 +PSBBYA,1,Multiple Choice (select 1),Multiple Choice,"

These two box plots show the distances of a standing jump, in inches, for a random sample of 10-year-olds and a random sample of 15-year-olds.

+

 

+

+

 

+

Is there a meaningful difference in median distance for the two populations?

+
 
",,,Yes || No,Yes,8405 +PRABEUG6,1,Multiple Choice (select all),Check All That Apply,

Select all expressions that show x increased by 35%.

,,,"

1.35x

||

35100x

|| + + + + + +
x+35100x
||

(1+0.35)x

||

100+35100x

||

(100+35)x

","

1.35x

|| + + + + + +
x+35100x
||

(1+0.35)x

||

100+35100x

",235425 +PRABEUDQ,1,Multiple Choice (select 1),Multiple Choice,"

Which event is more likely: rolling a standard number cube and getting an even number, or flipping a coin and having it land heads up?

",,,Rolling an even number || A coin landing heads-up || The events are equally likely,The events are equally likely,63338 +PRABETNT,1,Multiple Choice (select 1),Multiple Choice,"

Which decimal is the best estimate of the fraction 2940?

",,0,0.5 || 0.6 || 0.7 || 0.8,0.7,204565 +PRABEGKG,1,Multiple Choice (select all),Check All That Apply,"

Select all the points that are on a line with slope 2 that also contains the point (2, -1).

",,,"

(3, 1)

||

(1, 1)

||

(1, -3)

||

(4, 0)

||

(6, 7)

","

(3, 1)

||

(1, -3)

||

(6, 7)

",50741 +PRABPVSU,1,Multiple Choice (select all),Check All That Apply,

Select all of the equations where x = 3 is a solution.

,,,"

x - 3 = 0

||

1 + x = 2

||

9 - x = 3

||

6 = 2x

||

15x = 3

||

x2 = 9

","

x - 3 = 0

||

6 = 2x

||

x2 = 9

",367058 +PRABQPZY,1,Multiple Choice (select all),Check All That Apply,

Select all the equations that have no solution.

,,,x + 6 = 5 + x || -2(x - 3) = -2x + 6 || 4 - 4x = 3x + 2 || 4(x + 1) = 3(x + 2) || 5 - 3x = -3x + 4,x + 6 = 5 + x || 5 - 3x = -3x + 4,77227 +PRABFARX,1,Multiple Choice (select 1),Multiple Choice,"

Which polyhedron can be assembled from this net?

+

 

+

",,,

A triangular pyramid

||

A trapezoidal prism

||

A rectangular pyramid

||

A triangular prism

,

A triangular pyramid

,78121 +PSBCC5E,1,Multiple Choice (select 1),Multiple Choice,"

The dot plots show the amounts of time that ten South African students and ten Australian students took to get to school. Without calculating, answer the questions.

+

 

+

+

 

+

Which data set has the smaller mean? 

",,,South Africa || Australia,Australia,361179 +PRABE3F9,1,Multiple Choice (select all),Check All That Apply,"

The area of this shape is 24 square units. Which of these statements is true about the area? Select all that apply.

+

 

+

",,,The area can be found by counting the number of squares that touch the edge of the shape. || It takes 24 grid squares to cover the shape without gaps and overlaps. || The area can be found by multiplying the side lengths that are 6 units and 4 units. || The area can be found by counting the grid squares inside the shape. || The area can be found by adding 4 x 3 and 6 x 2,It takes 24 grid squares to cover the shape without gaps and overlaps. || The area can be found by counting the grid squares inside the shape. || The area can be found by adding 4 x 3 and 6 x 2,47557 +PSBBEJZ,2,Multiple Choice (select 1),Multiple Choice,

Use the graph to decide who got paid more after distributing 14 flyers.

,,,Elena || Jada,Elena,195004 +PRABG3XR,1,Multiple Choice (select 1),Multiple Choice,"

Is the value of the expression closer to 12, 1, or 112?

+

 

+

7 ÷ 5

",,,"

12

||

1

||

112

","

112

",128126 +PRABEVAW,1,Multiple Choice (select all),Check All That Apply,"

Select all the situations that can be represented by the tape diagram.

+

 

+

",,,"Clare buys 4 bouquets, each with the same number of flowers. The florist puts an extra flower in each bouquet before she leaves. She leaves with a total of 99 flowers. || Andre babysat 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $4 at the end of the month. Andre earned $99 from babysitting. || A family of 5 drove to a concert. They paid $4 for parking, and all of their tickets were the same price. They paid $99 in total. || 5 bags of marbles each contain 4 large marbles and the same number of small marbles. Altogether, the bags contain 99 marbles. || Han is baking five batches of muffins. Each batch needs the same amount of sugar in the muffins, and each batch needs four extra teaspoons of sugar for the topping. Han uses 99 total teaspoons of sugar.","Andre babysat 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $4 at the end of the month. Andre earned $99 from babysitting. || A family of 5 drove to a concert. They paid $4 for parking, and all of their tickets were the same price. They paid $99 in total.",308259 +PSBE24,1,Multiple Choice (select 1),Multiple Choice,"

Is the equation true or false?

+

 

+

8.4 × 103 × 2 = (8.4 × 2) × 10(3×2)

",,0,True || False,FALSE,25844 +PRABMTN7,1,Multiple Choice (select 1),Multiple Choice,"

For the equation, decide if it is always true or never true.

+

 

+

x − 3 = 2x − 3 − x

",,,Always True || Never True,Always True,148285 +PSB3Z,1,Multiple Choice (select 1),Multiple Choice,"

Which weighs more: a pumpkin that weighs 3.2 kilograms, or a cat that weighs 9 pounds?

+

 

+

Note: 1 pound is about 0.45 kilograms.

",,,a pumpkin that weighs 3.2 kilograms || a cat that weighs 9 pounds,a cat that weighs 9 pounds,3578 +PSBCR9A,1,Multiple Choice (select 1),Multiple Choice,"

Which figure is a scaled copy of Figure A? 

+

 

+

",,,Figure B || Figure C,Figure C,430037 +PSBDPJN,2,Multiple Choice (select 1),Multiple Choice,"

Which group shows greater variability? 

",,,Group P || Group Q,Group Q,591238 +PRABJK5Z,1,Multiple Choice (select all),Check All That Apply,"

Given a and b are numbers, and a + b = 180, which statements also must be true?

",,,a = 180 - b || a - 180 = b || 360 = 2a + 2b || a = 90 and b = 90,a = 180 - b || 360 = 2a + 2b,86798 +PSBB5Z7,1,Multiple Choice (select 1),Multiple Choice,"

¿Qué pesa más: una calabaza que pesa 3.2 kilogramos o un gato que pesa 9 libras?  

+

 

+

Nota: 1 libra es aproximadamente 0.45 kilogramos.

",,,Calabaza || Gato,Gato,319877 +PRABEPMB,1,Multiple Choice (select all),Check All That Apply,"

A square has an area of 81 square feet. Select all the expressions that equal the side length of this square, in feet.

",,,"

812

||

81

||

9

||

9

||

3

","

81

||

9

",423100 +PRABERFN,1,Multiple Choice (select 1),Multiple Choice,"

Which scale is equivalent to 1 cm to 1 km?

+
 
",,,"1 to 1,000 || 10,000 to 1 || 1 to 100,000 || 100,000 to 1 || 1 to 1,000,000","1 to 100,000",146478 +PSBJ4N,1,Multiple Choice (select 1),Multiple Choice,"

Which shape has a larger area: a rectangle that is 7 inches by  inch, or a square with side length of  inches?

",,,Rectangle || Square,Square,47078 +PSBCC7E,1,Multiple Choice (select 1),Multiple Choice,"

Two high school basketball teams have identical records of 15 wins and 2 losses. Sunnyside High School's mean score is 50 points and its MAD is 4 points. Shadyside High School's mean score is 60 points and its MAD is 15 points.

+

 

+

Lin read the records of each team’s score. She likes the team that had nearly the same score for every game it played. Which team do you think Lin likes?

",,,Sunnyside High School || Shadyside High School,Sunnyside High School,361989 +PRABEB5P,1,Multiple Choice (select all),Check All That Apply,

Select all the representations that are appropriate for comparing bite strength to weight for different carnivores.

,,,Histogram || Scatter plot || Dot plot || Table || Box plot,Scatter plot || Table,6116 +PSBCMZ4,1,Multiple Choice (select 1),Multiple Choice,

A rectangle has side lengths of 6 units and 3 units. Could you make a quadrilateral that is not identical using the same four side lengths?

,,,Yes || No,Yes,405080 +PSBTKM,2,Multiple Choice (select 1),Multiple Choice,"

Can you find a rational number that is exactly ?

",,,Yes || No,No,87272 +PSBCA6B,3,Multiple Choice (select 1),Multiple Choice,"

Two larger cubes are made out of unit cubes. Cube A is 2 by 2 by 2. Cube B is 4 by 4 by 4. The side length of Cube B is twice that of Cube A.

+

 

+

Is the volume of Cube B also twice that of Cube A?

+

 

+

",,,Yes || No,No,349875 +PSBH69,1,Multiple Choice (select 1),Multiple Choice,"

Which other expression has the same value as (-14)-(-8)?

+
 
",,,(-14) + 8 || 14 − (-8) || 14 + (-8) || (-14) + (-8),(-14) + 8,42642 +PSBHYF,3,Multiple Choice (select 1),Multiple Choice,"

Did Clare partition the figure into two identical shapes? 

+

 

+

",,,Yes || No,No,41469 +PRABMQH8,1,Multiple Choice (select all),Check All That Apply,"

Triangle Z is a scale copy of Triangle M.

+

+


Select all the sets of values that could be the side lengths of Triangle Z. 

",,,"

8,11,14

|| 10,17.5,25 || 6,9,11 || 6,10.5,15 || 8,14,20","10,17.5,25 || 6,10.5,15 || 8,14,20",569234 +PRABQP4K,1,Multiple Choice (select all),Check All That Apply,

Select all the relationships that demonstrate a negative association between variables.

,,,Number of absences from school and final grades || Outside temperature and ice cream sales || Price of houses and house sales || Number of rainy days and car accidents || Number of hours playing video games and grades,Number of absences from school and final grades || Price of houses and house sales || Number of hours playing video games and grades,77355 +PSBMYW,3,Multiple Choice (select 1),Multiple Choice,"

Which movie has a dot plot with ages that that center at about 30 years?

+

 

+

",,,Movie A || Movie B || Movie C,Movie C,57280 +PSB9QG,1,Multiple Choice (select 1),Multiple Choice,"

For the pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not.

+

 

+

 

+

Triangle A: 53, 71, ___; Triangle B: 53, 71, ___

",,,similar || not similar,similar,167382 +PRABQP6T,1,Multiple Choice (select 1),Multiple Choice,"

About 3.2×108 people live in the United States. About 3.9×107 people live in Canada. And about 1.1×108 people live in Mexico. About how many people live in all three countries altogether?

",,,"

4.69×107

||

4.69×108

||

8.2×107

||

8.2×108

","

4.69×108

",552392 +PRABFH7A,1,Multiple Choice (select all),Check All That Apply,"

The temperature at dawn is 6°C away from 0. Select all the temperatures that are possible.

",,,"

-12°C

||

-6°C

||

0°C

||

6°C

||

12°C

","

-6°C

||

6°C

",6346 +PSBCBW4,1,Multiple Choice (select 1),Multiple Choice,"

Andre and Jada are discussing how to write 1720 as a decimal.

+

 

+
+
    +
  • Andre says he can use long division to divide 17 by 20 to get the decimal.
    • +
+

 

+
    +
  • Jada says she can write an equivalent fraction with a denominator of 100 by multiplying by 55, then writing the number of hundredths as a decimal.
    • +
+

 

+

Do both of these strategies work?

+
",,,yes || no,yes,353991 +PSBBFAV,7,Multiple Choice (select 1),Multiple Choice,

Do you have any siblings? 

,,,Yes || No,Yes || No,198852 +PSBBZMW,1,Multiple Choice (select 1),Multiple Choice,"

Here are the nets of three cardboard boxes that are all rectangular prisms. The boxes will be packed with 1-centimeter cubes. All lengths are in centimeters.

+

+

 

+

Compare the surface areas of the boxes. Which box will use the least cardboard?

",,,"Box A || Box B || Box C || Boxes A,B,C uses the same amount of cardboard",Box A,295788 +PSBBBY3,1,Multiple Choice (select 1),Multiple Choice,"

A scientist is interested in whether certain species of butterflies like certain types of local flowers. The scientist captures butterflies in two zones with different flower types and records the number caught.

+

 

+ + + + + + + + + + + + + + + + + + +
 zone 1zone 2
eastern tiger swallowtail1634
monarch2446
+

 

+

 

+

Does the data show an association between butterfly type and zone? 

",,,Yes || No,No,180312 +PSB8AF,1,Multiple Choice (select 1),Multiple Choice,"

 

+

Clare started with a rectangular piece of paper. She folded up one corner, and then folded up the other corner, as shown in the photos.

+ + + + + + + + +
+

Try this yourself with any rectangular paper. Fold the left corner up at any angle, and then fold the right corner up so that the edges of the paper meet.

+

 

+

Clare thought that the angle at the bottom looked like a 90 degree angle. Does yours also look like it is 90 degrees?

",,,Yes || No,Yes,160140 +PRABEVCV,1,Multiple Choice (select 1),Multiple Choice,"

Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.

+

 

+

Which of these inequalities describes this situation, where n is the number of songs Lin wants to buy? 

+
 
",,,9.99 + 1.29n ≥ 50 || 9.99 + 1.29n ≤ 50 || 9.99 - 1.29n ≥ 50 || 9.99 - 1.29n ≤ 50,9.99 + 1.29n ≤ 50,189877 +PRABQMFK,1,Multiple Choice (select 1),Multiple Choice,

Which expression is equivalent to 20c − 8d?

,,,

2(10c + 4d)

|| 4(5c − 8d) || 4(5c − 2d) || c(20 − 8d),4(5c − 2d),427575 +PSBDW5,1,Multiple Choice (select all),Check All That Apply,"

For the situation, select all the equations that represent it.

+

 

+

Jada’s cat weighs 3.45 kg. Andre’s cat weighs 1.2 kg more than Jada’s cat. How much does Andre’s cat weigh?

",,,"

x = 3.45 + 1.2

||

x = 3.45 - 1.2

||

x + 1.2 = 3.45

||

x - 1.2 = 3.45

","

x = 3.45 + 1.2

||

x - 1.2 = 3.45

",19761 +PRABMTN6,1,Multiple Choice (select 1),Multiple Choice,"

For the equation, decide if it is always true or never true.

+

 

+

2(x + 3) = 5x + 6 − 3x 

",,,Always True || Never True,Always True,148145 +PSBFRY,1,Multiple Choice (select 1),Multiple Choice,"

Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre?

",,,Diego || Andre,Andre,29501 +PRABQTPQ,1,Multiple Choice (select 1),Multiple Choice,

A circle has radius 50 cm. Which of these is closest to its area?

,,,"157 cm² || 314 cm² || 7,854 cm² || 15,708 cm²","7,854 cm²",270553 +PRABERUD,1,Multiple Choice (select all),Check All That Apply,

Which of these scales is equivalent to the scale 1 cm to 5 km? Select all that apply.

,,,3 cm to 15 km || 1 mm to 150 km || 5 cm to 1 km || 5 mm to 2.5 km || 1 mm to 500 m,3 cm to 15 km || 5 mm to 2.5 km || 1 mm to 500 m,165767 +PRABQP3S,1,Multiple Choice (select 1),Multiple Choice,"

Which point is on the graph of the function y = 3x + 2?

",,,"(1, 5) || (2, 3) || (3, 2) || (5, 1)","(1, 5)",144266 +PSBBT89,1,Multiple Choice (select 1),Multiple Choice,"

Two different classes took a survey to determine the number of minutes spent on
homework one evening. Here is a box plot showing the results from Class A:

+

+

 

+

Here are the results from Class B:

+

10, 15, 20, 20, 25, 30, 30, 35, 40, 45, 45, 45, 60, 60, 80

+

 

+

In which class did students spend less time on their homework?

",,,Class A || Class B,Class B,265140 +PRABQPCM,1,Multiple Choice (select all),Check All That Apply,"

Select all expressions that are equivalent to 5n-30.

",,,n + n + n + n + n - 30 || 5(n - 30) || (n - 6) · 5 || 5n - 30n || 5n + -30,n + n + n + n + n - 30 || (n - 6) · 5 || 5n + -30,609697 +PSB4AR,1,Multiple Choice (select all),Check All That Apply,"

The table and graph represent two functions. Use the table and graph to answer the questions.

+

 

+

+

 

+ + + + + + + + + + + + + + + + + + + + + +
x123456
y3-1045-1
+

 

+

For which values of x is the output from the table less than the output from the graph?

",,,1 || 2 || 3 || 4 || 5 || 6,2 || 3,137984 +PRABEVHN,1,Multiple Choice (select all),Check All That Apply,

Select all the measures of variability or spread.

,,,mean || IQR (interquartile range) || MAD (mean absolute deviation) || median || range,IQR (interquartile range) || MAD (mean absolute deviation) || range,529857 +PSB2FK,4,Multiple Choice (select 1),Multiple Choice,"

If Mai is given the option to flip a coin and win if it comes up heads, is that a better option for her to win?

",,,Yes || No,Yes,126872 +PSBDPQ,1,Multiple Choice (select 1),Multiple Choice,"

For a suitcase to be checked on a flight (instead of carried by hand), it can weigh at most 50 pounds. Andre’s suitcase weighs 23 kilograms.

+

 

+

Can Andre check his suitcase? (Note: 10 kilograms ≈ 22 pounds)

",,,Yes || No,No,18501 +PSBCWTH,2,Multiple Choice (select 1),Multiple Choice,"

A circular lawn has a row of bricks around the edge. The diameter of the lawn is about 40 feet.

+

 

+

+

 

+

 

+

Which is the best estimate for the total length of the bricks? 

",,,"

125 feet

||

125 square feet

||

1,250 feet

||

1,250 square feet

",

125 feet

,456048 +PRABHGFH,1,Multiple Choice (select all),Check All That Apply,"

Which of these triangles are translations of Triangle A? Select all that apply.

+

 

+

+
 
",,,Triangle B || Triangle C || Triangle D || Triangle E || Triangle F,Triangle B || Triangle D,495451 +PSB88X,1,Multiple Choice (select 1),Multiple Choice,"

Jada and Lin are comparing inches and feet. Jada says that the constant of proportionality is 12, Lin says it is 112. Do you agree with either one of them?

",,,I agree with only Lin || I agree with only Jada || I agree with both Jada and Lin || I agree with neither Jada or Lin,I agree with both Jada and Lin,164771 +PSBDZX2,1,Multiple Choice (select all),Check All That Apply,"

Identify all pairs of parallel lines in the diagram.

+

 

+

",,,g and f || h and g || h and f || h and j || h and i || g and j || g and i || f and j || f and i || j and i,g and f,651306 +PSBBSQ,3,Multiple Choice (select all),Check All That Apply,"

Which measure of center- the mean or the median- better describes a typical value for the following distribution?

+

 

+

",,,Mean || Median,Median,7682 +PSBCJYT,1,Multiple Choice (select 1),Multiple Choice,"

Lin knows that there are 4 quarts in a gallon. She wants to convert 6 quarts to gallons, but cannot decide if she should multiply 6 by 4 or divide 6 by 4 to find her answer.

+

 

+

What should she do? If you get stuck, consider drawing a double number line or using a table.

",,,Multiply 6 by 4 || Divide 6 by 4,Divide 6 by 4,394101 +PSBBZSQ,1,Multiple Choice (select 1),Multiple Choice,"

Is the statement true or false?

+

 

+

16% of 250 is equal to 250% of 16

",,1,True || False,TRUE,296749 +PRABEVDK,1,Multiple Choice (select 1),Multiple Choice,"

A square pyramid is sliced parallel to the base and halfway up the pyramid.

+

 

+

Which of these describes the cross-section?

+

 

+

",,,A square smaller than the base || A quadrilateral that is not a square || A square the same size as the base || A triangle with a height the same as the pyramid,A square smaller than the base,68115 +PSBCGVT,1,Multiple Choice (select 1),Multiple Choice,"

The points (-2, 0) and (0, -6) are each on the graph of a linear equation. Is (2, 6) also on the graph of this linear equation?

",,,Yes || No,No,383239 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681 +PRABETDJ,1,Multiple Choice (select 1),Multiple Choice,"

At the beginning of the month, there were 80 ounces of peanut butter in the pantry. Since then, the family ate 0.3 of the peanut butter. How many ounces of peanut butter are in the pantry now?

",,,0.7 • 80 || 0.3 • 80 || 80 - 0.3 || (1 + 0.3) • 80,0.7 • 80,55885 +PRABFENN,1,Multiple Choice (select all),Check All That Apply,"
+

An orange has about 14 cup of juice. How many oranges are needed to make 212 cups of juice?

+

 

+

Select all the equations that represent this question.

+
",,,"

? · 14 = 212

||

14 ÷ 212 = ?

||

? ·  212 = 14

||

212 ÷ 14 = ?

","

? · 14 = 212

||

212 ÷ 14 = ?

",277226 +PRABQP5J,1,Multiple Choice (select 1),Multiple Choice,

Which segment has a length of 10 units?

,,,"

(3, 4) to (30, 40)

||

(0,0) to (10, 10)

||

(-1, -2) to (9, -2)

||

(-2, 8) to (-3, 7)

","

(-1, -2) to (9, -2)

",337475 +PRABQMFN,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that have the same value.

,,,

33

||

34

||

62

||

63

||

92

||

93

,

34

||

92

,350462 +PRABEU33,1,Multiple Choice (select 1),Multiple Choice,"

A car is 180 inches long. A truck is 75% longer than the car.

+

 

+
+

How long is the truck?

+
",,,135 inches || 240 inches || 255 inches || 315 inches,315 inches,248005 +PRABQM33,1,Multiple Choice (select all),Check All That Apply,"

Jada drew this line plot showing the hat sizes, in inches, of all the players on her softball team.

+

 

+

+

 

+

 

+

Select all the true statements.

",,,"

There are six players on the team.

||

The largest hat size is 8 inches.

||

Half of the hat sizes are less than 758 inches.

||

None of the players has a hat size of 768 inches.

||

 The difference between the maximum and minimum hat size is 78 inch.

","

The largest hat size is 8 inches.

||

Half of the hat sizes are less than 758 inches.

||

 The difference between the maximum and minimum hat size is 78 inch.

",4926 +PRABQP23,1,Multiple Choice (select all),Check All That Apply,"

Noah is three years younger than four times the age of his brother. Select all the equations that correctly represent the relationship between Noah's age n and his brother's age b.

",,,"

n=3-4b

||

n=4b-3

||

 n=4(b-3)

|| + + + + + +
b=n + 34
|| + + + + + +
b=4n-3
||

b=n4+3

","

n=4b-3

|| + + + + + +
b=n + 34
",674289 +PRABET9P,1,Multiple Choice (select 1),Multiple Choice,

Diego is solving the inequality 100 − 3x ≥ -50. He solves the equation 100 − 3x = -50 and gets x = 50. What is the solution to the inequality?

,,,x < 50 || x ≤ 50 || x > 50 || x ≥ 50,x ≤ 50,51606 +PRABFDGX,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that can represent the question: “How many groups of 45 are in 1?”

",,,"

? · 1 = 45

||

1 · 45 = ?

||

45 ÷ 1 = ?

||

? · 45 = 1

||

1 ÷ 45 = ?

","

? · 45 = 1

||

1 ÷ 45 = ?

",522821 +PSBCAMJ,1,Multiple Choice (select 1),Multiple Choice,"

The solution to 5 − 3x > 35 is either x > -10 or - 10 > x.

+

 

+

Which solution is correct?

",,,x > -10 || -10 > x,-10 > x,346366 +PSBKZU,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to . 

",,,9 - 10n || 14 - 3n || 14 - 21n || (2 - 3n) · 7 || 7 · 2 · (-3n),14 - 21n || (2 - 3n) · 7,51977 +PSBBSYB,1,Multiple Choice (select 1),Multiple Choice,"

State whether the following is in scientific notation.

+

 

+

36 x 105

",,,Already in scientific notation || Not in scientific notation,Not in scientific notation,257525 +PSBBSVC,1,Multiple Choice (select 1),Multiple Choice,"

State whether the following is in scientific notation.

+

 

+

48,200

",,,Already in scientific notation || Not in scientific notation,Not in scientific notation,257027 +PRABEG66,1,Multiple Choice (select 1),Multiple Choice,

An ice cream shop offers two ice cream cones. The waffle cone holds 12 ounces and is 5 inches tall. The sugar cone also holds 12 ounces and is 8 inches tall. Which cone has a larger radius? 

,,,waffle cone || sugar cone,waffle cone,115951 +PSBKYN,1,Multiple Choice (select 1),Multiple Choice,

There are 25 prime numbers between 1 and 100. There are 46 prime numbers between 1 and 200. Which situation below is more likely?

,,,"
    +
  • A computer produces a random number between 1 and 100 that is prime.
    • +
||
    +
  • A computer produces a random number between 1 and 200 that is prime.
    • +
","
    +
  • A computer produces a random number between 1 and 100 that is prime.
    • +
",51557 +PSBBU49,1,Multiple Choice (select 1),Multiple Choice,"

Do 4x and 15+x have the same value when x is 5?

",,,Yes || No,Yes,270010 +PSBTE,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of shapes, decide whether or not Shape A is congruent to Shape B. 

+

 

+

 

",,,"Yes, they are congruent || No, they are not congruent","No, they are not congruent",2234 +PRABESMD,1,Multiple Choice (select 1),Multiple Choice,"
+
+
+
+
+

Which question cannot be answered by the solution to the equation 3x = 27?

+

3

+
+
+
+
+
",,,Elena read three times as many pages as Noah. She read 27 pages. How many pages did Noah read? || Lin has 27 stickers. She gives 3 stickers to each of her friends. With how many friends did Lin share her stickers? || Diego paid $27 to have 3 pizzas delivered and $35 to have 4 pizzas delivered. What is the price of one pizza? || The coach splits a team of 27 students into 3 groups to practice skills. How many students are in each group?,Diego paid $27 to have 3 pizzas delivered and $35 to have 4 pizzas delivered. What is the price of one pizza?,67861 +PRABQPYS,1,Multiple Choice (select 1),Multiple Choice,"

Which graph is a translation of line n?

+

  

+

",,,Line A || Line B || Line C || Line D,Line D,172034 +PSBCRJR,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the inequality statement is true or false. 

+

 

+

-5 > 2

",,0,True || False,FALSE,426185 +PSBCB4Y,2,Multiple Choice (select 1),Multiple Choice,"

After Lin makes her way down the hall, will the 30th locker have no stickers, 1 sticker, or 2 stickers? 

",,,no stickers || 1 sticker || 2 stickers,1 sticker,355558 +PSBBZU2,1,Multiple Choice (select 1),Multiple Choice,"

If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle?

+

 

",,,Yes || No,Yes,297072 +PSBB27S,2,Multiple Choice (select 1),Multiple Choice,

Which of the graphs is most likely to represent the graph of daylight for the month after the autumnal equinox?

,,,"

||

||

||

 

","

",304606 +PSBBVT7,1,Multiple Choice (select all),Check All That Apply,"

Mai, Clare, and Tyler are hiking from a parking lot to the summit of a mountain. They pass a sign that gives distances.

+

 

+

Parking lot: 34 mile

+

Summit: 112 miles

+

 

+
    +
  • Mai says: “We are one-third of the way there.”

    • +
  • Clare says: “We have to go twice as far as we have already gone.”

    • +
  • Tyler says: “The total hike is three times as long as what we have already gone.”
    • +
  •  
    • +
+

 

+

Do you agree with any of them?  Select those you agree with. 

",,,Mai || Claire || Tyler,Mai || Claire || Tyler,274139 +PRABPTTC,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that have a solution of 27.

",,,"

x2=27

||

 x²=414

||

x²=449

||

x2=621

||

x3=8343

||

x3=67

","

x²=449

||

x3=8343

",478012 +PRABQNGF,1,Multiple Choice (select all),Check All That Apply,"

The ages of people dining in two restaurants are shown in the following box plots.

+

 

+

+

 

+

Select all the statements that must be true. 

",,,The median age of people dining in Restaurant B is greater than the median age of people dining in Restaurant A. || The MAD (mean absolute deviation) for Restaurant B is greater than the MAD (mean absolute deviation) for Restaurant A. || The youngest person was dining in Restaurant A. || The IQR (interquartile range) for Restaurant A is equal to the IQR (interquartile range) for Restaurant B. || Every person dining in Restaurant B is older than everyone dining in Restaurant A.,The median age of people dining in Restaurant B is greater than the median age of people dining in Restaurant A. || The youngest person was dining in Restaurant A.,258280 +PSBB3YN,1,Multiple Choice (select 1),Multiple Choice,"

Jada is using a computer’s random number generator to produce 6 random whole numbers between 1 and 100 so she can use a random sample. The computer produces the numbers: 1, 2, 3, 4, 5, and 6.

+

 

+

Should she use these numbers or have the computer generate a new set of random numbers?

",,,Use these numbers || Use new set of random numbers,Use these numbers,308995 +PRABEWFS,1,Multiple Choice (select 1),Multiple Choice,

Data collected from a survey of American teenagers aged 13 to 17 was used to estimate that 29% of teens believe in ghosts. This estimate was based on data from 510 American teenagers. What is the population that people carrying out the survey were interested in?

,,,All people in the United States. || The 510 teens that were surveyed. || All American teens who are between the ages of 13 and 17. || The 29% of the teens surveyed who said they believe in ghosts.,All American teens who are between the ages of 13 and 17.,310109 +PSBC99E,2,Multiple Choice (select 1),Multiple Choice,

Determine which data set is Tyler’s.

,,,Data Set A || Data Set B || Data Set C || Data Set D,Data Set B,520423 +PSBBQFD,1,Multiple Choice (select all),Check All That Apply,

Select all the prisms.

,,,"

||

||

||

||

","

||

||

||

",244435 +PSBZC7,1,Multiple Choice (select 1),Multiple Choice,

Suppose Quadrilaterals A and B are both squares. Are A and B necessarily scale copies of one another?

,,,Yes || No,Yes,120984 +PSBDMDU,1,Multiple Choice (select 1),Multiple Choice,"

A container of fuel dispenses fuel at the rate of 5 gallons per second. If y represents the amount of fuel remaining in the container, and x represents the number of seconds that have passed since the fuel started dispensing, then x and y satisfy a linear relationship.

+

In the coordinate plane, will the slope of the line representing that relationship have a positive, negative, or zero slope?

",,,Positive || Negative || Zero,Negative,578697 +PSB633,1,Multiple Choice (select 1),Multiple Choice,"

State whether you agree with the statement below. 

+

 

+

A temperature of 35 degrees Fahrenheit is as cold as a temperature of -35 degrees Fahrenheit.

",,,Agree || Disagree,Disagree,153519 +PSBS38,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3

",,1,True || False,TRUE,84110 +PSBNRS,1,Multiple Choice (select 1),Multiple Choice,"

Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8, and 10. Could one of the quadrilaterals be a scaled copy of the other?

",,,Yes || No,No,61151 +PRABQM8Z,1,Multiple Choice (select all),Check All That Apply,"

Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A.

+

Select all of the measurement pairs that could be the dimensions of Rectangle B.

",,,4.5 inches by 1.5 inches || 8 inches by 2 inches || 10 inches by 4 inches || 13.5 inches by 4.5 inches || 90 inches by 30 inches,4.5 inches by 1.5 inches || 13.5 inches by 4.5 inches || 90 inches by 30 inches,115930 +PRABEJTK,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equal to 4⋅10-3:

",,,"

4·110·110·110

||

4·(-10)·(-10)·(-10)

||

4·0.001

||

4·0.0001

||

0.004

||

0.0004

","

4·110·110·110

||

4·0.001

||

0.004

",490287 +PRABFDJM,1,Multiple Choice (select 1),Multiple Choice,"

Which question can be represented by the equation 4 ÷ 27 = ?

",,,"

What is 4 groups of 27?

||

How many 27s are in 4?

||

What is 27 of 4?

||

How many 4s are in 27?

","

How many 27s are in 4?

",184230 +PRABQPCF,1,Multiple Choice (select all),Check All That Apply,"

Lin is collecting coins. After giving away 13 coins, she has 75 coins remaining.

+

 

+

Select all the equations Lin can solve to find x, the number of coins she started with.

",,,"

x + 13 = 75

||

x - 13 = 75

||

x = 75 - 13

||

13x = 75

||

x = 75 + 13

||

x = 75 · 13

||

x = 7513

","

x - 13 = 75

||

x = 75 + 13

",178406 +PRABFG4K,1,Multiple Choice (select all),Check All That Apply,"

Which expressions are solutions to the equation 2.4y = 13.75?  Select all that apply.

+

 

+

 

",,,"

13.75 - 1.4

||

13.75 · 2.4

||

13.75 ÷ 2.4

||

13.752.4

||

2.4 ÷ 13.75

","

13.75 ÷ 2.4

||

13.752.4

",47917 +PRABQNDA,1,Multiple Choice (select all),Check All That Apply,"

The graph shows the cost C in dollars of w pounds of peanuts, a proportional relationship.

+

 

+

Select all the true statements.

+

 

+

",,,"2.5 pounds of peanuts costs $1. || 1 pound of peanuts costs $2.50. || 5 pounds of peanuts cost $12.50. || 9 pounds of peanuts cost $19.50. || The point (4, 10) is on the graph of the proportional relationship.","1 pound of peanuts costs $2.50. || 5 pounds of peanuts cost $12.50. || The point (4, 10) is on the graph of the proportional relationship.",409398 +PRABD477,1,Multiple Choice (select 1),Multiple Choice,"

Triangle DEF is a dilation of triangle ABC with scale factor 2. In triangle ABC, the largest angle measures 82°. What is the largest angle measure in triangle DEF?

",,,"

41°

||

82°

||

123°

||

164°

","

82°

",47390 +PRABQTD5,1,Multiple Choice (select 1),Multiple Choice,

Which graph represents a proportional relationship?

,,,"

||

||

||

","

",561011 +PSB47G,3,Multiple Choice (select 1),Multiple Choice,"

If x represents a number, does 25·x always represent 40% of that number?

",,,Yes || No,Yes,143123 +PSB5Y4,2,Multiple Choice (select 1),Multiple Choice,"

A different rectangular solid has length l, width 10, height 5, and volume V. Is the relationship between l and V a proportional relationship?

",,,Yes || No,Yes,148013 +PSBW2X,1,Multiple Choice (select 1),Multiple Choice,"

Tyler says that Figure B is a scaled copy of Figure A because all of the peaks are half as tall.

+

Do you agree with Tyler?

+

",,,Yes || No,No,108073 +PRABQMXH,1,Multiple Choice (select 1),Multiple Choice,"

It took 4 hours to drive 240 miles. At this rate, how long does it take to drive 90 miles?

",,,"

60 hours

||

6 hours

||

223 hours

||

112 hours

","

112 hours

",3980 +PRABEU6P,1,Multiple Choice (select all),Check All That Apply,"

Jada is collecting stickers. After getting 15 more stickers, she has 60 stickers in total.

+

 

+

Select all the equations Jada can solve to find x, the number of stickers she started with.

",,,"

x + 15 = 60

||

x − 15 = 60

||

x = 60 + 15

||

x = 60 − 15

||

15x = 60

||

 x = 60 · 15

||

x = 6015

",

x + 15 = 60

||

x = 60 − 15

,61779 +PSBCA6B,1,Multiple Choice (select 1),Multiple Choice,"

Two larger cubes are made out of unit cubes. Cube A is 2 by 2 by 2. Cube B is 4 by 4 by 4. The side length of Cube B is twice that of Cube A.

+

 

+

Is the surface area of Cube B also twice that Cube A?

+

 

+

",,,Yes || No,No,349598 +PSBR8T,1,Multiple Choice (select 1),Multiple Choice,"

Here is a story: Lin bought 4 bags of apples Each bag had the same number of apples. After eating 1 apple from each bag, she had 28 apples left.

+

 

+

Which diagram best represents the story? 

",,,"

||

||

","

",78866 +PRABEVX3,1,Multiple Choice (select all),Check All That Apply,"

Select all the right triangles, given the lengths of the sides.

+

+

 

",,,A. || B. || C. || D. || E.,A. || E.,46379 +PRABECZR,1,Multiple Choice (select all),Check All That Apply,

Select all the situations for which only zero or positive solutions make sense.

,,,

Measuring temperature in degrees Celsius at an Arctic outpost each day in January.

||

The height of a candle as it burns over an hour.

||

The elevation above sea level of a hiker descending into a canyon.

||

The number of students remaining in school after 6:00 p.m.

||

A bank account balance over a year.

||

The temperature in degrees Fahrenheit of an oven used on a hot summer day.

,

The height of a candle as it burns over an hour.

||

The number of students remaining in school after 6:00 p.m.

||

The temperature in degrees Fahrenheit of an oven used on a hot summer day.

,187169 +PSBBSFM,2,Multiple Choice (select 1),Multiple Choice,"

Which grade has the most students?

+

 

+

",,,Sixth grade || Seventh grade || Eighth grade,Sixth grade,255003 +PSBCZP4,2,Multiple Choice (select 1),Multiple Choice,"

Consider the statement: “A square with side lengths of  inch has an area of  square inches.” Do you agree?

",,,Agree || Disagree,Disagree,471899 +PSBN96,6,Multiple Choice (select 1),Multiple Choice,"

Which has more mass, the Burj Khalifa or the mass of the pennies it cost to build the Burj Khalifa?

",,,Burj Khalifa || Mass of pennies,Burj Khalifa,63961 +PSBHU8,1,Multiple Choice (select 1),Multiple Choice,"

If you mix blue and yellow paint in different ratios, you will get different shades of green paint. If the ratios are equivalent, the shades of green will be the same.

+

 

+
    +
  • Clare mixed a batch of green paint using 8 cups of yellow paint and 5 cups of blue paint.

    • +
  • Jada mixed another batch of green paint using 6 cups of yellow paint and 4 cups of blue paint.
    • +
+

 

+

Are these two batches the same shade of green?

+

 

",,,yes || no,no,40938 +PRABEUAV,1,Multiple Choice (select all),Check All That Apply,

You know x is a number less than 4. Select all the inequalities that must be true.

,,,x < 2 || x + 6 < 10 || 5x < 20 || x - 2 > 2 || x < 8,x + 6 < 10 || 5x < 20 || x < 8,73862 +PSBB8HF,2,Multiple Choice (select 1),Multiple Choice,

Are the swimmers on the 1984 team closer in age to one another than the swimmers on the 2016 team are to one another? 

,,,Yes || No,Yes,334286 +PSBBYTM,1,Multiple Choice (select 1),Multiple Choice,"

Here are two polygons on a grid.

+

 

+

+

 

+

Is PQRST a scaled copy of ABCDE?

",,,Yes || No,No,290885 +PRABQKNN,1,Multiple Choice (select all),Check All That Apply,"

Select all the true statements.

+

 

+

",,,The ratio of triangles to squares is 2 to 4. ||

The ratio of squares to smiley faces is 6 : 4.

|| The ratio of smiley faces to triangles is 6 to 4. || There are two squares for every triangle. || There are two triangles for every smiley face. || There are three smiley faces for every triangle.,The ratio of triangles to squares is 2 to 4. || There are two squares for every triangle. || There are three smiley faces for every triangle.,114950 +PSBBHSS,1,Multiple Choice (select 1),Multiple Choice,

Did it take more feet or meters to measure the indicated length?

,,,more feet || more meters,more feet,212942 +PRABQMT6,1,Multiple Choice (select all),Check All That Apply,

Select all the numbers that are a common multiple of 8 and 12.

,,,96 || 80 || 48 || 32 || 24 || 20 || 4,96 || 48 || 24,49409 +PRABQK7X,1,Multiple Choice (select all),Check All That Apply,

Select all the equations where x = 5 is a solution.

,,,"

x - 4 = 9

||

1 + x = 6

||

2 = 7 - x

||

10x = 5

||

110x = 12

||

x2 = 5

","

1 + x = 6

||

2 = 7 - x

||

110x = 12

",56477 +PRABETRF,1,Multiple Choice (select 1),Multiple Choice,"

Noah picked 3 kg of cherries. Jada picked half as many cherries as Noah. How many total kgs of cherries did Jada and Noah pick?

+
 
",,,3 + 0.5 || 3 - 0.5 || (1 + 0.5) · 3 || 1 + 0.5 · 3,(1 + 0.5) · 3,341602 +PSBBMG6,1,Multiple Choice (select 1),Multiple Choice,"

Kiran started his homework before 7:00 p.m. and finished his homework after 8:00 p.m. Let h represent the number of hours Kiran worked on his homework.

+

 

+

Decide if the statement it is definitely true, definitely not true, or possibly true.

+

 

+

h>1

+
 
",,,Definitely True || Definitely Not True || Possibly True,Definitely True,227553 +PSBB6PY,6,Multiple Choice (select 1),Multiple Choice,"

",,,< || = || >,=,324144 +PRABESGF,1,Multiple Choice (select all),Check All That Apply,"

Last week, the price, in dollars, of a gallon of gasoline was g. This week, the price of gasoline per gallon increased by 5%. Which expressions represent this week's price, in dollars, of a gallon of gasoline? Select all that apply.

",,,

g + 0.05

||

g + 0.05g

||

1.05g

||

0.05g

||

(1 + 0.05)g

,

g + 0.05g

||

1.05g

||

(1 + 0.05)g

,586483 +PSB6CY,1,Multiple Choice (select 1),Multiple Choice,"

Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base s. She asks Han what he thinks will happen to the volume of the prism if she triples s.

+

 

+

Han says the volume will be 9 times bigger. Is he right?

",,,Yes || No,Yes,149928 +PRABEEMF,1,Multiple Choice (select all),Check All That Apply,"

Select all of the given points in the coordinate plane that lie on the graph of the linear equation 4x − y = 3.

+
 
",,,"

(-1, -7)

||

(0, 3)

||

34, 0

||

(1, 1)

||

(2, 5)

||

(4, -1)

","

(-1, -7)

||

34, 0

||

(1, 1)

||

(2, 5)

",231799 +PRABFK4A,1,Multiple Choice (select 1),Multiple Choice,"

Priya asked each of five friends to attempt to throw a ball in a trash can until they succeeded. She recorded the number of unsuccessful attempts made by each friend as: 1, 8, 6, 2, 4. Priya made a mistake: The 8 in the data set should have been 18.

+

 

+

How would changing the 8 to 18 affect the mean and median of the data set?

",,,The mean would decrease and the median would not change. || The mean would increase and the median would not change. || The mean would decrease and the median would increase. || The mean would increase and the median would increase.,The mean would increase and the median would not change.,64548 +PSBJMA,3,Multiple Choice (select 1),Multiple Choice,

Which tomato variety should the farmer choose?

,,,Variety A || Variety B,Variety B,44782 +PRABQTPS,1,Multiple Choice (select all),Check All That Apply,"

Select all of the true statements.

+
 
",,,π is the area of a circle of radius 1. || π is the area of a circle of diameter 1. || π is the circumference of a circle of radius 1. || π is the circumference of a circle of diameter 1. || π is the constant of proportionality relating the diameter of a circle to its circumference. || π is the constant of proportionality relating the radius of a circle to its area.,π is the area of a circle of radius 1. || π is the circumference of a circle of diameter 1. || π is the constant of proportionality relating the diameter of a circle to its circumference.,270843 +PSBDBBT,1,Multiple Choice (select 1),Multiple Choice,"
+

Tyler and Priya were both measuring angle TUS.TU

+
+
 
+
 
+
Priya thinks the angle measures 40 degrees. Tyler thinks the angle measures 140 degrees. Do you agree with either of them?
+
",,,Tyler is correct || Priya is correct || Neither,Priya is correct,526525 +PRABEVTE,1,Multiple Choice (select 1),Multiple Choice,"

This table shows a linear relationship between the amount of water in a tank and time.

+

 

+ + + + + + + + + + + + + + + + + + + +
time(minutes)water(gallons)
030
520
1010
+

 

+

Which of these statements is true?

",,,The water in the tank is increasing at a rate of 2 gallons per minute. || The water in the tank is increasing at a rate of 10 gallons per minute. || The water in the tank is decreasing at a rate of 2 gallons per minute. || The water in the tank is decreasing at a rate of 10 gallons per minute.,The water in the tank is decreasing at a rate of 2 gallons per minute.,340440 +PRABQP5W,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 28·24.

",,,"

24

||

212

||

46

||

232

||

432

","

212

||

46

",156590 +PSBCE5U,3,Multiple Choice (select 1),Multiple Choice,"

At a farm, animals are fed bales of hay and buckets of grain. Each bale of hay is in the shape a rectangular prism. The base has side lengths 2 feet and 3 feet, and the height is 5 feet. Each bucket of grain is a cylinder with a diameter of 3 feet. The height of the bucket is 5 feet, the same as the height of the bale.

+

 

+

Which is larger in volume, the bale or the bucket?

",,,Bale || Bucket,Bucket,373766 +PSBQGS,1,Multiple Choice (select 1),Multiple Choice,"

A pollster attends a rally and surveys many of the participants about whether they associate with political Party A or political Party B and whether they are for or against Proposition 3.14 going up for vote soon. The results are sorted into the table shown.

+

 

+ + + + + + + + + + + + + + + + + + +
 foragainst
party A832165
party B80160
+

 

+
    +
  • A news station reports these results by saying, “A poll shows that about the same number of people from both parties are voting against Proposition 3.14.”
    • +
+

 

+
    +
  • A second news station shows this graphic. +

     

    +
    • +
+

+

 

+

Are any of the news reports misleading? 

",,,Yes || No,Yes,69854 +PSBB6PY,2,Multiple Choice (select 1),Multiple Choice,"

",,,< || = || >,<,323761 +PRABFBN3,1,Multiple Choice (select 1),Multiple Choice,"

Clare wants to mail a package that weighs 412 pounds. What could this weight be in kilograms?

",,,"

2.04

||

4.5

||

9.92

||

4,500

",

2.04

,14554 +PSBBMXK,1,Multiple Choice (select 1),Multiple Choice,"

A movie rating website has many people rate a new movie on a scale of 0 to 100. Here is a dot plot showing a random sample of 20 of these reviews.

+

 

+

+

 

+

Would the mean or median be a better measure for the center of this data?

",,,Median || Mean,Median,230527 +PSBDDG2,1,Multiple Choice (select 1),Multiple Choice,"

Suppose 45% of all the students at Andre’s school brought in a can of food to contribute to a canned food drive. Andre picks a representative sample of 25 students from the school and determines the sample’s percentage.

+

 

+

He expects the percentage for this sample will be 45%. Do you agree? 

+

 

",,,Yes || No,No,539325 +PSBMYW,1,Multiple Choice (select 1),Multiple Choice,"

A movie theater is showing three different movies. The dot plots represent the ages of the people who were at the Saturday afternoon showing of each of these movies.

+

+

 

+

One of these movies was an animated movie rated G for general audiences. Do you think it was movie A, B, or C?

",,,Movie A || Movie B || Movie C,Movie B,57030 +PSBBXQS,1,Multiple Choice (select all),Check All That Apply,

Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. 

,,,5 meters and 22 meters || 19 inches and 60 inches || 33 centimeters and 80 centimeters,19 inches and 60 inches,284643 +PRABFS5J,1,Multiple Choice (select all),Check All That Apply,"

Select the unit from the list that you would use to measure the object.

+

 

+

The weight or mass of a chalkboard or whiteboard

",,,centimeters || cups || feet || gallons || grams || inches || kilograms || kilometers || liters || meters || miles || milliliters || millimeters || ounces || pounds || quarts || tons || yards,kilograms || pounds,173917 +PRABQNEM,1,Multiple Choice (select 1),Multiple Choice,

Here are the dimensions of some rectangles. Which rectangle has an area of 12 square units and a perimeter of 14 units?

,,,a length of 1 units and a width of 12 units || a length of 6 units and a width of 1 unit || a length of 6 units and a width of 2 units || a length of 3 units and a width of 4 units,a length of 3 units and a width of 4 units,668776 +PSBCP3V,1,Multiple Choice (select 1),Multiple Choice,"

Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree with Lin? 

+

 

+

",,,I agree with Lin. || I do not agree with Lin. || Not enough information.,I agree with Lin.,417638 +PSBCBVV,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the quantity can be represented by a positive number or by a negative number. 

+

 

+

Tyler’s puppy gained 5 pounds.

",,,positive || negative,positive,353939 +PRABQP63,1,Multiple Choice (select all),Check All That Apply,"

Select all the numbers that are solutions to the equation x2=15.

",,,"

225

||

225

||

7.5

||

15

||

-15

","

15

||

-15

",315734 +PRABETPA,1,Multiple Choice (select all),Check All That Apply,"

The sales tax rate in New Mexico is 5.125%.  Select all the equations that represent the sales tax, t, you would pay in New Mexico for an item of cost c?

",,,"

t = 5.125c

||

t = 0.5125c

||

t = 0.05125c

||

t = c ÷ 0.05125

||

t = 5.125100c

","

t = 0.05125c

||

t = 5.125100c

",502720 +PSBCV8G,1,Multiple Choice (select 1),Multiple Choice,"

Are Figures A and B congruent? 

+

",,,Yes || No,No,452369 +PRABEVDJ,1,Multiple Choice (select all),Check All That Apply,

Select all the conditions for which it is possible to construct a triangle.

,,,"A triangle with angle measures 60°, 80°, and 80° || A triangle with side lengths 4 cm, 5 cm, and 6 cm || A triangle with side lengths 4 cm, 5 cm, and 15 cm || A triangle with side lengths 4 cm and 5 cm and a 50° angle || A triangle with angle measures 30° and 60°, and a 3 cm side length  ","A triangle with side lengths 4 cm, 5 cm, and 6 cm || A triangle with side lengths 4 cm and 5 cm and a 50° angle || A triangle with angle measures 30° and 60°, and a 3 cm side length  ",483519 +PSBBACU,1,Multiple Choice (select all),Check All That Apply,"

The manager of the concession stand keeps records of all of the supplies she buys and all of the items she sells. The table shows some of her records for Tuesday.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
itemquantityvalue in dollars
doughnuts-5837.70
straws3,000-10.35
hot dogs-3948.75
pizza13-116.87
apples-4014.00
french fries-88132.00
+

 

+

Which items did she sell? 

",,,doughnuts || straws || hot dogs || pizza || apples || french fries,doughnuts || hot dogs || apples || french fries,171270 +PRABPP7F,1,Multiple Choice (select 1),Multiple Choice,

Which expression is equivalent to 2(3x - 4)?

,,,3x - 4 || 5x - 6 || 6x - 4 || 6x - 8,6x - 8,195291 +PRABFG5R,1,Multiple Choice (select all),Check All That Apply,"

Here is a true statement -8.7 < -8.4.  Select all of the statements that are equivalent to -8.7 < -8.4.

",,,

-8.7 is further to the right on the number line than -8.4.

||

-8.7 is further to the left on the number line than -8.4.

||

-8.7 is less than -8.4.

||

-8.7 is greater than -8.4.

||

-8.4 is less than -8.7.

||

-8.4 is greater than -8.7.

,

-8.7 is further to the left on the number line than -8.4.

||

-8.7 is less than -8.4.

||

-8.4 is greater than -8.7.

,428161 +PRABE3GV,1,Multiple Choice (select all),Check All That Apply,

Which three of these parallelograms have the same area as each other?

,,,"

+

 

+

 

||

||

 

+

||

","

+

 

+

 

||

||

",503653 +PRABQXHZ,1,Multiple Choice (select 1),Multiple Choice,"

 

+

+

 

+

For the numbers a and b represented in the figure, which expression is equal to ?

",,,|a| + |b| || |a| - |b| || |b| - |a|,|b| - |a|,338572 +PRABP75T,1,Multiple Choice (select all),Check All That Apply,"

Salt and sugar give two distinctly different tastes, one salty and the other sweet. In a mixture of salt and sugar, it is possible for the mixture to be salty, sweet or both. Will any of these mixtures taste exactly the same?

",,,"Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture B: 1.5 cups water, 3 teaspoons salt, 0.2 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar || None of these mixtures taste the same.","Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar",48435 +PRABQNYX,1,Multiple Choice (select 1),Multiple Choice,

A circle has radius 40 cm. Which of these is closest to its area?

,,,"10,053 cm² || 5,026 cm² || 251 cm² || 126 cm²","5,026 cm²",26908 +PRABEPMA,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are equivalent to 38.

,,,"

324

||

83

||

3·3·3·3·3·3·3·3

||

342

||

363-2

||

36·102

","

324

||

3·3·3·3·3·3·3·3

||

342

||

363-2

",278747 +PSBYB5,4,Multiple Choice (select 1),Multiple Choice,

Are all of the possible outcomes equally likely?

,,,Yes || No,Yes,115545 +PSB6V2,2,Multiple Choice (select 1),Multiple Choice,

Did the average price of gas ever get below $2?

,,,Yes || No,Yes,152568 +PSBQG8,2,Multiple Choice (select 1),Multiple Choice,"

To represent , Elena drew another diagram. She also started by drawing 4 rectangles. She then replaced all 4 rectangles with 40 squares and crossed out 3 squares to represent subtraction of 0.03, leaving 37 squares in her diagram.

+

+

 

+

Is her diagram correct? Discuss your reasoning with a partner.

",,,Yes || No,Yes,70102 +PSBBKGB,1,Multiple Choice (select 1),Multiple Choice,

Triangle P has a base of 12 inches and a corresponding height of 8 inches. Triangle Q has a base of 15 inches and a corresponding height of 6.5 inches. Which triangle has a greater area? 

,,,Triangle P || Triangle Q,Triangle Q,222283 +PRABEDCQ,1,Multiple Choice (select 1),Multiple Choice,"

The linear model for some butterfly data is given by the equation y = 0.238x + 4.642. Which of the following best describes the slope of the model?

+

 

+

 

+

+
 
",,,"For every 1 mm the wingspan increases, the length of the butterfly increases 0.238 mm. || For every 1 mm the wingspan increases, the length of the butterfly increases 4.642 mm. || For every 1 mm the length of the butterfly increases, the wingspan increases 0.238 mm. || For every 1 mm the length of the butterfly increases, the wingspan increases 4.642 mm.","For every 1 mm the wingspan increases, the length of the butterfly increases 0.238 mm.",173897 +PRABQKVH,1,Multiple Choice (select 1),Multiple Choice,"

Andre used 412 sticks of butter to make multiple batches of brownies. The recipe calls for 34 of a stick of butter for each batch. How many batches did he make?

",,,"

6 batches

||

412 batches

||

338 batches

||

16 of a batch

",

6 batches

,518845 +PRABPUDC,1,Multiple Choice (select all),Check All That Apply,"

Lines CE and AD intersect at B.

+

+

Select all the true statements.

",,,The measure of angle CBA is equal to the measure of angle DBE. ||

The sum of the measures of angles CBA and DBE is 180 degrees.

|| The measure of angle CBD is equal to the measure of angle ABE. || The sum of the measures of angles CBD and CBA is 180 degrees. || The sum of the measures of angles CBA and DBE is 90 degrees.,The measure of angle CBA is equal to the measure of angle DBE. || The measure of angle CBD is equal to the measure of angle ABE. || The sum of the measures of angles CBD and CBA is 180 degrees.,544905 +PSBYKS,1,Multiple Choice (select 1),Multiple Choice,"

Which estimate is closest to the actual value of the expression? 

+

 

+

",,2,2 || 2.5 || 3,2.5,116703 +PSBW5U,3,Multiple Choice (select 1),Multiple Choice,"

For the situation, decide if it requires Noah to calculate surface area or volume. 

+

 

+

Noah is planning to use a box with a trapezoid base to hold modeling clay. He is unsure if the clay will all fit in the box.

",,,surface area || volume,volume,108867 +PRABQMAK,1,Multiple Choice (select 1),Multiple Choice,"

Mai biked 634 miles today, and Noah biked 412 miles. How many times the length of Noah’s bike ride was Mai’s bike ride?

",,,"

23 times as far

||

32 times as far

||

94 times as far

||

2438 times as far

","

32 times as far

",319507 +PRABEJDM,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements:

,,,"

28·29=217

||

82·92=722

||

82·92=724

||

28·29=417

","

28·29=217

||

82·92=722

",9879 +PRABFDGD,1,Multiple Choice (select 1),Multiple Choice,"

Which question can be represented by the equation  ? ·  18 = 3

",,,"

How many 3s are in 18?

||

What is 3 groups of 18?

||

How many 18s are in 3?

||

What is 18 of 3?

","

How many 18s are in 3?

",517428 +PSBU9U,1,Multiple Choice (select 1),Multiple Choice,"

Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster?

",,,Plane A || Plane B,Plane A,97062 +PRABQMFH,1,Multiple Choice (select 1),Multiple Choice,

Which expression is equal to 64? 

,,,"

10

||

24

||

46

||

6 · 6 · 6 · 6

",

6 · 6 · 6 · 6

,427314 +PSBBG,1,Multiple Choice (select 1),Multiple Choice,"

For the following pair of shapes, decide whether or not they are congruent. 

+

 

+

",,,"Yes, they are congruent || No, they are not congruent.","Yes, they are congruent",54 +PRABQP5U,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equal to 362·5.9.

",,,"361 · 6.9 || 3.62 · 5,900 || 36.2 · 59 || 36,200 · 0.059 || 0.362 · 0.0059","36.2 · 59 || 36,200 · 0.059",156407 +PSB76J,2,Multiple Choice (select 1),Multiple Choice,"

Jada has d dimes. She has more than 30 cents but less than a dollar.

+

 

+

Can d be 10?

",,,Yes || No,No,159146 +PSBH8S,4,Multiple Choice (select 1),Multiple Choice,

A four-year-old child is over 6 feet tall.

,,,impossible || unlikely || equally likely or unlikely || likely || certain,impossible || unlikely,42284 +PSBBD9R,2,Multiple Choice (select 1),Multiple Choice,

Which group shows greater variability?

,,,

Group A

|| group B,

Group A

,193337 +PSB5P,1,Multiple Choice (select 1),Multiple Choice,"

This is another diagram of an unbalanced hanger.

+
+

Andre writes the following inequality: c + p < s. Do you agree with his inequality?

",,,Yes || No,No,3858 +PRABD4TG,1,Multiple Choice (select 1),Multiple Choice,"

The point (-2, -3) is rotated 90 degrees counterclockwise using center (0, 0). What are the coordinates of the image?

",,,"

(-3,-2)

||

(-3,2)

||

(3,-2)

||

(3,2)

","

(3,-2)

",148617 +PRABD49X,1,Multiple Choice (select 1),Multiple Choice,"

The quadrilateral PQRS in the diagram is a parallelogram.

+

 

+

Let P'Q'R'S' be the image of PQRS after applying a dilation centered at a point O (not shown) with a scale factor of 3.

+

 

+

+

 

+

Which of the following is true?

",,,"P'Q' = PQ || P'Q' = 3PQ ||

PQ = 3P'Q'

||

P'Q' = 13PQ

",P'Q' = 3PQ,170317 +PSBCWTH,1,Multiple Choice (select 1),Multiple Choice,"

A circular lawn has a row of bricks around the edge. The diameter of the lawn is about 40 feet.

+

 

+

+

 

+

Which is the best estimate for the amount of grass in the lawn?

",,,"

125 feet

||

125 square feet

||

1,250 feet

||

1,250 square feet

","

1,250 square feet

",455884 +PSBDEVN,1,Multiple Choice (select 1),Multiple Choice,"

If you mix red and white paint in different ratios, you will get different shades of pink paint. If the ratios are equivalent, the shades of pink will be the same.

+

 

+
    +
  • +

    Mai mixed a batch of pink paint using 5 cups of red paint and 3 cups of white paint.

    +
    • +
+

 

+
    +
  • +

    Priya mixed another batch of pink paint using 7 cups of red paint and 4 cups of white paint.

    +
    • +
+

 

+

Are these two batches the same shade of pink?

",,,Yes || No,No,547864 +PRABEPK5,1,Multiple Choice (select 1),Multiple Choice,"

Evaluate (3.1×104) · (2×106). Choose the correct answer:

",,,"

5.1×1010

||

5.1×1024

||

6.2×1010

||

6.2×1024

","

6.2×1010

",278407 +PSBRVH,1,Multiple Choice (select 1),Multiple Choice,"

Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed.

+
    +
  • This graph shows how long, in minutes, it takes Runner #1 to run miles.
    • +
+

+
    +
  • The equation that relates Runner #2’s distance (in miles) with time (in minutes) is t = 8.5d.

    • +
  • Runner #3’s information is in the table:
    • +
+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
distance (miles)time (minutes)
218
436
654
872
1090
+



+

Which of the three runners has the fastest pace? 

",,,Runner #1 || Runner #2 || Runner #3,Runner #2,77471 +PSBWYC,1,Multiple Choice (select 1),Multiple Choice,"

A driver is traveling at a constant speed on Interstate 90 outside Chicago. If she traveled from Point A to Point B in 8 minutes, did she obey the speed limit of 55 miles per hour?

+

 

+

",,,Yes || No,No,107470 +PSBZWK,1,Multiple Choice (select 1),Multiple Choice,"

Choose the inequality that best matches the given situation.

+

 

+

The Garden Club is planting fruit trees in their school’s garden. There is one large tree that needs 5 pounds of fertilizer. The rest are newly planted trees that need 12 pound fertilizer each.

",,,"

25x+5≤12

||

12x+5≤25

||

12x+25≤5

||

5x+12≤25

","

12x+5≤25

",124074 +PRABESJW,1,Multiple Choice (select all),Check All That Apply,

Select all quantities that are proportional to the diagonal length of a square.

,,,

Area of a square

||

Perimeter of a square

||

Side length of a square

,

Perimeter of a square

||

Side length of a square

,123973 +PRABQPRP,1,Multiple Choice (select all),Check All That Apply,"

Clare created Figure A. Then she created Figure B by translating Triangle C and then translating Triangle D.

+

 

+

+

 

+

 

+

Select all the true statements.

",,,Figure A is congruent to Figure B || Figure B is a translation of Figure A. || Triangle C is congruent to Triangle C’. || Triangle D’ is congruent to Triangle D.,Triangle C is congruent to Triangle C’. || Triangle D’ is congruent to Triangle D.,504848 +PSBUC9,1,Multiple Choice (select 1),Multiple Choice,"

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

+

 

+

Will Mai and Clare complete a sign at the same time?

",,,Yes || No,Yes,90598 +PSBCEUM,1,Multiple Choice (select 1),Multiple Choice,"

Elena says that the thermometer shown here reads -2.5∘C because the line of the liquid is above -2∘C. Jada says that it is -1.5∘C.

+

 

+

Do you agree with either one of them? 

+

",,,Elena is correct || Jada is correct || Both are correct || Neither are correct,Jada is correct,371766 +PRABFFTG,1,Multiple Choice (select 1),Multiple Choice,

A bag of pennies weighs 5.1 kilograms. Each penny weighs 2.5 grams. About how many pennies are in the bag?

,,,"

20

||

200

||

2,000

||

20,000

","

2,000

",132787 +PSB3YT,1,Multiple Choice (select 1),Multiple Choice,"

Decide if the response will produce numerical data or categorical data.

+

 

+

What is your favorite breakfast food?

",,,Categorical || Numerical,Categorical,136119 +PRABD4S8,1,Multiple Choice (select all),Check All That Apply,

Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

,,,6 cm by 1.5 cm || 10 cm by 2 cm || 13 cm by 4 cm || 18 cm by 4.5 cm || 80 cm by 20 cm,6 cm by 1.5 cm || 18 cm by 4.5 cm || 80 cm by 20 cm,24106 +PSBBMSP,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

",,0,True || False,FALSE,229909 +PSB27N,1,Multiple Choice (select all),Check All That Apply,

Which of these solids are prisms? 

,,,"

||

||

||

||

||

","

||

||

||

",131558 +PSBBU49,2,Multiple Choice (select 1),Multiple Choice,"

Are 4x and 15+x equivalent expressions?

",,,Yes || No,No,270175 +PRABE57J,1,Multiple Choice (select 1),Multiple Choice,

Which figure has a greater surface area?

,,,"

||

|| They have the same surface area. || The answer cannot be determined.",They have the same surface area.,274073 +PRABPQDZ,1,Multiple Choice (select all),Check All That Apply,

Select all of the data sets for which you would use the mean to describe the center of the data.

,,,"

||

||

blue, red, blue, yellow, blue

||

||

71, 73, 75, 72, 78, 79, 70

","

||

||

71, 73, 75, 72, 78, 79, 70

",99379 +PRABET85,1,Multiple Choice (select 1),Multiple Choice,

Which inequality is true when the value of x is -3?

,,,-x − 6 < -3.5 || -x − 6 > 3.5 || -x − 6 > -3.5 || x − 6 > -3.5,-x − 6 > -3.5,347843 +PRABEU6Z,1,Multiple Choice (select all),Check All That Apply,"

Select all expressions that can be subtracted from 9x to result in the expression 3x+5.

",,,-5 + 6x || 5 - 6x || 6x + 5 || 6x - 5 || -6x + 5,-5 + 6x || 6x - 5,277069 +PSBBMJW,1,Multiple Choice (select 1),Multiple Choice,

A shopper needs 24 sandwich rolls. The store sells identical rolls in 2 differently sized packages. They sell a six-pack for $5.28 and a four-pack for $3.40. Should the shopper buy 4 six-packs or 6 four-packs?

,,,4 six-packs || 6 four-packs,6 four-packs,228746 +PSBN8P,1,Multiple Choice (select 1),Multiple Choice,"
+
+
+
+
+

Jada and Priya are trying to solve the equation 23 + x = 4.


+
    +
  • +

    Jada says, ""I think we should multiply each side by 32 because that is the reciprocal of 23.""

    +
    • +
  • +

    Priya says, ""I think we should add -23 to each side because that is the opposite of 23.""



    +
    • +
+

Which person's strategy should they use?

+
+
+
+
+
",,,Priya || Jada,Priya,63357 +PSBB2TW,1,Multiple Choice (select 1),Multiple Choice,"

For the inequality, decide whether the solution is represented by x < 4.5 or x > 4.5.

+

 

+

-24 > -6(x − 0.5)

+
 
",,,x < 4.5 || x > 4.5,x > 4.5,302140 +PRABQP44,1,Multiple Choice (select 1),Multiple Choice,"

A sphere has a volume of 972πcm3. What is its radius in centimeters? 

",,9,4.5 || 9 || 11 || 18,9,348910 +PSBED,1,Multiple Choice (select 1),Multiple Choice,"
+
+

Two cylinders, a and b, each started with different amounts of water.

+

 

+

The graph shows how the height of the water changed as the volume of water increased in each cylinder.

+

 

+

Which cylinder has the larger radius?

+

 

+
+
+
+
+

+
+
+
 
",,,

Cylinder a

||

Cylinder b

,

Cylinder b

,488 +PRABESJ8,1,Multiple Choice (select all),Check All That Apply,"

The point 3, 65 lies on the graph representing a proportional relationship. Which of the following points also lie on the same graph? Select all that apply.

",,,"

(1, 0.4)

||

1.5, 610

||

65, 3

||

4, 115

||

(15, 6)

","

(1, 0.4)

||

1.5, 610

||

(15, 6)

",296114 +PSBUC9,3,Multiple Choice (select 1),Multiple Choice,"

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

+

 

+

Will Mai and Noah complete a sign at the same time? 

",,,Yes || No,Yes,90903 +PRABFJZD,1,Multiple Choice (select 1),Multiple Choice,"

A corn field has an area of 28.6 acres. It requires about 15,000,000 gallons of water. About how many gallons of water per acre is that?

",,,"

5,000

||

50,000

||

500,000

||

5,000,000

","

500,000

",63719 +PRABQK7Q,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations represented by this tape diagram.

+

 

+

",,,2.5 + ? = 3.8 || 3.8 = ? + 2.5 || 3.8 - 2.5 = ? || 3.8 + 2.5 = ? || ? - 2.5 = 3.8,2.5 + ? = 3.8 || 3.8 = ? + 2.5 || 3.8 - 2.5 = ?,299700 +PRABEUGF,1,Multiple Choice (select all),Check All That Apply,"

M is a point on line segment KL. NM is a line segment. Select all the equations that represent the relationship between the measures of the angles in the figure.

+

 

+

",,,a = b || a + b = 90 || b = 90 - a || a + b = 180 || 180 - a = b || 180 = b - a,a + b = 180 || 180 - a = b,189053 +PRABQJTA,1,Multiple Choice (select all),Check All That Apply,

Select all the parallelograms that have an area of 12 square units.

,,,"

||

||

||

||

","

||

||

",383961 +PSBB4EW,1,Multiple Choice (select 1),Multiple Choice,"

Elena drank 3 liters of water yesterday. Jada drank 34 times as much water as Elena. Lin drank twice as much water as Jada.

+

 

+

 

+

Did Jada drink more or less water than Elena?

+

 

",,,More || Less,Less,311102 +PRABEPD8,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are equivalent to 4-3.

,,," + + + + + +
-12
|| + + + + + +
2-6
||

143

||

14·14·14

||

12

||

(-4)·(-4)·(-4)

||

8-122

"," + + + + + +
2-6
||

143

||

14·14·14

",105610 +PRABQK7Y,1,Multiple Choice (select 1),Multiple Choice,"

Which equation matches the hanger diagram?

+

",,,"

x · x · x = 1 · 1 · 1 · 1

||

x = 34

||

3x = 4

||

x + 1 = 4

",

3x = 4

,56614 +PSB724,3,Multiple Choice (select 1),Multiple Choice,

Which data set has greater spread? 

,,,Sixth-grade students || Seventh-grade students,Sixth-grade students,158585 +PRABQP6E,1,Multiple Choice (select 1),Multiple Choice,"

Which is closest to the quotient 2,967 ÷ 0.003?

",,,"1,000 || 10,000 || 100,000 || 1,000,000","1,000,000",505947 +PSBBTX3,1,Multiple Choice (select 1),Multiple Choice,"

Here are the approximate populations of three countries, expressed in scientific notation: Panama: 4 × 106; Peru: 3.2 × 107; Thailand: 7 × 107.

+

 

+

Lin says that more than 20 times as many people live in Thailand than in Panama. Is this correct?

",,,Yes || No,No,262979 +PRABHUKJ,1,Multiple Choice (select 1),Multiple Choice,"

Without solving, identify whether this equation has a solution that is positive, negative, or zero:

+

 

+

3x - 5 = -3

",,,

Positive

||

Negative

||

Zero

,

Positive

,190961 +PRABG2WG,1,Multiple Choice (select 1),Multiple Choice,"

True or false?

+

 

+

",,1,True || False,TRUE,348936 +PSBS86,2,Multiple Choice (select all),Check All That Apply,"

+

 

+

Which rectangles have the same perimeter as Rectangle R but different area?

",,,Rectangle A. || Rectangle B. || Rectangle C. || Rectangle D. || Rectangle E. || Rectangle F.,Rectangle D. || Rectangle F.,85142 +PRABFDG5,1,Multiple Choice (select 1),Multiple Choice,"

Andre is walking from home to a festival that is 158 kilometers away. He takes a quick rest after walking 13 kilometers.

+

 

+

In this situation, which question can be represented by the equation: 

+

?⋅158=13?

",,,What fraction of the trip has Andre completed? || How many more kilometers does he have to walk to get to the festival? || What fraction of the trip is left? || How many kilometers is it from home to the festival and back home?,What fraction of the trip has Andre completed?,184060 +PRABEQCP,1,Multiple Choice (select 1),Multiple Choice,"

A line contains the point (3, 5). If the line has negative slope, which of these points could also be on the line?

",,,"

(2, 0)

||

(4, 7)

||

(5, 4)

||

(6, 5)

","

(5, 4)

",487616 +PSBDVZB,1,Multiple Choice (select 1),Multiple Choice,"

The Empire State Building in New York City is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the Empire State Building on an 812-inch-by-11-inch piece of paper. Select a scale that you think is the most appropriate for the scale drawing.

+

 

",,,

1 inch to 1 foot

||

1  inch to 100 feet

||

1  inch to 1 mile

||

1  centimeter to 1 meter

||

1 centimeter to 50 meters

||

1  centimeter to 1 kilometer

,

1 centimeter to 50 meters

,628100 +PSB2SG,1,Multiple Choice (select 1),Multiple Choice,"

An equilateral triangle’s angles each have a measure of 60 degrees.

+

 

+

Can you put copies of an equilateral triangle together to form a straight angle?

",,,Yes || No,Yes,128818 +PRABHRJV,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that represent the large rectangle's total area.

+

 

+

",,,3(5 + b) || 5(b + 3) || 5b + 15 || 15 + 5b || 3 · 5 + 3b,5(b + 3) || 5b + 15 || 15 + 5b,69182 +PSB75H,1,Multiple Choice (select 1),Multiple Choice,

Which one of these relationships is different than the other three? 

,,,"

||

||

||

","

",159061 +PRABQPK3,1,Multiple Choice (select 1),Multiple Choice,"

In which pair of figures can Figure A be taken to Figure B by a rotation?

+

 

+

",,,Pair 1 || Pair 2 || Pair 3 || Pair 4,Pair 3,275383 +PRABQKJG,1,Multiple Choice (select 1),Multiple Choice,"

A mixture of orange paint contains 8 teaspoons of red paint and 12 teaspoons of yellow paint. To make the same shade of orange paint using 18 teaspoons of red paint, how much yellow paint would you need? Use the double number line diagram to help if needed. 

+

 

+

",,,27 teaspoons || 24 teaspoons || 22 teaspoons || 12 teaspoons,27 teaspoons,2433 +PSBDH8V,1,Multiple Choice (select 1),Multiple Choice,"

Your teacher will give your group several pairs of triangles. Each group member should take 1 or 2 pairs. 

+

 

+ + + + + + + + + + + + + + + +
+

 

+

Which pair(s) of triangles do you have? 

",,,P || Q || R || S || T || U || V || W,P || Q || R || S || T || U || V || W,566156 +PRABE9HG,1,Multiple Choice (select all),Check All That Apply,

Diego makes green paint by mixing 10 tablespoons of yellow paint and 2 tablespoons of blue paint. Which of these mixtures produce the same shade of green paint as Diego’s mixture? Select all that apply.

,,,"
+

For every 5 tablespoons of blue paint, mix in 1 tablespoon of yellow paint.

+
||

Mix tablespoons of blue paint and yellow paint in the ratio 1:5.

||

Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.

||

Mix 11 tablespoons of yellow paint and 3 tablespoons of blue paint.

||

For every tablespoon of blue paint, mix in 5 tablespoons of yellow paint.

","

Mix tablespoons of blue paint and yellow paint in the ratio 1:5.

||

Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.

||

For every tablespoon of blue paint, mix in 5 tablespoons of yellow paint.

",373794 +PRABHAAH,1,Multiple Choice (select 1),Multiple Choice,"

A circular field is set into a square with an 800 m side length. Estimate the field's area.

+

 

+

+
 
",,,"About 5,000 m² || About 50,000 m² || About 500,000 m² || About 5,000,000 m² || About 50,000,000 m²","About 500,000 m²",7396 +PSBBCQT,4,Multiple Choice (select 1),Multiple Choice,"

Is (9, 11) also on the line?

+

",,,Yes || No,Yes,184584 +PSBBMG6,5,Multiple Choice (select 1),Multiple Choice,"

Kiran started his homework before 7:00 p.m. and finished his homework after 8:00 p.m. Let h represent the number of hours Kiran worked on his homework.

+

 

+

Decide if the statement it is definitely true, definitely not true, or possibly true.

+

 

+

h<1

",,,Definitely True || Definitely Not True || Possibly True,Definitely Not True,228072 +PRABEVTC,1,Multiple Choice (select all),Check All That Apply,"

Select all the functions whose graphs include the point (16, 4).

",,,"

y=2x

||

y=x2

||

y=x+12

||

y=x-12

||

y=14x

","

y=x-12

||

y=14x

",340198 +PRABP8EV,1,Multiple Choice (select 1),Multiple Choice,"

In many countries, the standard paper size is not 8.5 inches by 11 inches (called “letter” size), but instead 210 millimeters by 297 millimeters (called “A4” size). Are these two rectangle sizes scaled copies of one another?

",,,Yes || No,No,81610 +PRABQJS8,1,Multiple Choice (select 1),Multiple Choice,"

What is the area of this parallelogram?

+

 

+

+
 
",,,30 cm² || 24 cm² || 22 cm² || 12 cm²,24 cm²,383708 +PSBX69,5,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

x=0 is a solution of the equation for line n.

",,0,True || False,FALSE,113562 +PRABHS2G,1,Multiple Choice (select all),Check All That Apply,"

Andre collected data measured in centimeters.

+

 

+ + + + + + + + + + + + + + + + + +
8.510.57.89.58.19.010.29.611.210.912.79.8
+

 

+

What could he be investigating? Select all that apply.

",,,

The weight of a dozen eggs.

||

The length of leaves from a tree.

||

The height of cups and mugs in a cupboard.

||

The length of songs on a music CD.

||

The length of colored pencils in a box.

,

The length of leaves from a tree.

||

The height of cups and mugs in a cupboard.

||

The length of colored pencils in a box.

,339343 +PRABEE27,1,Multiple Choice (select 1),Multiple Choice,"

Here are two points: (-3,4), (1,7). What is the slope of the line between them?

",,,"

43

||

34

||

16

||

23

","

34

",306325 +PRABFEZH,1,Multiple Choice (select all),Check All That Apply,

Select all the triangles that have an area of 30 square units.

,,,"

||

||

||

||

","

||

",55302 +PRABE3F4,1,Multiple Choice (select 1),Multiple Choice,"

Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure.

+

 

+
+
+
+
+

How does the area of her new figure compare with that of the original square? 

+

 

+

+
+
+
+
",,,The area of the new figure is greater. || The two figures have the same area. || The area of the original square is greater. || We don't know because neither the side length nor the area of the original square is known.,The two figures have the same area.,346945 +PSBCSH,1,Multiple Choice (select all),Check All That Apply,"

Here is an original drawing of the letter F and some other drawings.

+

 

+

+

 

+

Identify all the drawings that are scaled copies of the original letter F.  

",,,Drawing 1 || Drawing 2 || Drawing 3 || Drawing 4 || Drawing 5 || Drawing 6 || Drawing 7,Drawing 1 || Drawing 2 || Drawing 7,12898 +PSBVEV,2,Multiple Choice (select 1),Multiple Choice,

Which class had greater variability in the results?

,,,Class A || Class B,Class A,98346 +PRABD4TK,1,Multiple Choice (select 1),Multiple Choice,

Which of these sets of angle measures could be the three angles in a triangle?

,,,"40°, 50°, 60° || 50°, 60°, 70° || 60°, 70°, 80° || 70°, 80°, 90°","50°, 60°, 70°",24916 +PSBJKQ,1,Multiple Choice (select 1),Multiple Choice,"

Priya says that 13 · 13 · 13 · 13 = 43.  Do you agree with Priya? 

",,,Agree || Disagree,Disagree,44696 +PSBW5U,1,Multiple Choice (select 1),Multiple Choice,"

For the situation, decide if it requires Noah to calculate surface area or volume. 

+

 

+

Noah is planning to paint the bird house he built. He is unsure if he has enough paint.

",,,

Surface area

||

Volume

,

Surface area

,108650 +PSBBZPR,2,Multiple Choice (select 1),Multiple Choice,

Is there a linear relationship between height and volume? 

,,,Yes || No,Yes,296303 +PSBSA9,1,Multiple Choice (select 1),Multiple Choice,"

Two TV shows each asked 100 viewers for their ages. For one show, the mean age of the viewers was 35 years and the MAD was 20 years. For the other show, the mean age of the viewers was 30 years and the MAD was 5 years.

+

 

+

A sixth-grade student says he watches one of the shows. Which show do you think he watches?

",,,The first show || The second show,The first show,79667 +PRABHGF9,1,Multiple Choice (select all),Check All That Apply,"

Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.

+

",,,"Translate (-3,0) to (1,2). || Translate (2,1) to (-2,-1). || Translate (-4,-3) to (0,-1). || Translate (1,2) to (2,1).","Translate (-3,0) to (1,2). || Translate (-4,-3) to (0,-1).",137959 +PSBBE6C,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that describe the situation and then find the solution.

+

 

+

Han's house is 450 meters from school. Lin’s house is 135 meters closer to school. How far is Lin’s house from school?

+

 

",,,"

z = 450  + 135

||

z = 450 - 135

||

z - 135 = 450

||

z + 135 = 450

","

z = 450 - 135

||

z + 135 = 450

",198295 +PRABE52K,1,Multiple Choice (select all),Check All That Apply,

Select all drawings in which a corresponding height h for a given base b is correctly identified.

,,,"

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

","

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

",420787 +PSBH8S,3,Multiple Choice (select 1),Multiple Choice,

You will get an even number when you roll a standard number cube.

,,,impossible || unlikely || equally likely as not || likely || certain,equally likely as not,42186 +PSBC9Y8,2,Multiple Choice (select 1),Multiple Choice,"

If these numbers represent temperatures in degrees Celsius, which is the coldest?

",,,"

7

||

-3

||

12

||

-0.8

||

0.8

||

-110

||

-2

",

-3

,518599 +PSBDSR,1,Multiple Choice (select 1),Multiple Choice,"

Jada says, “I can tell that  equals 0 just by looking at it.” Is Jada correct?

",,,Yes || No,Yes,18664 +PSBN6A,2,Multiple Choice (select 1),Multiple Choice,"

The x-axis represents the number of hours before or after noon, and the y-axis represents the temperature in degrees Celsius.

+

 

+

+

 

+

At 11 a.m., it was 10°C. In what quadrant would this point be plotted?

+

 

",,,Quadrant I || Quadrant II || Quadrant III || Quadrant IV,Quadrant II,63205 +PSBEF3,1,Multiple Choice (select 1),Multiple Choice,"

When you add the distances of Mercury, Venus, Earth, and Mars from the Sun, would you reach as far as Jupiter?

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
objectdiameter (km)distance from the Sun (km)
Sun
Mercury
Venus
Earth
Mars
Jupiter
",,,Yes || No,No,22352 +PRABEVT5,1,Multiple Choice (select 1),Multiple Choice,"

Here is a scatter plot:

+

 

+

+

 

+

The graph of what linear equation is a good fit for this data?

",,,"

y=-13x+2

|| + + + + + +
+

y=-13x+6

+
||

y=13x+2

||

y=13x+6

","

y=-13x+2

",636416 +PSBBFG5,2,Multiple Choice (select 1),Multiple Choice,

What kind of data—categorical or numerical—do you think the variable “birth month” produces? 

,,,categorical || numerical,categorical,200269 +PRABQTD7,1,Multiple Choice (select 1),Multiple Choice,"

Andre rode his bike at a constant speed. He rode 1 mile in 5 minutes.

+

 

+

Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?

",,,"

t = 5d

||

t = 15d

||

t = d + 4

||

t = d − 4

","

t = 5d

",531136 +PSBJS4,1,Multiple Choice (select 1),Multiple Choice,"

The graph shows the temperature between noon and midnight in one day in a certain city.

+

 

+

+

 

+

Was it warmer at 3:00 p.m. or 9:00 p.m.?

",,,3:00 p.m. || 9:00 p.m. || Neither,9:00 p.m.,45204 +PSBZZQ,1,Multiple Choice (select 1),Multiple Choice,"

Choose the inequality that best matches the given situation.

+

 

+

The Hiking Club is on a hike down a cliff. They begin at an elevation of 12 feet and descend at the rate of 3 feet per minute.

",,,"

37x-3≥12

||

3x-37≥12

||

12-3x≥-37

||

12x-37≥-3

","

12-3x≥-37

",124637 +PSBV9Y,1,Multiple Choice (select 1),Multiple Choice,"

Kiran wants to know which three summer sports are most popular in his class. He surveyed his classmates on their favorite summer sport and collected these responses:

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
swimminggymnasticstrack and fieldvolleyball
swimmingswimmingdivingtrack and field
gymnasticsbasketballbasketballvolleyball
track and fieldtrack and fieldvolleyballgymnastics
divinggymnasticsvolleyballrowing
track and fieldtrack and fieldsoccerswimming
gymnasticstrack and fieldswimmingrowing
divingsoccer  
+

 

+

Did Kiran collect categorical or numerical data?

",,,categorical data || numerical data,categorical data,102850 +PSBBVTQ,1,Multiple Choice (select 1),Multiple Choice,"

Here are dot plots showing how long Diego’s trips to school took in minutes—which you studied earlier—and how long Andre’s trips to school took in minutes. The dot plots include the means for each data set, marked by triangles.

+

 

+

+

 

+

Which of the two data sets has a larger mean? 

+
 
",,,Diego's data set || Andre's data set,Andre's data set,274025 +PRABQPK4,1,Multiple Choice (select all),Check All That Apply,"

Select all the pairs where Figure H is the image of Figure G after a reflection, rotation, or translation.

",,,"

||

||

||

||

||

","

||

||

||

",275536 +PSBEZS,1,Multiple Choice (select 1),Multiple Choice,"

Is the equation true or false?

+

 

+

 

",,1,True || False,TRUE,25543 +PSBB8CU,1,Multiple Choice (select 1),Multiple Choice,

Elena said the equation 9x + 15 = 3x + 15 has no solutions because 9x is greater than 3x. Do you agree with Elena?

,,,Yes || No,No,333395 +PSBXSP,3,Multiple Choice (select 1),Multiple Choice,

Which of these is the solution to the equation?

,,5,2 || 3 || 5 || 7 || n,5,112678 +PSBFXY,1,Multiple Choice (select 1),Multiple Choice,"

Is there a rigid transformation taking Rhombus P to Rhombus Q? 

+

 

+

",,,Yes || No || Not enough information,No,30522 +PSBBMG6,7,Multiple Choice (select 1),Multiple Choice,"

Kiran started his homework before 7:00 p.m. and finished his homework after 8:00 p.m. Let h represent the number of hours Kiran worked on his homework.

+

 

+

Decide if the statement it is definitely true, definitely not true, or possibly true.

+

 

+

h<2

",,,Definitely True || Definitely Not True || Possibly True,Possibly True,228382 +PRABQJVG,1,Multiple Choice (select 1),Multiple Choice,"

For a cube whose side length is 4 inches, the expression could represent . . .

",,,"The length of 3 cubes lined up, in inches || The cube’s surface area in square inches || The cube’s volume in cubic inches || The total volume of 3 cubes, in cubic inches",The cube’s volume in cubic inches,503038 +PSB47G,1,Multiple Choice (select 1),Multiple Choice,"

To find 40% of 75, Priya calculates 25 · 75. Does her calculation give the correct value for 40% of 75?

",,,Yes || No,Yes,142840 +PSBBWRS,2,Multiple Choice (select 1),Multiple Choice,

Is there a proportional relationship between the area and perimeter of a square?

,,,Yes || No,No,278886 +PRABEUHG,1,Multiple Choice (select all),Check All That Apply,

Select all the sets of three side lengths that will make a triangle.

,,,"

3, 4, 8

||

7, 6, 12

||

5, 11, 13

||

4, 6, 12

||

4, 6, 10

","

7, 6, 12

||

5, 11, 13

",264186 +PSBC2VP,1,Multiple Choice (select 1),Multiple Choice,"

Two students are working on the same problem:

+

 

+

A juice box has 20% more juice in its new packaging. The original packaging held 12 fluid ounces. How much juice does the new packaging hold?

+

 

+ + + + + + + + + + + + + + + +
+
    +
  • Here is how Priya set up her double number line. 
    • +
+
+
    +
  • Here is how Clare set up her double number line. 
    • +
+
+

 

+

Do you agree with either of them?

",,,Agree with Priya || Agree with Clare || Agree with Both || Agree with Neither,Agree with Priya,478570 +PSBBBT9,1,Multiple Choice (select 1),Multiple Choice,"

An ecologist is studying a forest with a mixture of tree types. Since the average tree height in the area is 40 feet, he measures the height of the tree against that. He also records the type of tree. The results are shown in the table and segmented bar graph.

+

 

+

Is there evidence of an association between tree height and tree type? 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
 under 40 feet40 feet or tallertotal
deciduous453075
evergreen141024
total594099
+

 

+

",,,Yes || No,No,179563 +PSBBAC3,1,Multiple Choice (select 1),Multiple Choice,"

There are 2.54 cm in an inch, 12 inches in a foot, and 5,280 feet in a mile. Which expression gives the number of centimeters in a mile?

",,,"

2.5412·5,280

||

5,280·12·(2.54)

||

15,280·12·(2.54)

||

5,280+12+2.54

||

5,280·122.54

","

5,280·12·(2.54)

",171627 +PRABEWD6,1,Multiple Choice (select all),Check All That Apply,

Select all the reasons why random samples are preferred over other methods of getting a sample.

,,,"If you select a random sample, you can determine how many people you want in the sample. || A random sample is always the easiest way to select a sample from a population. || A random sample is likely to give you a sample that is representative of the population. || A random sample is a fair way to select a sample, because each person in the population has an equal chance of being selected. || If you use a random sample, the sample mean will always be the same as the population mean.","A random sample is likely to give you a sample that is representative of the population. || A random sample is a fair way to select a sample, because each person in the population has an equal chance of being selected.",309627 +PSBBBMY,1,Multiple Choice (select 1),Multiple Choice,"

Tyler claims that if two triangles each have a side length of 11 units and a side length of 8 units, and also an angle measuring 100 degrees, they must be identical to each other. Do you agree?

",,,Yes || No,No,178225 +PRABEAUM,1,Multiple Choice (select all),Check All That Apply,"

Select all of the ordered pairs (x, y) that are solutions to the linear equation 2x + 3y = 6.

+
 
",,,"

(0, 2)

||

(0, 6)

||

(2, 3)

||

(3, -2)

||

(3, 0)

||

(6, -2)

","

(0, 2)

||

(3, 0)

||

(6, -2)

",579648 +PSBBAK8,1,Multiple Choice (select all),Check All That Apply,

Which of these pairs of quantities are proportional to each other? 

,,,

Radius and diameter of a circle

||

Radius and circumference of a circle

||

Radius and area of a circle

||

Diameter and circumference of a circle

||

Diameter and area of a circle

,

Radius and diameter of a circle

||

Radius and circumference of a circle

||

Diameter and circumference of a circle

,172163 +PRABQPMT,1,Multiple Choice (select 1),Multiple Choice,"

This hanger is in balance. There are two labeled weights of 8 grams and 20 grams. The four circles each have the same weight.

+

 

+

+

 

+

What is the weight of each circle, in grams?

",,,"

3

||

7

||

5

||

2012

",

3

,90063 +PSBBK5S,1,Multiple Choice (select 1),Multiple Choice,"

Can the following net be assembled into a cube?

+

 

+

+
 
",,,Yes || No,No,226302 +PRABEQCH,1,Multiple Choice (select all),Check All That Apply,

Select all the sets that are the three side lengths of right triangles.

,,,"

8, 7, 15

||

4, 10, 84

||

8, 11, 129

||

1, 2, 3

","

4, 10, 84

||

8, 11, 129

||

1, 2, 3

",487468 +PSBBA5P,3,Multiple Choice (select 1),Multiple Choice,

Could 60 be a value of s?

,,,Yes || No,Yes,175861 +PSB347,5,Multiple Choice (select 1),Multiple Choice,

Is the graph of this function a line?

,,,Yes || No,No,137062 +PRABQMXG,1,Multiple Choice (select 1),Multiple Choice,

Lin’s family has completed 60% of a trip. They have traveled 30 miles. How long is the whole trip?

,,,50 miles || 48 miles || 30 miles || 18 miles,50 miles,3852 +PSB34B,1,Multiple Choice (select 1),Multiple Choice,"

Decide if the responses will produce numerical data or categorical data.

+

 

+

How many different teachers do you have?

",,,Categorical || Numerical,Numerical,136895 +PRABFEXP,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that give the area of the figure in square units.

+

",,,(5 + 6) × (3 + 2) || (8 × 6) − (3 × 4) || 6 × 8 × 2 × 3 × 4 × 5 || (5 × 6) + (3 × 2) || 8 × 6,(8 × 6) − (3 × 4) || (5 × 6) + (3 × 2),103748 +PSBQ3W,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that describe the situation.

+

 

+

Kiran’s backpack weighs 3 pounds less than Clare’s backpack. Clare’s backpack weighs 14 pounds. How much does Kiran’s backpack weigh?

+

 

",,,"

x + 3 = 14

||

3x = 14

||

x = 14 - 3

||

x = 14 ÷ 3

","

x + 3 = 14

||

x = 14 - 3

",73275 +PSBBGSF,1,Multiple Choice (select 1),Multiple Choice,"

Two trains are traveling at constant speeds on different tracks.

+

 

+

+

 

+
+

Which train is traveling faster?

+
",,,Train A || Train B,Train B,207470 +PRABUZ72,1,Multiple Choice (select all),Check All That Apply,"

The basketball coach says that based on Noah's free throws this season, Noah has a  probability of making each free throw. Select all the ways Noah could accurately simulate the number of free throws he will make in his next 6 attempts.

",,,"Flip a coin 6 times. Count the number of heads. || Make a spinner with 6 equally-sized sections, labeled with the numbers 1 through 6. Spin the spinner 6 times and count how many times the spinner lands on 3 or 4. || Put 3 red chips and 1 white chip in a bag. Draw a chip from the bag, record the result, and put it back in the bag. Do this 6 times and count the number of red chips drawn. || Make a spinner with 4 equally-sized sections. Color three sections green and one sections red. Spin the spinner 6 times and count the number of times the spinner lands on green. || Put the numbers 1 through 6 in a bag. Pick a number from the bag.","Put 3 red chips and 1 white chip in a bag. Draw a chip from the bag, record the result, and put it back in the bag. Do this 6 times and count the number of red chips drawn. || Make a spinner with 4 equally-sized sections. Color three sections green and one sections red. Spin the spinner 6 times and count the number of times the spinner lands on green.",350066 +PSBBX33,1,Multiple Choice (select 1),Multiple Choice,"

Can side d be the base of the triangle?

+

",,,Yes || No,Yes,286898 +PSBCN3V,2,Multiple Choice (select 1),Multiple Choice,

 Will a scale drawing where 1 cm represents 2 m be larger or smaller than this drawing?

,,,Larger || Smaller,Smaller,411000 +PSBC2H,2,Multiple Choice (select 1),Multiple Choice,"

The graph shows the temperature between noon and midnight in City A on a certain day.

+

 

+

+

 

+

The table shows the temperature, T, in degrees Fahrenheit, for h hours after noon, in City B.

+

 

+ + + + + + + + + + + + + + + + + + + + + +
h123456
T827875625859
+

 

+

Which city had a bigger change in temperature between 1:00 p.m. and 5:00 p.m.?

",,,City A || City B || Neither,City B,14654 +PSB7PK,2,Multiple Choice (select 1),Multiple Choice,"

Some T-shirts cost $8 each.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
xy
18
216
324
432
540
648
+

 

+

Is there a proportional relationship between x and y?

",,,Yes || No,Yes,156721 +PSBFGV,1,Multiple Choice (select 1),Multiple Choice,

Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? 

,,,

Store X: 4 cans for $2.48

||

Store Y: 5 cans for $3.00

||

Store Z: 59 cents per can

,

Store Z: 59 cents per can

,28051 +PRABEVTM,1,Multiple Choice (select 1),Multiple Choice,

A cylinder has volume 78 cm3. What is the volume of a cone with the same radius and height?

,,,26 cm³ || 39 cm³ || 156 cm³ || 234 cm³,26 cm³,596207 +PSBKVS,1,Multiple Choice (select 1),Multiple Choice,"

The likelihood that Han makes a free throw in basketball is 60%. The likelihood that he makes a 3-point shot is 0.345. Which event is more likely, Han making a free throw or making a 3-point shot?

",,,Han making a free throw || Han making a 3-point shot,Han making a free throw,51025 +PRABQPSJ,1,Multiple Choice (select 1),Multiple Choice,"

Han’s teacher asked him to draw a polygon similar to polygon A. Here is his work. Which explanation shows that polygons A and C are similar to each other?

+

 

+

",,,"Use a protractor to measure all four angles in polygon A and all four angles in polygon C. Since each angle in polygon A has a matching angle measure in polygon C, the polygons are similar. || Since each side in polygon C is three times as long as the corresponding side in polygon A, the figures are similar. || Dilate polygon C with center at the upper-left vertex and a scale factor of 1/3. Then, translate 7 units to the left. Since polygon C can be taken to polygon A with a dilation followed by a translation, the figures are similar. || Dilate polygon C with center at the upper-right corner and a scale factor of 3. Since polygon C can be taken to polygon A with a dilation, the polygons are similar.","Dilate polygon C with center at the upper-left vertex and a scale factor of 1/3. Then, translate 7 units to the left. Since polygon C can be taken to polygon A with a dilation followed by a translation, the figures are similar.",28093 +PRABFEXQ,1,Multiple Choice (select 1),Multiple Choice,"

Each small square in the graph paper represents 1 square unit.

+

 

+

Which expression is closest to the area of the rectangle, in square units?

+

",,,"

5 12 × 4 14

||

4 12 × 3 14

||

4 × 3

||

5 × 4

","

4 12 × 3 14

",103860 +PRABFG56,1,Multiple Choice (select all),Check All That Apply,"

Select all of the numbers that are greater than -5.

",,,"

1.3

||

-6

||

-12

||

17

||

-1

||

-4

","

1.3

||

17

||

-1

||

-4

",356660 +PRABD45B,1,Multiple Choice (select 1),Multiple Choice,"

In which pair of figures can Figure A be taken to Figure B by a rotation?

+

 

+

",,,Pair 1 || Pair 2 || Pair 3 || Pair 4,Pair 1,40911 +PSBC9Y8,3,Multiple Choice (select 1),Multiple Choice,"

If these numbers represent elevations in meters, which is the farthest away from sea level?

",,,"

7

||

-3

||

12

||

-0.8

||

0.8

||

-110

||

-2

","

7

",518807 +PRABP756,1,Multiple Choice (select all),Check All That Apply,"

Here are three problems. Select all problems that can be solved using division.

+

 

+

 

+

 

",,,"

Jada cut 4 pieces of ribbon that were equal in length. She used a total of 5 feet of ribbon. How long, in feet, was each piece of ribbon she cut?

||

A chef bought 3 bags of beans. Each bag contains 125 kilograms of beans. How many kilograms of beans did she buy?

||

A printer takes 212 seconds to print a flyer. It took 75 seconds to print a batch of flyers without stopping. How many flyers were in the batch?

","

Jada cut 4 pieces of ribbon that were equal in length. She used a total of 5 feet of ribbon. How long, in feet, was each piece of ribbon she cut?

||

A printer takes 212 seconds to print a flyer. It took 75 seconds to print a batch of flyers without stopping. How many flyers were in the batch?

",557055 +PRABETEY,1,Multiple Choice (select all),Check All That Apply,"

Priya bought x grams of flour. Clare bought 38 more than that. Select all equations that represent the relationship between the amount of flour that Priya bought, x, and the amount of flour that Clare bought, y.

",,,"

y = 38x

||

y = 58x

||

y = x + 38x

||
+
+
+
+
||

y = 118x

","

y = x + 38x

||

y = 118x

",383539 +PSB35H,1,Multiple Choice (select 1),Multiple Choice,

Are the ratios 3 : 6 and 6 : 3 equivalent?

,,,Yes || No,No,137170 +PRABQJVE,1,Multiple Choice (select all),Check All That Apply,

Select all of the nets that can be folded and assembled into a cube.

,,,"

||

||

","

||

",502795 +PRABPNVJ,1,Multiple Choice (select all),Check All That Apply,"

The air quality was tested in many office buildings in two cities. The results of the testing is shown in these box plots.

+

 

+

+

 

+

A level of less than 50 parts per million is considered healthy. A level of 50 or more parts per million is considered unhealthy.

+

 

+

Select all the statements that must be true.

",,,The lowest recorded measurement was in city Q. || All buildings tested in city P are in the healthy range. || The mean for city P is greater than the mean for city Q. || The range for city Q is greater than the range for city P. || The median for city P is greater than the median for city Q.,The lowest recorded measurement was in city Q. || All buildings tested in city P are in the healthy range. || The range for city Q is greater than the range for city P. || The median for city P is greater than the median for city Q.,183259 +PSBE3P,1,Multiple Choice (select 1),Multiple Choice,"

A class measured the radius r, circumference C, and area A of various circular objects. The results are recorded in this table.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
r(cm)C(cm)A(cm2)
42550
531.578.5
850201
1275452
+

 

+

Does there appear to be a proportional relationship between circumference and area?

",,,Yes || No,No,25643 +PSBY3C,1,Multiple Choice (select 1),Multiple Choice,"

Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote:

+

 

+

228 = 2 · 28 = 56

+

 

+

Elena said, “No, exponents mean repeated multiplication. It should be 28 ⋅ 28, which works out to be 784.” Do you agree with either of them? 

",,,Agree with both || Agree with Elena || Agree with Andre || Disagree with both,Disagree with both,119400 +PRABQP4J,1,Multiple Choice (select 1),Multiple Choice,"

Here is a scatter plot:

+

 

+

+

 

+

The graph of what linear equation is a good fit for this data?

",,,"

y=12x

||

y=-12x+1

||

y=-12x

||

y=12x+1

","

y=12x+1

",604573 +PRABFEWP,1,Multiple Choice (select all),Check All That Apply,"
+

Priya has 5 pencils, each x inches in length. When she lines up the pencils end to end, they measure 34.5 inches. Select all the equations that represent this situation.

+
",,,"

5 + x = 34.5

||

5x = 34.5

||

34.5 ÷ 5 = x

||

34.5 - 5 = x

||

x = (34.5) · 5

","

5x = 34.5

||

34.5 ÷ 5 = x

",155237 +PRABQTD6,1,Multiple Choice (select all),Check All That Apply,"

The graph shows the cost C in dollars of w pounds of blueberries, a proportional relationship.

+

 

+

Select all the true statements.

+

 

+

",,,"1 pound of blueberries costs $2.75. || 2.75 pounds of blueberries cost $1. || 5 pounds of blueberries cost $15.50. || 12 pounds of blueberries cost $33. || The point (3, 9) is on the graph of the proportional relationship.",1 pound of blueberries costs $2.75. || 12 pounds of blueberries cost $33.,530971 +PSBPAY,1,Multiple Choice (select 1),Multiple Choice,"

The line has been partitioned into three angles. Is there a triangle with these three angle measures? 

+

 

+

",,,Yes || No,Yes,64079 +PRABG4DP,1,Multiple Choice (select 1),Multiple Choice,

Which is more likely to happen?

,,,"When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes, you pull out a left shoe. || When listening to a playlist—which has 5 songs on it—in shuffle mode, the first song on the playlist plays first.","When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes, you pull out a left shoe.",44057 +PSBWYC,3,Multiple Choice (select 1),Multiple Choice,

A traffic helicopter flew directly from Point A to Point B in 8 minutes. Did the helicopter travel faster or slower than the driver?

,,,Faster || Slower,Slower,107783 +PRABFEXS,1,Multiple Choice (select all),Check All That Apply,

Select all the figures that have sides that appear to be perpendicular.

,,,"

||

||

||

||

","

||

",104131 +PSBBRW3,1,Multiple Choice (select 1),Multiple Choice,"

When he sorts the class’s scores on the last test, the teacher notices that exactly 12 students scored better than Clare and exactly 12 students scored worse than Clare. Does this mean that Clare’s score on the test is the median?

",,,Yes || No,Yes,252499 +PSBTME,2,Multiple Choice (select all),Check All That Apply,

Which of the following represents the amount a customer pays including the tip of 15% if the bill was b dollars? Select all that apply.

,,,"

15b

|| + + + + + +
b + 0.15b
|| + + + + + +
1.15b
|| + + + + + +
1.015b
|| + + + + + +
b+15100b
|| + + + + + +
b + 0.15
|| + + + + + +
0.15b
"," + + + + + +
b + 0.15b
|| + + + + + +
1.15b
|| + + + + + +
b+15100b
",87369 +PSBBK7W,1,Multiple Choice (select 1),Multiple Choice,"

Here are two nets. Mai said that both nets can be assembled into the same triangular prism. Do you agree?

+

 

+

 

+
 
",,,Agree || Disagree,Agree,226695 +PSBBV46,1,Multiple Choice (select 1),Multiple Choice,"

Andre says that 10x+6 and 5x+11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?

",,,Yes || No,No,275581 +PSBB4YA,3,Multiple Choice (select 1),Multiple Choice,

Your friend has a 15% off coupon and $10. What is the largest pizza that your friend can afford?

,,,

small

||

medium

||

large

,

small

,314006 +PSBWJZ,1,Multiple Choice (select 1),Multiple Choice,"

Andre sets up a rain gauge to measure rainfall in his back yard. On Tuesday, it rains off and on all day.

+
+

 

+
    +
  • He starts at 10 a.m. with an empty gauge when it starts to rain.
    • +
  • Two hours later, he checks, and the gauge has 2 cm of water in it.
    • +
  • It starts raining even harder, and at 4 p.m., the rain stops, so Andre checks the rain gauge and finds it has 10 cm of water in it.
    • +
  • While checking it, he accidentally knocks the rain gauge over and spills most of the water, leaving only 3 cm of water in the rain gauge.
    • +
  • When he checks for the last time at 5 p.m., there is no change.
    • +
+

 

+

 

+

Which of the two graphs could represent Andre’s story?

+
",,,"

||

","

",104928 +PSBWSA,1,Multiple Choice (select 1),Multiple Choice,"

Diego wants to survey a sample of students at his school to learn about the percentage of students who are satisfied with the food in the cafeteria. He decides to go to the cafeteria on a Monday and ask the first 25 students who purchase a lunch at the cafeteria if they are satisfied with the food.

+

 

+

Do you think this is a good way for Diego to select his sample?

",,,Yes || No,No,106494 +PRABTVKJ,1,Multiple Choice (select 1),Multiple Choice,"

Un automóvil tardó 4 horas recorriendo una distancia de 240 millas. A esa tasa, ¿cuánto tardaría en recorrer 90 millas?

",,,"60 horas || 6 horas ||

223 horas

||

112 horas

","

112 horas

",320230 +PSBEF3,2,Multiple Choice (select 1),Multiple Choice,"

Add all the diameters of all the planets except the Sun. Which is wider, all of these objects side by side, or the Sun?

",,,The first 5 planets || The Sun,The Sun,22473 +PRABESCB,1,Multiple Choice (select 1),Multiple Choice,

It was -5°C in Copenhagen and -12°C in Oslo. Which city was colder?

,,,Copenhagen || Oslo,Oslo,218498 +PSBX69,7,Multiple Choice (select 1),Multiple Choice,"

For the statement below, decide if it is true or false. 

+

 

+

(2, 0) makes both the equation for line m and the equation for line n true.

",,0,True || False,FALSE,113820 +PRABPESE,1,Multiple Choice (select 1),Multiple Choice,"

Kiran is using long division to find 696 ÷ 12.

+

 

+

12696

+

 

+

He starts by dividing 69 by 12. In which decimal place should Kiran place the first digit of the quotient (5)?

",,,Hundreds || Tens || Ones || Tenths,Tens,204459 +PRABFJQD,1,Multiple Choice (select all),Check All That Apply,"

Tyler has more than $10. Elena has more money than Tyler. Mai has more money than Elena. Let t be the amount of money that Tyler has, let e be the amount of money that Elena has, and let m be the amount of money that Mai has. Select all statements that are true.

",,,t < m || m > 10 || e > 10 || t > 10 || e > m || t < e,t < m || m > 10 || e > 10 || t > 10 || t < e,62003 +PRABETM6,1,Multiple Choice (select 1),Multiple Choice,

A circle’s circumference is 600 m. What is a good approximation of the circle’s area?

,,,"300 m2 || 3,000 m2 || 30,000 m2 || 300,000 m2","30,000 m2",25445 +PRABFGV9,1,Multiple Choice (select all),Check All That Apply,"
+

Andre ran 512 laps of a track in 8 minutes at a constant speed. It took Andre x minutes to run each lap. Select all the equations that represent this situation.

+

 

+
",,,"

512 x = 8

||

512 + x = 8

||

512 - x = 8

||

512 ÷ x = 8

||

x = 8 ÷  512

||

x = 512 ÷ 8

","

512 x = 8

||

x = 8 ÷  512

",189985 +PRABQP6R,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 6×105.

",,,"

(3×108)(2×10-2)

||

600,000,000×10-3

||

1.2×1072×102

||

600,000

||

605

","

600,000,000×10-3

||

600,000

",552200 +PSBB7UU,1,Multiple Choice (select 1),Multiple Choice,"

A participant in a 21-mile walkathon walks at a steady rate of 3 miles per hour. He thinks, “The relationship between the number of miles left to walk and the number of hours I already walked can be represented by a line with slope -3.” Do you agree with his claim?

",,,Yes || No,Yes,330357 +PRABQPKT,1,Multiple Choice (select 1),Multiple Choice,"

Which number line shows all the values of that make the inequality -6y - 2 ≥ 10 true?

",,,"

||

||

||

","

",163825 +PRABFJP8,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,"

-5 < -5

||

-6 < -5

||

-6 < 3

||

4 < -7

||

-7 < -8

","

-5 < -5

||

4 < -7

||

-7 < -8

",362112 +PRABQMBR,1,Multiple Choice (select all),Check All That Apply,"

Select all of the expressions that have the same value as 892÷8.

",,,8920 ÷ 80 || 894 ÷ 10 || 89.2 ÷ 0.08 || 8.92 ÷ 0.8 || 0.892 ÷ 0.008,8920 ÷ 80 || 0.892 ÷ 0.008,278345 +PRABEPV8,1,Multiple Choice (select all),Check All That Apply,"

Select all the statements that must be true for any scaled copy Q of Polygon P. 

+

",,,"

The side lengths are all whole numbers.

||

The angle measures are all whole numbers.

||

Q has exactly 1 right angle.

||

If the scale factor between P and Q is 15, then each side length of P is multiplied by 15 to get the corresponding side length of Q.

||

If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.

||

Q has 2 acute angles and 3 obtuse angles.

","

The angle measures are all whole numbers.

||

Q has exactly 1 right angle.

||

If the scale factor between P and Q is 15, then each side length of P is multiplied by 15 to get the corresponding side length of Q.

||

Q has 2 acute angles and 3 obtuse angles.

",209639 +PSBZ9M,1,Multiple Choice (select 1),Multiple Choice,

Noah gathered information on the home states of the swimmers on Team USA. He organized the data in a table. Would a dot plot be appropriate to display his data?

,,,Yes || No,No,125866 +PSBBD5P,1,Multiple Choice (select 1),Multiple Choice,"

Noah says that 24 ·32 = 66. Tyler says that 24 ·42 = 162.

+

 

+

Do you agree with Noah?

",,,Yes || No,No,192067 +PSBBSBU,2,Multiple Choice (select 1),Multiple Choice,

Priya says her elevation is less than the submarine’s and she is closer to sea level. Is this possible? 

,,,"Yes, it is possible. || No, it is not possible","No, it is not possible",254509 +PSBS9Q,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

 6+  6 + 6 = 63

",,0,True || False,FALSE,85308 +PRABFKT4,1,Multiple Choice (select all),Check All That Apply,"

Here is a histogram that summarizes the lengths, in feet, of a group of adult female sharks. Select all the statements that are true, according to the histogram.

+

 

+

",,,

A total of 9 sharks were measured.

||

A total of 50 sharks were measured.

||

The longest shark that was measured was 10 feet long.

||

Most of the sharks that were measured were over 16 feet long.

||

Two of the sharks that were measured were less than 14 feet long.

,

A total of 50 sharks were measured.

||

Two of the sharks that were measured were less than 14 feet long.

,65434 +PSBBHT5,1,Multiple Choice (select 1),Multiple Choice,"

Which is bigger, a quart or a liter?

",,,quart || liter,liter,213216 +PSBB6PY,1,Multiple Choice (select 1),Multiple Choice,"

Para cada pareja de números, llena el espacio con <, =, o > según corresponda.

+

 

+

0.75          34

",,,< || = || >,=,323658 +PRABQPME,1,Multiple Choice (select all),Check All That Apply,"

Elena would like to know the average height of seventh graders in her school district. She measures the heights of everyone in a random sample of 20 students. The mean height of Elena’s sample is 61 inches, and the MAD (mean absolute deviation) is 2 inches.

+

 

+

Select all the true statements.

",,,The median height of the sample must be between 59 and 63 inches. || Another random sample of 20 students is likely to have a mean between 57 and 65 inches. || The mean height of these 20 students is likely to be the same as the mean height of all students in the district. || The mean height of these 20 students is likely to be the same as the mean height of a second random sample of 20 students. || Elena would be more likely to get an accurate estimate of the mean height of the population by sampling 40 people instead of sampling 20 people.,Another random sample of 20 students is likely to have a mean between 57 and 65 inches. || Elena would be more likely to get an accurate estimate of the mean height of the population by sampling 40 people instead of sampling 20 people.,99112 +PRABEVTD,1,Multiple Choice (select all),Check All That Apply,"

This graph shows the temperature in Diego’s house between noon and midnight one day.

+

 

+

+

 

+

Select all the true statements.

",,,Time is a function of temperature. || The lowest temperature occurred between 4:00 and 5:00. || The temperature was increasing between 9:00 and 10:00. || The temperature was 74 degrees twice during the 12-hour period. || There was a four-hour period during which the temperature did not change.,The temperature was 74 degrees twice during the 12-hour period. || There was a four-hour period during which the temperature did not change.,340317 +PRABFGZ8,1,Multiple Choice (select all),Check All That Apply,"

Which expressions represent the total area of the large rectangle? Select all that apply. 

+

",,,6(m + n) || 6n + m || 6n + 6m || 6mn || (n + m)6,6(m + n) || 6n + 6m || (n + m)6,298817 +PSBBMNB,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

23 = 32

",,0,True || False,FALSE,229183 +PRABEDEK,1,Multiple Choice (select 1),Multiple Choice,"

Using the data in the scatter plot, what is a reasonable slope of a model that fits this data?

+

 

+

",,2,-2.5 || -1 || 1 || 2.5,2.5,36419 +PSBCHHJ,1,Multiple Choice (select 1),Multiple Choice,"

Han was looking at the equation 6x − 4 + 2(5x + 2) = 16x.

+

 

+

He said, “I can tell right away there are no solutions, because on the left side, you will have 6x + 10x and a bunch of constants, but you have just 16x on the right side.”

+

 

+

Do you agree with Han?

",,,Yes || No,No,386445 +PRABQPS5,1,Multiple Choice (select 1),Multiple Choice,

For which data set would the mean be a good way to describe the center of the data?

,,,"

white, blue, white, white, red

||

||

79, 80, 80, 88, 90, 92, 94

||

","

79, 80, 80, 88, 90, 92, 94

",266182 +PRABUUFB,1,Multiple Choice (select 1),Multiple Choice,"

State whether the following is in scientific notation.

+

 

+

8.7 x 10-12

",,,Already in scientific notation || Not in scientific notation,Already in scientific notation,258192 +PSBCBCJ,3,Multiple Choice (select 1),Multiple Choice,"

On a later day, he asked the same group of 10 friends to throw a ball again and collected another set of data. The median of the second data set is 49 feet, and the IQR is 6 feet.

+

 

+

Did the 10 friends, as a group, perform better (throw farther) in the second round compared to the first round? 

",,,

Better

||

Worse

,

Worse

,350745 +PRABQK68,1,Multiple Choice (select all),Check All That Apply,

Select all of the expressions that are equal to 2.

,,,"1,200 ÷ 60 || 1.2 ÷ 0.6 || 0.012 ÷ 0.06 || 0.5 ÷ 0.25 || 0.05 ÷ 0.025",1.2 ÷ 0.6 || 0.5 ÷ 0.25 || 0.05 ÷ 0.025,590847 +PSBBUMX,1,Multiple Choice (select 1),Multiple Choice,"

Clare estimates that her brother is 4 feet tall. When they get measured at the doctor’s office, her brother’s actual height is 4 feet, 2 inches.

+

 

+

Should Clare's or the doctor's measurement be considered the actual height?

",,,

Clare's measurement

||

Doctor's measurement

,

Doctor's measurement

,267340 +PRABEDCN,1,Multiple Choice (select 1),Multiple Choice,"

Which of these statements is true about the data in the scatter plot?

+

 

+

+
 
",,,"As x increases, y tends to increase. || As x increases, y tends to decrease. || As x increases, y tends to stay unchanged. || x and y are unrelated.","As x increases, y tends to decrease.",173561 +PSBCW78,1,Multiple Choice (select 1),Multiple Choice,"
+
+
+

Determine if the following is true or false.

+

 

+

|-5l < 3

+
+
+
",,0,True || False,FALSE,458234 +PSBCE5U,1,Multiple Choice (select 1),Multiple Choice,"

At a farm, animals are fed bales of hay and buckets of grain. Each bale of hay is in the shape a rectangular prism. The base has side lengths 2 feet and 3 feet, and the height is 5 feet. Each bucket of grain is a cylinder with a diameter of 3 feet. The height of the bucket is 5 feet, the same as the height of the bale.

+

 

+

Which is larger in area, the rectangular base of the bale or the circular base of the bucket? 

",,,Rectangular Base of the Bale || Circular Base of the Bucket,Circular Base of the Bucket,373493 +PSBZT4,3,Multiple Choice (select 1),Multiple Choice,"

Decide whether the table could represent a proportional relationship.

+

 

+

The number of wheels on a train.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
number of train carsnumber of wheelswheels per train car
20184 
30264 
40344 
50424 
+

 

",,,"

Yes, it is proportional

||

No, it is not proportional

","

No, it is not proportional

",123722 +PSBB4QM,2,Multiple Choice (select 1),Multiple Choice,"

If a compressed rubber sphere has a 6-inch width, is its height closer to 5 inches or to 11 inches?

",,,5 inches || 11 inches,5 inches,312938 +PRABEPJR,1,Multiple Choice (select all),Check All That Apply,"

Here is a picture of the Rose Bowl Stadium in Pasadena, CA.

+

 

+

+

 

+

Here are some copies of the picture. Select all the pictures that are scaled copies of the original picture.

",,,"

||

||

||

","

||

",108663 +PRABE3GW,1,Multiple Choice (select 1),Multiple Choice,

Which pair of base and height produces the greatest area? All measurements are in centimeters.

,,,"

b=4, h=3.5

||

b=0.8, h=20

||

b=6, h=2.25

||

b=10, h=1.4

","

b=0.8, h=20

",503799 +PSBCHZC,1,Multiple Choice (select all),Check All That Apply,"

Andre sometimes mows lawns on the weekend to make extra money. Two weeks ago, he mowed a neighbor’s lawn for 12 hour and earned $10. Last week, he mowed his uncle’s lawn for 32 hours and earned $30. This week, he mowed the lawn of a community center for 2 hours and earned $30.

+

 

+

 

+

Which jobs paid better than others? 

+

 

",,,

Neighbor's Lawn

||

Uncle's Lawn

||

Community Center

,

Neighbor's Lawn

||

Uncle's Lawn

,389028 +PSBBY9D,1,Multiple Choice (select 1),Multiple Choice,"

The equation a + b = c could be true or false.

+

 

+

If a is 3, b is 4, and c is 5, is the equation true or false?

+
 
",,0,True || False,FALSE,293491 +PRABD45A,1,Multiple Choice (select all),Check All That Apply,"

Select all the sequences of transformations could take figure P to figure Q.

+

 

+

",,,"a single reflection || a single rotation || a single translation || a translation, then a reflection || a reflection, then a different reflection","a single rotation || a reflection, then a different reflection",40714 +PRABPUJG,1,Multiple Choice (select all),Check All That Apply,

Select all the relationships that demonstrate a positive association between variables.

,,,Outside temperature and cost to heat a home || Length of time you have walked and distance you have traveled || Pounds of cherries you buy and amount of money you spend on cherries || Speed of a train and the amount of time it takes for the train to get to its destination || Number of people in a grocery check-out line and how long you have to wait to check out,Length of time you have walked and distance you have traveled || Pounds of cherries you buy and amount of money you spend on cherries || Number of people in a grocery check-out line and how long you have to wait to check out,296937 +PSBHNF,1,Multiple Choice (select 1),Multiple Choice,"

Noah is interested in comparing the number of movies watched by students and teachers over the winter break. He takes a random sample of 10 students and 10 teachers and makes a dot plot of their responses.

+

Students:

+

+

Teachers:

+

+


Noah then computes the measures of center and variability for each group:

+
    +
  • Students: Mean = 5.7 movies, MAD = 0.76 movies
    • +
  • Teachers: Mean = 2.7 movies, MAD = 0.9 movies
    • +
+

 

+

Is Noah's choice of mean and MAD appropriate for the data he has? 

",,,Yes || No,Yes,39360 +PRABEC25,1,Multiple Choice (select all),Check All That Apply,"
+

Here is the graph of a linear equation.  

+

 

+

Select all true statements about the line and its equation.

+
+
 
+
",,,"

One solution of the equation is (3, 2).

||

One solution of the equation is (-1, 1).

||

One solution of the equation is (1, 32).

||

There are 2 solutions.

||

There are infinitely many solutions.

||

The equation of the line is y = 14x + 54.

||

The equation of the line is y = 54x + 14.

","

One solution of the equation is (3, 2).

||

One solution of the equation is (-1, 1).

||

One solution of the equation is (1, 32).

||

There are infinitely many solutions.

||

The equation of the line is y = 14x + 54.

",331521 +PRABQPRE,1,Multiple Choice (select 1),Multiple Choice,"

A rectangular pyramid is sliced. The slice passes through the vertex of the pyramid and is perpendicular to the base of the pyramid. 

+

 

+

Which of these describes the cross section? 

+

",,,A rectangle smaller than the base || A quadrilateral that is not a rectangle || A rectangle the same size as the base || A triangle with a height the same as the pyramid,A triangle with a height the same as the pyramid,348992 +PRABFENR,1,Multiple Choice (select 1),Multiple Choice,"

Before refrigerators existed, some people had blocks of ice delivered to their homes.

+

 

+

A delivery wagon had a storage box in the shape of a rectangular prism that was 712 feet by 6 feet by 6 feet. The cubic ice blocks stored in the box had side lengths 112 feet.

+

 

+

 

+

How many ice blocks fit in the storage box?

",,,"

270

||

338

||

80

||

180

",

80

,277396 +PSBR2X,1,Multiple Choice (select 1),Multiple Choice,"

Han and Tyler are following a polenta recipe that uses 5 cups of water for every 2 cups of cornmeal.

+

 

+
    +
  • Han says, “I am using 3 cups of water. I will need 1 15 cups of cornmeal.”
    • +
  • Tyler says, “I am using 3 cups of cornmeal. I will need 7 12 cups of water.”
    • +
+

 

+

Do you agree with either of them?

",,,I agree with Han || I agree with Tyler || I agree with both || I don't agree with either,I agree with both,78262 +PRABPQ5B,1,Multiple Choice (select all),Check All That Apply,"

The equation  has two solutions. This is because both  , and also . So, 5 is a solution, and also -5 is a solution.

+


Select all the equations that have a solution of -4.

",,,10 + x = 6 || 10 - x = 6 || -3x = -12 || -3x = 12 || 8 = x² || x² = 16,10 + x = 6 || -3x = 12 || x² = 16,412709 +PRABEUGJ,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions that are the result of decreasing x by 80%.

,,,"

20100x

||

x - 80100x

||

100 - 20100x

||

0.80x

||

(1 - 0.8)x

","

20100x

||

x - 80100x

||

(1 - 0.8)x

",375713 +PSBBR5Q,1,Multiple Choice (select 1),Multiple Choice,"

Ten sixth-grade students reported the hours of sleep they get on nights before a school day. Their responses are recorded in the dot plot.

+



+

Looking at the dot plot, Lin estimated the mean number of hours of sleep to be 8.5 hours. Noah's estimate was 7.5 hours. Diego's estimate was 6.5 hours.

+

 

+

Which estimate do you think is best?

",,,Lin's estimate || Noah's estimate || Diego's estimate,Noah's estimate,253594 +PSBBMQF,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

161 = 82

",,0,True || False,FALSE,229517 +PRABHQW3,1,Multiple Choice (select all),Check All That Apply,"

Consider the division expression 712 ÷ 2.  Select all multiplication equations that correspond to this division expression.

",,,"

2 · ? = 712

||

712 · ? = 2

||

2 · 712 = ?

||

? · 712 = 2

||

? · 2 = 712

","

2 · ? = 712

||

? · 2 = 712

",490707 +PRABQMB2,1,Multiple Choice (select all),Check All That Apply,"

Without computing, select all of the expressions that have the same value as 81·(37+59).

",,,81 · (59+37) || (81 · 37) + 59 || (81 · 37) + (81 · 59) || 81 + (37 · 59) || (37 + 59) · 81,81 · (59+37) || (81 · 37) + (81 · 59) || (37 + 59) · 81,427706 +PSBBFAV,10,Multiple Choice (select all),Check All That Apply,"

Other than traveling from school, what do you do right after school on most days?

+
+
+
 
+
+
",,,Have a snack || Do homework || Read a book || Talk on the phone || Practice a sport || Do chores || Use the computer || Participate in an extracurricular activity,Have a snack || Do homework || Read a book || Talk on the phone || Practice a sport || Do chores || Use the computer || Participate in an extracurricular activity,199131 +PSBWQY,2,Multiple Choice (select 1),Multiple Choice,

Is the sample representative of the population?

,,,Yes || No,No,106396 +PRABFGZS,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that equal 34.

",,,

7

||

43

||

12

||

81

||

64

||

92

,

81

||

92

,297477 +PSBS86,3,Multiple Choice (select all),Check All That Apply,"

+

 

+

Which have the same area and the same perimeter as Rectangle R?

",,,Rectangle A. || Rectangle B. || Rectangle C. || Rectangle D. || Rectangle E. || Rectangle F.,Rectangle A. || Rectangle E.,85266 +PSBX69,1,Multiple Choice (select 1),Multiple Choice,"

Here are graphs representing three linear relationships. These relationships could also be represented with equations.

+

 

+

+

For the statement below, decide if it is true or false. 

+

 

+

(4, 0) is a solution of the equation for line m.

",,0,True || False,FALSE,113066 +PSBQM7,1,Multiple Choice (select 1),Multiple Choice,"

Priya looks at the inequality 12−x>5 and says “I subtract a number from 12 and want a result that is bigger than 5. That means that the solutions should be values of x that are smaller than something.”

+

 

+

Do you agree with Priya?

",,,Agree || Disagree,Agree,70471 +PSBH8S,7,Multiple Choice (select 1),Multiple Choice,

It will snow at our school on July 1.

,,,impossible || unlikely || equally likely as not || likely || certain,impossible || unlikely,42589 +PSBB7DK,1,Multiple Choice (select all),Check All That Apply,

Which graphs cannot represent a proportional relationship? Select all that apply.

,,,"

||

||

||

","

||

",327867 +PSBBR87,4,Multiple Choice (select 1),Multiple Choice,"

Noah said, “If a is a rational number, -a will always be a negative number.”

+

 

+

Do you agree with Noah? 

",,,"Yes, Noah is correct. || No, Noah is incorrect.","No, Noah is incorrect.",254122 +PRABFCCB,1,Multiple Choice (select all),Check All That Apply,

Select all the expressions whose value is larger than 100.

,,,"

120% of 100

||

50% of 150

||

150% of 50

||

20% of 800

||

200% of 30

||

500% of 400

||

1% of 1,000

",

120% of 100

||

20% of 800

||

500% of 400

,321235 +PSBV9Y,5,Multiple Choice (select all),Check All That Apply,

Which three summer sports are most popular in Kiran’s class?

,,,basketball || diving || gymnastics || rowing || soccer || swimming || track and field || volleyball,gymnastics || swimming || track and field,103242 +PSBC3Y7,1,Multiple Choice (select 1),Multiple Choice,"

At a restaurant, a trash can's opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 12 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening.

+

 

+

Do you agree or disagree with Jada’s explanation?

",,,Agree || Disagree,Disagree,485290 +PSBB2TW,2,Multiple Choice (select 1),Multiple Choice,"

For the inequality, decide whether the solution is represented by x < 4.5 or x > 4.5.

+

 

+

-8x + 6 > -30

",,,x < 4.5 || x > 4.5,x < 4.5,302326 +PRABDX3U,1,Multiple Choice (select all),Check All That Apply,"

The rectangle seen in Frame 1 is rotated to a new position, seen in Frame 2.

+



+

Select all the ways the rectangle could have been rotated to get from Frame 1 to Frame 2.

",,,40 degrees clockwise || 40 degrees counterclockwise || 90 degrees clockwise || 90 degrees counterclockwise || 140 degrees clockwise || 140 degrees counterclockwise,40 degrees counterclockwise || 140 degrees clockwise,1074 +PRABEE2J,1,Multiple Choice (select 1),Multiple Choice,"

Which equation, together with y = -1.5x + 3, makes a system with one solution?

",,,y = -1.5x + 6 || y = -1.5x || 2y = -3x + 6 || 2y + 3x = 6 || y = -2x + 3,y = -2x + 3,306064 +PSB9AQ,1,Multiple Choice (select 1),Multiple Choice,"

Which one of these pictures is not like the others?

+

 

+

",,,Picture L || Picture M || Picture N,Picture M,165102 +PSBQ67,1,Multiple Choice (select 1),Multiple Choice,"

For a science experiment, students need to find 25% of 60 grams.

+

 

+
    +
  • Jada says, “I can find this by calculating 14 of 60.”
    • +
  • Andre says, “25% of 60 means 25100 · 60.”
    • +
+

 

+

Do you agree with either of them? 

",,,I agree with only Jada || I agree with only Andre || I agree with both Jada and Andre || I agree with neither Jada or Andre,I agree with both Jada and Andre,73922 +PRABFEWM,1,Multiple Choice (select all),Check All That Apply,

Select all the true equations.

,,,"

5 + 0 = 0

||

15 · 0 = 0

||

1.4 + 2.7 = 4.1

||

23 · 59 = 712

||

423 = 5 - 13

","

15 · 0 = 0

||

1.4 + 2.7 = 4.1

||

423 = 5 - 13

",154867 +PRABMQH8,1,Multiple Choice (select all),Check All That Apply,"

Triangle Z is a scale copy of Triangle M.

+

+


Select all the sets of values that could be the side lengths of Triangle Z. 

",,,"

8,11,14

|| 10,17.5,25 || 6,9,11 || 6,10.5,15 || 8,14,20","10,17.5,25 || 6,10.5,15 || 8,14,20",569234 +PSBCNUB,1,Multiple Choice (select 1),Multiple Choice,"

Which temperature is warmer, -2 degrees Celsius, or -5 degrees Celsius?

",,,-2 degrees Celsius || -5 degrees Celsius,-2 degrees Celsius,409535 +PSBBXKW,1,Multiple Choice (select 1),Multiple Choice,"

While playing basketball, Jada’s heart rate goes up to 160 beats per minute. While jogging, her heart beats 25 times in 10 seconds. Assuming her heart beats at a constant rate while jogging, which of these activities resulted in a higher heart rate?

",,,jogging || playing basketball,playing basketball,283915 +PSBEXG,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the table could represent a proportional relationship.

+

 

+

Annie’s Attic is giving away $5 off coupons.

+

 

+ + + + + + + + + + + + + + + + + + + +
original pricesale price
$15$10
$25$20
$35$30
",,,"

Yes, it is proportional

||

No, it is not proportional

","

No, it is not proportional

",24484 +PRABQNZC,1,Multiple Choice (select 1),Multiple Choice,

Which of these expressions is equivalent to 0.04(x - 25)?

,,,

0.04x - 1

||

0.04x - 1.04

||

0.04x - 25

||

0.04x - 25.04

,

0.04x - 1

,498737 +PSBJF8,1,Multiple Choice (select 1),Multiple Choice,"

 

+

 

+

Diego and Jada were asked “How many rhombuses are in a trapezoid?”

+
    +
  • Diego says, “. If I put 1 rhombus on a trapezoid, the leftover shape is a triangle, which is  of the trapezoid.” 
    • +
  • Jada says, “I think it’s . Since we want to find out ‘how many rhombuses,’ we should compare the leftover triangle to a rhombus. A triangle is  of a rhombus.” 
    • +
+

 

+

Do you agree with either of them?

",,,I agree with Diego || I agree with Jada || I agree with neither || I agree with both,I agree with Jada,44207 +PSBH8S,8,Multiple Choice (select 1),Multiple Choice,

The sun will set today before 11:00 p.m.

,,,impossible || unlikely || equally likely as not || likely || certain,certain,42680 +PSBBCQT,6,Multiple Choice (select 1),Multiple Choice,"

Is (100, 193) also on the line?

+

",,,Yes || No,Yes,184867 +PRABDYF6,1,Multiple Choice (select 1),Multiple Choice,"

The point (-4,1) is rotated 180 degrees counterclockwise using center (0,0). What are the coordinates of the image?

",,,"

(-1,-4)

||

(-1,4)

||

(4,1)

||

(4,-1)

","

(4,-1)

",95407 +PSBBE76,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that describe the situation and then find the solution.

+

 

+

Tyler's playlist has 36 songs. Noah’s playlist has one quarter as many songs as Tyler's playlist. How many songs are on Noah’s playlist, w?

",,,"

w = 4 · 36

||

w = 36 ÷ 4

||

4w = 36

||

w4 = 36

","

w = 36 ÷ 4

||

4w = 36

",198693 +PSBG9G,2,Multiple Choice (select 1),Multiple Choice,"

A recipe for tropical fruit punch says, ""Combine 4 cups of pineapple juice with 5 cups of orange juice.""

+

 

+

If 12 cups of pineapple juice are used with 20 cups of orange juice, will the recipe taste the same?

",,,Yes || No,No,37441 +PSBBFYZ,1,Multiple Choice (select 1),Multiple Choice,

Could 7.2 inches and 28 inches be the diameter and circumference of the same circle?

,,,Yes || No,No,202903 +PSBCW5V,1,Multiple Choice (select 1),Multiple Choice,"
+
+
+

Determine if the following is true or false.

+

 

+

-5 > 3

+
+
+
",,0,True || False,FALSE,457920 +PRABPMJS,1,Multiple Choice (select all),Check All That Apply,

Select all the inequalities that have the same graph as x < 4.

,,,x < 2 || x + 6 < 10 || 5x < 20 || x-2 > 2 || x < 8,x + 6 < 10 || 5x < 20,233480 +PRABEUGG,1,Multiple Choice (select 1),Multiple Choice,"

Which equation represents the relationship between the angles in the figure?

+

 

+

",,,88 + b = 90 || 88 + b = 180 || 2b + 88 = 90 || 2b + 88 = 180,2b + 88 = 180,375373 +PRABETQK,1,Multiple Choice (select 1),Multiple Choice,

Noah picked 3 kg of cherries. Mai picked half as many cherries as Noah. How many total kg of cherries did Mai and Noah pick?

,,,"

3 + 12

||

3 - 12

||

1 + 12 · 3

||

1 + 12 · 3

","

1 + 12 · 3

",66914 +PSBBRHC,3,Multiple Choice (select 1),Multiple Choice,

Is the length of the shadow a function of time?

,,,Yes || No,Yes,250112 +PRABG423,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the solution is represented by x < 2.5 or x > 2.5.

+

 

+

-4x + 5 > -5

+
 
",,,x < 2.5 || x > 2.5,x < 2.5,237440 +PRABEDDW,1,Multiple Choice (select all),Check All That Apply,"

Here is a scatter plot:

+

 

+

+

 

+

Select all the following that describe the association in the scatter plot:

",,,Linear association || Non-linear association || Positive association || Negative association || No association,Non-linear association || Positive association,68650 +PSBUVN,1,Multiple Choice (select 1),Multiple Choice,"

Tyler and Han are discussing the question, ""Which sixth-grade student lives the farthest from school?""

+
    +
  • Tyler says, “I don’t think the question is a statistical question. There is only one person who lives the farthest from school, so there would not be variability in the data we collect.”
    • +
  • Han says: “I think it is a statistical question. To answer the question, we wouldn’t actually be asking everyone, 'Which student lives the farthest from school?' We would have to ask each student how far away from school they live, and we can expect their responses to have variability.”
    • +
+

Do you agree with either of them?

",,,Agree with Tyler || Agree with Han,Agree with Han,94609 +PSBBBD9,1,Multiple Choice (select 1),Multiple Choice,"

To make a friendship bracelet, some long strings are lined up then taking one string and tying it in a knot with each of the other strings to create a row of knots. A new string is chosen and knotted with the all the other strings to create a second row. This process is repeated until there are enough rows to make a bracelet to fit around your friend's wrist.

+

 

+

Are the number of knots proportional to the number of rows?

",,,Yes || No,Yes,177081 +PSBHNQ,1,Multiple Choice (select 1),Multiple Choice,"
    +
  • Noah says that 9x − 2x + 4x is equivalent to 3x because the subtraction sign tells us to subtract everything that comes after 9x.  
    • +
+

 

+
    +
  • Elena says that 9x − 2x + 4x is equivalent to 11x because the subtraction only applies to 2x.
    • +
+

 

+

Do you agree with either of these claims?

",,,Noah is correct || Elena is correct || Neither are correct || Both are correct,Elena is correct,39475 +PRABFS5H,1,Multiple Choice (select all),Check All That Apply,"

Select the unit from the list that you would use to measure the object.

+

 

+

The length of a chalkboard or whiteboard

",,,centimeters || cups || feet || gallons || grams || inches || kilograms || kilometers || liters || meters || miles || milliliters || millimeters || ounces || pounds || quarts || tons || yards,feet || meters || yards,173797 +PSBBMHD,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

3 + 3 + 3 + 3 + 3 = 35

",,0,True || False,FALSE,228402 +PSBBE7Q,1,Multiple Choice (select 1),Multiple Choice,"

The table shows how fast light waves or electricity can travel through different materials.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
materialspeed (meters per second)
space300,000,000
water
copper wire (electricity)280,000,000
diamond
ice
olive oil200,000,000
+

 

+

Which is faster, light through diamond or light through ice?

",,,light through diamond || light through ice,light through ice,198121 +PRABFKNZ,1,Multiple Choice (select all),Check All That Apply,"
+

Noah’s water bottle contains more than 1 quart of water but less than 112 quarts. Let w be the amount of water in Noah’s bottle, in quarts. Select all the true statements.

+
",,,"

w could be 34.

||

w could be 1.

||

w > 1

||

w could be 43.

||

w could be 54.

||

w could be 53.

||

w > 1.5

","

w > 1

||

w could be 43.

||

w could be 54.

",262820 +PSBCM9V,1,Multiple Choice (select all),Check All That Apply,"

Select all of the equations that describe the situation. If you get stuck, draw a diagram.

+

 

+

 

+

A coach formed teams of 8 from all the players in a soccer league. There are 14 teams. How many players are in the league?

",,,"

y = 14 ÷ 8

||

y8 = 14

||

18 y = 14 

||

y = 14 · 8

","

y8 = 14

||

18 y = 14 

||

y = 14 · 8

",406643 +PSBEPA,1,Multiple Choice (select 1),Multiple Choice,"

A restaurant sells 10 tacos for $8.49, or 6 of the same kind of taco for $5.40.

+

 

+

Which is the better deal?

+

 

",,,10 for $8.49 || 6 for $5.40,10 for $8.49,23593 +PSBCRHQ,3,Multiple Choice (select 1),Multiple Choice,

Is the percentage illumination of the moon's surface a linear function of the day?

,,,Yes || No,No,426071 +PRABQMWZ,1,Multiple Choice (select 1),Multiple Choice,"

These four numbers are plotted on a number line:  -23, 58, -35,-12

+

 

+

Which is the correct ordering on the number line, from left to right?

",,,"

-12, -35, -23, 58

||

-12, -35, 58, -23

||

-23, -35, -12, 58

||

-35, -23, -12, 58

","

-23, -35, -12, 58

",69186 +PSBCJQB,2,Multiple Choice (select 1),Multiple Choice,

Is there a proportional relationship between the perimeter and side length? 

,,,Yes || No,Yes,392468 +PRABEVSG,1,Multiple Choice (select all),Check All That Apply,"

Here is the graph for one of the equations in a system of two equations.

+

 

+

+

 

+

The solution to the system is (6, 2). Select all the equations that could be the other equation in the system.

",,,"

y=-3x

||

y=-32x+6

||

y=-16x+3

||

y=23x-1

||

y=12x-1

||

y=4x-2

","

y=-16x+3

||

y=12x-1

",297047 +PRABGY9N,1,Multiple Choice (select all),Check All That Apply,"

Study the examples and non-examples of bases and heights in a triangle. Answer the questions that follow.

+
    +
  • These dashed segments represent heights of the triangle.
    • +
+

+
    +
  • These dashed segments do not represent heights of the triangle.
    • +
+

+

 

+

Select all the statements that are true about bases and heights in a triangle.

",,,"Any side of a triangle can be a base. || There is only one possible height. || A height is always one of the sides of a triangle. || A height that corresponds to a base must be drawn at an acute angle to the base. || A height that corresponds to a base must be drawn at a right angle to the base. || Once we choose a base, there is only one segment that represents the corresponding height. || A segment representing a height must go through a vertex.",Any side of a triangle can be a base. || A height that corresponds to a base must be drawn at a right angle to the base.,306997 +PRABEVAJ,1,Multiple Choice (select 1),Multiple Choice,"

Let x=-118 and y=-114

+

 

+

+

 

+

Which expression has a negative value?

",,,"

x + y

||

x - y

||

x • y

||

xy

",

x + y

,69444 +PSBDA8S,1,Multiple Choice (select 1),Multiple Choice,"

We saw that it is possible to fit three copies of regular hexagons snugly around a point.

+

Each interior angle of a regular pentagon measures 108°. Is it possible to fit copies of a regular pentagon snugly around a point?

+

",,,Yes || No,No,525911 +PRABETN3,1,Multiple Choice (select all),Check All That Apply,"

Select all the options that have the same value as 312% of 20.

",,,"

3.5% of 20

||

312 · 20

||

(0.35) · 20

||

(0.035) · 20

||

7% of 10

",

3.5% of 20

||

(0.035) · 20

||

7% of 10

,184732 +PSBUPJ,2,Multiple Choice (select 1),Multiple Choice,"

Is the decimal of 1850 also 0.36?

+

 

",,,Yes || No,Yes,93346 +PRABQP65,1,Multiple Choice (select 1),Multiple Choice,"

Each of the following gives the lengths, in inches, of the sides of a triangle. Which one is a right triangle?

",,,"

3, 4, 6

||

4, 6, 8

||

5, 12, 13

||

5, 5, 10

","

5, 5, 10

",315914 +PSBD2M4,1,Multiple Choice (select 1),Multiple Choice,"

This diagram shows four small squares and one rectangle composed of 10 small squares.

+

 

+

+

 

+

Andre says that this diagram can represent 140. Do you agree with Andre?

",,,Yes || No,Yes,655190 +PRABQM3Q,1,Multiple Choice (select 1),Multiple Choice,

Which estimate is closest to the actual value of (3.99437) · (2.6851)?

,,10,14.2 || 12.6 || 10.8 || 8.3,10.8,61617 +PRABEQ3T,1,Multiple Choice (select 1),Multiple Choice,"

Which is the best explanation for why -10 is irrational?

",,,"

-10 is irrational because it is not rational.

||

- 10 is irrational because it is less than zero.

||

-10 is irrational because it is not a whole number.

||

-10 is irrational because if I put -10 into a calculator, I get -3.16227766, which does not make a repeating pattern.

","

-10 is irrational because if I put -10 into a calculator, I get -3.16227766, which does not make a repeating pattern.

",10283 +PRABEPN4,1,Multiple Choice (select 1),Multiple Choice,"

Which value is an exact solution of the equation m2 = 14?

",,,"

7

||

14

||

3.74

||

3.74

","

14

",146354 +PSBB9TA,1,Multiple Choice (select 1),Multiple Choice,"

Your teacher will give you 2 pieces of a 6-piece puzzle.

+

 

+

If you drew scaled copies of your puzzle pieces using a scale factor of 12, would they be larger or smaller than the original pieces?

",,,Larger || Smaller,Smaller,341397 +PSBCNJA,4,Multiple Choice (select 1),Multiple Choice,"

Andre surveyed a random sample of 20 students and found that 13 of them were in favor of having school start one hour later.

+

 

+

Do you think it would be surprising if 100 students out of 250 were in favor?

",,,Yes || No,Yes,408023 +PSBDDB9,1,Multiple Choice (select 1),Multiple Choice,"

Priya rewrites the expression 8y−24 as 8(y−3). Han rewrites 8y−24 as 2(4y−12).

+

Are Priya's and Han's expressions each equivalent to 8y−24?

",,,Yes || No,Yes,538288 +PRABQNC9,1,Multiple Choice (select 1),Multiple Choice,

Which table represents a proportional relationship?

,,," + + + + + + + + + + + + + + + + + + +
00
26
39
412
+

 

|| + + + + + + + + + + + + + + + + + + +
012
26
33
40
+

 

|| + + + + + + + + + + + + + + + + + + +
06
212
315
418
+

 

||

 

+ + + + + + + + + + + + + + + + + + + +
00
24
39
416
+

 

"," + + + + + + + + + + + + + + + + + + +
00
26
39
412
+

 

",409242 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681 +PSBBMG6,3,Multiple Choice (select 1),Multiple Choice,"

Kiran started his homework before 7:00 p.m. and finished his homework after 8:00 p.m. Let h represent the number of hours Kiran worked on his homework.

+

 

+

Decide if the statement it is definitely true, definitely not true, or possibly true.

+

 h>2

",,,Definitely True || Definitely Not True || Possibly True,Possibly True,227828 +PRABQP25,1,Multiple Choice (select all),Check All That Apply,

Select all the proportional relationships.

,,,"

|| + + + + + + + + + + + + + + + + + + + + + + + + + + +
xy
06
39
612
915
1218
|| + + + + + + + + + + + + + + + + +
day1234
number of cell phones sold5101520
||

y=13x, where x and y are both positive numbers.

||

Clare borrowed $100 from her father. She pays him back $10 each week. M is the amount of money Clare still owes, and W is the number of weeks: 100-10W=M

","

|| + + + + + + + + + + + + + + + + +
day1234
number of cell phones sold5101520
||

y=13x, where x and y are both positive numbers.

",595744 +PSBZP8,1,Multiple Choice (select all),Check All That Apply,"

The table shows records of money-related activities of a bakery owner over a period of a week.

+

 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DateItemsAmount in Dollars
May 1Rent-850.00
May 2Order (Birthday Cake and Cookies)106.75
May 3Utilities (Electricity, Gas, Phone)-294.50
May 5Order (Wedding Cake and Desserts)240.55
May 5Baking Supplies-147.95
May 6Order (Anniversary Cake)158.20
May 7Order (Breads and Desserts for a Conference)482.30
May 7Bakery Sales415.65
+

 

+

 

+

For which items did she receive money?

+

 

",,,

Rent

||

Orders

||

Utilities

||

Baking Supplies

||

Bakery Sales

,

Orders

||

Bakery Sales

,122792 +PSBU2,2,Multiple Choice (select 1),Multiple Choice,"

Is the point (1, 60) on the graph?

+

 

+

",,,Yes || No,Yes,2516 +PRABFJQN,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 123.

",,,"

12 · 12 · 12

||

123

||

132

||

16

||

18

","

12 · 12 · 12

||

123

||

18

",435477 +PSBBVZJ,1,Multiple Choice (select 1),Multiple Choice,

Circle A has a diameter of 1 foot. Circle B has a circumference of 1 meter. Which circle is bigger? (1 inch = 2.54 centimeters)

,,,Circle A || Circle B,Circle B,274856 +PSBC4G,1,Multiple Choice (select 1),Multiple Choice,"

The volume, V, of a cube with edge length s cm is given by the equation V=s3.

+

 

+

The volume of a sphere is a function of its radius (in centimeters), and the graph of the relationship is shown here.

+

 

+

+

 

+

Is the volume of the cube with edge length s = 3 greater or less than the volume of a sphere with radius 3?

",,,Greater than || Less than,Less than,15007 +PSBCRQU,5,Multiple Choice (select 1),Multiple Choice,

Use the decimal representations to decide which of these fractions has the greatest value.

,,,"

925

||

1130

||

411

","

1130

",427041 +PRABQKS5,1,Multiple Choice (select 1),Multiple Choice,

Jada made 6 cups of blueberry jam and divided the jam equally among 4 containers. How much jam went in each container?

,,,"

23 of a cup

||

1 cup

||

32 of a cup

||

24 cups

","

32 of a cup

",588423 +PSBS56,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

17 · 17 · 17 = 37

",,0,True || False,FALSE,84517 +PRABQPZA,1,Multiple Choice (select 1),Multiple Choice,"

A pool holds 19,900 gallons of water. There are two hoses that can be used to fill the pool, a large one and a small one. On an average day, it takes 5 hours to fill the pool with the large hose and 12 hours with the small hose. Which graph best represents this scenario?

",,,"

||

||

||

","

",211312 +PRABQPZZ,1,Multiple Choice (select 1),Multiple Choice,"

What is the solution to 3x + 30 + x = 10 + 2x + 5x + 2?

",,,"

18

||

6

||

92

||

-2

",

6

,150654 +PRABQKRX,1,Multiple Choice (select all),Check All That Apply,

Select all of the trips that would take 2 hours.

,,,"

Drive 60 miles per hour between Buffalo and Seneca Falls, which are 120 miles apart.

|| Walk 3 miles per hour to school, which is 1.5 miles away. || Take a train going 80 miles per hour from Albany to New York City, which are 160 miles apart.","

Drive 60 miles per hour between Buffalo and Seneca Falls, which are 120 miles apart.

|| Take a train going 80 miles per hour from Albany to New York City, which are 160 miles apart.",560316 +PSBBBHJ,3,Multiple Choice (select all),Check All That Apply,"

Select all heights that could be Andre's height in centimeters. If you get stuck, consider drawing a number line to help you.

",,,

150

||

154.5

||

160

||

162.5

||

164

,

154.5

||

160

||

162.5

,177985 +PRABEJZ2,1,Multiple Choice (select all),Check All That Apply,"

Here is a scatter plot that shows the number of points and assists by a set of hockey players. Select all the following that describe the association in the scatter plot:

+

 

+

",,,Linear association || Non-linear association || Positive association || Negative association || No association,Linear association || Positive association,400715 +PSBB8W,1,Multiple Choice (select 1),Multiple Choice,"
+

Here is a table that shows elevations of various cities.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
cityelevation (feet)
Harrisburg, PA320
Bethell, IN1,211
Denver, CO5,280
Coachella, CA-22
Death Valley, CA-282
New York City, NY33
Miami, FL0
+

 

+

On the list of cities, which city has the second highest elevation?

+
+
+

Here is a situation involving changes in temperature and a number line.

+

 

+

2. At noon, the temperature was 5 degrees Celsius. By late afternoon, it has risen 6 degrees Celsius. What was the temperature late in the afternoon?

+

a. Represent each change on a number line. 

+

+

Draw your number line on paper, take a picture, and upload it using the image upload icon 

+

If you do not have the ability to upload an image of your work type ""Number line is on paper.""

+
 
+
copied for free from openupresources.org
+
",,,"Harrisburg, PA || Bethell, IN || Denver, CO || Coachella, CA || Death Valley, CA || New York City, NY || Miami, FL","Bethell, IN",9624 +PSBBRM,1,Multiple Choice (select all),Check All That Apply,

Which of these triangles are definitely right triangles? (Note that not all triangles are drawn to scale.)

,,,"

||

||

||

||

","

||

||

",7398 +PSBNEN,1,Multiple Choice (select 1),Multiple Choice,"

Lin and Diego travel in cars on the highway at constant speeds. Decide who was traveling faster.

+

 

+

During the first half hour, Lin travels 23 miles while Diego travels 25 miles.

",,,Diego || Lin,Diego,59099 +PSBMSA,1,Multiple Choice (select 1),Multiple Choice,"

Two cars drive on the same highway in the same direction. The graphs show the distance, d, of each one as a function of time, t. Which car drives faster?

+

 

+

",,,Car A || Car B,Car B,55933 +PSBBUJU,2,Multiple Choice (select 1),Multiple Choice,

The mean weight of this sample of seventh-grade backpacks is 6.3 pounds. Do you think the mean weight of backpacks for all seventh-grade students is exactly 6.3 pounds?

,,,Yes || No,No,267394 +PSBYSU,1,Multiple Choice (select 1),Multiple Choice,"

Andre and Noah each drew a triangle with side lengths of 5 cm and 3 cm and an angle that measures 60º, and then they showed each other their drawings. 

+

 

+

+

 

+

Did Andre and Noah draw different triangles?

",,,Yes || No,No,117623 +PRABFEWN,1,Multiple Choice (select all),Check All That Apply,"

Mai's water bottle has 24 ounces in it. After she drank x ounces of water, there are 10 ounces left.

+

 

+

Select all the equations that represent this situation.

",,,"

24 ÷ 10 = x

||

24 + 10 = x

||

24 - 10 = x

||

x + 10 = 24

||

10x = 24

","

24 - 10 = x

||

x + 10 = 24

",155072 +PSBR7A,1,Multiple Choice (select 1),Multiple Choice,

A corn vendor at a farmer's market was selling a bag of 8 ears of corn for $2.56. Another vendor was selling a bag of 12 for $4.32. Which bag is the better deal?

,,,Bag of 8 for $2.56 || Bag of 12 for $4.32,Bag of 8 for $2.56,78992 +PSB9SV,1,Multiple Choice (select 1),Multiple Choice,"

For the pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not.

+

 

+

 

+

Triangle C: 90, 37, ___; Triangle D: 90, 53, ___

",,,similar || not similar,similar,167875 +PRABQMBH,1,Multiple Choice (select 1),Multiple Choice,"

For part of a science experiment, Andre adds 0.25 milliliters of dye to 12.3 milliliters of water. How many milliliters does the mixture contain?

+

 

",,12,12.05 || 12.325 || 12.55 || 14.8,12.55,8347 +PRABFHN7,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that are equivalent to 5x + 30x - 15x.

",,,"

5(x + 6x - 3x)

||

(5 + 30 - 15) · x

||

x(5 + 30x - 15x)

||

5x(1 + 6 - 3)

||

5(x + 30x - 15x)

","

5(x + 6x - 3x)

||

(5 + 30 - 15) · x

||

5x(1 + 6 - 3)

",70516 +PRABQPY9,1,Multiple Choice (select 1),Multiple Choice,"

A successful music app tracked the number of song downloads each day for a month for 4 music artists, represented by lines , j, m, and d over the course of a month. Which line represents an artist whose downloads remained constant over the month?

+

 

+

",,,ℓ || j || m || d,m,211231 +PRABET9R,1,Multiple Choice (select all),Check All That Apply,

Select all values of x that make the inequality -x + 6 ≥ 10 true.

,,,-3.9 || 4 || -4.01 || -4 || 4.01 || 3.9 || 0 || -7,-4.01 || -4 || -7,51952 +PRABPUPZ,1,Multiple Choice (select all),Check All That Apply,"

Select all the numbers that are solutions to the equation x3 = 27.

",,,"

27

||

3

||

273

||

273

||

9

","

3

||

273

",46264 +PRABQKRW,1,Multiple Choice (select 1),Multiple Choice,

There are 15 pieces of fruit in a bowl and 6 of them are apples. What percentage of the pieces of fruit in the bowl are apples?

,,,0.06% || 0.4% || 6% || 40%,40%,560175 +PSBCN9R,1,Multiple Choice (select 1),Multiple Choice,"

On a map with a scale of 1 inch to 12 feet, the area of a restaurant is 60 in2. Han says that the actual area of the restaurant is 720 ft2. Do you agree or disagree?

",,,I agree || I disagree,I disagree,412048 +PRABFFUD,1,Multiple Choice (select 1),Multiple Choice,"

Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet?

+
 
",,,Closer || Farther,Farther,197878 +PSBQGM,1,Multiple Choice (select all),Check All That Apply,"

Are any of the figures B, C, or D scaled copies of figure A? 

+

 

+

",,,B || C || D || None,C,69785 +PRABQPRV,1,Multiple Choice (select all),Check All That Apply,

Select all the measures of center.

,,,mean || IQR (interquartile range) || MAD (mean absolute deviation) || median || range,mean || median,202762 +PRABEU6S,1,Multiple Choice (select all),Check All That Apply,

Select all the equations that are true when x is -4.

,,,"

 -8 = 2x

||

-12 = x · -3

||

-12 = x + x + x

||

x4 = -1

||

x + 4 = -8

||

x2 = -16

","

 -8 = 2x

||

-12 = x + x + x

||

x4 = -1

",195193 +PSB4CN,3,Multiple Choice (select 1),Multiple Choice,"

Jada’s family bought 50 tacos for a party and paid $72.

+

 

+

Were Jada’s tacos the same price as Noah’s tacos?

",,,Yes || No,No,138414 +PSBDF4U,1,Multiple Choice (select 1),Multiple Choice,"

The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.”

+

 

+

Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water.

+

 

+

Which person will get a color mixture that is the same shade as Perfect Purple Water? 

",,,Jada || Andre,Jada,554651 +PRABQMP2,1,Multiple Choice (select all),Check All That Apply,"

Rectangle A is 10 times as long as rectangle B.


+



+

If rectangle A is 80 units long, select all the ways find the length of rectangle B.

",,,"

Multiply 80 by 10.

||

Multiply 80 by 110.

||

Multiply 10 by 80.

||

Divide 80 by 10.

||

Divide 10 by 80.

||

Divide 80 by 110.

","

Multiply 80 by 110.

||

Divide 80 by 10.

",445267 +PSBTWF,1,Multiple Choice (select 1),Multiple Choice,

Diego thinks that x = 3 is a solution to the equation x2 = 16. Do you agree?

,,,Yes || No,No,88806 +PSBBB4U,1,Multiple Choice (select 1),Multiple Choice,"
+
+

Clare went to a concession stand that sells pretzels for $3.25, drinks for $1.85, and bags of popcorn for $0.99 each. She bought at least one of each item and spent no more than $10.

+
+
+
 
+
Could Clare have purchased 2 pretzels, 2 drinks, and 2 bags of popcorn? 
",,,Yes || No,No,180865 +PRABQPYQ,1,Multiple Choice (select 1),Multiple Choice,"

At a grocery store, 2 gallons of milk cost $7.20, and 5 gallons of milk cost $18.

+

 

+

Which equation relates the total cost, t, to the gallons of milk purchased, m?

",,,m = 7.2t || t = 7.2m || m = 3.6t || t = 3.6m,t = 3.6m,171936 +PSBCNJA,2,Multiple Choice (select 1),Multiple Choice,"

Andre surveyed a random sample of 20 students and found that 13 of them were in favor of having school start one hour later.

+

 

+

Do you think it would be surprising if 150 students out of 250 were in favor?

",,,Yes || No,No,407824 +PSBB4EW,3,Multiple Choice (select 1),Multiple Choice,"

Elena drank 3 liters of water yesterday. Jada drank 34 times as much water as Elena. Lin drank twice as much water as Jada.

+

 

+

 

+

Did Lin drink more or less water than Elena drank?

",,,More || Less,More,311333 +PSBBUJU,1,Multiple Choice (select 1),Multiple Choice,"

Consider the question: Do tenth-grade students' backpacks generally weigh more than seventh-grade students' backpacks?

+

Here are dot plots showing the weights of backpacks for a random sample of students from these two grades:

+

 

+

+

 

+

Did any seventh-grade backpacks in this sample weigh more than a tenth-grade backpack?

",,,Yes || No,Yes,267307 +PRABEPUE,1,Multiple Choice (select all),Check All That Apply,

Figure B is a scaled copy of Figure A. Select all of the statements that must be true.

,,,Figure B is larger than Figure A || Figure B has the same number of edges as Figure A || Figure B has the same perimeter as Figure A || Figure B has the same number of angles as Figure A || Figure B has angles with the same measures as Figure A,Figure B has the same number of edges as Figure A || Figure B has the same number of angles as Figure A || Figure B has angles with the same measures as Figure A,117237 +PSBCBNU,3,Multiple Choice (select 1),Multiple Choice,"

If Andre made another courtyard scale drawing at a scale of 1 to 12, would this drawing be smaller or larger than the first drawing?  

",,,

smaller than the first drawing

||

larger than the first drawing

,

larger than the first drawing

,352677 +PRABQPZ2,1,Multiple Choice (select 1),Multiple Choice,"

Which of the systems of equations has a solution of (-2, 6)?

",,,"

y=2x+10y=3x-6

||

 y-2x=2y+2x=10

||

x-y=9y=x+9

||

 x+2y =10-4x-y=2

","

 x+2y =10-4x-y=2

",77479 +PSBH5E,1,Multiple Choice (select 1),Multiple Choice,"

Which other expression has the same value as (-14)-8?

",,,(-14) + 8 || 14 − (-8) || 14 + (-8) || (-14) + (-8),(-14) + (-8),42327 +PSBSP9,1,Multiple Choice (select 1),Multiple Choice,"

The Amazon rainforest covered 6.42 million square kilometers in 1994. In 2014, it covered only 5059 as much. Which is closest to the area of the Amazon Forest in 2014? 

",,,

6.4 million km2

||

5.4 million km2

||

4.4 million km2

||

3.4 million km2

||

2.4 million km2

,

5.4 million km2

,81898 +PRABE4MA,1,Multiple Choice (select all),Check All That Apply,

Select all of the pieces of information that would tell you x and y have a proportional relationship. Let y represent the distance between a rock and a turtle's current position in meters and x represent the number of minutes the turtle has been moving.

,,,"

y = 3x

||

After 4 minutes, the turtle has walked 12 feet away from the rock.

||

The turtle walks for a bit, then stops for a minute before walking again.

||

The turtle walks away from the rock at a constant rate.

",

y = 3x

||

The turtle walks away from the rock at a constant rate.

,103020 +PSBS57,2,Multiple Choice (select 1),Multiple Choice,"

Which of these values is closest to the slope of the linear model shown in the scatter plot?

+

 

+

",,,"1,000 || 3,000 || -1,000 || -3,000","1,000",84657 +PRABQKWB,1,Multiple Choice (select all),Check All That Apply,"

Select all equations that represent this question:

+


Diego has run 23 of a race’s distance. He has run 812 kilometers. How long is the whole race?

",,,"

812 ÷ 23 = ?

||

23 ÷ 812= ?

||

23 · ? = 812

||

812 · ? = 23

||

812 · 32 = ?

||

812 · 23 = ?

","

812 ÷ 23 = ?

||

23 · ? = 812

||

812 · 32 = ?

",20916 +PRABHK6C,1,Multiple Choice (select 1),Multiple Choice,"

If the net is assembled, which of the following polyhedra would it make?

+

 

+

 

+

+

 

+

 

+

 

",,,"

||

||

||

","

",475896 +PSBZ3D,1,Multiple Choice (select 1),Multiple Choice,"

Choose the inequality that best matches the given situation.

+

 

+

The Science Club is researching boiling points. They learn that at high altitudes, water boils at lower temperatures. At sea level, water boils at 212° F With each increase of 500 feet in elevation, the boiling point of water is lowered by about 1° F.

",,,"

212-1500e<195

||

1500e-195<212

||

195-212e<1500

||

212-195e<1500

","

212-1500e<195

",124948 +PSBZKN,1,Multiple Choice (select 1),Multiple Choice,"
+
Quadrilateral A has side lengths 3, 6, 6, and 9. Quadrilateral B is a scaled copy of A with a shortest side length equal to 2. Jada says, “Since the side lengths go down by 1 in this scaling, the perimeter goes down by 4 in total.” Do you agree with Jada?
+
",,,Yes || No,No,122126 +PRABQP4H,1,Multiple Choice (select 1),Multiple Choice,"

Jada gathered data at her school among 7th and 8th graders to see if there was an association between grade level and playing sports. The table shows her data, but the number of 8th graders who play sports is missing.

+

 

+ + + + + + + +
+ + + + + + + + + + + + + + + + + + +
 play sportsdon't play sports
7th graders11252
8th graders 84
+
+

 

+

Jada found there was no evidence of an association between grade level and playing sports. Which of these could be the number of 8th graders who play sports?

",,181,248 || 181 || 144 || 69,181,604503 +PSBBBXW,1,Multiple Choice (select 1),Multiple Choice,"

Are these faces congruent?

+

 

+

+
 
",,,"Yes, they are congruent || No, they are not congruent","No, they are not congruent",180206 +PRABQM34,1,Multiple Choice (select all),Check All That Apply,"

This line plot shows the amount of time, in seconds, that it took 20 sixth graders to complete a set of 10 sit ups in gym class.

+

 

+

+

 

+

 

+

Select all the true statements.

",,,The difference between the fastest and slowest times was 0.9 seconds. || The fastest time was 7.0 seconds. || The fastest 3 students’ total time was 23.6 seconds. || No student recorded a time of 7.1 seconds. || Exactly half of the students were faster than 7.6 seconds.,The fastest 3 students’ total time was 23.6 seconds. || No student recorded a time of 7.1 seconds.,5038 +PRABE37Q,1,Multiple Choice (select all),Check All That Apply,"

Select all segments that could represent a corresponding height if the side n is the base.

+

 

+

",,,e || f || g || h || j || k || m || n,g || h,43170 +PRABQP3T,1,Multiple Choice (select all),Check All That Apply,"

This table shows a linear relationship between the age of a newborn baby in weeks and their weight. 

+

 

+ + + + + + + + + + + + + + + + + + + + + + + +
age (weeks)weight (pounds)
16
38
1015
1217
+

 

+

Select all the true statements. 

",,,The weight of the baby increases at a constant rate of 2 lbs every week.  || The weight of the baby increases at a constant rate of 1 lb every week.  || The weight of the baby increases at a constant rate of 1/2 lb every week.  || Age is a function of weight.  || Weight is a function of age. ,The weight of the baby increases at a constant rate of 1 lb every week.  || Age is a function of weight.  || Weight is a function of age. ,144363 +PSBEX7,1,Multiple Choice (select 1),Multiple Choice,"

Is the equation true or false?

+

 

+

4 × 105 × 4 × 104 = 4 × 1020

",,0,True || False,FALSE,25252 +PSBBGHB,1,Multiple Choice (select 1),Multiple Choice,"

Which is greater, -920 or -0.5?

+

 

+

If you get stuck, consider plotting the numbers on a number line.

",,,"

-920

||

-0.5

","

-920

",205980 +PRABG2WF,1,Multiple Choice (select 1),Multiple Choice,"

True or false?

+

 

+

",,1,True || False,TRUE,348818 +PRABQP45,1,Multiple Choice (select all),Check All That Apply,"

The graph shows the relationship between a sphere's radius and volume. 

+

 

+

+

 

+

Select all the statements that are true about this relationship. 

",,,"If the radius doubles, the volume doubles.  || If the radius doubles, the volume becomes about 4 times bigger.  || If the radius doubles, the volume becomes about 8 times bigger. || The relationship is linear.  || The relationship is not linear.","If the radius doubles, the volume becomes about 8 times bigger. || The relationship is not linear.",348832 +PRABQP3U,1,Multiple Choice (select all),Check All That Apply,"

The graph shows the amount of water in a bathtub starting at 10:00. Select all true statements. 

+

 

+

",,,"The tub was filling faster at 10:14 than at 10:01.  || At 10:06, the tub was neither filling nor draining.  || The maximum amount of water in the tub was about 35 gallons.  || The amount of water in the tub stayed the same from 10:16 to 10:20.  || It took 4 minutes for the tub to drain. ","At 10:06, the tub was neither filling nor draining.  || The maximum amount of water in the tub was about 35 gallons.  || It took 4 minutes for the tub to drain. ",144504 +PSBBZBV,1,Multiple Choice (select 1),Multiple Choice,"

The equation x ⋅ y = z could be true or false.

+

 

+

If x is 3, y is 4, and z is 12, is the equation true or false?

+

 

",,1,True || False,TRUE,293965 +PRABFFUC,1,Multiple Choice (select 1),Multiple Choice,"

Is a temperature of -11 degrees warmer or colder than a temperature of -15 degrees?

+
 
",,,Warmer || Colder,Warmer,197626 +PSBNS,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of shapes, decide whether or not Shape A is congruent to Shape B. 

+

 

+

 

",,,"Yes, they are congruent || No, they are not congruent","No, they are not congruent",1543 +PRABEDYM,1,Multiple Choice (select 1),Multiple Choice,"

Which story matches the equation -6 + 3x = 2 + 4x?

",,,"

At 5 p.m., the temperatures recorded at two weather stations in Antarctica are -6 degrees and 2 degrees. The temperature changes at the same constant rate, x degrees per hour, throughout the night at both locations. The temperature at the first station 3 hours after this recording is the same as the temperature at the second station 4 hours after this recording.

||

Elena and Kiran play a card game. Every time they collect a pair of matching cards, they earn x points. At one point in the game, Kiran has -6 points and Elena has 2 points. After Elena collects 3 pairs and Kiran collects 4 pairs, they have the same number of points.

","

At 5 p.m., the temperatures recorded at two weather stations in Antarctica are -6 degrees and 2 degrees. The temperature changes at the same constant rate, x degrees per hour, throughout the night at both locations. The temperature at the first station 3 hours after this recording is the same as the temperature at the second station 4 hours after this recording.

",233998 +PSBHS,1,Multiple Choice (select 1),Multiple Choice,"

For the following pair of shapes, decide whether or not they are congruent. 

+

 

+

",,,"Yes, they are congruent || No, they are not congruent","No, they are not congruent",885 +PRABQMFP,1,Multiple Choice (select 1),Multiple Choice,

Which expression is equivalent to 45a - 10b?

,,,5(9a - 10b) || 45(a - 10b) || 5(9a + 2b) || 5(9a - 2b),5(9a - 2b),350591 +PSBB5XG,1,Multiple Choice (select 1),Multiple Choice,"

Is this equation true?

+

",,,Yes || No,No,319310 +PSBBM9E,1,Multiple Choice (select 1),Multiple Choice,"

For the same data, two different models are graphed. Which model more closely matches the data?

",,,"

||

","

",232667 +PSBB58,1,Multiple Choice (select 1),Multiple Choice,"

Now, let’s look at rectangles ABCD and EFGH.

+

+


Jada says, “These rectangles are similar because all of the side lengths differ by 2.” Lin says, “These rectangles are similar. I can dilate AD and BC using a scale factor of 2 and AB and CD using a scale factor of 1.5 to make the rectangles congruent. Then I can use a translation to line up the rectangles.” Do you agree with either Jada or Lin? 

",,,Jada || Lin || Neither,Neither,9569 +PRABEC2T,1,Multiple Choice (select 1),Multiple Choice,"

Choose the equation that has solutions (5, 7) and (8, 13).

",,,3x - y = 8 || y = x + 2 || y - x = 5 || y = 2x - 3,y = 2x - 3,382378 +PSBVM,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of shapes, decide whether or not Shape A is congruent to Shape B. 

+

 

+

 

",,,"Yes, they are congruent || No, they are not congruent","No, they are not congruent",2541 +PSBBT8B,1,Multiple Choice (select 1),Multiple Choice,"

Which of the three triangles has the greatest area?  If you get stuck, try using what you know about the area of parallelograms.

",,,"

 

+

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

||

All three triangles have areas that are equal.

",

All three triangles have areas that are equal.

,264860 +PSBYNG,1,Multiple Choice (select 1),Multiple Choice,"

Which estimate is closest to the actual value of the expression? 

+

 

+

",,6,6 || 6.5 || 7,6.5,117002 +PSBBHQQ,1,Multiple Choice (select all),Check All That Apply,

Which of the following numbers are greater than 6 and less than 8?

,,,"

7

||

60

||

80

","

60

",212585 +PRABEVAX,1,Multiple Choice (select 1),Multiple Choice,"

At practice, Diego does twice as many push-ups as Noah, and also 40 jumping jacks. He does 62 exercises in total. The equation  describes this situation.

+

 

+

What does the variable x represent?

+
 
",,,The number of jumping jacks Diego does || The number of push-ups Diego does || The number of jumping jacks Noah does || The number of push-ups Noah does,The number of push-ups Noah does,308414 +PSBYKR,1,Multiple Choice (select all),Check All That Apply,"

The table shows the speed of light or electricity through different materials. Identify the speeds that are written in scientific notation.

+

 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
materialspeed (meters per second)
space
water
copper (electricity)
diamond
ice
olive oil
+

 

+

",,,Space || Water || Copper (electricity) || Diamond || Ice || Olive Oil,Water || Ice,116755 +PSBZXP,1,Multiple Choice (select 1),Multiple Choice,

Diego paid $47 for 3 tickets to a concert. Andre paid $141 for 9 tickets to a concert. Did they pay at the same rate?

,,,Yes || No,Yes,124302 +PRABEVSY,1,Multiple Choice (select all),Check All That Apply,

Select all the proportional relationships.

,,,"

||

A train is traveling at a constant speed of 60 miles per hour. The number of hours the train has been traveling is t. The number of miles the train has traveled is d.

||

The relationship is represented by this table:  

+

 

+ + + + + + + + + + + + + + + + + + + +
xy
36
412
524
||

y=3x, where x and y are both positive numbers.

||

y=1x

","

A train is traveling at a constant speed of 60 miles per hour. The number of hours the train has been traveling is t. The number of miles the train has traveled is d.

||

y=3x, where x and y are both positive numbers.

",1089 +PSBBNG,1,Multiple Choice (select 1),Multiple Choice,"

Predict if the mean is greater than, less than, or approximately equal to the median.

+

 

+

Heights of 50 NBA basketball players

+

",,,Greater than || Less than || Equal to,Equal to,6560 +PRABFEZJ,1,Multiple Choice (select all),Check All That Apply,

Select all the parallelograms that have an area of 16 square units.

,,,"

||

||

||

","

||

||

",55428 +PSBBRHC,4,Multiple Choice (select 1),Multiple Choice,

Is it linear?

,,,Yes || No,No,250205 +PSBZV8,2,Multiple Choice (select 1),Multiple Choice,"

If each person ran at a constant speed the entire time, who was running faster? 

",,,Mai || Jada,Mai,124027 +PSBB7N6,1,Multiple Choice (select 1),Multiple Choice,"

Here is a 15-by-8 rectangle divided into triangles. Is the shaded triangle a right triangle? 

+

 

+
+

+
",,,Yes || No,No,329307 +PSBBSWV,1,Multiple Choice (select 1),Multiple Choice,"

State whether the following is in scientific notation.

+

 

+

0.00099

",,,Already in scientific notation || Not in scientific notation,Not in scientific notation,257260 +PSBB9D3,2,Multiple Choice (select 1),Multiple Choice,"

The reading on a car’s speedometer has 1.6% maximum error. The speed limit on a road is 65 mph.

+

 

+

The speedometer reads 66 mph. Is the car definitely going over the speed limit?

",,,Yes || No,No,339477 +PSBN96,3,Multiple Choice (select 1),Multiple Choice,"

Answer the question “Which is taller, the Burj Khalifa or a stack of the money it cost to build the Burj Khalifa?”

",,,Burj Khalifa || Stack of money,Stack of money,63639 +PSBBS2Y,3,Multiple Choice (select 1),Multiple Choice,

Clare estimates the students at her school spend an average of 1.2 hours each night doing homework. Priya estimates the students at her school spend an average of 2 hours each night watching TV. Which of these two estimates is likely to be closer to the actual mean value for all the students at their school?

,,,Clare's estimate || Priya's estimate,Clare's estimate,257987 +PSBF2G,1,Multiple Choice (select 1),Multiple Choice,"

Is there a rigid transformation taking Rectangle A to Rectangle B? 

+

",,,Yes || No || Not enough information,No,30936 +PSBCN6R,1,Multiple Choice (select 1),Multiple Choice,"
+

A map of a park has a scale of 1 inch to 1,000 feet. Another map of the same park has a scale of 1 inch to 500 feet. Which map is larger?

+
",,,"The map with scale 1 inch to 1,000 feet || The map with scale 1 inch to 500 feet",The map with scale 1 inch to 500 feet,411481 +PSBBMKA,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the equation is true or false.

+

 

+

53 = 5 ⋅ 5 ⋅ 5

",,1,True || False,TRUE,228808 +PRABHQC6,1,Multiple Choice (select 1),Multiple Choice,

Which figure has the largest shaded region?

,,,"

||

||

","

",91796 +PRABEJCQ,1,Multiple Choice (select all),Check All That Apply,"

Select all of the following that are equivalent to 110,000:

",,,"

(10,000)-1

||

(-10,000)

||

(100)-2

||

(10)-4

||

(-10)2

","

(10,000)-1

||

(100)-2

||

(10)-4

",208025 +PSBHNF,3,Multiple Choice (select 1),Multiple Choice,

Should Noah conclude that there is a meaningful difference in the mean number of movies watched over winter break between the two groups? 

,,,Yes || No,Yes,39707 +PRABQM83,1,Multiple Choice (select 1),Multiple Choice,"

A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area of the actual park, in square yards?

+

 

+

",,,"35 || 200 || 1,400 || 56,000","56,000",116142 +PRABQPRD,1,Multiple Choice (select all),Check All That Apply,

Select all the conditions for which it is possible to construct a triangle. 

,,,"A triangle with angle measures 40°, 60°, and 80° || A triangle with side lengths 3 cm, 7 cm, and 11 cm || A triangle with side lengths 6 in, 13 in, and 12 in || A triangle with side lengths 8 cm and 5 cm and a 90° angle || A triangle with angle measures 120° and 70°, and a 9 cm side length","A triangle with angle measures 40°, 60°, and 80° || A triangle with side lengths 6 in, 13 in, and 12 in || A triangle with side lengths 8 cm and 5 cm and a 90° angle",558187 +PSBVHS,2,Multiple Choice (select 1),Multiple Choice,

Which team improved the most?

,,,football team || basketball team || baseball team,baseball team,98864 +PRABEVTN,1,Multiple Choice (select all),Check All That Apply,"

The graph shows the relationship between the radius and volume for many cones whose height is 6 inches.

+

 

+

+

 

+

Select all the true statements about such cones.

",,,"The relationship between radius and volume is linear. || The relationship between radius and volume is not linear. || If the radius of the cone doubles, the volume of the cone doubles. || If the radius of the cone doubles, the volume of the cone is multiplied by 4. || If the radius of the cone is 2 inches, the volume of the cone is about 25 cubic inches.","The relationship between radius and volume is not linear. || If the radius of the cone doubles, the volume of the cone is multiplied by 4. || If the radius of the cone is 2 inches, the volume of the cone is about 25 cubic inches.",297716 +PSB7VY,1,Multiple Choice (select 1),Multiple Choice,"

A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says, “The snail was traveling faster because it went a greater distance.” Do you agree with Mai? 

",,,I agree || I disagree,I disagree,157878 +PSBCKRV,3,Multiple Choice (select 1),Multiple Choice,

Who won the race?

,,,Elena || Jada || It's a tie,It's a tie,398888 +PRABFG3G,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that represent the area of the shaded rectangle.

+

 

+

",,,"

3(10 - c)

||

3(c - 10)

||

10(c - 3)

||

10(3 - c)

||

30 - 3c

||

30 - 10c

","

3(10 - c)

||

30 - 3c

",87743 +PRABEEZR,1,Multiple Choice (select all),Check All That Apply,"

The solution to a system of equations is (5, -19). Choose two equations that might make up the system.

",,,y = -3x - 6 || y = 2x - 23 || y = -7x + 16 || y = x - 17 || y = -2x - 9,y = -7x + 16 || y = -2x - 9,104427 +PRABEQAX,1,Multiple Choice (select 1),Multiple Choice,

For which triangle does the Pythagorean Theorem express the relationship between the lengths of its three sides?

,,,"

||

||

||

","

",8202 +PSBBBY4,4,Multiple Choice (select 1),Multiple Choice,

The customer wants the window to have 5 feet of space above it. Is the customer describing a or b?

,,,a || b,a,180292 +PSBDBQU,2,Multiple Choice (select 1),Multiple Choice,

Which group shows greater variability?

,,,Group A || Group B,Group A,529063 +PSBYSB,2,Multiple Choice (select 1),Multiple Choice,

Who wins?

,,,Mai || Tyler,Mai,117709 +PSBCHEJ,1,Multiple Choice (select 1),Multiple Choice,"

Lin was looking at the equation 2x − 32 + 4(3x − 2462) = 14x.

+

 

+

She said, “I can tell right away there are no solutions, because on the left side, you will have 2x + 12x and a bunch of constants, but you have just 14x on the right side.”

+

 

+

Do you agree with Lin?

",,,Yes || No,Yes,386019 +PRABN748,1,Multiple Choice (select all),Check All That Apply,

Select all the ratios that are equivalent to each other. 

,,,

4 : 7

||

8 : 15

||

16 : 28

||

2 : 3

||

20 : 35

,

4 : 7

||

16 : 28

||

20 : 35

,650734 +PSBHA6,1,Multiple Choice (select 1),Multiple Choice,"

Noah says, “There are 212groups of 45 in 2."" Do you agree with him?

",,,Yes || No,Yes,37956 +PSBDG7H,1,Multiple Choice (select 1),Multiple Choice,"

The two lines represent the amount of water, over time, in two tanks that are the same size. Which container is filling more quickly?

+

 

+

",,,Container A || Container B,Container A,560139 +PSBKBK,1,Multiple Choice (select 1),Multiple Choice,

Which elevation is higher: 8 feet below sea level or 13 feet below sea level?

,,,8 feet below sea level || 13 feet below sea level,8 feet below sea level,48097 +PRABFF3M,1,Multiple Choice (select all),Check All That Apply,"

Which expressions are solutions to the equation 34x = 15?  Select all that apply.

",,,"

 

+

1534

+

 

||

 

+

1543

+

 

||

 

+

43 · 15

+

 

||

 

+

34 · 15

+

 

||

 

+

15 ÷ 34

","

 

+

1534

+

 

||

 

+

43 · 15

+

 

||

 

+

15 ÷ 34

",222789 +PSBN47,2,Multiple Choice (select all),Check All That Apply,

Which of the following could be points on the graph of your equation?

,,,"

(1.75, 1)

||

(2, 3.50)

||

(5, 8.75)

||

(17.50, 10)

||

(9, 15.35)

","

(2, 3.50)

||

(5, 8.75)

",63340 +PRABG2WE,1,Multiple Choice (select 1),Multiple Choice,"

True or false?

+

 

+

",,0,True || False,FALSE,348711 +PRABPUDN,1,Multiple Choice (select all),Check All That Apply,"

Diego made the shape on the left, and Elena made the shape on the right. Each shape uses 5 circles.

+

+

Select all the true statements. 

",,,The smallest circle in Diego's design is congruent to the smallest circle in Elena’s design. || Diego’s design is congruent to Elena’s design. || Elena’s design is a translation of Diego's design. || The largest circle in Elena's design is congruent to the largest circle in Diego's design. || Each circle in the Elena's design has a congruent circle within Diego's design.,The smallest circle in Diego's design is congruent to the smallest circle in Elena’s design. || The largest circle in Elena's design is congruent to the largest circle in Diego's design. || Each circle in the Elena's design has a congruent circle within Diego's design.,545012 +PSBEXG,2,Multiple Choice (select 1),Multiple Choice,"

Decide whether the table could represent a proportional relationship.

+

 

+

Bettie's Boutique is having a 20% off sale.

+

 

+ + + + + + + + + + + + + + + + + + + +
original pricesale price
$15$12
$25$20
$35$28
",,,"

Yes, it is proportional

||

No, it is not proportional

","

Yes, it is proportional

",24737 +PRABETM5,1,Multiple Choice (select all),Check All That Apply,

Elena walked 12 miles. Then she walked 0.25 that distance. How far did she walk altogether? Select all that apply.

,,,12 + 0.25 · 12 || 12(1 + 0.25) || 12 · 1.25 || 12 · 0.25 || 12 + 0.25,12 + 0.25 · 12 || 12(1 + 0.25) || 12 · 1.25,25178 +PRABFBT6,1,Multiple Choice (select 1),Multiple Choice,

A soccer field is 100 meters long. What could be its length in yards?

,,,

33.3

||

91

||

100

||

109

,

109

,79597 +PRABETDG,1,Multiple Choice (select all),Check All That Apply,"

Last week, it rained g inches. This week, the amount of rain decreased by 5%. Which expressions represent the amount of rain that fell this week? Select all that apply.

",,,

g - 0.05

||

g - 0.05g

||

0.95g

||

0.05g

||

(1 - 0.05)g

,

g - 0.05g

||

0.95g

||

(1 - 0.05)g

,181762 +PSBBRB7,1,Multiple Choice (select 1),Multiple Choice,"

Tyler thinks that this figure has enough information to figure out the values of a and b. Do you agree? 

+

",,,Yes || No,No,249250 +PSBQ5D,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations that describe the situation.

+

 

+
+
+
+

Each notebook contains 60 sheets of paper. Andre has 5 notebooks. How many sheets of paper do Andre’s notebooks contain?

+
+
+
",,,"

y = 60 ÷ 5

||

y = 5 · 60 

||

y5 = 60

||

5y= 60

","

y = 5 · 60 

||

y5 = 60

",73585 +PSBBHQ2,1,Multiple Choice (select 1),Multiple Choice,"

Which is larger, a cubic inch or a cubic centimeter?

",,,cubic inch || cubic centimeter,cubic inch,212537 +PSBBDBK,2,Multiple Choice (select 1),Multiple Choice,"

Based on the graph, can this be a proportional relationship?

",,,Yes || No,No,187804 +PSBCRPW,1,Multiple Choice (select 1),Multiple Choice,"

Decide whether the inequality statement is true or false. 

+

 

+

-12 > -15

",,1,True || False,TRUE,426918 +PRABEAG9,1,Multiple Choice (select all),Check All That Apply,"

Elena’s aunt pays her $1 for each call she makes to let people know about her aunt’s new business.

+

 

+

The table shows how much money Diego receives for washing windows for his neighbors.

+

 

+ + + + + + + + + + + + + + + + + + + +
number of windowsnumber of dollars
2730
4550
8190
+

 

+

 

+

Select all the statements about the situation that are true.

",,,"

Elena makes more money for making 10 calls than Diego makes for washing 10 windows.

||

Diego makes more money for washing each window than Elena makes for making each call.

||

Elena makes the same amount of money for 20 calls as Diego makes for 18 windows.

||

Diego needs to wash 35 windows to make as much money as Elena makes for 40 calls.

||

The equation y = 910x, where y is number of dollars and x is number of windows, represents Diego’s situation.

||

The equation y = x, where y is number of dollars and x is number of calls, represents Elena’s situation.

","

Diego makes more money for washing each window than Elena makes for making each call.

||

Elena makes the same amount of money for 20 calls as Diego makes for 18 windows.

||

The equation y = x, where y is number of dollars and x is number of calls, represents Elena’s situation.

",192118 +PSBCWSX,1,Multiple Choice (select all),Check All That Apply,"

Here are some fractions.

+

 

+

Select all the fractions that are equal to 8.2.

",,,"

820100

||

8201000

||

821000

||

82010

||

8210

||

82100

","

820100

||

8210

",455868 +PSBMG9,1,Multiple Choice (select 1),Multiple Choice,"

Without evaluating each expression, determine which value is the greatest.

",,,"

756 - 934

||

-756 + -934

||

-756 · 934

||

-756 ÷ -934

","

-756 ÷ -934

",54627 +PSBBVEV,1,Multiple Choice (select 1),Multiple Choice,"

A shopper needs 48 hot dogs. The store sells identical hot dogs in 2 differently sized packages. They sell a six-pack of hot dogs for $2.10, and an eight-pack of hot dogs for $3.12. Should the shopper buy 8 six-packs, or 6 eight-packs?

",,,8 six-packs || 6 eight-packs,8 six-packs,271838 +PSBYUC,3,Multiple Choice (select 1),Multiple Choice,

Which numbers—positive or negative—result in fewer bottles in the machine?

,,,positive || negative,negative,117788 +PSBF4M,1,Multiple Choice (select 1),Multiple Choice,"

Choose the equation that the diagram does not match.

+

",,,6 + 3x = 30 || 3(x + 6) = 30 || 3x = 30 − 6 || 30 = 3x + 6,3(x + 6) = 30,31406 +PSBH6F,1,Multiple Choice (select 1),Multiple Choice,"
    +
  •  Clare mixes 212 cups of water with 13 cup of orange juice concentrate.
    • +
+

 

+
    +
  • Han mixes 123 cups of water with 14 cup of orange juice concentrate.
    • +
+

 

+

 

+

Whose orange juice mixture tastes stronger?

",,,

Claire

|| Han,Han,42365 +PSBB3M4,2,Multiple Choice (select 1),Multiple Choice,

Did the student answer less than or more than 75% of the questions correctly?

,,,Less than 75% || More than 75%,More than 75%,307493 +PRABFK4F,1,Multiple Choice (select 1),Multiple Choice,"

Here is a table that shows student's scores for 10 rounds of a video game.

+

 

+ + + + + + + + + + + + + + + +
130150120170130120160160190140
+

 

+

What is the median score?

",,145,125 || 145 || 147 || 150,145,253922 +PSBKV,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of shapes, decide whether or not Shape A is congruent to Shape B. 

+

 

+

",,,"Yes, they are congruent || No, they are not congruent","Yes, they are congruent",1239 +PRABFG4D,1,Multiple Choice (select all),Check All That Apply,"

Andre says, “I multiplied 4 by 5, then cubed the result.”

+

Select all expressions that equal Andre’s answer.

",,,"4 · 5³ || (4 · 5)³ || (4 · 5)² || (5³) · 4 || 20³ || 500 || 8,000","(4 · 5)³ || 20³ || 8,000",47649 +PSBEQY,1,Multiple Choice (select 1),Multiple Choice,"

Last night, everyone at the school music concert wrote their age on a slip of paper and placed it in a box. Today, each of the students in a math class selected a random sample of size 10 from the box of papers. Here is a dot plot showing their sample means, rounded to the nearest year.

+

 

+

+

 

+

Does the number of dots on the dot plot tell you how many people were at the concert or how many students are in the math class?

",,,the concert || the math class,the math class,23449 +PSBGCD,1,Multiple Choice (select 1),Multiple Choice,

Angle A in triangle ABC is obtuse. Can angle B or angle C be obtuse?

,,,Yes || No,No,32656 +PSBBQJ,3,Multiple Choice (select all),Check All That Apply,"

Which measure of center - the mean or the median - better describes a typical value for this distribution?

+

 

+

",,,Mean || Median,Median,7254 +PSBNZB,1,Multiple Choice (select 1),Multiple Choice,"

Noah will select a letter at random from the word “FLUTE.” Lin will select a letter at random from the word “CLARINET.”

+

 

+

Which person is more likely to pick the letter “E?”

",,,Noah || Lin,Noah,62442 +PRABETDA,1,Multiple Choice (select all),Check All That Apply,"

Elena walked 12 miles. Then she walked 14 that distance. How far did she walk all together? Select all that apply.

",,,"

12 + 14

||

12 · 14

||

12 + 14·12

||

121 + 14

||

12 · 34

||

12 · 54

","

12 + 14·12

||

121 + 14

||

12 · 54

",362542 +PRABEVRU,1,Multiple Choice (select 1),Multiple Choice,"

Which of these expressions is equivalent to 3(x-2)?

",,,3x − 6 || 3x − 2 || 3x + 2 || 3x + 6,3x − 6,52890 +PSBBS2Y,1,Multiple Choice (select 1),Multiple Choice,"

Clare and Priya each took a random sample of 25 students at their school.

+

 

+
    +
  • Clare asked each student in her sample how much time they spend doing homework each night. The sample mean was 1.2 hours and the MAD was 0.6 hours.
    • +
+

 

+
    +
  • Priya asked each student in her sample how much time they spend watching TV each night. The sample mean was 2 hours and the MAD was 1.3 hours.
    • +
+

 

+

At their school, do you think there is more variability in how much time students spend doing homework or watching TV?

",,,Doing homework || Watching TV,Watching TV,257569 +PSB4WS,2,Multiple Choice (select 1),Multiple Choice,"

A graph of a linear equation passes through (-2,0) and (0,-6).

+

 

+

Is  an equation for this graph?

+
 
",,,Yes || No,No,141750 +PSBBTTH,1,Multiple Choice (select 1),Multiple Choice,"

Noah said, “When you divide a number by a second number, the result will always be smaller than the first number.”

+

 

+

Jada said, “I think the result could be larger or smaller, depending on the numbers.”

+

 

+

Do you agree with either of them?

",,,I agree with Noah || I agree with Jada || I agree with both || I don't agree with either,I agree with Jada,262449 +PRABPH7F,1,Multiple Choice (select all),Check All That Apply,

Select all the ratios that are equivalent to the ratio 12:3.

,,,"6 : 1 || 1 : 4 || 4 : 1 || 24 : 6 || 15 : 6 || 1,200 : 300 || 112 : 13","4 : 1 || 24 : 6 || 1,200 : 300",218802 +PRABQM99,1,Multiple Choice (select all),Check All That Apply,

Rectangle A measures 8 inches by 2 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

,,,40 inches by 10 inches || 10 inches by 2.5 inches || 9 inches by 3 inches || 7 inches by 1 inch || 6.4 inches by 1.6 inches,40 inches by 10 inches || 10 inches by 2.5 inches || 6.4 inches by 1.6 inches,12129 +PRABFKNQ,1,Multiple Choice (select all),Check All That Apply,"

Lin and her friends went out for ice cream after school. The following questions came up during their trip.

+

 

+

Select all the questions that are statistical questions.

",,,

How far are we from the ice cream shop?

||

What is the most popular ice cream flavor this week?

||

What does a group of 4 people typically spend on ice cream at this shop?

||

Do kids usually prefer to get a cup or a cone?

||

How many toppings are there to choose from?

,

What is the most popular ice cream flavor this week?

||

What does a group of 4 people typically spend on ice cream at this shop?

||

Do kids usually prefer to get a cup or a cone?

,43132 +PRABE3F3,1,Multiple Choice (select all),Check All That Apply,"

The area of the square is 1 square unit. Two small triangles can be put together to make a square or to make a medium triangle.

+

 

+

 

+

+

 

+

 

+

Which figure also has an area of 112 square units? Select all that apply.

",,,"

||

||

||

","

||

||

",347199 +PRABPVSX,1,Multiple Choice (select all),Check All That Apply,"

Select all the expressions that represent the total area of the rectangle.

+

 

+

",,,"

4s

||

13s + 12

||

13 · s + 13 · 12

||

13s + 4

||

13 (s + 12)

","

13 · s + 13 · 12

||

13s + 4

||

13 (s + 12)

",367311 +PRABEDB2,1,Multiple Choice (select 1),Multiple Choice,"

For the equation, decide if it is always true or never true.

+

 

+

x − 13 = x + 1

",,,Always True || Never True,Never True,147769 +PSB72T,1,Multiple Choice (select 1),Multiple Choice,"

Tulip bulbs are on sale at store A at 5 for $11.00, and the regular price at store B is 6 for $13. Is each store pricing tulip bulbs at the same rate?

",,,Yes || No,No,158629 +PSB9AY,2,Multiple Choice (select 1),Multiple Choice,"

Without calculating, do you expect the slope of the line through (1, 11) and (8, 2) to be positive or negative?

",,,Positive || Negative,Negative,165038 +PRABG3XP,1,Multiple Choice (select 1),Multiple Choice,"

Is the value of the expression closer to 12, 1, or 112?

+

 

+

20 ÷ 18

+

 

+

 

",,,"

12

||

1

||

112

","

1

",127860 +PRABFFX6,1,Multiple Choice (select all),Check All That Apply,"

Select all of the nets that can be folded and assembled into a triangular prism like this one.

+

 

+

",,,"

||

||

||

","

||

",558559 +PRABFDN6,1,Multiple Choice (select all),Check All That Apply,"

Select all the statements that show correct reasoning for finding 1415 ÷ 75.  

",,,"

Multiplying 1415 by 5 and then by 17 .

||

Dividing 1415 by 5, and then multiplying by 17.

||

Multiplying 1415 by 7, and then multiplying by 15

||

Multiplying 1415 by 5 and then dividing by 7.

||

Multiplying 1514 by 7 and then dividing by 5.

","

Multiplying 1415 by 5 and then by 17 .

||

Multiplying 1415 by 5 and then dividing by 7.

",477073 +PSBUC9,5,Multiple Choice (select 1),Multiple Choice,"

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

+

 

+

Will Clare and Noah complete a sign at the same time?

",,,Yes || No,No,91177 +PSBBESN,2,Multiple Choice (select 1),Multiple Choice,"

If you connect the ends of the sides you drew to make a triangle, is the third side longer or shorter than 5 centimeters? 

",,,longer || shorter,shorter,196033 +PSB5PB,3,Multiple Choice (select 1),Multiple Choice,"

Here are some line segments.

+

 

+

+

 

+

 

+

Which segment is not a dilation of BC?

",,,ED || GJ || FH,ED,146131 +PRABETQQ,1,Multiple Choice (select 1),Multiple Choice,"

At the beginning of the month, there were 80 ounces of peanut butter in the pantry. Now, there is 13 less than that. How many ounces of peanut butter is in the pantry now?

",,,"

23 · 80

||

13 · 80

||

80 - 13

||

1 + 13 · 80

","

23 · 80

",327306 +PRABEVSF,1,Multiple Choice (select all),Check All That Apply,

Select all the systems of equations that have exactly one solution.

,,,"

y=3x+1y=-3x+7

||

y=3x+1y=x+1

||

y=3x+1y=3x+7

||

x+y=102x+2y=20

||

x+y=10x+y=12

","

y=3x+1y=-3x+7

||

y=3x+1y=x+1

",296856 +PRABQNDB,1,Multiple Choice (select 1),Multiple Choice,"

Kiran walked at a constant speed. He walked 1 mile in 15 minutes.

+

 

+

Which of these equations represents the distance d (in miles) that Kiran walks in t minutes?

",,,"

d = t + 14

||

d = t - 14

||

d = 15t

||

d = 115t

","

d = 115t

",409526 +PSB6ZC,1,Multiple Choice (select 1),Multiple Choice,"

Which travels faster: a car that travels 6 miles in 10 minutes at a constant speed, or a train that travels 6 miles in 8 minutes at a constant speed? 

",,,a car that travels 6 miles in 10 minutes at a constant speed || or a train that travels 6 miles in 8 minutes at a constant speed,or a train that travels 6 miles in 8 minutes at a constant speed,153145 +PSBKVA,1,Multiple Choice (select all),Check All That Apply,

A micrometer is an instrument that can measure lengths to the nearest micron (a micron is a millionth of a meter). Would this instrument be useful for measuring any of the following things?

,,,"1. The thickness of an eyelash, which is typically about 0.1 millimeters. || 2. The diameter of a red blood cell, which is typically about 8 microns. ||

3. The diameter of a hydrogen atom, which is about 100 picometers (a picometer is a trillionth of a meter).

","1. The thickness of an eyelash, which is typically about 0.1 millimeters. || 2. The diameter of a red blood cell, which is typically about 8 microns.",51243 +PSBDVUA,2,Multiple Choice (select all),Check All That Apply,"

Select all pairs of lines that appear to be parallel.

+

 

+

",,,m and p || m and r || m and s || m and t || p and r || p and s || p and t || r and s || r and t || s and t,s and t,627506 +PRABQPYP,1,Multiple Choice (select 1),Multiple Choice,"

To mix a particular shade of pink paint, white paint and red paint are mixed in the ratio 4 : 3. If 12 gallons of red paint are mixed with some white paint to make this same shade of pink, how many total gallons of pink paint result?

",,28,48 || 36 || 28 || 16,28,171809 +PSBCU6,3,Multiple Choice (select 1),Multiple Choice,"

Ten people can dig five holes in three hours. If n people digging at the same rate dig m holes in d hours:

+

 

+

Is m proportional to d when n = 10?

",,,Yes || No,Yes,13937 +PSBCNBJ,1,Multiple Choice (select 1),Multiple Choice,"

Here is Elena's work for finding the surface area of a rectangular prism that is 1 foot by 1 foot by 2 feet.

+

+

 

+

 

+

She concluded that the surface area of the prism is 296 square feet.

+

 

+

Do you agree with her conclusion?

",,,Yes || No,No,406876 +PSBFJW,1,Multiple Choice (select 1),Multiple Choice,"

Is the point (20, 13) on this line? 

+

 

+

",,,Yes || No,Yes,28352 +PRABQTQQ,1,Multiple Choice (select 1),Multiple Choice,"

Which of these expressions is equivalent to 0.05(x−40)?

+
 
",,,

0.05x - 40.05

||

0.05x - 40

||

0.05x - 2.05

||

0.05x - 2

,

0.05x - 2

,33992 +PRABQPRX,1,Multiple Choice (select 1),Multiple Choice,"

How far away is the point (-5, 2) from the x-axis? 

",,,7 units || 5 units || 3 units || 2 units,2 units,430244 +PSBBXYF,1,Multiple Choice (select all),Check All That Apply,

Select all triangles that have an area of 8 square units. 

,,,"

+

 

+

 

+

 

||

+

 

+

 

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

","

+

 

+

 

+

 

||

+

 

+

 

+

 

+

 

+

 

||

+

 

+

 

+

 

||

+

 

+

 

+

 

",286192 +PSBCW3W,1,Multiple Choice (select 1),Multiple Choice,"

Determine if the following is true or false.

+

 

+

-5 < 3

",,1,True || False,TRUE,457584 +PRABFBNV,1,Multiple Choice (select 1),Multiple Choice,

Tyler’s height is 57 inches. What could be his height in centimeters?

,,,"

3,551

||

22.4

||

57

||

144.8

",

144.8

,14257 +PSBS27,1,Multiple Choice (select 1),Multiple Choice,"

Jada is making a scale model of the solar system. The distance from Earth to the moon is about 2.389 × 105 miles. The distance from Earth to the sun is about 9.296 × 107 miles. She decides to put Earth on one corner of her dresser and the moon on another corner, about a foot away. Where should she put the sun?

+

 

+
+
    +
  • On a windowsill in the same room?
    • +
  • In her kitchen, which is down the hallway?
    • +
  • A city block away?
    • +
+

 

+
",,,"on a windowsill in the same room || in her kitchen, which is down the hallway || a city block away",a city block away,83841 +PSBBSG,1,Multiple Choice (select 1),Multiple Choice,"

The triangle has side lengths 7, 10, and 12. Is it a right triangle?

+
 
",,,Yes || No,No,7541 +PSBCNE9,1,Multiple Choice (select all),Check All That Apply,"

Select all of the equations that describe the situation. If you get stuck, draw a diagram.

+

 

+

 

+

Mai ran 27 miles last week, which was three times as far as Jada ran. How far did Jada run?

",,,"

3w = 27

||

w = 13 · 27

||

w = 27 ÷ 3

||

w = 3 · 27

","

3w = 27

||

w = 13 · 27

||

w = 27 ÷ 3

",407444 +PSBMYP,1,Multiple Choice (select 1),Multiple Choice,"

Kiran and Clare like to race each other home from school. They run at the same speed, but Kiran's house is slightly closer to school than Clare's house. On a graph, their distance from their homes in meters is a function of the time from when they begin the race in seconds.

+

 

+

As you read the graphs left to right, would the lines go up or down?

",,,up || down,down,56987 +PRABQPTU,1,Multiple Choice (select 1),Multiple Choice,"

Which of these expressions is equivalent to -4(5-2x)?

",,,-20 + 8x || -20 - 8x || -20x + 8 || 20x + 8,-20 + 8x,35877 +PSBZEE,1,Multiple Choice (select 1),Multiple Choice,"

Andre says that x is 7 because he can move the two 1s with the x to the other side.

+
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
Do you agree with Andre?
",,,Yes || No,No,121352 +PRABPJHD,1,Multiple Choice (select all),Check All That Apply,

Which graphs could represent a proportional relationship? 

,,,"

||

||

||

","

||

",552378 +PSBFCE,6,Multiple Choice (select 1),Multiple Choice,"

Is the point (0, -2) on this line?

",,,Yes || No,Yes,27460 +PSBHTM,1,Multiple Choice (select 1),Multiple Choice,"

Identify the error in generating an expression equivalent to 4 + 2x − 12(10 − 4x).

+

 Line 1: 4 + 2x + ‐1  210 +‐4xLine 2: 4 + 2x +‐5 + 2xLine 3: 4 + 2x‐5 + 2xLine 4: ‐1

+

 

+

Which line contains the error?

",,,Line 1 || Line 2 || Line 3 || Line 4,Line 4,40142 +PSBBBY4,1,Multiple Choice (select 1),Multiple Choice,"

A room is 15 feet tall. An architect wants to include a window that is 6 feet tall. The distance between the floor and the bottom of the window is b feet. The distance between the ceiling and the top of the window is a feet. This relationship can be described by the equation

+
a = 15 − (b + 6)
+

 

+

Which variable is independent based on the equation given?

",,,a || b,b,179830 +PSBBN78,1,Multiple Choice (select all),Check All That Apply,"

Here are some polygons:

+

 

+

+

 

+

Which of Polygons B, C, D, E, and F are similar to Polygon A?

+
 
",,,Polygon B || Polygon C || Polygon D || Polygon E || Polygon F,Polygon B || Polygon C || Polygon E,238263 +PSBCU6,1,Multiple Choice (select 1),Multiple Choice,"

Ten people can dig five holes in three hours. If n people digging at the same rate dig m holes in d hours:

+


Is n proportional to m when d = 3?

",,,Yes || No,Yes,13763 +PSB347,3,Multiple Choice (select 1),Multiple Choice,"

If the radius of a cylinder is doubled, does the volume double?

",,,Yes || No,No,136717 +PRABQM8Y,1,Multiple Choice (select all),Check All That Apply,"

Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select all of the true statements.

+

 

+

+

 

",,,Segment EF is twice as long as segment AB. || Segment CD is twice as long as segment FG. || The measure of angle HEF is twice the measure of angle DAB. || The length of segment EH is 16 units. || The area of EFGH is twice the area of ABCD.,Segment EF is twice as long as segment AB. || The length of segment EH is 16 units.,115829 +PSBT77,2,Multiple Choice (select all),Check All That Apply,"

Which years in this period of time had fewer than 100,000 cases of whooping cough?

",,,1939 || 1940 || 1941 || 1942 || 1943 || 1944 || 1945 || 1946 || 1947 || 1948 || 1949 || 1950 || 1951 || 1952 || 1953 || 1954 || 1955,1948 || 1949 || 1951 || 1952 || 1953 || 1954 || 1955,90496 +PRABECYW,1,Multiple Choice (select all),Check All That Apply,"

Here is a balanced hanger diagram.

+

 

+ + + + + + + +
Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and x represents the weight of each square. Select all equations that represent the hanger.
",,,"

x + x + x + x + 11 = x + 11.5

||

 2x = 0.5

||

4x + 5 + 6 = 2x + 2.5 + 6

||

2x + 2.5 = 3

||

4x + 2.5 + 2.5 + 3 + 3 = 2x + 2.5 + 3 + 3 + 3

","

 2x = 0.5

||

2x + 2.5 = 3

||

4x + 2.5 + 2.5 + 3 + 3 = 2x + 2.5 + 3 + 3 + 3

",530004 +PSBBNXQ,1,Multiple Choice (select 1),Multiple Choice,

Mai says that -8 > -4. Do you agree with her?

,,,Yes || No,No,236733 +PRABEVDM,1,Multiple Choice (select 1),Multiple Choice,

Which of these describes a unique polygon?

,,,"A triangle with angles 30°, 50°, and 100° || A quadrilateral with each side length 5 cm || A triangle with side lengths 6 cm, 7 cm, and 8 cm || A triangle with side lengths 4 cm and 5 cm and a 50° angle","A triangle with side lengths 6 cm, 7 cm, and 8 cm",483667 +PRABQPY8,1,Multiple Choice (select all),Check All That Apply,"

Select all the equations on which the point (10, 0) lies.

",,,5x + 2y = 15 || 2x + 4y = 20 || x + 6y = 10 || 3x + 3y = 13 || 4x + 2y = 20 || 6x + y = 50,2x + 4y = 20 || x + 6y = 10,211131 +PSB724,1,Multiple Choice (select 1),Multiple Choice,"

These two histograms show the number of text messages sent in one week by two groups of 100 students. The first histogram summarizes data from sixth-grade students. The second histogram summarizes data from seventh-grade students.

+

 

+

+

 

+

Do the two data sets have approximately the same center? 

",,,Yes || No,Yes,158316 +PSBBR6V,2,Multiple Choice (select 1),Multiple Choice,

Are the flawed erasers associated with certain colors?

,,,Yes || No,Yes,253836 +PRABD8GT,1,Multiple Choice (select all),Check All That Apply,"

Select all the pairs of points so that the line between those points has slope .

",,,"(0,0) and (2,3) || (0,0) and (3,2) || (1,5) and (4,7) || (-2,-2) and (4,2) || (20,30) and (-20,-30)","(0,0) and (3,2) || (1,5) and (4,7) || (-2,-2) and (4,2)",20361 +PSBCQD8,1,Multiple Choice (select 1),Multiple Choice,"

Which is a scaled copy of Polygon A?

+

 

+

",,,B || C || D || E || F,D,419376 +PSBBPFG,1,Multiple Choice (select 1),Multiple Choice,"

Noah says that to find 20% of a number he divides the number by 5. For example, 20% of 60 is 12, because 60 ÷ 5 = 12.

+

Does Noah’s method always work? 

",,,Yes || No,Yes,239466 +PSBTXU,5,Multiple Choice (select 1),Multiple Choice,"

A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is the statement true or false? 

+

 

+

Speed is a function of number of students racing.

",,0,True || False,FALSE,88607 diff --git a/Data/Skill_Set.csv b/Data/Skill_Set.csv new file mode 100644 index 0000000000000000000000000000000000000000..663c4f0627dfeb0da04f9df136ceb35e50318e32 --- /dev/null +++ b/Data/Skill_Set.csv @@ -0,0 +1,165 @@ +index,skill_code,full_description +1,2.MD.B.5,"Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem." +2,3.MD.B.3,"Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ""how many more"" and ""how many less"" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets." +3,3.MD.C.6,"Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)." +4,3.MD.C.7a,"Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths." +5,3.MD.C.7d,"Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems." +6,3.MD.D.8,"Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters." +7,3.NF.A.2a,Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. +8,3.NF.A.2b,Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. +9,3.NF.A.3b,"Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model." +10,3.NF.A.3d,"Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model." +11,3.OA.A.1,"Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7." +12,3.OA.A.4,"Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?." +13,3.OA.B.5,Apply properties of operations as strategies to multiply and divide. +14,4.G.A.1,"Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures." +15,4.G.A.2,"Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles." +16,4.MD.A.1,"Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …" +17,4.MD.A.3,"Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor." +18,4.NBT.A.1,"Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division." +19,4.NBT.B.6,"Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." +20,4.NF.A.1,"Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions." +21,4.NF.A.2,"Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model." +22,4.NF.B.4b,"Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)" +23,4.NF.C.6,"Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram." +24,4.OA.A.1,"Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations." +25,4.OA.B.4,Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite. +26,5.G.A.1,"Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate)." +27,5.G.A.2,"Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation." +28,5.G.B.4,Classify two-dimensional figures in a hierarchy based on properties. +29,5.MD.A.1,"Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems." +30,5.MD.B.2,"Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally." +31,5.MD.C.3b,A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. +32,5.MD.C.4,"Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units." +33,5.MD.C.5a,"Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication." +34,5.MD.C.5b,Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. +35,5.NBT.A.1,"Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left." +36,5.NBT.A.2,"Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10." +37,5.NBT.A.3b,"Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons." +38,5.NBT.B.5,Fluently multiply multi-digit whole numbers using the standard algorithm. +39,5.NBT.B.6,"Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." +40,5.NBT.B.7,"Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used." +41,5.NF.A.1,"Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)" +42,5.NF.A.2,"Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7" +43,5.NF.B.3,"Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?" +44,5.NF.B.4a,"Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)" +45,5.NF.B.4b,"Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas." +46,5.NF.B.5a,"Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication." +47,5.NF.B.5b,Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. +48,5.NF.B.6,"Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem." +49,5.NF.B.7a,"Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3." +50,5.NF.B.7b,"Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4." +51,5.NF.B.7c,"Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?" +52,5.OA.A.1,"Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols." +53,5.OA.A.2,"Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ""add 8 and 7, then multiply by 2"" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product." +54,6.EE.A.1,Write and evaluate numerical expressions involving whole-number exponents. +55,6.EE.A.2a,"Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation ""Subtract y from 5"" as 5 - y." +56,6.EE.A.2b,"Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms." +57,6.EE.A.2c,"Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2." +58,6.EE.A.3,"Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y." +59,6.EE.A.4,"Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for." +60,6.EE.B.5,"Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true." +61,6.EE.B.6,"Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set." +62,6.EE.B.7,"Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers." +63,6.EE.B.8,Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. +64,6.EE.C.9,"Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time." +65,6.G.A.1,"Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems." +66,6.G.A.2,"Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems." +67,6.G.A.3,Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. +68,6.G.A.4,"Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems." +69,6.NS.A.1,"Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?" +70,6.NS.B.2,Fluently divide multi-digit numbers using the standard algorithm. +71,6.NS.B.3,"Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation." +72,6.NS.B.4,"Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)." +73,6.NS.C.5,"Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation." +74,6.NS.C.6a,"Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite." +75,6.NS.C.6c,Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. +76,6.NS.C.7a,"Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right." +77,6.NS.C.7b,"Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer than -7 °C." +78,6.NS.C.7c,"Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars." +79,6.NS.C.7d,"Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars." +80,6.NS.C.8,Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. +81,6.RP.A.1,"Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, ""The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak."" ""For every vote candidate A received, candidate C received nearly three votes.""" +82,6.RP.A.2,"Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship." +83,6.RP.A.3a,"Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios." +84,6.RP.A.3b,"Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?" +85,6.RP.A.3c,"Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent." +86,6.RP.A.3d,Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. +87,6.SP.A.1,"Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, ""How old am I?"" is not a statistical question, but ""How old are the students in my school?"" is a statistical question because one anticipates variability in students' ages." +88,6.SP.A.2,"Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape." +89,6.SP.A.3,"Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number." +90,6.SP.B.4,"Display numerical data in plots on a number line, including dot plots, histograms, and box plots." +91,6.SP.B.5a,Reporting the number of observations. +92,6.SP.B.5b,"Describing the nature of the attribute under investigation, including how it was measured and its units of measurement." +93,6.SP.B.5c,"Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered." +94,6.SP.B.5d,Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. +95,7.EE.A.1,"Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients." +96,7.EE.A.2,"Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ""increase by 5%"" is the same as ""multiply by 1.05.""" +97,7.EE.B.3,"Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation." +98,7.EE.B.4a,"Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?" +99,7.EE.B.4b,"Solve word problems leading to inequalities of the form px + q > r or px + q For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions." +100,7.G.A.1,"Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale." +101,7.G.A.2,"Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle." +102,7.G.A.3,"Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids." +103,7.G.B.4,Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. +104,7.G.B.5,"Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure." +105,7.G.B.6,"Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms." +106,7.NS.A.1a,"Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged." +107,7.NS.A.1b,"Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts." +108,7.NS.A.1c,"Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts." +109,7.NS.A.1d,Apply properties of operations as strategies to add and subtract rational numbers. +110,7.NS.A.2a,"Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts." +111,7.NS.A.2b,"Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts." +112,7.NS.A.2c,Apply properties of operations as strategies to multiply and divide rational numbers. +113,7.NS.A.2d,Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. +114,7.NS.A.3,Solve real-world and mathematical problems involving the four operations with rational numbers. +115,7.RP.A.1,"Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour." +116,7.RP.A.2a,"Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin." +117,7.RP.A.2b,"Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships." +118,7.RP.A.2c,"Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn." +119,7.RP.A.2d,"Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate." +120,7.RP.A.3,Use proportional relationships to solve multistep ratio and percent problems. +121,7.SP.A.1,Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. +122,7.SP.A.2,"Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be." +123,7.SP.B.3,"Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable." +124,7.SP.B.4,"Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book." +125,7.SP.C.5,"Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event." +126,7.SP.C.6,"Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times." +127,7.SP.C.7a,"Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected." +128,7.SP.C.7b,"Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?" +129,7.SP.C.8a,"Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs." +130,7.SP.C.8b,"Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., ""rolling double sixes""), identify the outcomes in the sample space which compose the event." +131,7.SP.C.8c,"Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?" +132,8.EE.A.1,"Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27." +133,8.EE.A.2,"Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational." +134,8.EE.A.3,"Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger." +135,8.EE.A.4,"Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology." +136,8.EE.B.5,"Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed." +137,8.EE.B.6,Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. +138,8.EE.C.7a,"Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers)." +139,8.EE.C.7b,"Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms." +140,8.EE.C.8a,"Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously." +141,8.EE.C.8b,"Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6." +142,8.EE.C.8c,"Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair." +143,8.F.A.1,Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. +144,8.F.A.2,"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change." +145,8.F.A.3,"Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line." +146,8.F.B.4,"Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values." +147,8.F.B.5,"Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally." +148,8.G.A.1a,"Lines are taken to lines, and line segments to line segments of the same length." +149,8.G.A.1b,Angles are taken to angles of the same measure. +150,8.G.A.1c,Parallel lines are taken to parallel lines. +151,8.G.A.2,"Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them." +152,8.G.A.3,"Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates." +153,8.G.A.4,"Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them." +154,8.G.A.5,"Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so." +155,8.G.B.6,Explain a proof of the Pythagorean Theorem and its converse. +156,8.G.B.7,Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. +157,8.G.B.8,Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. +158,8.G.C.9,"Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems." +159,8.NS.A.1,"Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number." +160,8.NS.A.2,"Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations." +161,8.SP.A.1,"Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association." +162,8.SP.A.2,"Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line." +163,8.SP.A.3,"Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height." +164,8.SP.A.4,"Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?" diff --git a/Data/Skills.csv b/Data/Skills.csv new file mode 100644 index 0000000000000000000000000000000000000000..0bbadab5a0c201c913315858345d137e839915f1 --- /dev/null +++ b/Data/Skills.csv @@ -0,0 +1,3798 @@ +problem_id,skill_id,node_code,node_name +299836,1,3.OA.A.1,Interpret Products of Whole Numbers +427946,1,3.OA.A.1,Interpret Products of Whole Numbers +299836,4,3.OA.A.4,Determine the Unknown Whole Number in a Multiplication/Division Equation +427946,4,3.OA.A.4,Determine the Unknown Whole Number in a Multiplication/Division Equation +299546,5,3.OA.B.5,Apply Properties of Operations To Multiply & Divide +427706,5,3.OA.B.5,Apply Properties of Operations To Multiply & Divide +151911,15,3.NF.A.2a,Represent Unit Fractions on a Number Line +323486,16,3.NF.A.2b,Represent Fractions on a Number Line +323395,16,3.NF.A.2b,Represent Fractions on a Number Line +323318,16,3.NF.A.2b,Represent Fractions on a Number Line +259422,16,3.NF.A.2b,Represent Fractions on a Number Line +151911,16,3.NF.A.2b,Represent Fractions on a Number Line +151911,19,3.NF.A.3b,Recognize & Generate Simple Equivalent Fractions +323959,21,3.NF.A.3d,Comprare Fractions with Like Numerators or Denominators +3501,24,3.MD.B.3,Draw & Apply Knowledge of Bar & Pictures Graphs +255003,24,3.MD.B.3,Draw & Apply Knowledge of Bar & Pictures Graphs +103462,29,3.MD.C.6,Measure Area by Counting Unit Squares +543579,29,3.MD.C.6,Measure Area by Counting Unit Squares +543579,31,3.MD.C.7a,Find the Area of a Rectangle by Tiling +103462,31,3.MD.C.7a,Find the Area of a Rectangle by Tiling +1366,31,3.MD.C.7a,Find the Area of a Rectangle by Tiling +54202,31,3.MD.C.7a,Find the Area of a Rectangle by Tiling +595379,31,3.MD.C.7a,Find the Area of a Rectangle by Tiling +543878,34,3.MD.C.7d,Find Area of Rectangles by Decomposing +103748,34,3.MD.C.7d,Find Area of Rectangles by Decomposing +1366,35,3.MD.D.8,Solve Word Problems Involving Perimeter of Polygons +595520,35,3.MD.D.8,Solve Word Problems Involving Perimeter of Polygons +151389,38,4.OA.A.1,Interpret & Represent Multiplicative Comparisons as Multiplication Equations +151533,38,4.OA.A.1,Interpret & Represent Multiplicative Comparisons as Multiplication Equations +258849,38,4.OA.A.1,Interpret & Represent Multiplicative Comparisons as Multiplication Equations +151647,38,4.OA.A.1,Interpret & Represent Multiplicative Comparisons as Multiplication Equations +258984,38,4.OA.A.1,Interpret & Represent Multiplicative Comparisons as Multiplication Equations +259128,38,4.OA.A.1,Interpret & Represent Multiplicative Comparisons as Multiplication Equations +322962,41,4.OA.B.4,Find & Use Factors of to Determine if a Number is Prime or Composite +608636,41,4.OA.B.4,Find & Use Factors of to Determine if a Number is Prime or Composite +258849,44,4.NBT.A.1,Recognize & Apply Concepts of Place Value Relationships +259128,44,4.NBT.A.1,Recognize & Apply Concepts of Place Value Relationships +258984,44,4.NBT.A.1,Recognize & Apply Concepts of Place Value Relationships +151389,44,4.NBT.A.1,Recognize & Apply Concepts of Place Value Relationships +151647,44,4.NBT.A.1,Recognize & Apply Concepts of Place Value Relationships +151533,44,4.NBT.A.1,Recognize & Apply Concepts of Place Value Relationships +655353,50,4.NBT.B.6,Divide Whole Numbers using Place Value Models & Strategies +456745,50,4.NBT.B.6,Divide Whole Numbers using Place Value Models & Strategies +258570,51,4.NF.A.1,"Explain, Recognize & Generate Equivalent Fractions" +151128,51,4.NF.A.1,"Explain, Recognize & Generate Equivalent Fractions" +324036,52,4.NF.A.2,Compare Fractions with Different Numerators & Denominators +323873,52,4.NF.A.2,Compare Fractions with Different Numerators & Denominators +324144,52,4.NF.A.2,Compare Fractions with Different Numerators & Denominators +323959,52,4.NF.A.2,Compare Fractions with Different Numerators & Denominators +133202,52,4.NF.A.2,Compare Fractions with Different Numerators & Denominators +133338,52,4.NF.A.2,Compare Fractions with Different Numerators & Denominators +151389,61,4.NF.B.4b,Multiply a Fraction by a Whole Number +151533,61,4.NF.B.4b,Multiply a Fraction by a Whole Number +259128,61,4.NF.B.4b,Multiply a Fraction by a Whole Number +258849,61,4.NF.B.4b,Multiply a Fraction by a Whole Number +258984,61,4.NF.B.4b,Multiply a Fraction by a Whole Number +151647,61,4.NF.B.4b,Multiply a Fraction by a Whole Number +325103,64,4.NF.C.6,Convert Fractions to Decimals (Denominators of 10 or 100) +355920,64,4.NF.C.6,Convert Fractions to Decimals (Denominators of 10 or 100) +455868,64,4.NF.C.6,Convert Fractions to Decimals (Denominators of 10 or 100) +455995,64,4.NF.C.6,Convert Fractions to Decimals (Denominators of 10 or 100) +356245,64,4.NF.C.6,Convert Fractions to Decimals (Denominators of 10 or 100) +488652,64,4.NF.C.6,Convert Fractions to Decimals (Denominators of 10 or 100) +668634,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +174042,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +172779,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +173266,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +605230,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +173140,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +173797,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +173917,66,4.MD.A.1,Convert Measurements Within a System & Display in Two-Column Tables +25823,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +47078,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +25576,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +25682,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +543579,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +25949,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +46209,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +605230,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +88850,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +103462,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +347425,68,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +668634,69,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +605230,69,4.MD.A.3,Apply Area & Perimeter Formulas for Rectangles +651370,76,4.G.A.1,Draw & Identify Types of Lines and Angles +104004,76,4.G.A.1,Draw & Identify Types of Lines and Angles +651306,76,4.G.A.1,Draw & Identify Types of Lines and Angles +627401,76,4.G.A.1,Draw & Identify Types of Lines and Angles +12623,76,4.G.A.1,Draw & Identify Types of Lines and Angles +627506,76,4.G.A.1,Draw & Identify Types of Lines and Angles +115085,76,4.G.A.1,Draw & Identify Types of Lines and Angles +104131,77,4.G.A.1,Draw & Identify Types of Lines and Angles +23769,78,4.G.A.2,Classify 2D Figures by Parallel & Perpendicular Lines and Angles +104004,78,4.G.A.2,Classify 2D Figures by Parallel & Perpendicular Lines and Angles +544510,78,4.G.A.2,Classify 2D Figures by Parallel & Perpendicular Lines and Angles +427706,80,5.OA.A.1,Evaluate Expressions Using Groupings +299546,80,5.OA.A.1,Evaluate Expressions Using Groupings +543878,81,5.OA.A.2,Write & Interpret Simple Expressions +103748,81,5.OA.A.2,Write & Interpret Simple Expressions +655039,83,5.NBT.A.1,Understand Base Ten Place Value Relationships +455078,83,5.NBT.A.1,Understand Base Ten Place Value Relationships +454858,83,5.NBT.A.1,Understand Base Ten Place Value Relationships +655190,83,5.NBT.A.1,Understand Base Ten Place Value Relationships +455397,83,5.NBT.A.1,Understand Base Ten Place Value Relationships +654938,83,5.NBT.A.1,Understand Base Ten Place Value Relationships +104252,84,5.NBT.A.2,Explain Patterns when Multiplying & Dividing Powers of 10 +323658,87,5.NBT.A.3b,Compare Decimals to Thousandths +323761,87,5.NBT.A.3b,Compare Decimals to Thousandths +284725,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +508769,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +508616,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +509009,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +508887,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +45675,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +457114,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +78754,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +92677,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +78619,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +445524,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +92205,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +421967,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +421838,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +332052,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +331934,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +289975,89,5.NBT.B.5,Multiply Multi-Digit Whole Numbers Using the Standard Algorithm +421173,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +421448,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +421310,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +421588,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +407583,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +531410,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +531190,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +531647,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +445641,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +530879,90,5.NBT.B.6,Divide Whole Numbers (Up to 4-Digit Dividends & 2-Digit Divisors) +5038,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +3036,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +254457,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +445374,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +2930,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +254589,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +256627,91,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +154867,94,5.NF.A.1,Add & Subtract Fractions with Unlike Denominators +256500,95,5.NF.A.1,Add & Subtract Fractions with Unlike Denominators +4926,95,5.NF.A.1,Add & Subtract Fractions with Unlike Denominators +274139,96,5.NF.A.2,Solve Word Problems Involving Addition/Subtraction of Fractions +127860,97,5.NF.B.3,Interpret Fractions as Division in Word Problems +128010,97,5.NF.B.3,Interpret Fractions as Division in Word Problems +128126,97,5.NF.B.3,Interpret Fractions as Division in Word Problems +132213,97,5.NF.B.3,Interpret Fractions as Division in Word Problems +154867,99,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +474069,99,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +474198,99,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +103860,100,5.NF.B.4b,Find the Area of a Rectangle with Fractional Side Lengths +471899,100,5.NF.B.4b,Find the Area of a Rectangle with Fractional Side Lengths +648,102,5.NF.B.5a,Compare the Size of Products & Factors +576826,102,5.NF.B.5a,Compare the Size of Products & Factors +438,102,5.NF.B.5a,Compare the Size of Products & Factors +311333,102,5.NF.B.5a,Compare the Size of Products & Factors +311102,102,5.NF.B.5a,Compare the Size of Products & Factors +420156,102,5.NF.B.5a,Compare the Size of Products & Factors +420156,103,5.NF.B.5b,Explain Results Less or Greater Than 1 when Multiplying Fractions +576826,103,5.NF.B.5b,Explain Results Less or Greater Than 1 when Multiplying Fractions +429356,104,5.NF.B.6,Solve Real-World Problems Involving Multiplication of Fractions +420156,104,5.NF.B.6,Solve Real-World Problems Involving Multiplication of Fractions +445267,106,5.NF.B.7a,Interpret & Compute Quotients of Unit Fractions & Whole Numbers +131914,107,5.NF.B.7b,Interpret & Compute Quotients of Whole Numbers & Unit Fractions +445267,107,5.NF.B.7b,Interpret & Compute Quotients of Whole Numbers & Unit Fractions +457262,107,5.NF.B.7b,Interpret & Compute Quotients of Whole Numbers & Unit Fractions +131914,108,5.NF.B.7c,Solve Word Problems Involving Division of Fractions & Whole Numbers +445267,108,5.NF.B.7c,Solve Word Problems Involving Division of Fractions & Whole Numbers +310779,110,5.MD.A.1,Convert Among Standard Measurement Units +95,110,5.MD.A.1,Convert Among Standard Measurement Units +242,110,5.MD.A.1,Convert Among Standard Measurement Units +310891,110,5.MD.A.1,Convert Among Standard Measurement Units +4926,112,5.MD.B.2,Create Line Plots with Fractions +256500,112,5.MD.B.2,Create Line Plots with Fractions +256627,112,5.MD.B.2,Create Line Plots with Fractions +5038,112,5.MD.B.2,Create Line Plots with Fractions +601993,115,5.MD.C.3b,Understand that Unit Cubes Can be Used to Construct Volume +247085,116,5.MD.C.4,Measure Volumes with Unit Cubes +48585,118,5.MD.C.5a,Find the Volume of a Rectangular Prism Without a Formula +48967,118,5.MD.C.5a,Find the Volume of a Rectangular Prism Without a Formula +133518,119,5.MD.C.5b,Find the Volume of a Rectangular Prism With a Formula +48762,119,5.MD.C.5b,Find the Volume of a Rectangular Prism With a Formula +248037,119,5.MD.C.5b,Find the Volume of a Rectangular Prism With a Formula +324806,121,5.G.A.1,Understand Components of the Coordinate Plane +324554,121,5.G.A.1,Understand Components of the Coordinate Plane +324709,121,5.G.A.1,Understand Components of the Coordinate Plane +324631,121,5.G.A.1,Understand Components of the Coordinate Plane +324900,121,5.G.A.1,Understand Components of the Coordinate Plane +488471,122,5.G.A.2,Graph points in Quadrant 1 & Interpret Coordinate Values +243115,124,5.G.B.4,Classify 2D Figures Based on Properties +544510,125,5.G.B.4,Classify 2D Figures Based on Properties +23769,125,5.G.B.4,Classify 2D Figures Based on Properties +54134,126,6.RP.A.1,Understand & Describe Ratios +88681,126,6.RP.A.1,Understand & Describe Ratios +2196,126,6.RP.A.1,Understand & Describe Ratios +437233,126,6.RP.A.1,Understand & Describe Ratios +547591,126,6.RP.A.1,Understand & Describe Ratios +40656,126,6.RP.A.1,Understand & Describe Ratios +373794,126,6.RP.A.1,Understand & Describe Ratios +39085,126,6.RP.A.1,Understand & Describe Ratios +199800,126,6.RP.A.1,Understand & Describe Ratios +83745,126,6.RP.A.1,Understand & Describe Ratios +114950,126,6.RP.A.1,Understand & Describe Ratios +4213,127,6.RP.A.2,Understand & Describe Unit Rate +547864,127,6.RP.A.2,Understand & Describe Unit Rate +547291,127,6.RP.A.2,Understand & Describe Unit Rate +261537,127,6.RP.A.2,Understand & Describe Unit Rate +320443,127,6.RP.A.2,Understand & Describe Unit Rate +559407,127,6.RP.A.2,Understand & Describe Unit Rate +39959,127,6.RP.A.2,Understand & Describe Unit Rate +3098,127,6.RP.A.2,Understand & Describe Unit Rate +39724,127,6.RP.A.2,Understand & Describe Unit Rate +40426,127,6.RP.A.2,Understand & Describe Unit Rate +560590,127,6.RP.A.2,Understand & Describe Unit Rate +40293,127,6.RP.A.2,Understand & Describe Unit Rate +40938,127,6.RP.A.2,Understand & Describe Unit Rate +546982,127,6.RP.A.2,Understand & Describe Unit Rate +546775,127,6.RP.A.2,Understand & Describe Unit Rate +547415,127,6.RP.A.2,Understand & Describe Unit Rate +261766,127,6.RP.A.2,Understand & Describe Unit Rate +559654,127,6.RP.A.2,Understand & Describe Unit Rate +559546,127,6.RP.A.2,Understand & Describe Unit Rate +164620,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +164748,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +287230,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +287949,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +370906,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +370138,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +371156,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +42395,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +40656,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +174455,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +370357,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +371046,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +370431,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +347969,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +40938,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +37441,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +283575,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +286756,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +282992,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +42567,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +279063,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +363127,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +360494,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +284919,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +360123,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +78262,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +77267,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +91684,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +91913,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +91811,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +240818,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +72272,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +72169,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +650734,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +426575,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +537832,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +2319,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +30276,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +547591,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +426461,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +360011,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +2433,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +320230,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +69590,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +115193,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +547864,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +115064,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +347269,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +114344,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +59778,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +554651,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +495575,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +229328,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +229131,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +359683,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +15930,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +137170,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +139424,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +138970,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +406068,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +138263,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +138414,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +53422,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +139112,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +143888,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +147205,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +53714,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +348393,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +146848,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +147031,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +15805,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +287601,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +164198,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +164090,129,6.RP.A.3a,Create Tables to Compare Equivalent Ratios +3418,130,6.RP.A.3b,Solve Unit Rate Problems +4344,130,6.RP.A.3b,Solve Unit Rate Problems +3980,130,6.RP.A.3b,Solve Unit Rate Problems +3098,130,6.RP.A.3b,Solve Unit Rate Problems +3256,130,6.RP.A.3b,Solve Unit Rate Problems +11914,130,6.RP.A.3b,Solve Unit Rate Problems +12985,130,6.RP.A.3b,Solve Unit Rate Problems +13384,130,6.RP.A.3b,Solve Unit Rate Problems +12177,130,6.RP.A.3b,Solve Unit Rate Problems +24870,130,6.RP.A.3b,Solve Unit Rate Problems +23593,130,6.RP.A.3b,Solve Unit Rate Problems +27697,130,6.RP.A.3b,Solve Unit Rate Problems +28051,130,6.RP.A.3b,Solve Unit Rate Problems +28432,130,6.RP.A.3b,Solve Unit Rate Problems +30898,130,6.RP.A.3b,Solve Unit Rate Problems +31058,130,6.RP.A.3b,Solve Unit Rate Problems +30779,130,6.RP.A.3b,Solve Unit Rate Problems +28730,130,6.RP.A.3b,Solve Unit Rate Problems +30604,130,6.RP.A.3b,Solve Unit Rate Problems +31250,130,6.RP.A.3b,Solve Unit Rate Problems +30601,130,6.RP.A.3b,Solve Unit Rate Problems +31856,130,6.RP.A.3b,Solve Unit Rate Problems +39724,130,6.RP.A.3b,Solve Unit Rate Problems +42395,130,6.RP.A.3b,Solve Unit Rate Problems +39959,130,6.RP.A.3b,Solve Unit Rate Problems +40426,130,6.RP.A.3b,Solve Unit Rate Problems +40293,130,6.RP.A.3b,Solve Unit Rate Problems +42567,130,6.RP.A.3b,Solve Unit Rate Problems +43293,130,6.RP.A.3b,Solve Unit Rate Problems +41676,130,6.RP.A.3b,Solve Unit Rate Problems +62872,130,6.RP.A.3b,Solve Unit Rate Problems +59099,130,6.RP.A.3b,Solve Unit Rate Problems +61003,130,6.RP.A.3b,Solve Unit Rate Problems +59398,130,6.RP.A.3b,Solve Unit Rate Problems +62539,130,6.RP.A.3b,Solve Unit Rate Problems +63719,130,6.RP.A.3b,Solve Unit Rate Problems +61761,130,6.RP.A.3b,Solve Unit Rate Problems +61363,130,6.RP.A.3b,Solve Unit Rate Problems +62707,130,6.RP.A.3b,Solve Unit Rate Problems +62166,130,6.RP.A.3b,Solve Unit Rate Problems +63037,130,6.RP.A.3b,Solve Unit Rate Problems +67685,130,6.RP.A.3b,Solve Unit Rate Problems +76912,130,6.RP.A.3b,Solve Unit Rate Problems +78012,130,6.RP.A.3b,Solve Unit Rate Problems +78634,130,6.RP.A.3b,Solve Unit Rate Problems +77528,130,6.RP.A.3b,Solve Unit Rate Problems +77847,130,6.RP.A.3b,Solve Unit Rate Problems +77688,130,6.RP.A.3b,Solve Unit Rate Problems +78992,130,6.RP.A.3b,Solve Unit Rate Problems +96695,130,6.RP.A.3b,Solve Unit Rate Problems +97491,130,6.RP.A.3b,Solve Unit Rate Problems +97813,130,6.RP.A.3b,Solve Unit Rate Problems +97062,130,6.RP.A.3b,Solve Unit Rate Problems +103888,130,6.RP.A.3b,Solve Unit Rate Problems +108169,130,6.RP.A.3b,Solve Unit Rate Problems +107470,130,6.RP.A.3b,Solve Unit Rate Problems +108047,130,6.RP.A.3b,Solve Unit Rate Problems +108478,130,6.RP.A.3b,Solve Unit Rate Problems +108354,130,6.RP.A.3b,Solve Unit Rate Problems +108670,130,6.RP.A.3b,Solve Unit Rate Problems +107783,130,6.RP.A.3b,Solve Unit Rate Problems +124302,130,6.RP.A.3b,Solve Unit Rate Problems +124027,130,6.RP.A.3b,Solve Unit Rate Problems +127489,130,6.RP.A.3b,Solve Unit Rate Problems +132567,130,6.RP.A.3b,Solve Unit Rate Problems +132256,130,6.RP.A.3b,Solve Unit Rate Problems +132144,130,6.RP.A.3b,Solve Unit Rate Problems +132877,130,6.RP.A.3b,Solve Unit Rate Problems +132432,130,6.RP.A.3b,Solve Unit Rate Problems +132758,130,6.RP.A.3b,Solve Unit Rate Problems +144489,130,6.RP.A.3b,Solve Unit Rate Problems +144285,130,6.RP.A.3b,Solve Unit Rate Problems +149859,130,6.RP.A.3b,Solve Unit Rate Problems +153145,130,6.RP.A.3b,Solve Unit Rate Problems +149750,130,6.RP.A.3b,Solve Unit Rate Problems +157878,130,6.RP.A.3b,Solve Unit Rate Problems +158629,130,6.RP.A.3b,Solve Unit Rate Problems +159000,130,6.RP.A.3b,Solve Unit Rate Problems +158226,130,6.RP.A.3b,Solve Unit Rate Problems +164198,130,6.RP.A.3b,Solve Unit Rate Problems +164090,130,6.RP.A.3b,Solve Unit Rate Problems +159196,130,6.RP.A.3b,Solve Unit Rate Problems +173472,130,6.RP.A.3b,Solve Unit Rate Problems +174088,130,6.RP.A.3b,Solve Unit Rate Problems +173863,130,6.RP.A.3b,Solve Unit Rate Problems +207470,130,6.RP.A.3b,Solve Unit Rate Problems +219121,130,6.RP.A.3b,Solve Unit Rate Problems +219244,130,6.RP.A.3b,Solve Unit Rate Problems +228746,130,6.RP.A.3b,Solve Unit Rate Problems +237868,130,6.RP.A.3b,Solve Unit Rate Problems +238070,130,6.RP.A.3b,Solve Unit Rate Problems +261537,130,6.RP.A.3b,Solve Unit Rate Problems +261766,130,6.RP.A.3b,Solve Unit Rate Problems +260638,130,6.RP.A.3b,Solve Unit Rate Problems +677513,130,6.RP.A.3b,Solve Unit Rate Problems +271838,130,6.RP.A.3b,Solve Unit Rate Problems +1638,130,6.RP.A.3b,Solve Unit Rate Problems +283915,130,6.RP.A.3b,Solve Unit Rate Problems +287949,130,6.RP.A.3b,Solve Unit Rate Problems +288360,130,6.RP.A.3b,Solve Unit Rate Problems +287601,130,6.RP.A.3b,Solve Unit Rate Problems +306784,130,6.RP.A.3b,Solve Unit Rate Problems +319717,130,6.RP.A.3b,Solve Unit Rate Problems +319607,130,6.RP.A.3b,Solve Unit Rate Problems +320538,130,6.RP.A.3b,Solve Unit Rate Problems +319516,130,6.RP.A.3b,Solve Unit Rate Problems +324446,130,6.RP.A.3b,Solve Unit Rate Problems +644155,130,6.RP.A.3b,Solve Unit Rate Problems +324260,130,6.RP.A.3b,Solve Unit Rate Problems +643786,130,6.RP.A.3b,Solve Unit Rate Problems +644011,130,6.RP.A.3b,Solve Unit Rate Problems +333185,130,6.RP.A.3b,Solve Unit Rate Problems +349252,130,6.RP.A.3b,Solve Unit Rate Problems +347954,130,6.RP.A.3b,Solve Unit Rate Problems +348162,130,6.RP.A.3b,Solve Unit Rate Problems +353584,130,6.RP.A.3b,Solve Unit Rate Problems +353327,130,6.RP.A.3b,Solve Unit Rate Problems +353461,130,6.RP.A.3b,Solve Unit Rate Problems +354136,130,6.RP.A.3b,Solve Unit Rate Problems +388358,130,6.RP.A.3b,Solve Unit Rate Problems +387984,130,6.RP.A.3b,Solve Unit Rate Problems +388660,130,6.RP.A.3b,Solve Unit Rate Problems +389028,130,6.RP.A.3b,Solve Unit Rate Problems +395051,130,6.RP.A.3b,Solve Unit Rate Problems +395419,130,6.RP.A.3b,Solve Unit Rate Problems +395593,130,6.RP.A.3b,Solve Unit Rate Problems +407824,130,6.RP.A.3b,Solve Unit Rate Problems +408023,130,6.RP.A.3b,Solve Unit Rate Problems +430257,130,6.RP.A.3b,Solve Unit Rate Problems +430376,130,6.RP.A.3b,Solve Unit Rate Problems +564514,130,6.RP.A.3b,Solve Unit Rate Problems +564997,130,6.RP.A.3b,Solve Unit Rate Problems +447809,130,6.RP.A.3b,Solve Unit Rate Problems +564837,130,6.RP.A.3b,Solve Unit Rate Problems +564678,130,6.RP.A.3b,Solve Unit Rate Problems +559546,130,6.RP.A.3b,Solve Unit Rate Problems +560316,130,6.RP.A.3b,Solve Unit Rate Problems +559654,130,6.RP.A.3b,Solve Unit Rate Problems +559407,130,6.RP.A.3b,Solve Unit Rate Problems +560733,130,6.RP.A.3b,Solve Unit Rate Problems +546982,130,6.RP.A.3b,Solve Unit Rate Problems +546775,130,6.RP.A.3b,Solve Unit Rate Problems +478871,130,6.RP.A.3b,Solve Unit Rate Problems +547291,130,6.RP.A.3b,Solve Unit Rate Problems +478760,130,6.RP.A.3b,Solve Unit Rate Problems +547415,130,6.RP.A.3b,Solve Unit Rate Problems +593802,131,6.RP.A.3c,Solve Problems Involving Percents +275922,131,6.RP.A.3c,Solve Problems Involving Percents +142840,131,6.RP.A.3c,Solve Problems Involving Percents +210383,131,6.RP.A.3c,Solve Problems Involving Percents +142483,131,6.RP.A.3c,Solve Problems Involving Percents +143123,131,6.RP.A.3c,Solve Problems Involving Percents +370522,131,6.RP.A.3c,Solve Problems Involving Percents +275754,131,6.RP.A.3c,Solve Problems Involving Percents +185126,131,6.RP.A.3c,Solve Problems Involving Percents +143514,131,6.RP.A.3c,Solve Problems Involving Percents +127791,131,6.RP.A.3c,Solve Problems Involving Percents +128001,131,6.RP.A.3c,Solve Problems Involving Percents +236371,131,6.RP.A.3c,Solve Problems Involving Percents +19386,131,6.RP.A.3c,Solve Problems Involving Percents +129075,131,6.RP.A.3c,Solve Problems Involving Percents +185395,131,6.RP.A.3c,Solve Problems Involving Percents +238851,131,6.RP.A.3c,Solve Problems Involving Percents +128360,131,6.RP.A.3c,Solve Problems Involving Percents +128108,131,6.RP.A.3c,Solve Problems Involving Percents +236051,131,6.RP.A.3c,Solve Problems Involving Percents +199099,131,6.RP.A.3c,Solve Problems Involving Percents +172534,131,6.RP.A.3c,Solve Problems Involving Percents +10241,131,6.RP.A.3c,Solve Problems Involving Percents +185277,131,6.RP.A.3c,Solve Problems Involving Percents +4091,131,6.RP.A.3c,Solve Problems Involving Percents +593590,131,6.RP.A.3c,Solve Problems Involving Percents +350776,131,6.RP.A.3c,Solve Problems Involving Percents +129183,131,6.RP.A.3c,Solve Problems Involving Percents +361789,131,6.RP.A.3c,Solve Problems Involving Percents +307493,131,6.RP.A.3c,Solve Problems Involving Percents +361669,131,6.RP.A.3c,Solve Problems Involving Percents +307360,131,6.RP.A.3c,Solve Problems Involving Percents +239163,131,6.RP.A.3c,Solve Problems Involving Percents +55067,131,6.RP.A.3c,Solve Problems Involving Percents +497933,131,6.RP.A.3c,Solve Problems Involving Percents +497078,131,6.RP.A.3c,Solve Problems Involving Percents +237316,131,6.RP.A.3c,Solve Problems Involving Percents +237612,131,6.RP.A.3c,Solve Problems Involving Percents +271538,131,6.RP.A.3c,Solve Problems Involving Percents +154014,131,6.RP.A.3c,Solve Problems Involving Percents +228454,131,6.RP.A.3c,Solve Problems Involving Percents +560175,131,6.RP.A.3c,Solve Problems Involving Percents +270745,131,6.RP.A.3c,Solve Problems Involving Percents +164748,131,6.RP.A.3c,Solve Problems Involving Percents +153748,131,6.RP.A.3c,Solve Problems Involving Percents +171639,131,6.RP.A.3c,Solve Problems Involving Percents +172131,131,6.RP.A.3c,Solve Problems Involving Percents +172318,131,6.RP.A.3c,Solve Problems Involving Percents +164620,131,6.RP.A.3c,Solve Problems Involving Percents +237456,131,6.RP.A.3c,Solve Problems Involving Percents +271396,131,6.RP.A.3c,Solve Problems Involving Percents +271644,131,6.RP.A.3c,Solve Problems Involving Percents +19578,131,6.RP.A.3c,Solve Problems Involving Percents +382646,131,6.RP.A.3c,Solve Problems Involving Percents +324952,131,6.RP.A.3c,Solve Problems Involving Percents +155392,131,6.RP.A.3c,Solve Problems Involving Percents +270541,131,6.RP.A.3c,Solve Problems Involving Percents +231744,131,6.RP.A.3c,Solve Problems Involving Percents +228285,131,6.RP.A.3c,Solve Problems Involving Percents +320333,131,6.RP.A.3c,Solve Problems Involving Percents +231330,131,6.RP.A.3c,Solve Problems Involving Percents +296749,131,6.RP.A.3c,Solve Problems Involving Percents +321235,131,6.RP.A.3c,Solve Problems Involving Percents +171838,131,6.RP.A.3c,Solve Problems Involving Percents +418297,131,6.RP.A.3c,Solve Problems Involving Percents +164090,131,6.RP.A.3c,Solve Problems Involving Percents +47523,131,6.RP.A.3c,Solve Problems Involving Percents +263662,131,6.RP.A.3c,Solve Problems Involving Percents +498428,131,6.RP.A.3c,Solve Problems Involving Percents +208182,131,6.RP.A.3c,Solve Problems Involving Percents +239810,131,6.RP.A.3c,Solve Problems Involving Percents +496936,131,6.RP.A.3c,Solve Problems Involving Percents +497355,131,6.RP.A.3c,Solve Problems Involving Percents +238558,131,6.RP.A.3c,Solve Problems Involving Percents +239466,131,6.RP.A.3c,Solve Problems Involving Percents +237164,131,6.RP.A.3c,Solve Problems Involving Percents +32378,131,6.RP.A.3c,Solve Problems Involving Percents +153894,131,6.RP.A.3c,Solve Problems Involving Percents +370230,131,6.RP.A.3c,Solve Problems Involving Percents +32696,131,6.RP.A.3c,Solve Problems Involving Percents +515648,131,6.RP.A.3c,Solve Problems Involving Percents +263496,131,6.RP.A.3c,Solve Problems Involving Percents +496551,131,6.RP.A.3c,Solve Problems Involving Percents +32069,131,6.RP.A.3c,Solve Problems Involving Percents +231535,131,6.RP.A.3c,Solve Problems Involving Percents +263152,131,6.RP.A.3c,Solve Problems Involving Percents +497385,131,6.RP.A.3c,Solve Problems Involving Percents +498194,131,6.RP.A.3c,Solve Problems Involving Percents +370835,131,6.RP.A.3c,Solve Problems Involving Percents +19738,131,6.RP.A.3c,Solve Problems Involving Percents +276105,131,6.RP.A.3c,Solve Problems Involving Percents +229674,131,6.RP.A.3c,Solve Problems Involving Percents +236208,131,6.RP.A.3c,Solve Problems Involving Percents +262990,131,6.RP.A.3c,Solve Problems Involving Percents +78711,131,6.RP.A.3c,Solve Problems Involving Percents +263336,131,6.RP.A.3c,Solve Problems Involving Percents +272713,131,6.RP.A.3c,Solve Problems Involving Percents +271030,131,6.RP.A.3c,Solve Problems Involving Percents +143860,131,6.RP.A.3c,Solve Problems Involving Percents +497698,131,6.RP.A.3c,Solve Problems Involving Percents +73922,131,6.RP.A.3c,Solve Problems Involving Percents +365680,131,6.RP.A.3c,Solve Problems Involving Percents +127673,131,6.RP.A.3c,Solve Problems Involving Percents +164198,131,6.RP.A.3c,Solve Problems Involving Percents +174579,131,6.RP.A.3c,Solve Problems Involving Percents +10342,131,6.RP.A.3c,Solve Problems Involving Percents +382388,131,6.RP.A.3c,Solve Problems Involving Percents +228118,131,6.RP.A.3c,Solve Problems Involving Percents +110306,132,6.RP.A.3c,Solve Problems Involving Percents +119836,132,6.RP.A.3c,Solve Problems Involving Percents +365680,132,6.RP.A.3c,Solve Problems Involving Percents +35357,132,6.RP.A.3c,Solve Problems Involving Percents +172957,132,6.RP.A.3c,Solve Problems Involving Percents +119704,132,6.RP.A.3c,Solve Problems Involving Percents +119945,132,6.RP.A.3c,Solve Problems Involving Percents +221668,132,6.RP.A.3c,Solve Problems Involving Percents +361669,132,6.RP.A.3c,Solve Problems Involving Percents +222018,132,6.RP.A.3c,Solve Problems Involving Percents +10241,132,6.RP.A.3c,Solve Problems Involving Percents +31188,132,6.RP.A.3c,Solve Problems Involving Percents +325149,132,6.RP.A.3c,Solve Problems Involving Percents +361789,132,6.RP.A.3c,Solve Problems Involving Percents +240555,132,6.RP.A.3c,Solve Problems Involving Percents +320133,132,6.RP.A.3c,Solve Problems Involving Percents +142055,132,6.RP.A.3c,Solve Problems Involving Percents +113478,132,6.RP.A.3c,Solve Problems Involving Percents +560450,132,6.RP.A.3c,Solve Problems Involving Percents +111728,132,6.RP.A.3c,Solve Problems Involving Percents +271394,132,6.RP.A.3c,Solve Problems Involving Percents +323049,132,6.RP.A.3c,Solve Problems Involving Percents +10342,132,6.RP.A.3c,Solve Problems Involving Percents +3852,132,6.RP.A.3c,Solve Problems Involving Percents +33334,132,6.RP.A.3c,Solve Problems Involving Percents +221830,132,6.RP.A.3c,Solve Problems Involving Percents +45372,132,6.RP.A.3c,Solve Problems Involving Percents +496354,132,6.RP.A.3c,Solve Problems Involving Percents +33021,132,6.RP.A.3c,Solve Problems Involving Percents +45043,132,6.RP.A.3c,Solve Problems Involving Percents +150918,133,6.RP.A.3c,Solve Problems Involving Percents +31856,133,6.RP.A.3c,Solve Problems Involving Percents +114889,133,6.RP.A.3c,Solve Problems Involving Percents +497669,133,6.RP.A.3c,Solve Problems Involving Percents +407530,133,6.RP.A.3c,Solve Problems Involving Percents +407150,133,6.RP.A.3c,Solve Problems Involving Percents +33653,133,6.RP.A.3c,Solve Problems Involving Percents +407285,133,6.RP.A.3c,Solve Problems Involving Percents +132871,133,6.RP.A.3c,Solve Problems Involving Percents +114762,133,6.RP.A.3c,Solve Problems Involving Percents +407421,133,6.RP.A.3c,Solve Problems Involving Percents +133098,133,6.RP.A.3c,Solve Problems Involving Percents +115027,133,6.RP.A.3c,Solve Problems Involving Percents +114644,133,6.RP.A.3c,Solve Problems Involving Percents +171809,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +3578,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +272435,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +11608,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +14371,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +393738,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +212537,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +42715,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +394746,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +393425,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +18501,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +272220,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +319877,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +29501,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +14554,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +394101,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +350310,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +213216,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +394487,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +212653,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +213954,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +98240,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +79597,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +14257,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +57665,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +319813,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +42388,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +42486,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +559856,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +212942,134,6.RP.A.3d,Use Ratios to Convert Measurement Units +163759,135,6.NS.A.1,Interpret & Compute using Division of Fractions +20000,135,6.NS.A.1,Interpret & Compute using Division of Fractions +320253,135,6.NS.A.1,Interpret & Compute using Division of Fractions +490707,135,6.NS.A.1,Interpret & Compute using Division of Fractions +557055,135,6.NS.A.1,Interpret & Compute using Division of Fractions +320033,135,6.NS.A.1,Interpret & Compute using Division of Fractions +319914,135,6.NS.A.1,Interpret & Compute using Division of Fractions +21032,135,6.NS.A.1,Interpret & Compute using Division of Fractions +163575,135,6.NS.A.1,Interpret & Compute using Division of Fractions +517428,135,6.NS.A.1,Interpret & Compute using Division of Fractions +37956,135,6.NS.A.1,Interpret & Compute using Division of Fractions +37276,135,6.NS.A.1,Interpret & Compute using Division of Fractions +515041,135,6.NS.A.1,Interpret & Compute using Division of Fractions +201709,135,6.NS.A.1,Interpret & Compute using Division of Fractions +36501,135,6.NS.A.1,Interpret & Compute using Division of Fractions +275405,135,6.NS.A.1,Interpret & Compute using Division of Fractions +37735,135,6.NS.A.1,Interpret & Compute using Division of Fractions +288230,135,6.NS.A.1,Interpret & Compute using Division of Fractions +111092,135,6.NS.A.1,Interpret & Compute using Division of Fractions +91335,135,6.NS.A.1,Interpret & Compute using Division of Fractions +36911,135,6.NS.A.1,Interpret & Compute using Division of Fractions +277226,135,6.NS.A.1,Interpret & Compute using Division of Fractions +44687,135,6.NS.A.1,Interpret & Compute using Division of Fractions +201829,135,6.NS.A.1,Interpret & Compute using Division of Fractions +44207,135,6.NS.A.1,Interpret & Compute using Division of Fractions +275212,135,6.NS.A.1,Interpret & Compute using Division of Fractions +576579,135,6.NS.A.1,Interpret & Compute using Division of Fractions +576243,135,6.NS.A.1,Interpret & Compute using Division of Fractions +45097,135,6.NS.A.1,Interpret & Compute using Division of Fractions +350118,135,6.NS.A.1,Interpret & Compute using Division of Fractions +351102,135,6.NS.A.1,Interpret & Compute using Division of Fractions +349260,135,6.NS.A.1,Interpret & Compute using Division of Fractions +35549,135,6.NS.A.1,Interpret & Compute using Division of Fractions +201571,135,6.NS.A.1,Interpret & Compute using Division of Fractions +46664,135,6.NS.A.1,Interpret & Compute using Division of Fractions +288530,135,6.NS.A.1,Interpret & Compute using Division of Fractions +287888,135,6.NS.A.1,Interpret & Compute using Division of Fractions +349546,135,6.NS.A.1,Interpret & Compute using Division of Fractions +45479,135,6.NS.A.1,Interpret & Compute using Division of Fractions +264456,135,6.NS.A.1,Interpret & Compute using Division of Fractions +416720,135,6.NS.A.1,Interpret & Compute using Division of Fractions +263940,135,6.NS.A.1,Interpret & Compute using Division of Fractions +264639,135,6.NS.A.1,Interpret & Compute using Division of Fractions +263156,135,6.NS.A.1,Interpret & Compute using Division of Fractions +264344,135,6.NS.A.1,Interpret & Compute using Division of Fractions +264992,135,6.NS.A.1,Interpret & Compute using Division of Fractions +263570,135,6.NS.A.1,Interpret & Compute using Division of Fractions +261929,135,6.NS.A.1,Interpret & Compute using Division of Fractions +36743,135,6.NS.A.1,Interpret & Compute using Division of Fractions +262501,135,6.NS.A.1,Interpret & Compute using Division of Fractions +277396,135,6.NS.A.1,Interpret & Compute using Division of Fractions +263466,135,6.NS.A.1,Interpret & Compute using Division of Fractions +288005,135,6.NS.A.1,Interpret & Compute using Division of Fractions +35817,135,6.NS.A.1,Interpret & Compute using Division of Fractions +518589,135,6.NS.A.1,Interpret & Compute using Division of Fractions +262837,135,6.NS.A.1,Interpret & Compute using Division of Fractions +10794,135,6.NS.A.1,Interpret & Compute using Division of Fractions +263960,135,6.NS.A.1,Interpret & Compute using Division of Fractions +514446,135,6.NS.A.1,Interpret & Compute using Division of Fractions +348977,135,6.NS.A.1,Interpret & Compute using Division of Fractions +125069,135,6.NS.A.1,Interpret & Compute using Division of Fractions +36318,135,6.NS.A.1,Interpret & Compute using Division of Fractions +477073,135,6.NS.A.1,Interpret & Compute using Division of Fractions +262987,135,6.NS.A.1,Interpret & Compute using Division of Fractions +125391,135,6.NS.A.1,Interpret & Compute using Division of Fractions +417385,135,6.NS.A.1,Interpret & Compute using Division of Fractions +415185,135,6.NS.A.1,Interpret & Compute using Division of Fractions +126203,135,6.NS.A.1,Interpret & Compute using Division of Fractions +469563,135,6.NS.A.1,Interpret & Compute using Division of Fractions +522821,135,6.NS.A.1,Interpret & Compute using Division of Fractions +127330,135,6.NS.A.1,Interpret & Compute using Division of Fractions +414393,135,6.NS.A.1,Interpret & Compute using Division of Fractions +414757,135,6.NS.A.1,Interpret & Compute using Division of Fractions +131258,135,6.NS.A.1,Interpret & Compute using Division of Fractions +86400,135,6.NS.A.1,Interpret & Compute using Division of Fractions +184230,135,6.NS.A.1,Interpret & Compute using Division of Fractions +417173,135,6.NS.A.1,Interpret & Compute using Division of Fractions +416968,135,6.NS.A.1,Interpret & Compute using Division of Fractions +287627,135,6.NS.A.1,Interpret & Compute using Division of Fractions +476732,135,6.NS.A.1,Interpret & Compute using Division of Fractions +184060,135,6.NS.A.1,Interpret & Compute using Division of Fractions +587537,135,6.NS.A.1,Interpret & Compute using Division of Fractions +518845,135,6.NS.A.1,Interpret & Compute using Division of Fractions +517656,135,6.NS.A.1,Interpret & Compute using Division of Fractions +407357,135,6.NS.A.1,Interpret & Compute using Division of Fractions +132330,135,6.NS.A.1,Interpret & Compute using Division of Fractions +131386,135,6.NS.A.1,Interpret & Compute using Division of Fractions +131506,135,6.NS.A.1,Interpret & Compute using Division of Fractions +182148,135,6.NS.A.1,Interpret & Compute using Division of Fractions +183695,135,6.NS.A.1,Interpret & Compute using Division of Fractions +588744,135,6.NS.A.1,Interpret & Compute using Division of Fractions +130932,135,6.NS.A.1,Interpret & Compute using Division of Fractions +182258,135,6.NS.A.1,Interpret & Compute using Division of Fractions +81470,135,6.NS.A.1,Interpret & Compute using Division of Fractions +407929,135,6.NS.A.1,Interpret & Compute using Division of Fractions +588423,135,6.NS.A.1,Interpret & Compute using Division of Fractions +183784,135,6.NS.A.1,Interpret & Compute using Division of Fractions +183482,135,6.NS.A.1,Interpret & Compute using Division of Fractions +518730,135,6.NS.A.1,Interpret & Compute using Division of Fractions +407757,135,6.NS.A.1,Interpret & Compute using Division of Fractions +218311,135,6.NS.A.1,Interpret & Compute using Division of Fractions +218537,135,6.NS.A.1,Interpret & Compute using Division of Fractions +81228,135,6.NS.A.1,Interpret & Compute using Division of Fractions +182395,135,6.NS.A.1,Interpret & Compute using Division of Fractions +588631,135,6.NS.A.1,Interpret & Compute using Division of Fractions +518962,135,6.NS.A.1,Interpret & Compute using Division of Fractions +218191,135,6.NS.A.1,Interpret & Compute using Division of Fractions +588511,135,6.NS.A.1,Interpret & Compute using Division of Fractions +81337,135,6.NS.A.1,Interpret & Compute using Division of Fractions +521139,135,6.NS.A.1,Interpret & Compute using Division of Fractions +243534,135,6.NS.A.1,Interpret & Compute using Division of Fractions +199749,135,6.NS.A.1,Interpret & Compute using Division of Fractions +242767,135,6.NS.A.1,Interpret & Compute using Division of Fractions +243888,135,6.NS.A.1,Interpret & Compute using Division of Fractions +564260,135,6.NS.A.1,Interpret & Compute using Division of Fractions +287470,135,6.NS.A.1,Interpret & Compute using Division of Fractions +243107,135,6.NS.A.1,Interpret & Compute using Division of Fractions +563384,135,6.NS.A.1,Interpret & Compute using Division of Fractions +594494,135,6.NS.A.1,Interpret & Compute using Division of Fractions +243693,135,6.NS.A.1,Interpret & Compute using Division of Fractions +511103,135,6.NS.A.1,Interpret & Compute using Division of Fractions +77264,135,6.NS.A.1,Interpret & Compute using Division of Fractions +76458,135,6.NS.A.1,Interpret & Compute using Division of Fractions +242498,135,6.NS.A.1,Interpret & Compute using Division of Fractions +243402,135,6.NS.A.1,Interpret & Compute using Division of Fractions +242315,135,6.NS.A.1,Interpret & Compute using Division of Fractions +241877,135,6.NS.A.1,Interpret & Compute using Division of Fractions +562131,135,6.NS.A.1,Interpret & Compute using Division of Fractions +561849,135,6.NS.A.1,Interpret & Compute using Division of Fractions +76591,135,6.NS.A.1,Interpret & Compute using Division of Fractions +77616,135,6.NS.A.1,Interpret & Compute using Division of Fractions +349832,135,6.NS.A.1,Interpret & Compute using Division of Fractions +311,135,6.NS.A.1,Interpret & Compute using Division of Fractions +76716,135,6.NS.A.1,Interpret & Compute using Division of Fractions +103383,135,6.NS.A.1,Interpret & Compute using Division of Fractions +318942,135,6.NS.A.1,Interpret & Compute using Division of Fractions +21767,135,6.NS.A.1,Interpret & Compute using Division of Fractions +238362,135,6.NS.A.1,Interpret & Compute using Division of Fractions +320140,135,6.NS.A.1,Interpret & Compute using Division of Fractions +319778,135,6.NS.A.1,Interpret & Compute using Division of Fractions +20500,135,6.NS.A.1,Interpret & Compute using Division of Fractions +20916,135,6.NS.A.1,Interpret & Compute using Division of Fractions +20788,135,6.NS.A.1,Interpret & Compute using Division of Fractions +318653,135,6.NS.A.1,Interpret & Compute using Division of Fractions +319507,135,6.NS.A.1,Interpret & Compute using Division of Fractions +319658,135,6.NS.A.1,Interpret & Compute using Division of Fractions +156504,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +126648,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +92479,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +62644,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +262449,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +354320,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +204595,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +490267,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +93346,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +102028,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +262674,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +204768,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +204459,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +278232,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +103383,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +590968,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +133100,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +591069,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +473981,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +590738,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +590413,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +505947,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +92124,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +515874,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +215013,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +278455,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +137305,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +203679,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +92835,136,6.NS.B.2,Divide Multi-Digit Whole Numbers +62040,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +7096,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +319310,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +249213,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8347,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +249867,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8869,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +9017,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +249667,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +71526,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +69196,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8476,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +9184,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +154867,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +61905,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +277881,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +61764,137,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8476,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +70629,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +197306,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +70299,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +305101,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +277053,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +405351,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +470590,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +274984,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +274077,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +275825,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +61764,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +204143,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +71223,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +7207,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +276696,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +94160,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +7369,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +94419,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +7710,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273109,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +94291,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +197603,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +304746,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273482,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +70102,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +70912,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273269,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8064,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +61905,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273819,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +470213,138,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273482,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +465121,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +14749,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8234,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +354320,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +60703,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +10467,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +88,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +156407,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +132787,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +342597,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +342329,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +75189,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +45068,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +77299,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +342865,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +342027,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +91787,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8563,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +7381,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8540,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +204910,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273819,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +61617,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +343161,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +81898,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +77578,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +15038,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +403777,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +403421,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8390,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +8659,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +181356,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +180865,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +405944,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273269,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +156504,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +343445,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +138228,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +10585,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +81543,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +274077,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +130191,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +215152,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +77861,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273109,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +181066,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +75309,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +81261,139,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +117528,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +272660,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +273049,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +117994,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +278232,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +117735,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +118786,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +126091,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +262087,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +126362,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +127324,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +505841,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +412825,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +126628,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +590847,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +262715,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +134242,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +591069,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +132551,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +590968,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +590738,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +137139,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +136828,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +137016,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +81543,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +81261,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +78269,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +22078,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +22349,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +641896,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +222661,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +278455,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +277925,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +46049,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +45439,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +351353,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +278345,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +45750,140,6.NS.B.3,"Add, Subtract, Multiply & Divide Multi-Digit Decimals" +436594,141,6.NS.B.4,Find Common Factors & Multiples +436482,141,6.NS.B.4,Find Common Factors & Multiples +437180,141,6.NS.B.4,Find Common Factors & Multiples +436921,141,6.NS.B.4,Find Common Factors & Multiples +92677,141,6.NS.B.4,Find Common Factors & Multiples +436717,141,6.NS.B.4,Find Common Factors & Multiples +437042,141,6.NS.B.4,Find Common Factors & Multiples +436208,141,6.NS.B.4,Find Common Factors & Multiples +414444,141,6.NS.B.4,Find Common Factors & Multiples +92361,141,6.NS.B.4,Find Common Factors & Multiples +414639,141,6.NS.B.4,Find Common Factors & Multiples +261290,141,6.NS.B.4,Find Common Factors & Multiples +414817,141,6.NS.B.4,Find Common Factors & Multiples +90903,142,6.NS.B.4,Find Common Factors & Multiples +592258,142,6.NS.B.4,Find Common Factors & Multiples +489519,142,6.NS.B.4,Find Common Factors & Multiples +90598,142,6.NS.B.4,Find Common Factors & Multiples +238849,142,6.NS.B.4,Find Common Factors & Multiples +591850,142,6.NS.B.4,Find Common Factors & Multiples +91177,142,6.NS.B.4,Find Common Factors & Multiples +91453,142,6.NS.B.4,Find Common Factors & Multiples +489770,142,6.NS.B.4,Find Common Factors & Multiples +92518,142,6.NS.B.4,Find Common Factors & Multiples +592027,142,6.NS.B.4,Find Common Factors & Multiples +92677,142,6.NS.B.4,Find Common Factors & Multiples +355558,142,6.NS.B.4,Find Common Factors & Multiples +324197,144,6.NS.B.4,Find Common Factors & Multiples +410833,144,6.NS.B.4,Find Common Factors & Multiples +324258,144,6.NS.B.4,Find Common Factors & Multiples +49409,144,6.NS.B.4,Find Common Factors & Multiples +66602,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +171657,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +153519,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +354803,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +355654,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +122792,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +62772,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +195577,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +409535,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +354353,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +48097,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +198077,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +66748,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +197878,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +236452,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +154138,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +353939,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +187169,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +153861,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +355221,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +117788,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +197626,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +9624,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +9946,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +171270,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +198319,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +10141,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +63725,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +373578,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +195392,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +236567,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +118176,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +117977,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +66472,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +195675,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +522388,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +123053,145,6.NS.C.5,Use Positive & Negative Numbers to Represent Quantities +254122,147,6.NS.C.6a,Identify Opposites of Integers +355221,147,6.NS.C.6a,Identify Opposites of Integers +354353,147,6.NS.C.6a,Identify Opposites of Integers +353939,147,6.NS.C.6a,Identify Opposites of Integers +354803,147,6.NS.C.6a,Identify Opposites of Integers +39966,147,6.NS.C.6a,Identify Opposites of Integers +64016,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +385260,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +19594,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +63205,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +63054,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +406337,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +5125,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +32363,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +49246,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +356879,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +32600,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +337576,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +202997,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +69186,149,6.NS.C.6c,Plot Integers Points on a Number Line & Coordinate Planes +86693,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +28640,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +427265,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +457584,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +426918,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +5429,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +191727,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +457920,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +426185,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +426543,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +20763,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +522597,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +428161,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +205980,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +371766,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +6476,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +356660,151,6.NS.C.7a,Interpret & Compare Integers Using a Number Line +5669,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +518807,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +254509,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +236733,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +218498,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +48097,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +518347,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +518599,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +409535,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +522597,152,6.NS.C.7b,Interpret & Compare Rational Numbers in Real-World Contexts +135943,153,6.NS.C.7c,Understand & Interpret Absolute Value +49529,153,6.NS.C.7c,Understand & Interpret Absolute Value +356457,153,6.NS.C.7c,Understand & Interpret Absolute Value +136203,153,6.NS.C.7c,Understand & Interpret Absolute Value +458234,153,6.NS.C.7c,Understand & Interpret Absolute Value +458552,153,6.NS.C.7c,Understand & Interpret Absolute Value +6158,153,6.NS.C.7c,Understand & Interpret Absolute Value +254509,154,6.NS.C.7d,Understand & Interpret Absolute Value in Real-World Contexts +6346,154,6.NS.C.7d,Understand & Interpret Absolute Value in Real-World Contexts +17938,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +1910,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +3724,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +430244,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +132573,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +324288,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +486785,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +17631,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +17786,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +19594,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +137129,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +238060,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +523482,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +3634,155,6.NS.C.8,Solve Real-World Problems by Graphing on a Coordinate Plane +503178,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +198552,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +247781,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +198429,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +348715,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +350322,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46539,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +348833,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46924,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +435477,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +97579,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +44696,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46683,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +350462,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46425,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46285,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46811,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +48302,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +337576,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +48123,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +427314,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +425797,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +427433,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +425926,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +89104,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +296064,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +557307,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +59107,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +295642,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +58258,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +221748,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +119400,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +295883,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +297160,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +88806,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +558716,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +89321,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +506037,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +373136,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +557481,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +86962,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +297477,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +86722,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +85308,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +84944,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +20908,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +128141,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +87135,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +21399,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +228008,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +228402,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +228808,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +128547,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +128322,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +230550,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +229909,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +21258,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +231607,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +229517,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +230244,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +229183,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +21076,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +156590,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +503038,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +133477,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +404191,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +404451,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +21595,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +404343,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +307185,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +501827,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +83709,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +141384,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +247608,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +501955,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +247357,156,6.EE.A.1,Write & Evaluate Numerical Expressions with Exponents +46101,158,6.EE.A.2a,Write Expressions with Numbers & Variables +605052,158,6.EE.A.2a,Write Expressions with Numbers & Variables +47649,158,6.EE.A.2a,Write Expressions with Numbers & Variables +189985,158,6.EE.A.2a,Write Expressions with Numbers & Variables +604967,158,6.EE.A.2a,Write Expressions with Numbers & Variables +668776,158,6.EE.A.2a,Write Expressions with Numbers & Variables +367186,158,6.EE.A.2a,Write Expressions with Numbers & Variables +19255,158,6.EE.A.2a,Write Expressions with Numbers & Variables +426116,159,6.EE.A.2b,Identify Parts of an Expression +349167,159,6.EE.A.2b,Identify Parts of an Expression +349044,159,6.EE.A.2b,Identify Parts of an Expression +426220,159,6.EE.A.2b,Identify Parts of an Expression +605052,159,6.EE.A.2b,Identify Parts of an Expression +604967,159,6.EE.A.2b,Identify Parts of an Expression +207,160,6.EE.A.2c,Evaluate Expression in Real-World Context +425926,160,6.EE.A.2c,Evaluate Expression in Real-World Context +668776,160,6.EE.A.2c,Evaluate Expression in Real-World Context +312,160,6.EE.A.2c,Evaluate Expression in Real-World Context +93,160,6.EE.A.2c,Evaluate Expression in Real-World Context +348833,160,6.EE.A.2c,Evaluate Expression in Real-World Context +604967,160,6.EE.A.2c,Evaluate Expression in Real-World Context +425797,160,6.EE.A.2c,Evaluate Expression in Real-World Context +348715,160,6.EE.A.2c,Evaluate Expression in Real-World Context +605052,160,6.EE.A.2c,Evaluate Expression in Real-World Context +372951,161,6.EE.A.2c,Evaluate Expression in Real-World Context +372761,161,6.EE.A.2c,Evaluate Expression in Real-World Context +46711,161,6.EE.A.2c,Evaluate Expression in Real-World Context +373740,161,6.EE.A.2c,Evaluate Expression in Real-World Context +46527,161,6.EE.A.2c,Evaluate Expression in Real-World Context +47109,161,6.EE.A.2c,Evaluate Expression in Real-World Context +373537,161,6.EE.A.2c,Evaluate Expression in Real-World Context +47479,161,6.EE.A.2c,Evaluate Expression in Real-World Context +373325,161,6.EE.A.2c,Evaluate Expression in Real-World Context +46909,161,6.EE.A.2c,Evaluate Expression in Real-World Context +47289,161,6.EE.A.2c,Evaluate Expression in Real-World Context +46338,161,6.EE.A.2c,Evaluate Expression in Real-World Context +53138,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +94031,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +33992,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +56749,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +110609,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +349044,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +35877,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +538288,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +93868,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +195291,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +367311,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +6876,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +94199,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +349167,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +298817,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +35781,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +350591,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +69182,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +498737,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +426220,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +426116,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +113030,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +189623,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +186704,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +52890,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +184709,162,6.EE.A.3,Generate Equivalent Expressions using Properties of Operations +427575,163,6.EE.A.4,Identify Equivalent Expressions +70516,163,6.EE.A.4,Identify Equivalent Expressions +189763,163,6.EE.A.4,Identify Equivalent Expressions +609697,163,6.EE.A.4,Identify Equivalent Expressions +350591,163,6.EE.A.4,Identify Equivalent Expressions +270175,163,6.EE.A.4,Identify Equivalent Expressions +362327,163,6.EE.A.4,Identify Equivalent Expressions +35632,163,6.EE.A.4,Identify Equivalent Expressions +84110,163,6.EE.A.4,Identify Equivalent Expressions +270010,163,6.EE.A.4,Identify Equivalent Expressions +56749,163,6.EE.A.4,Identify Equivalent Expressions +367311,163,6.EE.A.4,Identify Equivalent Expressions +84517,163,6.EE.A.4,Identify Equivalent Expressions +21566,163,6.EE.A.4,Identify Equivalent Expressions +296344,163,6.EE.A.4,Identify Equivalent Expressions +541977,163,6.EE.A.4,Identify Equivalent Expressions +50267,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +194547,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +510935,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +361147,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +121352,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +50865,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +50477,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +112678,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +56477,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +112511,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +130824,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +367058,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +112350,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +360938,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +293965,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +50674,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +195193,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +113676,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +109056,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +50042,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +361805,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +293491,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +179454,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +361341,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +109501,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +361546,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +130584,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +109387,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +109628,164,6.EE.B.5,Solve 1-Step Equations & Inequalities Using Substitution +244242,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +187657,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +406364,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +406161,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +55944,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +406962,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +54562,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +677527,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +123623,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +54441,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +556824,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +366543,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +187859,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +19761,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +19879,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +365152,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +78941,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +15120,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +198406,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +15569,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +407575,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +364872,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +406771,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +206088,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +407444,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +155072,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +206599,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +406643,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +15414,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +407163,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +198693,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +80072,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +198805,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +229303,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +155237,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +229143,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +677544,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +15269,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +677536,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +87743,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +54317,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +207052,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +54666,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +365306,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +228800,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +198295,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +365017,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +228973,165,6.EE.B.6,Write Expressions with Variables to Solve Problems +292292,166,6.EE.B.7,Write & Solve 1-Step Equations +197182,166,6.EE.B.7,Write & Solve 1-Step Equations +74581,166,6.EE.B.7,Write & Solve 1-Step Equations +196505,166,6.EE.B.7,Write & Solve 1-Step Equations +292175,166,6.EE.B.7,Write & Solve 1-Step Equations +179341,166,6.EE.B.7,Write & Solve 1-Step Equations +407444,166,6.EE.B.7,Write & Solve 1-Step Equations +61779,166,6.EE.B.7,Write & Solve 1-Step Equations +198295,166,6.EE.B.7,Write & Solve 1-Step Equations +367186,166,6.EE.B.7,Write & Solve 1-Step Equations +298057,166,6.EE.B.7,Write & Solve 1-Step Equations +110852,166,6.EE.B.7,Write & Solve 1-Step Equations +298258,166,6.EE.B.7,Write & Solve 1-Step Equations +407163,166,6.EE.B.7,Write & Solve 1-Step Equations +223118,166,6.EE.B.7,Write & Solve 1-Step Equations +74258,166,6.EE.B.7,Write & Solve 1-Step Equations +178686,166,6.EE.B.7,Write & Solve 1-Step Equations +406643,166,6.EE.B.7,Write & Solve 1-Step Equations +366764,166,6.EE.B.7,Write & Solve 1-Step Equations +74416,166,6.EE.B.7,Write & Solve 1-Step Equations +298444,166,6.EE.B.7,Write & Solve 1-Step Equations +54317,166,6.EE.B.7,Write & Solve 1-Step Equations +406161,166,6.EE.B.7,Write & Solve 1-Step Equations +406364,166,6.EE.B.7,Write & Solve 1-Step Equations +179089,166,6.EE.B.7,Write & Solve 1-Step Equations +366543,166,6.EE.B.7,Write & Solve 1-Step Equations +122576,166,6.EE.B.7,Write & Solve 1-Step Equations +196111,166,6.EE.B.7,Write & Solve 1-Step Equations +74735,166,6.EE.B.7,Write & Solve 1-Step Equations +54666,166,6.EE.B.7,Write & Solve 1-Step Equations +54562,166,6.EE.B.7,Write & Solve 1-Step Equations +365017,166,6.EE.B.7,Write & Solve 1-Step Equations +178835,166,6.EE.B.7,Write & Solve 1-Step Equations +122450,166,6.EE.B.7,Write & Solve 1-Step Equations +142047,166,6.EE.B.7,Write & Solve 1-Step Equations +179212,166,6.EE.B.7,Write & Solve 1-Step Equations +222789,166,6.EE.B.7,Write & Solve 1-Step Equations +365152,166,6.EE.B.7,Write & Solve 1-Step Equations +56163,166,6.EE.B.7,Write & Solve 1-Step Equations +206901,166,6.EE.B.7,Write & Solve 1-Step Equations +196907,166,6.EE.B.7,Write & Solve 1-Step Equations +206730,166,6.EE.B.7,Write & Solve 1-Step Equations +406771,166,6.EE.B.7,Write & Solve 1-Step Equations +350665,166,6.EE.B.7,Write & Solve 1-Step Equations +198805,166,6.EE.B.7,Write & Solve 1-Step Equations +56614,166,6.EE.B.7,Write & Solve 1-Step Equations +64813,166,6.EE.B.7,Write & Solve 1-Step Equations +407575,166,6.EE.B.7,Write & Solve 1-Step Equations +61624,166,6.EE.B.7,Write & Solve 1-Step Equations +55067,166,6.EE.B.7,Write & Solve 1-Step Equations +64410,166,6.EE.B.7,Write & Solve 1-Step Equations +64605,166,6.EE.B.7,Write & Solve 1-Step Equations +47917,166,6.EE.B.7,Write & Solve 1-Step Equations +64054,166,6.EE.B.7,Write & Solve 1-Step Equations +223323,166,6.EE.B.7,Write & Solve 1-Step Equations +606133,166,6.EE.B.7,Write & Solve 1-Step Equations +178963,166,6.EE.B.7,Write & Solve 1-Step Equations +48838,166,6.EE.B.7,Write & Solve 1-Step Equations +141837,166,6.EE.B.7,Write & Solve 1-Step Equations +64237,166,6.EE.B.7,Write & Solve 1-Step Equations +406962,166,6.EE.B.7,Write & Solve 1-Step Equations +198693,166,6.EE.B.7,Write & Solve 1-Step Equations +198406,166,6.EE.B.7,Write & Solve 1-Step Equations +73717,166,6.EE.B.7,Write & Solve 1-Step Equations +73585,166,6.EE.B.7,Write & Solve 1-Step Equations +73287,166,6.EE.B.7,Write & Solve 1-Step Equations +178406,166,6.EE.B.7,Write & Solve 1-Step Equations +122331,166,6.EE.B.7,Write & Solve 1-Step Equations +223535,166,6.EE.B.7,Write & Solve 1-Step Equations +178546,166,6.EE.B.7,Write & Solve 1-Step Equations +73275,166,6.EE.B.7,Write & Solve 1-Step Equations +222907,166,6.EE.B.7,Write & Solve 1-Step Equations +73395,166,6.EE.B.7,Write & Solve 1-Step Equations +364872,166,6.EE.B.7,Write & Solve 1-Step Equations +54441,166,6.EE.B.7,Write & Solve 1-Step Equations +365306,166,6.EE.B.7,Write & Solve 1-Step Equations +444018,166,6.EE.B.7,Write & Solve 1-Step Equations +298615,166,6.EE.B.7,Write & Solve 1-Step Equations +159146,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +362112,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +62003,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +227043,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +262820,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +227828,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +410688,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +177985,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +175861,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +228072,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +2951,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +159292,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +175247,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +3858,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +227553,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +228382,167,6.EE.B.8,Write Simple Inequalities to Represent a Condition +43771,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +44015,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +63146,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +68783,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +68963,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +20430,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +18187,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +18301,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +19984,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +426461,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +96224,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +426575,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +96079,168,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +68783,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +349368,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +105867,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +349505,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +68963,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +60015,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +63340,169,6.EE.C.9,Write & Analyze Relationships Between Dependent & Independent Variables +276338,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +24929,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +503274,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +150868,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +501827,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +150514,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +383037,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +227577,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +372037,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +145962,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +383334,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +149451,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +403617,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +501955,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +173259,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +89233,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +37379,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +47557,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +444018,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +276196,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +287214,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +276480,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +24639,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +383524,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +273241,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +88316,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +346945,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +266614,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +276040,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +149829,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +10047,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +89569,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +26348,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +390139,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +54527,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +150161,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +336859,170,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +557307,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +383961,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +503799,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +383708,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +375982,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +347199,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +10364,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +10254,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +97230,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +88950,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +504115,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +42515,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +565173,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +503653,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +201855,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +25226,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +557481,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +375655,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +42671,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +433197,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +566156,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +24293,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +42913,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +503982,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +668776,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +42371,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +43170,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +14144,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +565046,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +97111,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +55428,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +336859,171,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +242072,172,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +1630,172,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +41185,172,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +41469,172,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +12774,172,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +418012,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +176469,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +306997,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +242640,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +668703,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +77648,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +286560,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +577430,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +138605,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +337992,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +577269,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +383830,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +421017,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +185261,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +272768,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +185386,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +286898,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +420787,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +605478,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +253000,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +323410,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +230682,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +323128,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +323266,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +264860,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +323003,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +55302,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +286192,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +166613,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +418178,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +222283,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +323746,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +419590,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +375305,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +375493,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +175939,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +176215,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +417861,173,6.G.A.1,"Find the Area of Triangles, Quadrilaterals & Polygons" +256912,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +79361,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +21181,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +151049,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +115417,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +20286,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +115789,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +278648,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +115025,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +166007,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +87339,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +165863,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +1468,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +320405,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +87535,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +319193,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +176751,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +177695,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +20500,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +150895,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +503038,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +579223,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +278504,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +176895,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +115625,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +256677,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +115150,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +60349,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +318942,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +167762,174,6.G.A.2,Find the Volume of Rectangular Prisms with Fractional Sides +316168,175,6.G.A.3,Use Coordinates on a Graph to Create Polygons & Find Side Lengths +316462,175,6.G.A.3,Use Coordinates on a Graph to Create Polygons & Find Side Lengths +138605,175,6.G.A.3,Use Coordinates on a Graph to Create Polygons & Find Side Lengths +337475,175,6.G.A.3,Use Coordinates on a Graph to Create Polygons & Find Side Lengths +37999,175,6.G.A.3,Use Coordinates on a Graph to Create Polygons & Find Side Lengths +137129,175,6.G.A.3,Use Coordinates on a Graph to Create Polygons & Find Side Lengths +502795,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +78121,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +250066,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +558559,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +249682,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +382659,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +382382,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +382737,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +382485,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +226695,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +226302,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115417,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115789,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115025,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +475896,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115625,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +47990,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115150,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +36768,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +144713,176,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +137690,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +198387,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +199131,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +199218,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +94609,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +198852,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +262608,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +362897,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +43132,177,6.SP.A.1,Recognize Statistical Questions Account for Variablility +44782,178,6.SP.A.2,Understand Properties of Distribution with (or for) Data +57280,178,6.SP.A.2,Understand Properties of Distribution with (or for) Data +21754,178,6.SP.A.2,Understand Properties of Distribution with (or for) Data +21866,178,6.SP.A.2,Understand Properties of Distribution with (or for) Data +57030,178,6.SP.A.2,Understand Properties of Distribution with (or for) Data +181770,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +528780,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +256621,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +64548,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +520423,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +256519,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +181647,179,6.SP.A.3,Recognize Properties of Measure of Center with Variation +65288,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +258280,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +183259,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +529063,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +591536,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +80061,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +193572,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +55325,181,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +6843,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +65434,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +591536,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +158855,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +158316,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +158585,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +6560,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +206643,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +193572,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +206824,183,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +103242,186,6.SP.B.5a,Report the Number of Observations in a Data Set +136119,187,6.SP.B.5b,Describe the Attributes of a Data Set +136895,187,6.SP.B.5b,Describe the Attributes of a Data Set +200269,187,6.SP.B.5b,Describe the Attributes of a Data Set +339343,187,6.SP.B.5b,Describe the Attributes of a Data Set +102850,187,6.SP.B.5b,Describe the Attributes of a Data Set +137297,187,6.SP.B.5b,Describe the Attributes of a Data Set +136547,187,6.SP.B.5b,Describe the Attributes of a Data Set +258280,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +256519,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +351005,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +201945,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +202431,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +202762,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +350745,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +350634,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +193337,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +350537,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +361422,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +361179,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +361989,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +363244,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +181770,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +591238,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +79667,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +46358,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +46235,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +46015,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +46116,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +45665,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +45802,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +528780,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +529581,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +529857,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +529063,188,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +529389,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +182704,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +99939,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +5236,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +182285,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +252396,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +529857,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +88478,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +253594,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +6735,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +99247,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +183259,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +274025,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +256621,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +188655,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +252066,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +193691,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +6006,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +591659,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +99606,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +202276,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +202762,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +288503,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +519985,189,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +202762,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +529857,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +528652,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +182285,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +181647,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +289171,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +182483,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +252499,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +253922,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +183259,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +288926,190,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +528780,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +6560,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +7682,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +6843,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +7018,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +7452,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +7254,191,6.SP.B.5c,Give & Describe Quantitative Measures of Center & Variability +334286,192,6.SP.B.5d,Relate Measures of Center & Variablity to Distribution of Data +182704,192,6.SP.B.5d,Relate Measures of Center & Variablity to Distribution of Data +182483,192,6.SP.B.5d,Relate Measures of Center & Variablity to Distribution of Data +182285,192,6.SP.B.5d,Relate Measures of Center & Variablity to Distribution of Data +382565,193,7.RP.A.1,Compute Unit Rates with Fractions +303033,193,7.RP.A.1,Compute Unit Rates with Fractions +559523,193,7.RP.A.1,Compute Unit Rates with Fractions +382916,193,7.RP.A.1,Compute Unit Rates with Fractions +75212,193,7.RP.A.1,Compute Unit Rates with Fractions +409731,193,7.RP.A.1,Compute Unit Rates with Fractions +558351,193,7.RP.A.1,Compute Unit Rates with Fractions +558648,193,7.RP.A.1,Compute Unit Rates with Fractions +302809,193,7.RP.A.1,Compute Unit Rates with Fractions +221711,193,7.RP.A.1,Compute Unit Rates with Fractions +222861,193,7.RP.A.1,Compute Unit Rates with Fractions +559181,193,7.RP.A.1,Compute Unit Rates with Fractions +42365,193,7.RP.A.1,Compute Unit Rates with Fractions +221573,193,7.RP.A.1,Compute Unit Rates with Fractions +501551,193,7.RP.A.1,Compute Unit Rates with Fractions +558904,193,7.RP.A.1,Compute Unit Rates with Fractions +56172,194,7.RP.A.2a,Identify Proportional Relationships +56590,194,7.RP.A.2a,Identify Proportional Relationships +184732,194,7.RP.A.2a,Identify Proportional Relationships +552378,194,7.RP.A.2a,Identify Proportional Relationships +48435,194,7.RP.A.2a,Identify Proportional Relationships +19558,194,7.RP.A.2a,Identify Proportional Relationships +221711,194,7.RP.A.2a,Identify Proportional Relationships +122274,194,7.RP.A.2a,Identify Proportional Relationships +123317,194,7.RP.A.2a,Identify Proportional Relationships +221573,194,7.RP.A.2a,Identify Proportional Relationships +26568,194,7.RP.A.2a,Identify Proportional Relationships +263683,194,7.RP.A.2a,Identify Proportional Relationships +584015,194,7.RP.A.2a,Identify Proportional Relationships +584326,194,7.RP.A.2a,Identify Proportional Relationships +584537,194,7.RP.A.2a,Identify Proportional Relationships +121533,194,7.RP.A.2a,Identify Proportional Relationships +86074,194,7.RP.A.2a,Identify Proportional Relationships +278886,194,7.RP.A.2a,Identify Proportional Relationships +123500,194,7.RP.A.2a,Identify Proportional Relationships +85726,194,7.RP.A.2a,Identify Proportional Relationships +123973,194,7.RP.A.2a,Identify Proportional Relationships +106336,194,7.RP.A.2a,Identify Proportional Relationships +123722,194,7.RP.A.2a,Identify Proportional Relationships +24737,194,7.RP.A.2a,Identify Proportional Relationships +584429,194,7.RP.A.2a,Identify Proportional Relationships +9419,194,7.RP.A.2a,Identify Proportional Relationships +9673,194,7.RP.A.2a,Identify Proportional Relationships +408662,194,7.RP.A.2a,Identify Proportional Relationships +103020,194,7.RP.A.2a,Identify Proportional Relationships +225175,194,7.RP.A.2a,Identify Proportional Relationships +131274,194,7.RP.A.2a,Identify Proportional Relationships +409242,194,7.RP.A.2a,Identify Proportional Relationships +259215,194,7.RP.A.2a,Identify Proportional Relationships +263438,194,7.RP.A.2a,Identify Proportional Relationships +259069,194,7.RP.A.2a,Identify Proportional Relationships +135345,194,7.RP.A.2a,Identify Proportional Relationships +135491,194,7.RP.A.2a,Identify Proportional Relationships +135638,194,7.RP.A.2a,Identify Proportional Relationships +136814,194,7.RP.A.2a,Identify Proportional Relationships +135233,194,7.RP.A.2a,Identify Proportional Relationships +135753,194,7.RP.A.2a,Identify Proportional Relationships +135875,194,7.RP.A.2a,Identify Proportional Relationships +136282,194,7.RP.A.2a,Identify Proportional Relationships +225359,194,7.RP.A.2a,Identify Proportional Relationships +136020,194,7.RP.A.2a,Identify Proportional Relationships +36971,194,7.RP.A.2a,Identify Proportional Relationships +136496,194,7.RP.A.2a,Identify Proportional Relationships +259356,194,7.RP.A.2a,Identify Proportional Relationships +327867,194,7.RP.A.2a,Identify Proportional Relationships +136146,194,7.RP.A.2a,Identify Proportional Relationships +100712,194,7.RP.A.2a,Identify Proportional Relationships +34746,194,7.RP.A.2a,Identify Proportional Relationships +109969,194,7.RP.A.2a,Identify Proportional Relationships +24963,194,7.RP.A.2a,Identify Proportional Relationships +110096,194,7.RP.A.2a,Identify Proportional Relationships +36440,194,7.RP.A.2a,Identify Proportional Relationships +144928,194,7.RP.A.2a,Identify Proportional Relationships +595744,194,7.RP.A.2a,Identify Proportional Relationships +144794,194,7.RP.A.2a,Identify Proportional Relationships +147904,194,7.RP.A.2a,Identify Proportional Relationships +9567,194,7.RP.A.2a,Identify Proportional Relationships +303033,194,7.RP.A.2a,Identify Proportional Relationships +24484,194,7.RP.A.2a,Identify Proportional Relationships +148013,194,7.RP.A.2a,Identify Proportional Relationships +152397,194,7.RP.A.2a,Identify Proportional Relationships +302809,194,7.RP.A.2a,Identify Proportional Relationships +35010,194,7.RP.A.2a,Identify Proportional Relationships +36700,194,7.RP.A.2a,Identify Proportional Relationships +1089,194,7.RP.A.2a,Identify Proportional Relationships +22967,194,7.RP.A.2a,Identify Proportional Relationships +109845,194,7.RP.A.2a,Identify Proportional Relationships +37662,194,7.RP.A.2a,Identify Proportional Relationships +561011,194,7.RP.A.2a,Identify Proportional Relationships +511978,194,7.RP.A.2a,Identify Proportional Relationships +37332,194,7.RP.A.2a,Identify Proportional Relationships +308662,194,7.RP.A.2a,Identify Proportional Relationships +343125,194,7.RP.A.2a,Identify Proportional Relationships +343609,194,7.RP.A.2a,Identify Proportional Relationships +392468,194,7.RP.A.2a,Identify Proportional Relationships +36149,194,7.RP.A.2a,Identify Proportional Relationships +156721,194,7.RP.A.2a,Identify Proportional Relationships +42014,194,7.RP.A.2a,Identify Proportional Relationships +100983,194,7.RP.A.2a,Identify Proportional Relationships +13937,194,7.RP.A.2a,Identify Proportional Relationships +225864,194,7.RP.A.2a,Identify Proportional Relationships +343945,194,7.RP.A.2a,Identify Proportional Relationships +98864,194,7.RP.A.2a,Identify Proportional Relationships +101254,194,7.RP.A.2a,Identify Proportional Relationships +12129,194,7.RP.A.2a,Identify Proportional Relationships +560745,194,7.RP.A.2a,Identify Proportional Relationships +100386,194,7.RP.A.2a,Identify Proportional Relationships +43417,194,7.RP.A.2a,Identify Proportional Relationships +13763,194,7.RP.A.2a,Identify Proportional Relationships +13854,194,7.RP.A.2a,Identify Proportional Relationships +110217,194,7.RP.A.2a,Identify Proportional Relationships +225766,194,7.RP.A.2a,Identify Proportional Relationships +560139,194,7.RP.A.2a,Identify Proportional Relationships +25209,194,7.RP.A.2a,Identify Proportional Relationships +42156,194,7.RP.A.2a,Identify Proportional Relationships +512430,194,7.RP.A.2a,Identify Proportional Relationships +650373,194,7.RP.A.2a,Identify Proportional Relationships +177081,194,7.RP.A.2a,Identify Proportional Relationships +61559,194,7.RP.A.2a,Identify Proportional Relationships +351684,194,7.RP.A.2a,Identify Proportional Relationships +114159,194,7.RP.A.2a,Identify Proportional Relationships +105953,194,7.RP.A.2a,Identify Proportional Relationships +179199,194,7.RP.A.2a,Identify Proportional Relationships +179693,194,7.RP.A.2a,Identify Proportional Relationships +178727,194,7.RP.A.2a,Identify Proportional Relationships +178978,194,7.RP.A.2a,Identify Proportional Relationships +182437,194,7.RP.A.2a,Identify Proportional Relationships +24484,195,7.RP.A.2b,Identify the Constant of Proportionality +35102,195,7.RP.A.2b,Identify the Constant of Proportionality +23822,195,7.RP.A.2b,Identify the Constant of Proportionality +24963,195,7.RP.A.2b,Identify the Constant of Proportionality +102385,195,7.RP.A.2b,Identify the Constant of Proportionality +296114,195,7.RP.A.2b,Identify the Constant of Proportionality +225359,195,7.RP.A.2b,Identify the Constant of Proportionality +408074,195,7.RP.A.2b,Identify the Constant of Proportionality +225175,195,7.RP.A.2b,Identify the Constant of Proportionality +129451,195,7.RP.A.2b,Identify the Constant of Proportionality +124164,195,7.RP.A.2b,Identify the Constant of Proportionality +24737,195,7.RP.A.2b,Identify the Constant of Proportionality +650519,195,7.RP.A.2b,Identify the Constant of Proportionality +196819,195,7.RP.A.2b,Identify the Constant of Proportionality +196523,195,7.RP.A.2b,Identify the Constant of Proportionality +164771,195,7.RP.A.2b,Identify the Constant of Proportionality +560139,195,7.RP.A.2b,Identify the Constant of Proportionality +124698,195,7.RP.A.2b,Identify the Constant of Proportionality +270843,195,7.RP.A.2b,Identify the Constant of Proportionality +197156,195,7.RP.A.2b,Identify the Constant of Proportionality +25520,195,7.RP.A.2b,Identify the Constant of Proportionality +27175,195,7.RP.A.2b,Identify the Constant of Proportionality +101024,195,7.RP.A.2b,Identify the Constant of Proportionality +24068,195,7.RP.A.2b,Identify the Constant of Proportionality +97850,196,7.RP.A.2c,Represent Proportional Relationships with Equations +270760,196,7.RP.A.2c,Represent Proportional Relationships with Equations +294659,196,7.RP.A.2c,Represent Proportional Relationships with Equations +118275,196,7.RP.A.2c,Represent Proportional Relationships with Equations +118986,196,7.RP.A.2c,Represent Proportional Relationships with Equations +271395,196,7.RP.A.2c,Represent Proportional Relationships with Equations +270281,196,7.RP.A.2c,Represent Proportional Relationships with Equations +118610,196,7.RP.A.2c,Represent Proportional Relationships with Equations +119756,196,7.RP.A.2c,Represent Proportional Relationships with Equations +122934,196,7.RP.A.2c,Represent Proportional Relationships with Equations +269923,196,7.RP.A.2c,Represent Proportional Relationships with Equations +119432,196,7.RP.A.2c,Represent Proportional Relationships with Equations +294155,196,7.RP.A.2c,Represent Proportional Relationships with Equations +123580,196,7.RP.A.2c,Represent Proportional Relationships with Equations +124698,196,7.RP.A.2c,Represent Proportional Relationships with Equations +263961,196,7.RP.A.2c,Represent Proportional Relationships with Equations +124164,196,7.RP.A.2c,Represent Proportional Relationships with Equations +1195,196,7.RP.A.2c,Represent Proportional Relationships with Equations +101733,196,7.RP.A.2c,Represent Proportional Relationships with Equations +408662,196,7.RP.A.2c,Represent Proportional Relationships with Equations +129738,196,7.RP.A.2c,Represent Proportional Relationships with Equations +409526,196,7.RP.A.2c,Represent Proportional Relationships with Equations +271051,196,7.RP.A.2c,Represent Proportional Relationships with Equations +137922,196,7.RP.A.2c,Represent Proportional Relationships with Equations +144928,196,7.RP.A.2c,Represent Proportional Relationships with Equations +144794,196,7.RP.A.2c,Represent Proportional Relationships with Equations +595853,196,7.RP.A.2c,Represent Proportional Relationships with Equations +247607,196,7.RP.A.2c,Represent Proportional Relationships with Equations +247330,196,7.RP.A.2c,Represent Proportional Relationships with Equations +74204,196,7.RP.A.2c,Represent Proportional Relationships with Equations +460042,196,7.RP.A.2c,Represent Proportional Relationships with Equations +460209,196,7.RP.A.2c,Represent Proportional Relationships with Equations +560745,196,7.RP.A.2c,Represent Proportional Relationships with Equations +383539,196,7.RP.A.2c,Represent Proportional Relationships with Equations +168477,196,7.RP.A.2c,Represent Proportional Relationships with Equations +168704,196,7.RP.A.2c,Represent Proportional Relationships with Equations +460374,196,7.RP.A.2c,Represent Proportional Relationships with Equations +375713,196,7.RP.A.2c,Represent Proportional Relationships with Equations +171936,196,7.RP.A.2c,Represent Proportional Relationships with Equations +182778,196,7.RP.A.2c,Represent Proportional Relationships with Equations +182948,196,7.RP.A.2c,Represent Proportional Relationships with Equations +182080,196,7.RP.A.2c,Represent Proportional Relationships with Equations +20510,196,7.RP.A.2c,Represent Proportional Relationships with Equations +183159,196,7.RP.A.2c,Represent Proportional Relationships with Equations +187804,196,7.RP.A.2c,Represent Proportional Relationships with Equations +47104,196,7.RP.A.2c,Represent Proportional Relationships with Equations +531136,196,7.RP.A.2c,Represent Proportional Relationships with Equations +47181,196,7.RP.A.2c,Represent Proportional Relationships with Equations +19877,196,7.RP.A.2c,Represent Proportional Relationships with Equations +42964,196,7.RP.A.2c,Represent Proportional Relationships with Equations +42156,196,7.RP.A.2c,Represent Proportional Relationships with Equations +202480,196,7.RP.A.2c,Represent Proportional Relationships with Equations +42014,196,7.RP.A.2c,Represent Proportional Relationships with Equations +24068,196,7.RP.A.2c,Represent Proportional Relationships with Equations +35102,196,7.RP.A.2c,Represent Proportional Relationships with Equations +23822,196,7.RP.A.2c,Represent Proportional Relationships with Equations +129133,197,7.RP.A.2d,Interpret Points on Proportional Graphs +409398,197,7.RP.A.2d,Interpret Points on Proportional Graphs +1449,197,7.RP.A.2d,Interpret Points on Proportional Graphs +2516,197,7.RP.A.2d,Interpret Points on Proportional Graphs +23819,197,7.RP.A.2d,Interpret Points on Proportional Graphs +24277,197,7.RP.A.2d,Interpret Points on Proportional Graphs +530971,197,7.RP.A.2d,Interpret Points on Proportional Graphs +21201,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +323501,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +316809,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +20885,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +323812,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +318309,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +20199,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +316941,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +496354,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +317074,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +61531,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +267646,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +171238,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +338281,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +238173,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +62350,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +479240,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +318171,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +21043,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +338629,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +171421,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +313685,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +97107,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +113440,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +317429,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +323576,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15629,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +324897,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +502720,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +96761,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +16005,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15881,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +324443,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +97399,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +314006,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +246686,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +97648,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +244895,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +314324,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +113646,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +313329,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +97533,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +247727,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +245930,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +203426,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +97961,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +31433,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +246966,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +499714,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +477606,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +74049,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +24461,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +96895,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +245546,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +248005,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +156692,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +245240,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +246376,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15059,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +73890,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +478570,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +251426,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +22470,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +389538,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +98095,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +289043,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +203873,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15333,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +429590,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +504254,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +153106,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15138,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +14960,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +153479,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +389890,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +153291,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +478342,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +479016,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15760,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +153688,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +152711,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +101005,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +77978,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +78165,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +152894,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +100544,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +505561,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +477986,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +24484,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +505118,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +429767,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +429393,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +146150,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +509509,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +96632,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +24777,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +100670,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +504695,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +146018,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +24963,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +23144,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +428623,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +137401,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +137056,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +218838,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +137232,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +205498,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +235060,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +553614,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +57624,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +317307,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +367651,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +120403,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +367113,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +317741,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +232655,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems 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Solve Ratio & Percent Problems +317639,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +20669,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +503044,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +316680,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +317833,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +15492,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +62493,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +359617,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +553198,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +498194,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +178224,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +236501,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +21347,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +418897,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +267340,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +499326,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +178110,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +177927,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +61213,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +428993,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +506119,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +84788,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +131934,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +205959,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +204231,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +339221,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +84918,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +338934,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +509942,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +339477,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +86791,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +205281,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +326880,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +31188,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +205821,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +205401,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +87236,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +205649,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +586483,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +331301,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +86471,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +24737,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +87369,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +123995,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +87154,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +125385,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems 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Ratio & Percent Problems +113830,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +497355,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +50795,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +121257,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +51243,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +20026,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +52062,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +360293,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +359196,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +185005,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +181762,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +233047,198,7.RP.A.3,Use Proportional Relationships to Solve Ratio & Percent Problems +14063,200,7.NS.A.1a,Describe Situations Where Opposite Quantities Combine to Make 0 +450077,201,7.NS.A.1b,Interpret Sums of Rational Numbers +449847,201,7.NS.A.1b,Interpret Sums of Rational Numbers +114294,201,7.NS.A.1b,Interpret Sums of Rational Numbers +214107,201,7.NS.A.1b,Interpret Sums of Rational Numbers +338572,201,7.NS.A.1b,Interpret Sums of Rational Numbers +214762,201,7.NS.A.1b,Interpret Sums of Rational Numbers +214460,201,7.NS.A.1b,Interpret Sums of Rational Numbers +333811,201,7.NS.A.1b,Interpret Sums of Rational Numbers +24438,201,7.NS.A.1b,Interpret Sums of Rational Numbers +11247,201,7.NS.A.1b,Interpret Sums of Rational Numbers +91688,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +42327,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +42642,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +179142,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +114294,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +24438,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +91790,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +179464,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +162021,202,7.NS.A.1c,Understand Properties of Subtracting Rational Numbers +154547,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +153749,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +405832,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +67623,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +615367,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +60534,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +60862,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +61160,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +60187,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +615225,203,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +120094,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +119645,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +131027,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +407999,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +131322,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +130668,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +131590,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +407631,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +279176,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +195193,204,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +222978,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +223345,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +223087,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +223225,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +223453,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +24564,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +312,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +69320,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +64016,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +207,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +69444,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +93,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +87614,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +585630,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +585877,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +442008,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +586044,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +442127,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +586212,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +441900,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +441780,205,7.NS.A.1d,Apply Properties of Operations to Add/Subtract Rational Numbers +112497,206,7.NS.A.2a,Understand Applied Context for Multiplying Rational Numbers +24564,206,7.NS.A.2a,Understand Applied Context for Multiplying Rational Numbers +180087,206,7.NS.A.2a,Understand Applied Context for Multiplying Rational Numbers +179837,206,7.NS.A.2a,Understand Applied Context for Multiplying Rational Numbers +180403,206,7.NS.A.2a,Understand Applied Context for Multiplying Rational Numbers +112290,206,7.NS.A.2a,Understand Applied Context for Multiplying Rational Numbers +24564,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +112931,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +112644,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +24305,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +584854,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +112797,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +226035,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +226116,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +584945,207,7.NS.A.2b,Understand Applied Context for Dividing Rational Numbers +60187,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +61160,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +60862,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +60534,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +22023,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +22552,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +37975,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +22322,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +147088,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +407631,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +24305,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +407999,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +184690,208,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +61160,209,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +60187,209,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +60534,209,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +60862,209,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +38524,209,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +278775,209,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +112644,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +69444,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +93,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +177679,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +54627,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +362542,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +25486,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +26296,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +312,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +112931,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +195193,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +408499,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +279032,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +55885,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +112497,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +26005,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +55569,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +177979,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +65010,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +278908,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +207,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +64437,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +64758,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +38766,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +25718,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +65369,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +177403,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +112797,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +178227,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +112290,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +38268,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +278653,210,7.NS.A.2c,Apply Properties of Operations to Multiply/Divide Rational Numbers +354272,211,7.NS.A.2d,Convert a Rational Number to a Decimal +316024,211,7.NS.A.2d,Convert a Rational Number to a Decimal +204565,211,7.NS.A.2d,Convert a Rational Number to a Decimal +426537,211,7.NS.A.2d,Convert a Rational Number to a Decimal +355272,211,7.NS.A.2d,Convert a Rational Number to a Decimal +426703,211,7.NS.A.2d,Convert a Rational Number to a Decimal +426376,211,7.NS.A.2d,Convert a Rational Number to a Decimal +427041,211,7.NS.A.2d,Convert a Rational Number to a Decimal +355634,211,7.NS.A.2d,Convert a Rational Number to a Decimal +353991,211,7.NS.A.2d,Convert a Rational Number to a Decimal +112290,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +64354,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +112644,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +112797,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +112497,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +48612,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +112931,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +24305,212,7.NS.A.3,Solve Applied Problems Involving All Operations of Rational Numbers +2894,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +3056,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +18664,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +21711,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +22093,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +40142,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +40512,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +39475,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +43371,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +62186,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +146878,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +158903,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +158297,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +158771,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +162630,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +163965,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +190106,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +188812,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +214651,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +218163,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +277069,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +277314,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +327384,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +599220,213,7.EE.A.1,Apply Properties of Operations to Create Equivalent Expressions +66914,214,7.EE.A.2,Understand Equivalent Expressions in Context +171627,214,7.EE.A.2,Understand Equivalent Expressions in Context +257823,214,7.EE.A.2,Understand Equivalent Expressions in Context +537870,214,7.EE.A.2,Understand Equivalent Expressions in Context +25178,214,7.EE.A.2,Understand Equivalent Expressions in Context +51977,214,7.EE.A.2,Understand Equivalent Expressions in Context +341602,214,7.EE.A.2,Understand Equivalent Expressions in Context +275581,214,7.EE.A.2,Understand Equivalent Expressions in Context +303522,214,7.EE.A.2,Understand Equivalent Expressions in Context +235425,214,7.EE.A.2,Understand Equivalent Expressions in Context +327306,214,7.EE.A.2,Understand Equivalent Expressions in Context +56910,214,7.EE.A.2,Understand Equivalent Expressions in Context +109572,214,7.EE.A.2,Understand Equivalent Expressions in Context +171459,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +156692,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +246686,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +257823,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +244895,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +171630,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +97533,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +184283,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +97399,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +96761,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +245546,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +152091,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +245240,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +246376,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +184392,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +184499,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +152206,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +152004,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +78866,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +96632,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +506119,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +171543,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +246966,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +96895,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +97648,215,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +506119,216,7.EE.B.3,Solve Applied Problems Using Numerical and Algebraic Expressions and Equations +75928,217,7.EE.B.4a,Solve 2-Step Equations +308593,217,7.EE.B.4a,Solve 2-Step Equations +308146,217,7.EE.B.4a,Solve 2-Step Equations +156494,217,7.EE.B.4a,Solve 2-Step Equations +157401,217,7.EE.B.4a,Solve 2-Step Equations +308518,217,7.EE.B.4a,Solve 2-Step Equations +157655,217,7.EE.B.4a,Solve 2-Step Equations +154770,217,7.EE.B.4a,Solve 2-Step Equations +156087,217,7.EE.B.4a,Solve 2-Step Equations +157516,217,7.EE.B.4a,Solve 2-Step Equations +375908,217,7.EE.B.4a,Solve 2-Step Equations +63357,217,7.EE.B.4a,Solve 2-Step Equations +155183,217,7.EE.B.4a,Solve 2-Step Equations +156936,217,7.EE.B.4a,Solve 2-Step Equations +155484,217,7.EE.B.4a,Solve 2-Step Equations +157262,217,7.EE.B.4a,Solve 2-Step Equations +442685,217,7.EE.B.4a,Solve 2-Step Equations +524787,217,7.EE.B.4a,Solve 2-Step Equations +158652,217,7.EE.B.4a,Solve 2-Step Equations +55829,217,7.EE.B.4a,Solve 2-Step Equations +56136,217,7.EE.B.4a,Solve 2-Step Equations +54008,217,7.EE.B.4a,Solve 2-Step Equations +56457,217,7.EE.B.4a,Solve 2-Step Equations +443136,217,7.EE.B.4a,Solve 2-Step Equations +53735,217,7.EE.B.4a,Solve 2-Step Equations +55691,217,7.EE.B.4a,Solve 2-Step Equations +367805,217,7.EE.B.4a,Solve 2-Step Equations +63291,217,7.EE.B.4a,Solve 2-Step Equations +376399,217,7.EE.B.4a,Solve 2-Step Equations +178835,217,7.EE.B.4a,Solve 2-Step Equations +179212,217,7.EE.B.4a,Solve 2-Step Equations +179341,217,7.EE.B.4a,Solve 2-Step Equations +183371,217,7.EE.B.4a,Solve 2-Step Equations +369393,217,7.EE.B.4a,Solve 2-Step Equations +525202,217,7.EE.B.4a,Solve 2-Step Equations +341780,217,7.EE.B.4a,Solve 2-Step Equations +131999,217,7.EE.B.4a,Solve 2-Step Equations +341553,217,7.EE.B.4a,Solve 2-Step Equations +131796,217,7.EE.B.4a,Solve 2-Step Equations +376894,217,7.EE.B.4a,Solve 2-Step Equations +131886,217,7.EE.B.4a,Solve 2-Step Equations +132093,217,7.EE.B.4a,Solve 2-Step Equations +369146,217,7.EE.B.4a,Solve 2-Step Equations +337756,217,7.EE.B.4a,Solve 2-Step Equations +11040,217,7.EE.B.4a,Solve 2-Step Equations +90428,217,7.EE.B.4a,Solve 2-Step Equations +90560,217,7.EE.B.4a,Solve 2-Step Equations +368501,217,7.EE.B.4a,Solve 2-Step Equations +90063,217,7.EE.B.4a,Solve 2-Step Equations +368816,217,7.EE.B.4a,Solve 2-Step Equations +368183,217,7.EE.B.4a,Solve 2-Step Equations +153281,217,7.EE.B.4a,Solve 2-Step Equations +155769,217,7.EE.B.4a,Solve 2-Step Equations +76294,217,7.EE.B.4a,Solve 2-Step Equations +194628,217,7.EE.B.4a,Solve 2-Step Equations +376600,217,7.EE.B.4a,Solve 2-Step Equations +179089,217,7.EE.B.4a,Solve 2-Step Equations +178963,217,7.EE.B.4a,Solve 2-Step Equations +194530,217,7.EE.B.4a,Solve 2-Step Equations +31406,217,7.EE.B.4a,Solve 2-Step Equations +178546,217,7.EE.B.4a,Solve 2-Step Equations +178686,217,7.EE.B.4a,Solve 2-Step Equations +190220,217,7.EE.B.4a,Solve 2-Step Equations +274694,217,7.EE.B.4a,Solve 2-Step Equations +195078,217,7.EE.B.4a,Solve 2-Step Equations +194712,217,7.EE.B.4a,Solve 2-Step Equations +376147,217,7.EE.B.4a,Solve 2-Step Equations +194986,217,7.EE.B.4a,Solve 2-Step Equations +194802,217,7.EE.B.4a,Solve 2-Step Equations +194900,217,7.EE.B.4a,Solve 2-Step Equations +341553,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +51952,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +51606,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +163825,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +341780,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +189992,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +80087,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +302140,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +302326,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +110803,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +323597,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +233480,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +302522,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +346366,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +347843,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +73862,218,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +386124,219,7.G.A.1,Solve Scale Drawing Problems +110217,219,7.G.A.1,Solve Scale Drawing Problems +115930,219,7.G.A.1,Solve Scale Drawing Problems +116350,219,7.G.A.1,Solve Scale Drawing Problems +114882,219,7.G.A.1,Solve Scale Drawing Problems +115829,219,7.G.A.1,Solve Scale Drawing Problems +114557,219,7.G.A.1,Solve Scale Drawing Problems +114712,219,7.G.A.1,Solve Scale Drawing Problems +116142,219,7.G.A.1,Solve Scale Drawing Problems +3216,219,7.G.A.1,Solve Scale Drawing Problems +3108,219,7.G.A.1,Solve Scale Drawing Problems +2532,219,7.G.A.1,Solve Scale Drawing Problems +240434,219,7.G.A.1,Solve Scale Drawing Problems +218802,219,7.G.A.1,Solve Scale Drawing Problems +10706,219,7.G.A.1,Solve Scale Drawing Problems +10844,219,7.G.A.1,Solve Scale Drawing Problems +11049,219,7.G.A.1,Solve Scale Drawing Problems +12289,219,7.G.A.1,Solve Scale Drawing Problems +12898,219,7.G.A.1,Solve Scale Drawing Problems +12006,219,7.G.A.1,Solve Scale Drawing Problems +12129,219,7.G.A.1,Solve Scale Drawing Problems +15259,219,7.G.A.1,Solve Scale Drawing Problems +209639,219,7.G.A.1,Solve Scale Drawing Problems +247183,219,7.G.A.1,Solve Scale Drawing Problems +209207,219,7.G.A.1,Solve Scale Drawing Problems +208077,219,7.G.A.1,Solve Scale Drawing Problems +24106,219,7.G.A.1,Solve Scale Drawing Problems +208921,219,7.G.A.1,Solve Scale Drawing Problems +24870,219,7.G.A.1,Solve Scale Drawing Problems +257011,219,7.G.A.1,Solve Scale Drawing Problems +207210,219,7.G.A.1,Solve Scale Drawing Problems +256312,219,7.G.A.1,Solve Scale Drawing Problems +24640,219,7.G.A.1,Solve Scale Drawing Problems +208594,219,7.G.A.1,Solve Scale Drawing Problems +27571,219,7.G.A.1,Solve Scale Drawing Problems +27844,219,7.G.A.1,Solve Scale Drawing Problems +28656,219,7.G.A.1,Solve Scale Drawing Problems +26892,219,7.G.A.1,Solve Scale Drawing Problems +27332,219,7.G.A.1,Solve Scale Drawing Problems +28087,219,7.G.A.1,Solve Scale Drawing Problems +28347,219,7.G.A.1,Solve Scale Drawing Problems +36042,219,7.G.A.1,Solve Scale Drawing Problems +181638,219,7.G.A.1,Solve Scale Drawing Problems +176239,219,7.G.A.1,Solve Scale Drawing Problems +176093,219,7.G.A.1,Solve Scale Drawing Problems +508521,219,7.G.A.1,Solve Scale Drawing Problems +44235,219,7.G.A.1,Solve Scale Drawing Problems +290885,219,7.G.A.1,Solve Scale Drawing Problems +509883,219,7.G.A.1,Solve Scale Drawing Problems +44380,219,7.G.A.1,Solve Scale Drawing Problems +165102,219,7.G.A.1,Solve Scale Drawing Problems +294072,219,7.G.A.1,Solve Scale Drawing Problems +51489,219,7.G.A.1,Solve Scale Drawing Problems +52116,219,7.G.A.1,Solve Scale Drawing Problems +51828,219,7.G.A.1,Solve Scale Drawing Problems +569234,219,7.G.A.1,Solve Scale Drawing Problems +510249,219,7.G.A.1,Solve Scale Drawing Problems +165767,219,7.G.A.1,Solve Scale Drawing Problems +61151,219,7.G.A.1,Solve Scale Drawing Problems +301410,219,7.G.A.1,Solve Scale Drawing Problems +303155,219,7.G.A.1,Solve Scale Drawing Problems +301201,219,7.G.A.1,Solve Scale Drawing Problems +60631,219,7.G.A.1,Solve Scale Drawing Problems +160506,219,7.G.A.1,Solve Scale Drawing Problems +303079,219,7.G.A.1,Solve Scale Drawing Problems +509539,219,7.G.A.1,Solve Scale Drawing Problems +303219,219,7.G.A.1,Solve Scale Drawing Problems +230204,219,7.G.A.1,Solve Scale Drawing Problems +69785,219,7.G.A.1,Solve Scale Drawing Problems +429837,219,7.G.A.1,Solve Scale Drawing Problems +430037,219,7.G.A.1,Solve Scale Drawing Problems +77198,219,7.G.A.1,Solve Scale Drawing Problems +76811,219,7.G.A.1,Solve Scale Drawing Problems +146478,219,7.G.A.1,Solve Scale Drawing Problems +419376,219,7.G.A.1,Solve Scale Drawing Problems +145212,219,7.G.A.1,Solve Scale Drawing Problems +230683,219,7.G.A.1,Solve Scale Drawing Problems +4480,219,7.G.A.1,Solve Scale Drawing Problems +413713,219,7.G.A.1,Solve Scale Drawing Problems +3378,219,7.G.A.1,Solve Scale Drawing Problems +411481,219,7.G.A.1,Solve Scale Drawing Problems +412048,219,7.G.A.1,Solve Scale Drawing Problems +341397,219,7.G.A.1,Solve Scale Drawing Problems +341023,219,7.G.A.1,Solve Scale Drawing Problems +411000,219,7.G.A.1,Solve Scale Drawing Problems +352275,219,7.G.A.1,Solve Scale Drawing Problems +341117,219,7.G.A.1,Solve Scale Drawing Problems 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Shapes & Unique Triangles +97230,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +196033,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +365643,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +123610,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +483667,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +259177,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +258731,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +177311,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +97111,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +303405,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +130499,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +117623,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +177761,220,7.G.A.2,Draw Geometric Shapes & Unique Triangles +114275,221,7.G.A.3,Describe 2D Cross Sections of 3D figures +7407,221,7.G.A.3,Describe 2D Cross Sections of 3D figures +7158,221,7.G.A.3,Describe 2D Cross Sections of 3D figures 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Facts About Angles to Write & Solve Equations +448452,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +160140,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +92551,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +128818,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +92939,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +154657,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +153940,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +246605,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +449555,225,7.G.B.5,Use Facts About Angles to Write & Solve Equations +130937,227,7.G.B.5,Use Facts About Angles to Write & Solve Equations +475938,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +674301,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +475820,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +162087,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +155972,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +156411,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +6562,228,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +3195,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +296039,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153688,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +251994,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +251573,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +156599,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153479,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +151997,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +53711,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +302658,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +108867,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +348314,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +226658,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +226452,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +152711,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +44592,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153291,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +44926,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +108650,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +53415,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153106,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +207279,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +156219,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +251741,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +132812,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +152894,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +133008,229,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +244435,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +244865,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +295905,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +110217,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +128308,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +226249,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +674301,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +108650,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +251741,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +152894,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +80588,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +245152,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +131558,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +152711,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +244645,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153688,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +227110,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153291,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153479,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +153106,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +330320,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +348188,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +251573,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +110096,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +373766,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +209528,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +209221,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +156797,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +226658,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +244890,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +124486,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +246416,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +209608,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +162201,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +227295,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +109845,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +109969,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +373493,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +302268,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +124819,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +108867,230,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +258429,232,7.SP.A.1,Interpret Methods of Sampling +310109,232,7.SP.A.1,Interpret Methods of Sampling +99239,232,7.SP.A.1,Interpret Methods of Sampling +308995,232,7.SP.A.1,Interpret Methods of Sampling +539325,232,7.SP.A.1,Interpret Methods of Sampling +99112,232,7.SP.A.1,Interpret Methods of Sampling +106396,232,7.SP.A.1,Interpret Methods of Sampling +309627,232,7.SP.A.1,Interpret Methods of Sampling +266053,232,7.SP.A.1,Interpret Methods of Sampling +100451,232,7.SP.A.1,Interpret Methods of Sampling +106494,232,7.SP.A.1,Interpret Methods of Sampling +266182,233,7.SP.A.2,Use Random Samples to Draw Influences +99379,233,7.SP.A.2,Use Random Samples to Draw Influences +23659,233,7.SP.A.2,Use Random Samples to Draw Influences +298906,233,7.SP.A.2,Use Random Samples to Draw Influences +104881,233,7.SP.A.2,Use Random Samples to Draw Influences +215871,233,7.SP.A.2,Use Random Samples to Draw Influences +297237,233,7.SP.A.2,Use Random Samples to Draw Influences +105229,233,7.SP.A.2,Use Random Samples to Draw Influences +106945,233,7.SP.A.2,Use Random Samples to Draw Influences +99112,233,7.SP.A.2,Use Random Samples to Draw Influences +23449,233,7.SP.A.2,Use Random Samples to Draw Influences +298063,233,7.SP.A.2,Use Random Samples to Draw Influences +24873,233,7.SP.A.2,Use Random Samples to Draw Influences +539841,233,7.SP.A.2,Use Random Samples to Draw Influences +298561,233,7.SP.A.2,Use Random Samples to Draw Influences +105511,233,7.SP.A.2,Use Random Samples to Draw Influences +325378,233,7.SP.A.2,Use Random Samples to Draw Influences +403293,233,7.SP.A.2,Use Random Samples to Draw Influences +297976,233,7.SP.A.2,Use Random Samples to Draw Influences +298486,233,7.SP.A.2,Use Random Samples to Draw Influences +266053,233,7.SP.A.2,Use Random Samples to Draw Influences +297138,233,7.SP.A.2,Use Random Samples to Draw Influences +8405,234,7.SP.B.3,Compare Populations using Center & Variability +187130,234,7.SP.B.3,Compare Populations using Center & Variability +267394,234,7.SP.B.3,Compare Populations using Center & Variability +265806,234,7.SP.B.3,Compare Populations using Center & Variability +267307,234,7.SP.B.3,Compare Populations using Center & Variability +187602,234,7.SP.B.3,Compare Populations using Center & Variability +187451,234,7.SP.B.3,Compare Populations using Center & Variability +39707,234,7.SP.B.3,Compare Populations using Center & Variability +39360,234,7.SP.B.3,Compare Populations using Center & Variability +98828,234,7.SP.B.3,Compare Populations using Center & Variability +187306,234,7.SP.B.3,Compare Populations using Center & Variability +187772,234,7.SP.B.3,Compare Populations using Center & Variability +256298,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +99606,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +298063,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +169705,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +99939,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +257987,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +9612,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +98346,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +257090,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +169437,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +265806,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +265301,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +106008,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +170227,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +99247,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +230845,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +230527,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +266182,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +256603,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +257569,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +99379,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +265140,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +98217,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +98828,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +255819,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +230731,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +297976,235,7.SP.B.4,Draw Inferences using Measures of Center & Variability +22103,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +43887,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42186,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +43505,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42284,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42864,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42680,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42766,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42491,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42091,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +41980,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42589,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +44057,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +63338,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +53108,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +43774,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +51557,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +349992,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +42389,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +51025,236,7.SP.C.5,Understand that Probability is Between 0-1 & Describes the Likelihood of an Event Occurring +265967,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +126872,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +123919,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +43700,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +265593,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +111989,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +1805,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +126669,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +124041,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +61911,237,7.SP.C.6,Approximate Probability of an Event by Collecting Data +97915,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +115723,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +100714,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +350066,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +115545,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +44248,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +44115,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +44396,239,7.SP.C.7a,Develop a Uniform Probabilty Model of a Single Event +62442,240,7.SP.C.7b,Develop a Probability Model of a Single Event +350066,240,7.SP.C.7b,Develop a Probability Model of a Single Event +37832,240,7.SP.C.7b,Develop a Probability Model of a Single Event +37467,240,7.SP.C.7b,Develop a Probability Model of a Single Event +43208,240,7.SP.C.7b,Develop a Probability Model of a Single Event +349910,242,7.SP.C.8a,Understand Probability of a Compound Event +159519,242,7.SP.C.8a,Understand Probability of a Compound Event +250867,242,7.SP.C.8a,Understand Probability of a Compound Event +250608,242,7.SP.C.8a,Understand Probability of a Compound Event +279365,242,7.SP.C.8a,Understand Probability of a Compound Event +277185,242,7.SP.C.8a,Understand Probability of a Compound Event +250727,242,7.SP.C.8a,Understand Probability of a Compound Event +279742,242,7.SP.C.8a,Understand Probability of a Compound Event +350160,243,7.SP.C.8b,Represent Sample Spaces for Compound Events +194852,243,7.SP.C.8b,Represent Sample Spaces for Compound Events +196019,243,7.SP.C.8b,Represent Sample Spaces for Compound Events +195315,243,7.SP.C.8b,Represent Sample Spaces for Compound Events +194307,243,7.SP.C.8b,Represent Sample Spaces for Compound Events +3705,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +207655,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +633159,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +71072,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +3566,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +633512,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +278217,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +96485,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +126669,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +126872,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +632697,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +207427,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +207084,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +96902,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +350160,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +207316,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +277725,244,7.SP.C.8b,Represent Sample Spaces for Compound Events +198767,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +350066,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +390129,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +390558,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +390823,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +77989,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +78469,245,7.SP.C.8c,Design & Use a Simulation for Compound Events +312048,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +522651,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +87272,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +523084,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +311896,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +522897,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +10283,246,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +15689,247,8.NS.A.2,Approximate Irrational Numbers +46660,247,8.NS.A.2,Approximate Irrational Numbers +423932,247,8.NS.A.2,Approximate Irrational Numbers +423768,247,8.NS.A.2,Approximate Irrational Numbers +423100,247,8.NS.A.2,Approximate Irrational Numbers +423276,247,8.NS.A.2,Approximate Irrational Numbers +423601,247,8.NS.A.2,Approximate Irrational Numbers +423450,247,8.NS.A.2,Approximate Irrational Numbers +424081,247,8.NS.A.2,Approximate Irrational Numbers +116435,247,8.NS.A.2,Approximate Irrational Numbers +117002,247,8.NS.A.2,Approximate Irrational Numbers +116703,247,8.NS.A.2,Approximate Irrational Numbers +117298,247,8.NS.A.2,Approximate Irrational Numbers +146354,247,8.NS.A.2,Approximate Irrational Numbers +146523,247,8.NS.A.2,Approximate Irrational Numbers +315827,247,8.NS.A.2,Approximate Irrational Numbers +307803,247,8.NS.A.2,Approximate Irrational Numbers +307502,247,8.NS.A.2,Approximate Irrational Numbers +277038,247,8.NS.A.2,Approximate Irrational Numbers +276480,247,8.NS.A.2,Approximate Irrational Numbers +276874,247,8.NS.A.2,Approximate Irrational Numbers +276040,247,8.NS.A.2,Approximate Irrational Numbers +276338,247,8.NS.A.2,Approximate Irrational Numbers +276196,247,8.NS.A.2,Approximate Irrational Numbers +276705,247,8.NS.A.2,Approximate Irrational Numbers +277212,247,8.NS.A.2,Approximate Irrational Numbers +316129,248,8.NS.A.2,Approximate Irrational Numbers +10115,248,8.NS.A.2,Approximate Irrational Numbers +469527,249,8.EE.A.1,Know & Apply Properties of Exponents +278747,249,8.EE.A.1,Know & Apply Properties of Exponents +192377,249,8.EE.A.1,Know & Apply Properties of Exponents +192067,249,8.EE.A.1,Know & Apply Properties of Exponents +58041,249,8.EE.A.1,Know & Apply Properties of Exponents +58180,249,8.EE.A.1,Know & Apply Properties of Exponents +263567,249,8.EE.A.1,Know & Apply Properties of Exponents +263664,249,8.EE.A.1,Know & Apply Properties of Exponents +552296,249,8.EE.A.1,Know & Apply Properties of Exponents +25252,249,8.EE.A.1,Know & Apply Properties of Exponents +425079,249,8.EE.A.1,Know & Apply Properties of Exponents +424891,249,8.EE.A.1,Know & Apply Properties of Exponents +424251,249,8.EE.A.1,Know & Apply Properties of Exponents +424722,249,8.EE.A.1,Know & Apply Properties of Exponents +424393,249,8.EE.A.1,Know & Apply Properties of Exponents +424567,249,8.EE.A.1,Know & Apply Properties of Exponents +469703,249,8.EE.A.1,Know & Apply Properties of Exponents +12211,249,8.EE.A.1,Know & Apply Properties of Exponents +12381,249,8.EE.A.1,Know & Apply Properties of Exponents +12541,249,8.EE.A.1,Know & Apply Properties of Exponents +469613,249,8.EE.A.1,Know & Apply Properties of Exponents +9879,249,8.EE.A.1,Know & Apply Properties of Exponents +7829,249,8.EE.A.1,Know & Apply Properties of Exponents +7635,249,8.EE.A.1,Know & Apply Properties of Exponents +552200,249,8.EE.A.1,Know & Apply Properties of Exponents +359589,249,8.EE.A.1,Know & Apply Properties of Exponents +221966,250,8.EE.A.1,Know & Apply Properties of Exponents +91640,250,8.EE.A.1,Know & Apply Properties of Exponents +552200,250,8.EE.A.1,Know & Apply Properties of Exponents +263567,250,8.EE.A.1,Know & Apply Properties of Exponents +245814,251,8.EE.A.1,Know & Apply Properties of Exponents +356718,252,8.EE.A.2,Evaluate Square & Cube Roots +356901,252,8.EE.A.2,Evaluate Square & Cube Roots +355425,252,8.EE.A.2,Evaluate Square & Cube Roots +357082,252,8.EE.A.2,Evaluate Square & Cube Roots +357261,252,8.EE.A.2,Evaluate Square & Cube Roots +355769,252,8.EE.A.2,Evaluate Square & Cube Roots +355074,252,8.EE.A.2,Evaluate Square & Cube Roots +212585,252,8.EE.A.2,Evaluate Square & Cube Roots +356075,252,8.EE.A.2,Evaluate Square & Cube Roots +94804,252,8.EE.A.2,Evaluate Square & Cube Roots +412709,252,8.EE.A.2,Evaluate Square & Cube Roots +332084,252,8.EE.A.2,Evaluate Square & Cube Roots +331279,252,8.EE.A.2,Evaluate Square & Cube Roots +331115,252,8.EE.A.2,Evaluate Square & Cube Roots +330781,252,8.EE.A.2,Evaluate Square & Cube Roots +330621,252,8.EE.A.2,Evaluate Square & Cube Roots +332235,252,8.EE.A.2,Evaluate Square & Cube Roots +330959,252,8.EE.A.2,Evaluate Square & Cube Roots +331947,252,8.EE.A.2,Evaluate Square & Cube Roots +331773,252,8.EE.A.2,Evaluate Square & Cube Roots +331447,252,8.EE.A.2,Evaluate Square & Cube Roots +330485,252,8.EE.A.2,Evaluate Square & Cube Roots +331613,252,8.EE.A.2,Evaluate Square & Cube Roots +86904,252,8.EE.A.2,Evaluate Square & Cube Roots +252048,252,8.EE.A.2,Evaluate Square & Cube Roots +315734,252,8.EE.A.2,Evaluate Square & Cube Roots +316129,252,8.EE.A.2,Evaluate Square & Cube Roots +478012,252,8.EE.A.2,Evaluate Square & Cube Roots +161350,252,8.EE.A.2,Evaluate Square & Cube Roots +162174,252,8.EE.A.2,Evaluate Square & Cube Roots +161838,252,8.EE.A.2,Evaluate Square & Cube Roots +161664,252,8.EE.A.2,Evaluate Square & Cube Roots +46264,252,8.EE.A.2,Evaluate Square & Cube Roots +238057,253,8.EE.A.3,Expressing Quantities in Scientific Notation +398365,253,8.EE.A.3,Expressing Quantities in Scientific Notation +262979,253,8.EE.A.3,Expressing Quantities in Scientific Notation +116755,253,8.EE.A.3,Expressing Quantities in Scientific Notation +263239,253,8.EE.A.3,Expressing Quantities in Scientific Notation +551634,253,8.EE.A.3,Expressing Quantities in Scientific Notation +198955,253,8.EE.A.3,Expressing Quantities in Scientific Notation +104232,253,8.EE.A.3,Expressing Quantities in Scientific Notation +105610,253,8.EE.A.3,Expressing Quantities in Scientific Notation +104560,253,8.EE.A.3,Expressing Quantities in Scientific Notation +199191,253,8.EE.A.3,Expressing Quantities in Scientific Notation +490287,253,8.EE.A.3,Expressing Quantities in Scientific Notation +83409,253,8.EE.A.3,Expressing Quantities in Scientific Notation +208025,253,8.EE.A.3,Expressing Quantities in Scientific Notation +551805,253,8.EE.A.3,Expressing Quantities in Scientific Notation +552200,254,8.EE.A.4,Apply Scientific Notation Operations +11875,254,8.EE.A.4,Apply Scientific Notation Operations +552392,254,8.EE.A.4,Apply Scientific Notation Operations +551805,254,8.EE.A.4,Apply Scientific Notation Operations +398730,254,8.EE.A.4,Apply Scientific Notation Operations +399091,254,8.EE.A.4,Apply Scientific Notation Operations +278407,254,8.EE.A.4,Apply Scientific Notation Operations +63961,254,8.EE.A.4,Apply Scientific Notation Operations +263239,254,8.EE.A.4,Apply Scientific Notation Operations +551634,254,8.EE.A.4,Apply Scientific Notation Operations +198121,254,8.EE.A.4,Apply Scientific Notation Operations +263567,254,8.EE.A.4,Apply Scientific Notation Operations +198440,254,8.EE.A.4,Apply Scientific Notation Operations +63639,254,8.EE.A.4,Apply Scientific Notation Operations +58527,254,8.EE.A.4,Apply Scientific Notation Operations +263739,254,8.EE.A.4,Apply Scientific Notation Operations +25543,254,8.EE.A.4,Apply Scientific Notation Operations +25844,254,8.EE.A.4,Apply Scientific Notation Operations +262979,254,8.EE.A.4,Apply Scientific Notation Operations +198635,254,8.EE.A.4,Apply Scientific Notation Operations +257027,254,8.EE.A.4,Apply Scientific Notation Operations +258192,254,8.EE.A.4,Apply Scientific Notation Operations +258045,254,8.EE.A.4,Apply Scientific Notation Operations +257260,254,8.EE.A.4,Apply Scientific Notation Operations +257525,254,8.EE.A.4,Apply Scientific Notation Operations +257604,254,8.EE.A.4,Apply Scientific Notation Operations +257097,254,8.EE.A.4,Apply Scientific Notation Operations +257352,254,8.EE.A.4,Apply Scientific Notation Operations +22352,254,8.EE.A.4,Apply Scientific Notation Operations +83841,254,8.EE.A.4,Apply Scientific Notation Operations +22473,254,8.EE.A.4,Apply Scientific Notation Operations +79163,255,8.EE.B.5,Compare Slopes of Proportional Relationships +211231,255,8.EE.B.5,Compare Slopes of Proportional Relationships +211131,255,8.EE.B.5,Compare Slopes of Proportional Relationships +192118,255,8.EE.B.5,Compare Slopes of Proportional Relationships +157579,255,8.EE.B.5,Compare Slopes of Proportional Relationships +195004,255,8.EE.B.5,Compare Slopes of Proportional Relationships +211312,255,8.EE.B.5,Compare Slopes of Proportional Relationships +77471,255,8.EE.B.5,Compare Slopes of Proportional Relationships +209506,255,8.EE.B.5,Compare Slopes of Proportional Relationships +79065,255,8.EE.B.5,Compare Slopes of Proportional Relationships +79256,255,8.EE.B.5,Compare Slopes of Proportional Relationships +236549,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +239904,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +27019,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +146496,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +381490,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +33513,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +159061,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +158484,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +381865,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +184584,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +197850,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +27460,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +158769,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +165287,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +184366,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +165038,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +27276,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +49232,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +28352,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +190990,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +190411,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +184867,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +190835,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +43045,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +184505,256,8.EE.B.6,Find Slope of a Line using Similar Triangles +16728,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +147962,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +148145,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +148466,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +524173,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +147769,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +16591,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +77227,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +386019,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +17667,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +386445,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +146938,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +333395,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +500624,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +16856,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +148285,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +360720,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +146473,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +150654,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +108574,258,8.EE.C.7a,"Solve Linear Equations with One, Multiple or No Solutions" +155556,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +328823,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +155341,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +184908,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +104135,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +382378,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +231799,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +93475,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +498517,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +83813,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +331322,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131672,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +579648,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +55154,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +148754,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +294102,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131293,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +190961,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +95029,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +231522,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +230038,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +128305,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +248217,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +94737,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +132416,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131112,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +328341,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +219375,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131520,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +132200,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +219253,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +530004,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +592014,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +132688,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +388305,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +329327,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +94876,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +155730,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +330016,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +387953,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +132932,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +191140,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +150076,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +148929,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +387531,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +231289,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +234184,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +149101,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +360109,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131367,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131899,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +131134,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +430695,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +591787,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +233384,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +331070,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +330854,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +133257,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +527725,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +293786,259,8.EE.C.7b,Solve Multi-Step Linear Equations with Rational Number Coefficients +113306,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +114103,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +84475,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +84315,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +84651,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +141750,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +113820,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +113562,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +129599,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +297047,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +384509,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +126461,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +194106,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +129804,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +398888,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +114342,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +130008,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +114797,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +223780,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +114584,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +113066,261,8.EE.C.8a,Identify Solutions to Systems of Equations Using Graphs +296856,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +91020,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +99441,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +14761,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +227799,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +77479,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +99193,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +104427,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +306064,262,8.EE.C.8b,Solve Systems of Linear Equations Algebraically +225929,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +503,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +253,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +105121,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +153081,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +1867,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +232017,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +180036,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +232208,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +226545,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +180127,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +682,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +233998,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +47808,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +89416,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +146750,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +225403,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +232533,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +233780,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +232362,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +19954,263,8.EE.C.8c,Solve Systems of Linear Equations Word Problems +144266,264,8.F.A.1,Understand Definition of a Function +89069,264,8.F.A.1,Understand Definition of a Function +88965,264,8.F.A.1,Understand Definition of a Function +297716,264,8.F.A.1,Understand Definition of a Function +88607,264,8.F.A.1,Understand Definition of a Function +89270,264,8.F.A.1,Understand Definition of a Function +296303,264,8.F.A.1,Understand Definition of a Function +89478,264,8.F.A.1,Understand Definition of a Function +87902,264,8.F.A.1,Understand Definition of a Function +88255,264,8.F.A.1,Understand Definition of a Function +340198,264,8.F.A.1,Understand Definition of a Function +348832,264,8.F.A.1,Understand Definition of a Function +292178,264,8.F.A.1,Understand Definition of a Function +211131,264,8.F.A.1,Understand Definition of a Function +269076,265,8.F.A.2,Compare Functions in Different Forms +138133,265,8.F.A.2,Compare Functions in Different Forms +137984,265,8.F.A.2,Compare Functions in Different Forms +180476,266,8.F.A.3,Identify Linear & Non-Linear Functions +297716,266,8.F.A.3,Identify Linear & Non-Linear Functions +348832,266,8.F.A.3,Identify Linear & Non-Linear Functions +149599,266,8.F.A.3,Identify Linear & Non-Linear Functions +291134,266,8.F.A.3,Identify Linear & Non-Linear Functions +291282,266,8.F.A.3,Identify Linear & Non-Linear Functions +180143,266,8.F.A.3,Identify Linear & Non-Linear Functions +179830,266,8.F.A.3,Identify Linear & Non-Linear Functions +348674,266,8.F.A.3,Identify Linear & Non-Linear Functions +180292,266,8.F.A.3,Identify Linear & Non-Linear Functions +296303,266,8.F.A.3,Identify Linear & Non-Linear Functions +524173,267,8.F.B.4,Use Functions to Model Relationships Between Quantities +296303,267,8.F.B.4,Use Functions to Model Relationships Between Quantities +17046,268,8.F.B.4,Use Functions to Model Relationships Between Quantities +109764,269,8.F.B.4,Use Functions to Model Relationships Between Quantities +110017,269,8.F.B.4,Use Functions to Model Relationships Between Quantities +165645,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +236767,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +132337,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +144363,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +331866,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +165535,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +306325,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +237129,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +166028,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +332048,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +132090,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +325132,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +487616,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +383239,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +412814,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +165896,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +340440,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +50741,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +20361,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +165778,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +236954,270,8.F.B.4,Use Functions to Model Relationships Between Quantities +186281,271,8.F.B.4,Use Functions to Model Relationships Between Quantities +187219,271,8.F.B.4,Use Functions to Model Relationships Between Quantities +187127,271,8.F.B.4,Use Functions to Model Relationships Between Quantities +185874,271,8.F.B.4,Use Functions to Model Relationships Between Quantities +18591,271,8.F.B.4,Use Functions to Model Relationships Between Quantities +18775,271,8.F.B.4,Use Functions to Model Relationships Between Quantities +87931,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +87609,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +330357,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +578697,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +579179,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +88244,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +132090,273,8.F.B.4,Use Functions to Model Relationships Between Quantities +342229,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +190990,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +426071,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +99193,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +148105,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +190835,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +99441,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +190411,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +161738,274,8.F.B.4,Use Functions to Model Relationships Between Quantities +56987,275,8.F.B.4,Use Functions to Model Relationships Between Quantities +55933,275,8.F.B.4,Use Functions to Model Relationships Between Quantities +304444,275,8.F.B.4,Use Functions to Model Relationships Between Quantities +304606,275,8.F.B.4,Use Functions to Model Relationships Between Quantities +250205,277,8.F.B.4,Use Functions to Model Relationships Between Quantities +43045,277,8.F.B.4,Use Functions to Model Relationships Between Quantities +331521,277,8.F.B.4,Use Functions to Model Relationships Between Quantities +250112,277,8.F.B.4,Use Functions to Model Relationships Between Quantities +249681,277,8.F.B.4,Use Functions to Model Relationships Between Quantities +2034,277,8.F.B.4,Use Functions to Model Relationships Between Quantities +121116,278,8.F.B.5,Qualitatively Describe & Graph Relationships +488,278,8.F.B.5,Qualitatively Describe & Graph Relationships +121281,278,8.F.B.5,Qualitatively Describe & Graph Relationships +121482,278,8.F.B.5,Qualitatively Describe & Graph Relationships +105377,278,8.F.B.5,Qualitatively Describe & Graph Relationships +104928,278,8.F.B.5,Qualitatively Describe & Graph Relationships +340581,278,8.F.B.5,Qualitatively Describe & Graph Relationships +340317,278,8.F.B.5,Qualitatively Describe & Graph Relationships +144504,278,8.F.B.5,Qualitatively Describe & Graph Relationships +152409,278,8.F.B.5,Qualitatively Describe & Graph Relationships +152568,278,8.F.B.5,Qualitatively Describe & Graph Relationships +155954,278,8.F.B.5,Qualitatively Describe & Graph Relationships +60012,278,8.F.B.5,Qualitatively Describe & Graph Relationships +60170,278,8.F.B.5,Qualitatively Describe & Graph Relationships +45497,278,8.F.B.5,Qualitatively Describe & Graph Relationships +45704,278,8.F.B.5,Qualitatively Describe & Graph Relationships +45204,278,8.F.B.5,Qualitatively Describe & Graph Relationships +45592,278,8.F.B.5,Qualitatively Describe & Graph Relationships +14567,278,8.F.B.5,Qualitatively Describe & Graph Relationships 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Segments +35246,281,8.G.A.1b,Apply the Properties of Transformations to Angles +249173,281,8.G.A.1b,Apply the Properties of Transformations to Angles +495451,281,8.G.A.1b,Apply the Properties of Transformations to Angles +388718,281,8.G.A.1b,Apply the Properties of Transformations to Angles +389082,281,8.G.A.1b,Apply the Properties of Transformations to Angles +350622,281,8.G.A.1b,Apply the Properties of Transformations to Angles +40911,281,8.G.A.1b,Apply the Properties of Transformations to Angles +53019,281,8.G.A.1b,Apply the Properties of Transformations to Angles +40714,281,8.G.A.1b,Apply the Properties of Transformations to Angles +275383,281,8.G.A.1b,Apply the Properties of Transformations to Angles +322590,281,8.G.A.1b,Apply the Properties of Transformations to Angles +275670,281,8.G.A.1b,Apply the Properties of Transformations to Angles +30522,281,8.G.A.1b,Apply the Properties of Transformations to Angles +322882,281,8.G.A.1b,Apply the Properties of Transformations to Angles 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Sequences +1239,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +146791,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +85142,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +452369,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +504583,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +2541,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +2234,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +544776,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +48569,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +336,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +417638,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +577,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences +54,283,8.G.A.2,Understand & Describe Geometric Transformation Sequences 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Transformations to Determine Similarity in 2D figures +9287,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +47390,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +238263,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +168353,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +26752,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +26857,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +167875,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +168820,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +9569,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +167382,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +232166,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +62717,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +155904,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +37464,287,8.G.A.4,use Transformations to Determine Similarity in 2D figures +189375,288,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +174309,288,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +32656,289,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +64079,289,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +24916,289,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +8680,289,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +504284,289,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +504078,289,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +196678,290,8.G.B.6,Prove the Pythagorean Theorem & it's Converse +315914,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +46379,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +315454,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +329307,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +118107,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +222860,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +222626,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +222741,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +65477,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +65337,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +487312,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +117709,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +162829,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +10729,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +10564,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +162661,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +8050,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +162490,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +52069,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +9217,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +7398,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +162344,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +52189,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +10412,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +354813,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +354090,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +354627,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +487468,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +485290,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +7859,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +8202,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +223006,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +118016,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +7541,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +222369,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +46033,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +454526,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +222494,291,8.G.B.7,Apply the Pythagorean Theorem to 2D & 3D FIgures +136977,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +118522,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +46660,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +118249,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +136831,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +136694,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +332409,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +117898,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +118376,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +315827,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +99309,292,8.G.B.8,Apply the Pythagorean Theorem to Find the Distance Between Points on the Coordinate Plane +351813,293,8.G.C.9,Know & Use Volume Formulas +374368,293,8.G.C.9,Know & Use Volume Formulas +213558,293,8.G.C.9,Know & Use Volume Formulas +115324,293,8.G.C.9,Know & Use Volume Formulas +137062,293,8.G.C.9,Know & Use Volume Formulas +17475,293,8.G.C.9,Know & Use Volume Formulas +15072,293,8.G.C.9,Know & Use Volume Formulas +48656,293,8.G.C.9,Know & Use Volume Formulas +223692,293,8.G.C.9,Know & Use Volume Formulas +373766,293,8.G.C.9,Know & Use Volume Formulas +373493,293,8.G.C.9,Know & Use Volume Formulas +114806,293,8.G.C.9,Know & Use Volume Formulas +46033,293,8.G.C.9,Know & Use Volume Formulas +86322,293,8.G.C.9,Know & Use Volume Formulas +150182,293,8.G.C.9,Know & Use Volume Formulas +90927,293,8.G.C.9,Know & Use Volume Formulas +91237,293,8.G.C.9,Know & Use Volume Formulas +351677,293,8.G.C.9,Know & Use Volume Formulas +180722,293,8.G.C.9,Know & Use Volume Formulas +374418,293,8.G.C.9,Know & Use Volume Formulas +140189,293,8.G.C.9,Know & Use Volume Formulas +150288,293,8.G.C.9,Know & Use Volume Formulas +114637,293,8.G.C.9,Know & Use Volume Formulas +15627,293,8.G.C.9,Know & Use Volume Formulas +114450,293,8.G.C.9,Know & Use Volume Formulas +136717,293,8.G.C.9,Know & Use Volume Formulas +86515,293,8.G.C.9,Know & Use Volume Formulas +374058,293,8.G.C.9,Know & Use Volume Formulas +89267,293,8.G.C.9,Know & Use Volume Formulas +351988,293,8.G.C.9,Know & Use Volume Formulas +115049,293,8.G.C.9,Know & Use Volume Formulas +374220,293,8.G.C.9,Know & Use Volume Formulas +15234,293,8.G.C.9,Know & Use Volume Formulas +596384,293,8.G.C.9,Know & Use Volume Formulas +674243,293,8.G.C.9,Know & Use Volume Formulas +165493,293,8.G.C.9,Know & Use Volume Formulas +36511,293,8.G.C.9,Know & Use Volume Formulas +91074,293,8.G.C.9,Know & Use Volume Formulas +14914,293,8.G.C.9,Know & Use Volume Formulas +213135,293,8.G.C.9,Know & Use Volume Formulas +115187,293,8.G.C.9,Know & Use Volume Formulas +48968,293,8.G.C.9,Know & Use Volume Formulas +157411,293,8.G.C.9,Know & Use Volume Formulas +223532,293,8.G.C.9,Know & Use Volume Formulas +48812,293,8.G.C.9,Know & Use Volume Formulas +151258,294,8.G.C.9,Know & Use Volume Formulas +151596,294,8.G.C.9,Know & Use Volume Formulas +351813,294,8.G.C.9,Know & Use Volume Formulas +352230,294,8.G.C.9,Know & Use Volume Formulas +353101,294,8.G.C.9,Know & Use Volume Formulas +58785,294,8.G.C.9,Know & Use Volume Formulas +154066,294,8.G.C.9,Know & Use Volume Formulas +212876,294,8.G.C.9,Know & Use Volume Formulas +139860,294,8.G.C.9,Know & Use Volume Formulas +151429,294,8.G.C.9,Know & Use Volume Formulas +351677,294,8.G.C.9,Know & Use Volume Formulas +351988,294,8.G.C.9,Know & Use Volume Formulas +333800,294,8.G.C.9,Know & Use Volume Formulas +352921,294,8.G.C.9,Know & Use Volume Formulas +125853,294,8.G.C.9,Know & Use Volume Formulas +348910,294,8.G.C.9,Know & Use Volume Formulas +333981,294,8.G.C.9,Know & Use Volume Formulas +297864,294,8.G.C.9,Know & Use Volume Formulas +58581,294,8.G.C.9,Know & Use Volume Formulas +352595,294,8.G.C.9,Know & Use Volume Formulas +164833,294,8.G.C.9,Know & Use Volume Formulas +350639,294,8.G.C.9,Know & Use Volume Formulas +125684,294,8.G.C.9,Know & Use Volume Formulas +352750,294,8.G.C.9,Know & Use Volume Formulas +333699,294,8.G.C.9,Know & Use Volume Formulas +333895,294,8.G.C.9,Know & Use Volume Formulas +352407,294,8.G.C.9,Know & Use Volume Formulas +86515,295,8.G.C.9,Know & Use Volume Formulas +89267,295,8.G.C.9,Know & Use Volume Formulas +138533,295,8.G.C.9,Know & Use Volume Formulas +26678,295,8.G.C.9,Know & Use Volume Formulas +36673,295,8.G.C.9,Know & Use Volume Formulas +138360,295,8.G.C.9,Know & Use Volume Formulas +315454,295,8.G.C.9,Know & Use Volume Formulas +348674,295,8.G.C.9,Know & Use Volume Formulas +151987,295,8.G.C.9,Know & Use Volume Formulas +151827,295,8.G.C.9,Know & Use Volume Formulas +27930,295,8.G.C.9,Know & Use Volume Formulas +26766,295,8.G.C.9,Know & Use Volume Formulas +351813,295,8.G.C.9,Know & Use Volume Formulas +115951,295,8.G.C.9,Know & Use Volume Formulas +596207,295,8.G.C.9,Know & Use Volume Formulas +165245,295,8.G.C.9,Know & Use Volume Formulas +351677,295,8.G.C.9,Know & Use Volume Formulas +27699,295,8.G.C.9,Know & Use Volume Formulas +351988,295,8.G.C.9,Know & Use Volume Formulas +297716,295,8.G.C.9,Know & Use Volume Formulas +674266,295,8.G.C.9,Know & Use Volume Formulas +27604,295,8.G.C.9,Know & Use Volume Formulas +50592,295,8.G.C.9,Know & Use Volume Formulas +233520,295,8.G.C.9,Know & Use Volume Formulas +203778,295,8.G.C.9,Know & Use Volume Formulas +116167,295,8.G.C.9,Know & Use Volume Formulas +233319,295,8.G.C.9,Know & Use Volume Formulas +180722,295,8.G.C.9,Know & Use Volume Formulas +86322,295,8.G.C.9,Know & Use Volume Formulas +152166,295,8.G.C.9,Know & Use Volume Formulas +6116,296,8.SP.A.1,Construct & Interpret Scatter Plots +173561,296,8.SP.A.1,Construct & Interpret Scatter Plots +124523,296,8.SP.A.1,Construct & Interpret Scatter Plots +400715,296,8.SP.A.1,Construct & Interpret Scatter Plots +33514,296,8.SP.A.1,Construct & Interpret Scatter Plots +296937,296,8.SP.A.1,Construct & Interpret Scatter Plots +68821,296,8.SP.A.1,Construct & Interpret Scatter Plots +68650,296,8.SP.A.1,Construct & Interpret Scatter Plots +312938,296,8.SP.A.1,Construct & Interpret Scatter Plots +77355,296,8.SP.A.1,Construct & Interpret Scatter Plots +90496,296,8.SP.A.1,Construct & Interpret Scatter Plots +327381,296,8.SP.A.1,Construct & Interpret Scatter Plots +90685,296,8.SP.A.1,Construct & Interpret Scatter Plots +480902,296,8.SP.A.1,Construct & Interpret Scatter Plots +33779,296,8.SP.A.1,Construct & Interpret Scatter Plots +233989,296,8.SP.A.1,Construct & Interpret Scatter Plots +533341,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +604573,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +636416,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +296579,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +296489,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +232667,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +186153,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +185871,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +170280,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +170383,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +36419,297,8.SP.A.2,Determine Line of Best Fit for Scatter Plots +480902,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +23029,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +22573,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +22902,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +296489,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +296579,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +180839,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +76975,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +76861,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +604573,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +636416,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +84657,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +173897,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +12777,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +84521,298,8.SP.A.3,Use Linear Equations Applied to Bivariate Data +253836,299,8.SP.A.4,Construct & Interpret Two Way Tables +69854,299,8.SP.A.4,Construct & Interpret Two Way Tables +604503,299,8.SP.A.4,Construct & Interpret Two Way Tables +179563,299,8.SP.A.4,Construct & Interpret Two Way Tables +180312,299,8.SP.A.4,Construct & Interpret Two Way Tables +636346,299,8.SP.A.4,Construct & Interpret Two Way Tables +254278,299,8.SP.A.4,Construct & Interpret Two Way Tables +299700,340,2.MD.B.5,Solve Word Problems Involving Lengths using Addition & Subtraction +427819,340,2.MD.B.5,Solve Word Problems Involving Lengths using Addition & Subtraction +222136,1129,5.NBT.A.2,Explain Patterns when Multiplying & Dividing Powers of 10 +2695,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +254319,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +3201,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +2812,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +48374,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +5038,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +256627,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +254716,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +254190,1131,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +422237,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +422084,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508887,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508769,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +509009,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508616,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +445524,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +79155,1132,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +421173,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508286,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +134923,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508172,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +135051,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +134784,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508017,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +508402,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +421310,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +421448,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +445641,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +421588,1133,5.NBT.B.7,Compute Decimal Problems Involving All 4 Operations +457262,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +421967,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +421838,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +348598,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +348818,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +348936,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +348711,1134,5.NF.B.4a,Interpret & Compute Products of Fractions and Whole Numbers +475491,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115625,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +60186,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +79708,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +502515,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +54974,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +274073,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +349598,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +502164,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115025,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +273669,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +406876,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +272246,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +637195,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115789,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +558257,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +248279,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +14173,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +273879,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +295992,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +55545,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +168559,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115150,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +502927,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +349875,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +115417,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +79262,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +295788,1135,6.G.A.4,Represent 3D Figures Using Nets to Find Surface Area +389120,1136,7.EE.B.4a,Solve 2-Step Equations +388622,1136,7.EE.B.4a,Solve 2-Step Equations +11331,1136,7.EE.B.4a,Solve 2-Step Equations +118504,1136,7.EE.B.4a,Solve 2-Step Equations +314711,1136,7.EE.B.4a,Solve 2-Step Equations +104742,1136,7.EE.B.4a,Solve 2-Step Equations +257823,1136,7.EE.B.4a,Solve 2-Step Equations +55274,1136,7.EE.B.4a,Solve 2-Step Equations +162424,1136,7.EE.B.4a,Solve 2-Step Equations +48612,1136,7.EE.B.4a,Solve 2-Step Equations +196520,1136,7.EE.B.4a,Solve 2-Step Equations +156040,1136,7.EE.B.4a,Solve 2-Step Equations +90188,1136,7.EE.B.4a,Solve 2-Step Equations +308259,1136,7.EE.B.4a,Solve 2-Step Equations +186074,1136,7.EE.B.4a,Solve 2-Step Equations +54241,1136,7.EE.B.4a,Solve 2-Step Equations +180669,1136,7.EE.B.4a,Solve 2-Step Equations +168704,1136,7.EE.B.4a,Solve 2-Step Equations +64354,1136,7.EE.B.4a,Solve 2-Step Equations +247400,1136,7.EE.B.4a,Solve 2-Step Equations +344535,1136,7.EE.B.4a,Solve 2-Step Equations +10359,1136,7.EE.B.4a,Solve 2-Step Equations +156315,1136,7.EE.B.4a,Solve 2-Step Equations +10737,1136,7.EE.B.4a,Solve 2-Step Equations +178070,1136,7.EE.B.4a,Solve 2-Step Equations +11235,1136,7.EE.B.4a,Solve 2-Step Equations +67861,1136,7.EE.B.4a,Solve 2-Step Equations +11131,1136,7.EE.B.4a,Solve 2-Step Equations +11040,1136,7.EE.B.4a,Solve 2-Step Equations +347162,1136,7.EE.B.4a,Solve 2-Step Equations +54233,1136,7.EE.B.4a,Solve 2-Step Equations +247823,1136,7.EE.B.4a,Solve 2-Step Equations +156598,1136,7.EE.B.4a,Solve 2-Step Equations +674289,1136,7.EE.B.4a,Solve 2-Step Equations +168477,1136,7.EE.B.4a,Solve 2-Step Equations +308414,1136,7.EE.B.4a,Solve 2-Step Equations +129703,1136,7.EE.B.4a,Solve 2-Step Equations +54349,1136,7.EE.B.4a,Solve 2-Step Equations +124948,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +189877,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +124074,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +104597,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +124637,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +163692,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +129703,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +237641,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +124358,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +237440,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +70471,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +85212,1137,7.EE.B.4b,"Solve, Graph & Interpret 2-Step Inequalities" +316024,1138,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +74236,1138,8.NS.A.1,Understand & Approximate Rational & Irrational Numbers +103419,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +150918,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +193572,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +125866,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +285834,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +57280,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +283170,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +57030,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +21754,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +591536,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +188925,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +21866,2277,6.SP.B.4,"Display Numerical Data Using Dot Plots, Histograms & Box Plots" +10007,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +96584,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +9804,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +319333,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +504723,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +319240,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +96780,2279,7.G.B.5,Use Facts About Angles to Write & Solve Equations +149928,2281,7.G.B.6,"Find Area, Volume & Surface Area of 2D/3D Objects" +145971,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +309708,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +145792,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +146131,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +175643,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +170317,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +28184,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +81610,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +239691,2283,8.G.A.3,Describe the Effect of Transformations on 2D Figures +77888,2284,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles +239815,2284,8.G.A.5,Use Informal Arguments to Establish Facts about Angles for Similar Triangles diff --git a/README.md b/README.md new file mode 100644 index 0000000000000000000000000000000000000000..40d0e11aab3ff9375f4508986e965d85a6139231 --- /dev/null +++ b/README.md @@ -0,0 +1,246 @@ +--- +license: cc-by-nc-4.0 + +extra_gated_prompt: "You agree to our [Responsible Use Guidelines](https://www.etrialstestbed.org/mathnet57963-guidelines)." + +extra_gated_fields: + First and Last Name: text + Affiliation(university, company, etc): text + Country: country + Why are you asking to use this dataset?: text + How are you going to use this dataset?: text + How will you store and secure this data?: text + Do you have a university-affiliated email we could use to verify your request? If so, please enter it, if not, please explain why: text + + I agree to use this dataset for non-commercial use ONLY: checkbox + While we think it's impossible for you to identify a student from these answers, you need to agree to not try to do so, and you also need to inform us if you find any PII in any of the images with the filenames: checkbox + Check box - I agree that this data will be stored on secured institutional systems, will not be shared with unauthorized parties and will deleted or returned to ASSISTments when my research is complete: checkbox + +configs: + - config_name: Foundational ASSIST Dataset + data_files: Data/Problems.csv + - config_name: Interactions + data_files: Data/Interactions.csv + - config_name: Skills + data_files: Data/Skills.csv + +--- + +**IMPORTANT UPDATE ON 3/19:** Due to an issue with git LFS 700k rows in interactions.csv were missing. Please redownload the dataset to use these rows. + +# Overview of Foundational ASSIST +Foundational ASSIST is a dataset containing all natural text of problems and student answers as recorded by ASSISTments. The problems are from from Illustrative Mathematics 6th - 8th grade math curriculum, a common core aligned curriculum popular in the United States. + +The data is in the "Data" folder. The code used to generate results in the original paper by Worden et al. is in the Code folder, and the results (in case you do not wish to reinference) are in the "Results" folder. + +The dataset is comprised of three files: +1. **Interactions**, which contains students attempts of problems, +2. **Problems**, which includes information relevant to problems, and +3. **Skills**, which links Problems to skills. +The dataset was curated to include 5,000 unique students who have each completed between 211-421 problems in ASSISTments. The dataset includes 1.7 million instances of students solving problems, complete with the answer text, problem text, distractor text, and more. + +# Interactions File +Interactions consists of 1,722,169 unique instances of students solving problems. The information provided includes a) problem_id, linking to Problems b) hint_count, the number of hints the student requested c) answer_text, the exact text of their first answer d) saw_answer, a boolean indicating whether the student requested to see the correct answer e) discrete_score, 0 the students score f) end_time, the time at which the student put in the correct answer to the problem g) user_xid, a unique identifier for each student. + +Note that ASSISTments provides a discrete_score of 1 only if the student gets the problem correct on their first attempt, without requesting any support. If the student requests a hint, requests the answer, or has multiple tries they receive a 0. Accordingly, a student's answer can be the correct answer, but they can receive a 0 if the student requests a hint or sees the answer before entering the answer. This is shown in “table 7 cognitive accuracy when answers are incorrect” in our paper. + +# Problems File +This file consists of information about 3,395 unique problems. The columns include +1. Problem Set Id, which links problems that follow one another +2. Problem Part, which indicates where in the Problem Set the problem occurs +3. Problem Type, describing the type of problem +4. Answer Type, describing the type of answer (see below table or more information) +5. Problem Body, the problem text with HTML or markup illustrating exactly what the student saw (code to convert to natural language is available on the github) +6. Fill-in Options +7. Fill-in Answers +8. Multiple Choice Options +9. Multiple Choice Answers +10. problem_id + +Problem Set example: PSB6N4 consists of three problems. The first is problem_id 151389 (as it has ‘Problem Part’ = 1, the second is problem_id 151533, and the third/last is 151647. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Answer Type + Description + Fill-in Options + Fill-in Answers + Multiple Choice Options + Multiple Choice Answers +
Numeric + The student must type in the correct number + The correct answer. If there are multiple correct answers they are separated by a “,”. + The correct answer. If there are multiple correct answers they are separated by a “,”. + n/a + n/a +
Drop Down + The student must select the correct option from a drop-down menu. These are similar to multiple choice + All the drop down options, separated by “</p>,” + The correct dropdown option. + n/a + n/a +
Algebraic Expression + The student must type in the correct, short, algebraic expression, or a similar equivalent expression. E.g. if the answer is a^2+b^2 then b^2+a^2 would also be correct. + The correct answer. If there are multiple correct answers they are separated by a “,”. + The correct answer. If there are multiple correct answers they are separated by a “,”. + n/a + n/a +
Ordering + The student must order some values in some order. Note the initial order of how these are presented to students is randomized. + The correct order of objects, separated by “,”. + The correct order of objects, separated by “,”. + n/a + n/a +
Exact Match + The student must type in exactly the correct answer. This could be a number, expression, point, list, etc. + The correct answer. If there are multiple correct answers they are separated by a “,”. Note that some answers, e.g. lists, require the whole text (1,2,3) and there is only a single answer. + The correct answer. If there are multiple correct answers they are separated by a “,”. Note that some answers, e.g. lists, require the whole text (1,2,3) and there is only a single answer. + n/a + n/a +
Exact Fraction + The student must type in exactly the correct fraction. + The correct answer. If there are multiple correct answers they are separated by a “,”. + The correct answer. If there are multiple correct answers they are separated by a “,”. + n/a + n/a +
Numeric Expression + The student must type in a numeric expression. Note that simplification occurs, e.g. if the answer is 11^3, 1331 is also considered correct. + The correct answer. If there are multiple correct answers they are separated by a “,”. + The correct answer. If there are multiple correct answers they are separated by a “,”. + n/a + n/a +
Multiple Choice + The student must select the correct option. + n/a + n/a + A list of options, separated by ‘||’. + The correct option. +
Check all that apply + The student must select all correct option(s). + n/a + n/a + A list of options, separated by ‘||’. + The correct option(s), separated by ‘||’. +
+ +# Skills File +The skills file consists of +1) problem_id, linking to problems in the Problems file +2) skill_id, a unique identifier per skill +3) node_code, which identifies the ASSISTments Skill tag Illustrative Math code for the skill and +4) node_name, a description of the skill. In total there are 224 unique skills. + +# Data Source +All data across each file are from [ASSISTments](https://new.assistments.org/), where students complete in-class work as well as homework and receive support and feedback from the platform. This work was done in conjunction with [Dr. Heffernan’s lab at WPI](https://www.neilheffernan.net/home). To ensure student privacy, our team attempted to remove all Personal Identifiable Information (PII). However, it is possible students could type PII into fill-in problems, which we aimed to detect and remove, but short of a manual review of 1.7 million interaction logs becomes infeasible. Accordingly, we ask that if people using this dataset come across PII to please contact us at [etrials@assistments.org](etrials@assistments.org) so it can be removed. + +# License and Sharing Agreement +This dataset is licensed under CC-BY-NC-4.0. We require that this dataset is used for research and educational purposes following this +[Responsible Use Guidelines](https://www.etrialstestbed.org/mathnet57963-guidelines). + +# Citation + +If you use the **FoundationalASSIST** dataset in your research, please cite the following paper: + +> Worden, E., Heffernan, C., Heffernan, N., & Sonkar, S. (2026). FoundationalASSIST: An Educational Dataset for Foundational Knowledge Tracing and Pedagogical Grounding of LLMs. *arXiv preprint arXiv:2602.00070*. + +### BibTeX + +```bibtex +@article{worden2026foundationalassist, + title={FoundationalASSIST: An Educational Dataset for Foundational Knowledge Tracing and Pedagogical Grounding of LLMs}, + author={Worden, Eamon and Heffernan, Cristina and Heffernan, Neil and Sonkar, Shashank}, + journal={arXiv preprint arXiv:2602.00070}, + year={2026} +} +``` + +### FAQs +Q: Where is the code that cleans the problem text? +A: This repository, in Code/clean_utils.py or cleantext.py, both are similar. + +Q: How does discrete_score work? +A: Discrete score is 1 if the student solved the problem on their first try without requesting a hint (hint_count) or an explanation/seeing the answer (saw_answer). +Note this is recorded by ASSISTments. There are 433 rows where discrete_score = 1 despite saw_answer = True or hint_count > 0. In these instances, the student correctly solved the problem then requested hints/explanation/the answer anyways. + +Q: Does the dataset track multiple attempts? (E.g. the student first incorrectly said 3, then incorrectly answered 6, then correctly answered 9) +A: No. We recognize it may be valuable to have this data. However, currently, answer_text (in Interactions.csv) is the first answer (right or wrong) the student submitted for the problem. Second/future attempts are not included in this dataset, but stay tuned. \ No newline at end of file diff --git a/Results/Problems_duplicated_problem_id.csv b/Results/Problems_duplicated_problem_id.csv new file mode 100644 index 0000000000000000000000000000000000000000..d7ebe708e1d8df54f2eec3efa921c7005cb715cc --- /dev/null +++ b/Results/Problems_duplicated_problem_id.csv @@ -0,0 +1,209 @@ +Problem Set Id,Problem Part,Problem Type,Answer Types,Problem Body,Fill-in Options,Fill-in Answers,Multiple Choice Options,Multiple Choice Answers,problem_id,duplicate_group_id,duplicate_problem_id_count,distinct_problem_body_count +PSBBP4J,2,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.

+

 

+

square units.

+

 

+

",11,11,,,242640,1,2,1 +PSBBP4J,2,Fill-in-the-blank(s),Numeric,"

Find the area of the triangle.

+

 

+

square units.

+

 

+

",11,11,,,242640,1,2,1 +PSBBPYN,1,Fill-in-the-blank(s),Numeric,"

Find the area of this trapezoid.

+

 

+

+

 

+

square units

",18,18,,,242072,2,2,1 +PSBBPYN,1,Fill-in-the-blank(s),Numeric,"

Find the area of this trapezoid.

+

 

+

+

 

+

square units

",18,18,,,242072,2,2,1 +PSBBUFM,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region in square units.

+

 

+

+

 

+

square units

",40,40,,,266614,3,2,1 +PSBBUFM,1,Fill-in-the-blank(s),Numeric,"

Find the area of the shaded region in square units.

+

 

+

+

 

+

square units

",40,40,,,266614,3,2,1 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","2, 4","2, 4",,,437233,4,4,1 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","2, 4","2, 4",,,437233,4,4,1 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","2, 4","2, 4",,,437233,4,4,1 +PSBCTHE,3,Fill-in-the-blank(s),Numeric,"

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail.

+

 

+

+

 

+

 

+

 

+

Complete each statement:

+

 

+

There are paws for every tail.

+

There are paws for every ear.

","4, 2","4, 2",,,437233,4,4,1 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104,5,4,1 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104,5,4,1 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104,5,4,1 +PRABFEFN,1,Fill-in-the-blank(s),Numeric,"

A square has a side length of 5 feet. What is its area?

+

 

+

square feet

",25,25,,,89104,5,4,1 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850,6,4,1 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850,6,4,1 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850,6,4,1 +PRABE64P,1,Fill-in-the-blank(s),Numeric,"

A square is 3 inches by 3 inches. What is its area?

+

 

+

square inches

",9,9,,,88850,6,4,1 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321,7,4,1 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321,7,4,1 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321,7,4,1 +PRABFEFP,1,Fill-in-the-blank(s),Numeric,"

The area of a square is 36 square centimeters. What is the length of each side of the square?

+

 

+

centimeters

",6,6,,,89321,7,4,1 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316,8,4,1 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316,8,4,1 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316,8,4,1 +PSBTTU,1,Fill-in-the-blank(s),Numeric,"

Find the area of this quadrilateral.

+

 

+

+

 

+

square units

",24,24,,,88316,8,4,1 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681,9,4,1 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681,9,4,1 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681,9,4,1 +PRABE64M,1,Multiple Choice (select all),Check All That Apply,"

Here is a diagram that describes the cups of green and white paint in a mixture.

+

 

+ + + + + + + + + + + +
green paint (cups)
white paint (cups)
+

 

+

Select all the statements that accurately describe this diagram.

",,,"The ratio of cups of white paint to cups of green paint is 2 to 4. || For every cup of green paint, there are two cups of white paint. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint. ||

The ratio of cups of green paint to cups of white paint is 2 : 4.

","The ratio of cups of white paint to cups of green paint is 2 to 4. ||

The ratio of cups of green paint to cups of white paint is 4 : 2.

|| For every cup of white paint, there are two cups of green paint.",88681,9,4,1 +PRABERFN,1,Multiple Choice (select 1),Multiple Choice,"

Which scale is equivalent to 1 cm to 1 km?

+
 
",,,"1 to 1,000 || 10,000 to 1 || 1 to 100,000 || 100,000 to 1 || 1 to 1,000,000","1 to 100,000",146478,10,2,1 +PRABERFN,1,Multiple Choice (select 1),Multiple Choice,"

Which scale is equivalent to 1 cm to 1 km?

+
 
",,,"1 to 1,000 || 10,000 to 1 || 1 to 100,000 || 100,000 to 1 || 1 to 1,000,000","1 to 100,000",146478,10,2,1 +PSB5BQ,1,Multiple Choice (select 1),Multiple Choice,"

In one version of trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes?

",,,Yes || No,Yes,143888,11,2,1 +PSB5BQ,1,Multiple Choice (select 1),Multiple Choice,"

In one version of trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes?

",,,Yes || No,Yes,143888,11,2,1 +PRABE55W,1,Multiple Choice (select all),Check All That Apply,

Select all the polygons.

,,,"

||

||

||

||

||

","

||

",243115,12,2,1 +PRABE55W,1,Multiple Choice (select all),Check All That Apply,

Select all the polygons.

,,,"

||

||

||

||

||

","

||

",243115,12,2,1 +PRABP75T,1,Multiple Choice (select all),Check All That Apply,"

Salt and sugar give two distinctly different tastes, one salty and the other sweet. In a mixture of salt and sugar, it is possible for the mixture to be salty, sweet or both. Will any of these mixtures taste exactly the same?

",,,"Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture B: 1.5 cups water, 3 teaspoons salt, 0.2 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar || None of these mixtures taste the same.","Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar",48435,13,2,1 +PRABP75T,1,Multiple Choice (select all),Check All That Apply,"

Salt and sugar give two distinctly different tastes, one salty and the other sweet. In a mixture of salt and sugar, it is possible for the mixture to be salty, sweet or both. Will any of these mixtures taste exactly the same?

",,,"Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture B: 1.5 cups water, 3 teaspoons salt, 0.2 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar || None of these mixtures taste the same.","Mixture A: 2 cups water, 4 teaspoons salt, 0.25 cup sugar || Mixture C: 1 cup water, 2 teaspoons salt, 0.125 cup sugar",48435,13,2,1 +PSBGXA,1,Multiple Choice (select 1),Multiple Choice,

The side lengths of Triangle B are all 5 more than the side lengths of Triangle A. Can Triangle B be a scaled copy of Triangle A?

,,,Yes || No,Yes,36042,14,2,1 +PSBGXA,1,Multiple Choice (select 1),Multiple Choice,

The side lengths of Triangle B are all 5 more than the side lengths of Triangle A. Can Triangle B be a scaled copy of Triangle A?

,,,Yes || No,Yes,36042,14,2,1 +PRABMQH8,1,Multiple Choice (select all),Check All That Apply,"

Triangle Z is a scale copy of Triangle M.

+

+


Select all the sets of values that could be the side lengths of Triangle Z. 

",,,"

8,11,14

|| 10,17.5,25 || 6,9,11 || 6,10.5,15 || 8,14,20","10,17.5,25 || 6,10.5,15 || 8,14,20",569234,15,2,1 +PRABMQH8,1,Multiple Choice (select all),Check All That Apply,"

Triangle Z is a scale copy of Triangle M.

+

+


Select all the sets of values that could be the side lengths of Triangle Z. 

",,,"

8,11,14

|| 10,17.5,25 || 6,9,11 || 6,10.5,15 || 8,14,20","10,17.5,25 || 6,10.5,15 || 8,14,20",569234,15,2,1 diff --git a/Results/Problems_same_body_different_problem_id.csv b/Results/Problems_same_body_different_problem_id.csv new file mode 100644 index 0000000000000000000000000000000000000000..ec078271f46937ef0d1dc70b4a1f6f5691f73335 --- /dev/null +++ b/Results/Problems_same_body_different_problem_id.csv @@ -0,0 +1,55 @@ +Problem Set Id,Problem Part,Problem Type,Answer Types,Problem Body,Fill-in Options,Fill-in Answers,Multiple Choice Options,Multiple Choice Answers,problem_id,duplicate_group_id,distinct_problem_id_count,distinct_problem_ids +PSB2CK,6,Fill-in-the-blank(s),Numeric,"

What is its answer?

+

 

+

",2.64,2.64,,,126628,1,3,126091;126362;126628 +PSB2CK,2,Fill-in-the-blank(s),Numeric,"

What is its answer?

+

 

+

",264,264,,,126091,1,3,126091;126362;126628 +PSB2CK,4,Fill-in-the-blank(s),Numeric,"

What is its answer?

+

 

+

",26.4,26.4,,,126362,1,3,126091;126362;126628 +PSBBS8M,2,Fill-in-the-blank(s),Numeric,"

How many different triangles are there?

+

 

+

different triangles

",3,3,,,259177,2,2,258731;259177 +PSBBS6F,2,Fill-in-the-blank(s),Numeric,"

How many different triangles are there?

+

 

+

different triangles

",4,4,,,258731,2,2,258731;259177 +PRABFG57,1,Order / Sort,Ordering,

Order these numbers from least to greatest:

,"

-12

,

12

,

-1

,

-112

,

1

,

0

","

-12

,

12

,

-1

,

-112

,

1

,

0

",,,406337,3,2,406337;6158 +PRABFKN2,1,Order / Sort,Ordering,

Order these numbers from least to greatest:

,"

-18

,

-17

,

-18

,

19

,

20

","

-18

,

-17

,

-18

,

19

,

20

",,,6158,3,2,406337;6158 +PSBDASC,2,Fill-in-the-blank(s),Numeric,"

What is the decimal representation of that number?

+

 

+

",0.5,0.5,,,522651,4,2,522651;523084 +PSBDASC,6,Fill-in-the-blank(s),Numeric,"

What is the decimal representation of that number?

+

 

+

",0.125,0.125,,,523084,4,2,522651;523084 +PSBCDYX,3,Fill-in-the-blank(s),Numeric,"

Solve the equation you wrote.

+

 

+

x =

",7.8,7.8,,,366764,5,2,366764;56163 +PSBMSN,3,Fill-in-the-blank(s),Numeric,"

Solve the equation you wrote.

+

 

+

x =

",11.6,11.6,,,56163,5,2,366764;56163 +PSBBSYB,2,Fill-in-the-blank(s),Numeric,"

If not, write it in scientific notation.

+

 

+

×10

","6, 3.6","6, 3.6",,,257604,6,3,257097;257352;257604 +PSBBSWV,2,Fill-in-the-blank(s),Numeric,"

If not, write it in scientific notation.

+

 

+

×10

","-4, 9.9","-4, 9.9",,,257352,6,3,257097;257352;257604 +PSBBSVC,2,Fill-in-the-blank(s),Numeric,"

If not, write it in scientific notation.

+

 

+

×10

","4, 4.82","4, 4.82",,,257097,6,3,257097;257352;257604 +PSBGBG,4,Fill-in-the-blank(s),Numeric,"

On which day did it occur?

+

 

+

Day

",11,11,,,32600,7,2,32363;32600 +PSBGBG,2,Fill-in-the-blank(s),Numeric,"

On which day did it occur?

+

 

+

Day

",14,14,,,32363,7,2,32363;32600 +PRABQM8U,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,"Given a box plot, it is always possible to calculate the mean of the data. || Given a box plot, it is always possible to calculate the median of the data. || Given a box plot, it is always possible to construct a corresponding dot plot. || Given a dot plot, it is always possible to construct a corresponding box plot. || Given a histogram, it is always possible to construct a corresponding box plot.","Given a box plot, it is always possible to calculate the median of the data. || Given a dot plot, it is always possible to construct a corresponding box plot.",193572,8,3,193572;362112;69320 +PRABEVAG,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,"

2.3 + (-2.3) is equal to zero.

||

(-3.7) + (-4.1) is positive.

||

-2.6 - -124 is positive.

||

52 + -2.5 is negative.

||

72 - (-100) is negative.

","

2.3 + (-2.3) is equal to zero.

||

-2.6 - -124 is positive.

",69320,8,3,193572;362112;69320 +PRABFJP8,1,Multiple Choice (select all),Check All That Apply,

Select all the true statements.

,,,"

-5 < -5

||

-6 < -5

||

-6 < 3

||

4 < -7

||

-7 < -8

","

-5 < -5

||

4 < -7

||

-7 < -8

",362112,8,3,193572;362112;69320 +PSBCKT6,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of numbers below, select the number that is greater.

",,,"

42 · 107

||

8.5 · 108

","

8.5 · 108

",399091,9,3,398365;398730;399091 +PSBCKRX,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of numbers below, select the number that is greater.

",,,"

2 · 106 

||

7.839 · 106 

","

7.839 · 106 

",398730,9,3,398365;398730;399091 +PSBCKP4,1,Multiple Choice (select 1),Multiple Choice,"

For the pair of numbers below, select the number that is greater.

",,,"

17·108   

||

4·108

","

17·108   

",398365,9,3,398365;398730;399091 +PRABQPRF,1,Multiple Choice (select 1),Multiple Choice,

Which of these describes a unique polygon?

,,,"A quadrilateral with 4 right angles || A triangle with angles 30°, 80°, and 70° || A triangle with side lengths 7 cm and 8 cm and a 70° angle || A triangle with each side length 5 inches",A triangle with each side length 5 inches,558308,10,2,483667;558308 +PRABEVDM,1,Multiple Choice (select 1),Multiple Choice,

Which of these describes a unique polygon?

,,,"A triangle with angles 30°, 50°, and 100° || A quadrilateral with each side length 5 cm || A triangle with side lengths 6 cm, 7 cm, and 8 cm || A triangle with side lengths 4 cm and 5 cm and a 50° angle","A triangle with side lengths 6 cm, 7 cm, and 8 cm",483667,10,2,483667;558308 +PSBBD9R,2,Multiple Choice (select 1),Multiple Choice,

Which group shows greater variability?

,,,

Group A

|| group B,

Group A

,193337,11,2,193337;529063 +PSBDBQU,2,Multiple Choice (select 1),Multiple Choice,

Which group shows greater variability?

,,,Group A || Group B,Group A,529063,11,2,193337;529063 diff --git a/Results/day_student_attempt_distribution.png b/Results/day_student_attempt_distribution.png new file mode 100644 index 0000000000000000000000000000000000000000..be9e7d9e58e30f31bc8306ee5bba8dff9661f8f4 --- /dev/null +++ b/Results/day_student_attempt_distribution.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d9f59cee525d97c2d4002c888725b17c8e49d1881249f83dbf44582f250dc74c +size 175846 diff --git a/Results/day_student_attempt_distribution_00173df52c65a9c13b45978c5a56ea2db67b17deded674486f7af64f7c5fd9ac.png b/Results/day_student_attempt_distribution_00173df52c65a9c13b45978c5a56ea2db67b17deded674486f7af64f7c5fd9ac.png new file mode 100644 index 0000000000000000000000000000000000000000..19281091e356710a14d5d74d17fe3f7364262d9d --- /dev/null +++ b/Results/day_student_attempt_distribution_00173df52c65a9c13b45978c5a56ea2db67b17deded674486f7af64f7c5fd9ac.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4ca130170fdcc3e821ab21ccc262d091b088c0fa069f585d20485e1cfec0e0f1 +size 133826 diff --git a/Results/day_student_attempt_distribution_001849d40d6bf1e2ed5826e4420e291e54655a2b6b77a9ab701faaeb4e899abe.png b/Results/day_student_attempt_distribution_001849d40d6bf1e2ed5826e4420e291e54655a2b6b77a9ab701faaeb4e899abe.png new file mode 100644 index 0000000000000000000000000000000000000000..a35613b5bb124c2e2bcb70d11dd4e5152d042533 --- /dev/null +++ b/Results/day_student_attempt_distribution_001849d40d6bf1e2ed5826e4420e291e54655a2b6b77a9ab701faaeb4e899abe.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e54a86b81d0221edd7bfc2449b2ef8cca2ed2cefcfef096ff6e23447d03e3ada +size 132799 diff --git a/Results/day_student_attempt_distribution_counts.csv b/Results/day_student_attempt_distribution_counts.csv new file mode 100644 index 0000000000000000000000000000000000000000..4aeaa4b1c771d380e6fd97528576ff1ff50936ae --- /dev/null +++ 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+302400.0,345600.0,43200.0,48,0.13150684931506848,13.150684931506849 +345600.0,388800.0,43200.0,18,0.049315068493150684,4.931506849315069 diff --git a/Results/pedagogical_grounding/README.md b/Results/pedagogical_grounding/README.md new file mode 100644 index 0000000000000000000000000000000000000000..6bf4b6fa34c3feacb8015605b3faac75418bd88c --- /dev/null +++ b/Results/pedagogical_grounding/README.md @@ -0,0 +1,275 @@ +# Pedagogical Grounding + +This module provides tools for analyzing educational assessment data and benchmarking LLMs on pedagogical reasoning tasks. + +## Overview + +The pedagogical grounding work consists of two parts: + +1. **Analysis Scripts** - Compute pedagogical metrics from student response data +2. **LLM Benchmark** - Evaluate LLMs on pedagogical reasoning tasks + +--- + +## Part 1: Analysis Scripts + +These scripts analyze the FoundationalKT dataset to compute pedagogical metrics. + +### IRT Parameters (`irt_parameters.py`) + +Computes Item Response Theory parameters for assessment items using Bayesian inference. + +```bash +python pedagogical_grounding/irt_parameters.py \ + --data-dir foundationalktdataset/ \ + --output-dir pedagogical_grounding/output/ +``` + +**Output:** `irt_parameters.json` (~2,548 problems) + +| Field | Description | +|-------|-------------| +| `problem_id` | Unique problem identifier | +| `difficulty_1pl` | 1PL (Rasch) difficulty parameter | +| `difficulty_2pl` | 2PL difficulty parameter (primary metric) | +| `discrimination_2pl` | 2PL discrimination parameter | +| `percent_correct` | Empirical accuracy rate | +| `n_responses` | Number of student responses | + +**Interpretation:** +- `difficulty_2pl`: Higher = harder (range: -1.35 to 0.91) +- `discrimination_2pl`: Higher = better at distinguishing student ability (range: 0.01 to 0.91) + +### Distractor Analysis (`distractor_analysis.py`) + +Analyzes the effectiveness of wrong answer choices in multiple-choice questions. + +```bash +python pedagogical_grounding/distractor_analysis.py \ + --data-dir foundationalktdataset/ \ + --output-dir pedagogical_grounding/output/ +``` + +**Output:** `distractor_stats.json` (~236 MC problems) + +| Field | Description | +|-------|-------------| +| `problem_id` | Unique problem identifier | +| `n_choices` | Number of answer options | +| `correct_rate` | Fraction choosing correct answer | +| `distractors` | Dict of wrong answers → count | +| `distractor_frequencies` | Dict of wrong answers → frequency | +| `most_common_distractor` | Most frequently chosen wrong answer | +| `least_common_distractor` | Least frequently chosen wrong answer | + +--- + +## Part 2: LLM Benchmark + +Benchmarks LLMs on 4 pedagogical reasoning tasks using zero-shot evaluation. + +### Tasks + +| Task | Description | Data Source | Metric | +|------|-------------|-------------|--------| +| `difficulty` | Which of two questions is harder? | IRT params | Binary accuracy | +| `discrimination` | Which question better distinguishes ability? | IRT params | Binary accuracy | +| `distractor_most` | Which wrong answer is most commonly chosen? | Distractor stats | Multi-class accuracy | +| `distractor_least` | Which wrong answer is least commonly chosen? | Distractor stats | Multi-class accuracy | + +### Scripts + +All benchmark scripts are located in this folder (`pedagogical_grounding/`): + +| File | Description | +|------|-------------| +| `pedagogical_inference_base.py` | Base module with data loading, sampling, prompts, inference | +| `gptoss120b_pedagogical.py` | GPT-OSS-120B model config | +| `qwen3next80b_instruct_pedagogical.py` | Qwen3-Next-80B-Instruct model config | +| `qwen3next80b_thinking_pedagogical.py` | Qwen3-Next-80B-Thinking model config | +| `evaluate_pedagogical.py` | Evaluation script for accuracy metrics | + +### Usage + +**Run all commands from the project root directory.** + +#### Run Inference + +```bash +# Difficulty comparison (stratified sampling, 1000 pairs) +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \ + --task difficulty \ + --num-samples 1000 \ + --sampling-mode stratified \ + --num-gpus 4 + +# Discrimination comparison +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \ + --task discrimination \ + --num-samples 1000 \ + --num-gpus 4 + +# Most common distractor prediction +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \ + --task distractor_most \ + --num-gpus 4 + +# Least common distractor prediction +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \ + --task distractor_least \ + --num-gpus 4 + +# All tasks at once +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \ + --task all \ + --num-samples 500 \ + --num-gpus 4 +``` + +#### Evaluate Results + +```bash +python pedagogical_grounding/evaluate_pedagogical.py --input gptoss120b_pedagogical_difficulty_n1000_stratified.jsonl +python pedagogical_grounding/evaluate_pedagogical.py --input results.jsonl --output metrics.json +``` + +### CLI Arguments + +| Argument | Description | Default | +|----------|-------------|---------| +| `--task` | Task to run: `difficulty`, `discrimination`, `distractor_most`, `distractor_least`, `all` | Required | +| `--sampling-mode` | `random` or `stratified` (ensures meaningful differences) | `stratified` | +| `--num-samples` | Number of pairs/problems to sample | 1000 | +| `--min-difference` | Minimum difference for stratified sampling | 0.2 | +| `--batch-size` | Batch size for vLLM inference | 500 | +| `--num-gpus` | Number of GPUs for tensor parallelism | 1 | +| `--data-dir` | Base directory containing data files | `.` | + +### Sampling Modes + +**Random:** Any two questions randomly paired (may include trivial comparisons). + +**Stratified:** Ensures meaningful differences between pairs: +- Small: 0.2–0.5 difference +- Medium: 0.5–1.0 difference +- Large: >1.0 difference + +### Output Format (JSONL) + +**Comparison tasks:** +```json +{ + "prediction_id": "difficulty_405080_448452", + "task": "difficulty", + "problem_id_a": 405080, + "problem_id_b": 448452, + "value_a": -0.234, + "value_b": -0.533, + "difference": 0.299, + "stratum": "small", + "ground_truth": "A", + "predicted_answer": "A", + "is_correct": true +} +``` + +**Distractor tasks:** +```json +{ + "prediction_id": "distractor_most_74236", + "task": "distractor_most", + "problem_id": 74236, + "n_choices": 4, + "ground_truth_letter": "B", + "ground_truth_text": "Elena is correct", + "ground_truth_freq": 0.207, + "predicted_answer": "B", + "is_correct": true +} +``` + +### Baselines + +| Task | Random Baseline | +|------|-----------------| +| Difficulty comparison | 50% | +| Discrimination comparison | 50% | +| Distractor (3 options) | 33% | +| Distractor (4 options) | 25% | + +### Evaluation Metrics + +The evaluation script computes: + +- **Overall accuracy** vs random baseline +- **By stratum** (for comparison tasks): small/medium/large difference +- **By difference magnitude**: very_small/small/medium/large +- **By number of distractors** (for distractor tasks) +- **By ground truth frequency**: rare/moderate/common distractors + +--- + +## Data Flow + +``` +foundationalktdataset/ +├── Interactions.csv # Student responses +├── Problems.csv # Problem text and answers +└── Skills.csv # Skill metadata + │ + ▼ +┌───────────────────────────────────────┐ +│ Analysis Scripts (Part 1) │ +│ irt_parameters.py, distractor_analysis.py │ +└───────────────────────────────────────┘ + │ + ▼ +pedagogical_grounding/output/ +├── irt_parameters.json # 2,548 problems with IRT params +└── distractor_stats.json # 236 MC problems with distractor data + │ + ▼ +┌───────────────────────────────────────┐ +│ LLM Benchmark (Part 2) │ +│ pedagogical_inference_base.py │ +│ + model configs │ +└───────────────────────────────────────┘ + │ + ▼ +Output: JSONL predictions + evaluation metrics +``` + +--- + +## File Structure + +``` +foundationalKT-ss/ +├── pedagogical_grounding/ +│ ├── README.md # This file +│ │ +│ │ # Analysis Scripts (Part 1) +│ ├── irt_parameters.py # IRT parameter computation +│ ├── distractor_analysis.py # Distractor effectiveness analysis +│ │ +│ │ # LLM Benchmark (Part 2) +│ ├── pedagogical_inference_base.py # Benchmark base module +│ ├── gptoss120b_pedagogical.py # GPT-OSS-120B config +│ ├── qwen3next80b_instruct_pedagogical.py # Qwen3 Instruct config +│ ├── qwen3next80b_thinking_pedagogical.py # Qwen3 Thinking config +│ ├── evaluate_pedagogical.py # Evaluation script +│ │ +│ │ # Output Data +│ └── output/ +│ ├── irt_parameters.json # IRT results (2,548 problems) +│ ├── irt_parameters.png # IRT visualizations +│ ├── distractor_stats.json # Distractor results (236 problems) +│ └── distractor_analysis.png # Distractor visualizations +│ +├── foundationalktdataset/ # Source data +│ ├── Interactions.csv +│ ├── Problems.csv +│ └── Skills.csv +│ +└── clean_utils.py # Text cleaning utilities +``` diff --git a/Results/pedagogical_grounding/batch_evaluate.py b/Results/pedagogical_grounding/batch_evaluate.py new file mode 100644 index 0000000000000000000000000000000000000000..a54a9e83a7c562488d5090434a274d30b6f2f30d --- /dev/null +++ b/Results/pedagogical_grounding/batch_evaluate.py @@ -0,0 +1,328 @@ +""" +Batch evaluation script for Pedagogical Grounding LLM Benchmark. + +Analyzes all result files in a directory and creates aggregate comparison tables. + +Usage: + python pedagogical_grounding/batch_evaluate.py --input-dir pedagogical_grounding/results + python pedagogical_grounding/batch_evaluate.py --input-dir results --output summary.json +""" + +import argparse +import glob +import json +import os +import re +from collections import defaultdict +from typing import Dict, List, Tuple + +from evaluate_pedagogical import ( + load_results, + evaluate_comparison_task, + evaluate_distractor_task, +) + + +def extract_model_name(filename: str) -> str: + """Extract model name from filename.""" + basename = os.path.basename(filename) + # Pattern: {model}_pedagogical_{task}_... + match = re.match(r'^(.+?)_pedagogical_', basename) + if match: + return match.group(1) + return basename.replace('.jsonl', '') + + +def evaluate_file(filepath: str) -> Tuple[str, Dict]: + """Evaluate a single file and return model name and metrics.""" + model_name = extract_model_name(filepath) + results = load_results(filepath) + + metrics = { + 'file': os.path.basename(filepath), + 'total_predictions': len(results), + 'tasks': {} + } + + # Identify and evaluate tasks + tasks = set(r.get('task') for r in results if r.get('task')) + + for task in tasks: + if task in ['difficulty', 'discrimination']: + task_metrics = evaluate_comparison_task(results, task) + elif task in ['distractor_most', 'distractor_least']: + task_metrics = evaluate_distractor_task(results, task) + else: + continue + + if 'error' not in task_metrics: + metrics['tasks'][task] = task_metrics + + return model_name, metrics + + +def print_header(title: str, width: int = 80) -> None: + """Print a formatted header.""" + print() + print("=" * width) + print(f" {title}") + print("=" * width) + + +def print_accuracy_table(all_metrics: Dict[str, Dict], task: str) -> None: + """Print accuracy comparison table for a task.""" + models = sorted(all_metrics.keys()) + + # Get baseline + if task in ['difficulty', 'discrimination']: + baseline = 0.5 + baseline_label = "50.0%" + else: + baseline = None # Varies by model + baseline_label = "varies" + + # Header + print(f"\n{'Model':<35} {'Accuracy':>10} {'Lift':>10} {'N':>8}") + print("-" * 65) + + # Data rows + for model in models: + task_metrics = all_metrics[model]['tasks'].get(task) + if task_metrics and 'error' not in task_metrics: + acc = task_metrics['accuracy'] + lift = task_metrics['lift_over_random'] + n = task_metrics['total'] + print(f"{model:<35} {acc:>9.1%} {lift:>+9.1%} {n:>8}") + else: + print(f"{model:<35} {'N/A':>10} {'N/A':>10} {'N/A':>8}") + + print("-" * 65) + print(f"{'Random Baseline':<35} {baseline_label:>10}") + + +def print_stratum_table(all_metrics: Dict[str, Dict], task: str) -> None: + """Print stratum breakdown comparison table.""" + models = sorted(all_metrics.keys()) + strata = ['small', 'medium', 'large'] + + # Header + header = f"{'Model':<30}" + for s in strata: + header += f" {s:>12}" + print(f"\n{header}") + print("-" * (30 + 13 * len(strata))) + + # Data rows + for model in models: + task_metrics = all_metrics[model]['tasks'].get(task) + if task_metrics and 'error' not in task_metrics: + row = f"{model:<30}" + by_stratum = task_metrics.get('by_stratum', {}) + for s in strata: + if s in by_stratum: + acc = by_stratum[s]['accuracy'] + row += f" {acc:>11.1%}" + else: + row += f" {'N/A':>12}" + print(row) + + +def print_summary_table(all_metrics: Dict[str, Dict]) -> None: + """Print overall summary table with all tasks.""" + models = sorted(all_metrics.keys()) + tasks = ['difficulty', 'discrimination', 'distractor_most', 'distractor_least'] + task_abbrev = { + 'difficulty': 'Diff', + 'discrimination': 'Disc', + 'distractor_most': 'D-Most', + 'distractor_least': 'D-Least' + } + + # Header + header = f"{'Model':<30}" + for t in tasks: + header += f" {task_abbrev[t]:>10}" + header += f" {'Avg':>10}" + print(f"\n{header}") + print("-" * (30 + 11 * (len(tasks) + 1))) + + # Data rows + for model in models: + row = f"{model:<30}" + accs = [] + for t in tasks: + task_metrics = all_metrics[model]['tasks'].get(t) + if task_metrics and 'error' not in task_metrics: + acc = task_metrics['accuracy'] + row += f" {acc:>9.1%}" + accs.append(acc) + else: + row += f" {'N/A':>10}" + + # Average + if accs: + avg = sum(accs) / len(accs) + row += f" {avg:>9.1%}" + else: + row += f" {'N/A':>10}" + + print(row) + + # Baseline row + print("-" * (30 + 11 * (len(tasks) + 1))) + baseline_row = f"{'Random Baseline':<30}" + baseline_row += f" {'50.0%':>10}" # difficulty + baseline_row += f" {'50.0%':>10}" # discrimination + baseline_row += f" {'~35%':>10}" # distractor_most + baseline_row += f" {'~35%':>10}" # distractor_least + baseline_row += f" {'~43%':>10}" # avg + print(baseline_row) + + +def print_lift_table(all_metrics: Dict[str, Dict]) -> None: + """Print lift over random baseline table.""" + models = sorted(all_metrics.keys()) + tasks = ['difficulty', 'discrimination', 'distractor_most', 'distractor_least'] + task_abbrev = { + 'difficulty': 'Diff', + 'discrimination': 'Disc', + 'distractor_most': 'D-Most', + 'distractor_least': 'D-Least' + } + + # Header + header = f"{'Model':<30}" + for t in tasks: + header += f" {task_abbrev[t]:>10}" + header += f" {'Avg Lift':>10}" + print(f"\n{header}") + print("-" * (30 + 11 * (len(tasks) + 1))) + + # Data rows + for model in models: + row = f"{model:<30}" + lifts = [] + for t in tasks: + task_metrics = all_metrics[model]['tasks'].get(t) + if task_metrics and 'error' not in task_metrics: + lift = task_metrics['lift_over_random'] + row += f" {lift:>+9.1%}" + lifts.append(lift) + else: + row += f" {'N/A':>10}" + + # Average lift + if lifts: + avg_lift = sum(lifts) / len(lifts) + row += f" {avg_lift:>+9.1%}" + else: + row += f" {'N/A':>10}" + + print(row) + + +def print_best_model_per_task(all_metrics: Dict[str, Dict]) -> None: + """Print best model for each task.""" + tasks = ['difficulty', 'discrimination', 'distractor_most', 'distractor_least'] + + print(f"\n{'Task':<20} {'Best Model':<30} {'Accuracy':>10} {'Lift':>10}") + print("-" * 72) + + for task in tasks: + best_model = None + best_acc = -1 + best_lift = 0 + + for model, metrics in all_metrics.items(): + task_metrics = metrics['tasks'].get(task) + if task_metrics and 'error' not in task_metrics: + if task_metrics['accuracy'] > best_acc: + best_acc = task_metrics['accuracy'] + best_lift = task_metrics['lift_over_random'] + best_model = model + + if best_model: + print(f"{task:<20} {best_model:<30} {best_acc:>9.1%} {best_lift:>+9.1%}") + else: + print(f"{task:<20} {'N/A':<30} {'N/A':>10} {'N/A':>10}") + + +def main(): + parser = argparse.ArgumentParser( + description="Batch evaluate Pedagogical Grounding Benchmark results" + ) + parser.add_argument( + "--input-dir", "-i", + type=str, + required=True, + help="Directory containing JSONL result files" + ) + parser.add_argument( + "--output", "-o", + type=str, + default=None, + help="Output JSON file for aggregate metrics (optional)" + ) + parser.add_argument( + "--pattern", + type=str, + default="*.jsonl", + help="Glob pattern for result files (default: *.jsonl)" + ) + args = parser.parse_args() + + # Find all result files + pattern = os.path.join(args.input_dir, args.pattern) + files = sorted(glob.glob(pattern)) + + if not files: + print(f"No files found matching: {pattern}") + return + + print(f"Found {len(files)} result files in {args.input_dir}") + + # Evaluate all files + all_metrics = {} + for filepath in files: + print(f" Loading: {os.path.basename(filepath)}") + model_name, metrics = evaluate_file(filepath) + all_metrics[model_name] = metrics + + # Print aggregate tables + print_header("PEDAGOGICAL GROUNDING BENCHMARK - AGGREGATE RESULTS") + + # Summary table + print_header("ACCURACY BY TASK", width=72) + print_summary_table(all_metrics) + + # Lift table + print_header("LIFT OVER RANDOM BASELINE", width=72) + print_lift_table(all_metrics) + + # Best model per task + print_header("BEST MODEL PER TASK", width=72) + print_best_model_per_task(all_metrics) + + # Detailed stratum breakdown for comparison tasks + print_header("DIFFICULTY - ACCURACY BY STRATUM", width=70) + print_stratum_table(all_metrics, 'difficulty') + + print_header("DISCRIMINATION - ACCURACY BY STRATUM", width=70) + print_stratum_table(all_metrics, 'discrimination') + + # Individual task tables + for task in ['difficulty', 'discrimination', 'distractor_most', 'distractor_least']: + print_header(f"{task.upper()} - DETAILED", width=65) + print_accuracy_table(all_metrics, task) + + # Save aggregate metrics if output specified + if args.output: + with open(args.output, 'w') as f: + json.dump(all_metrics, f, indent=2) + print(f"\nAggregate metrics saved to {args.output}") + + print() + + +if __name__ == "__main__": + main() diff --git a/Results/pedagogical_grounding/distractor_analysis.py b/Results/pedagogical_grounding/distractor_analysis.py new file mode 100644 index 0000000000000000000000000000000000000000..eafcc3cbac5f981ea7df9ced1801028e0e7ed1f2 --- /dev/null +++ b/Results/pedagogical_grounding/distractor_analysis.py @@ -0,0 +1,299 @@ +""" +Distractor Analysis for Pedagogical Grounding + +Computes distractor effectiveness for Multiple Choice (select 1) questions +with more than 2 choices. Identifies most/least common wrong answers. +""" + +import argparse +import os +import json +import pandas as pd +import numpy as np +import matplotlib.pyplot as plt +from collections import Counter + +# Configuration +DEFAULT_DATA_DIR = "foundationalktdataset" +STUDENT_FILE = "Interactions.csv" +PROBLEMS_FILE = "Problems.csv" + + +def parse_args(): + parser = argparse.ArgumentParser(description="Analyze distractor effectiveness") + parser.add_argument( + "--data-dir", "-d", + type=str, + default=DEFAULT_DATA_DIR, + help=f"Directory containing input CSV files (default: {DEFAULT_DATA_DIR})" + ) + parser.add_argument( + "--output-dir", "-o", + type=str, + default="pedagogical_grounding/output", + help="Directory to save output (default: pedagogical_grounding/output)" + ) + parser.add_argument( + "--no-plots", + action="store_true", + help="Skip generating plots" + ) + return parser.parse_args() + + +def load_data(data_dir): + """Load student and problem data.""" + print(f"Loading data from {data_dir}...") + + student_df = pd.read_csv(os.path.join(data_dir, STUDENT_FILE)) + problems_df = pd.read_csv(os.path.join(data_dir, PROBLEMS_FILE)) + + print(f" Loaded {len(student_df):,} student interactions") + print(f" Loaded {len(problems_df):,} problems") + + return student_df, problems_df + + +def get_answer_options(answer_string): + """Parse pipe-delimited answer options.""" + if pd.isna(answer_string) or answer_string == '': + return [] + return [opt.strip() for opt in answer_string.split('||') if opt.strip()] + + +def get_correct_answers(correct_string): + """Parse pipe-delimited correct answers.""" + if pd.isna(correct_string) or correct_string == '': + return [] + return [ans.strip() for ans in correct_string.split('||') if ans.strip()] + + +def normalize_answer(text): + """Normalize answer text for comparison.""" + if pd.isna(text): + return "" + import re + # Remove HTML tags + text = re.sub(r'<[^>]+>', '', str(text)) + # Normalize whitespace + text = ' '.join(text.split()) + return text.strip().lower() + + +def analyze_distractors(student_df, problems_df): + """Analyze distractor effectiveness for MC (select 1) with >2 choices.""" + print("\n" + "=" * 60) + print(" DISTRACTOR ANALYSIS") + print("=" * 60) + + # Filter to MC (select 1) problems + mc_problems = problems_df[problems_df['Problem Type'] == 'Multiple Choice (select 1)'].copy() + + # Count choices + mc_problems['answer_options'] = mc_problems['Multiple Choice Options'].apply(get_answer_options) + mc_problems['n_choices'] = mc_problems['answer_options'].apply(len) + + # Filter to >2 choices + mc_problems = mc_problems[mc_problems['n_choices'] > 2].copy() + print(f"\nMC (select 1) problems with >2 choices: {len(mc_problems)}") + + # Get correct answers + mc_problems['correct_answers'] = mc_problems['Multiple Choice Answers'].apply(get_correct_answers) + + # Filter student data to these problems + problem_ids = set(mc_problems['problem_id']) + mc_interactions = student_df[student_df['problem_id'].isin(problem_ids)].copy() + print(f"Student interactions for these problems: {len(mc_interactions):,}") + + # Merge to get answer options + mc_interactions = mc_interactions.merge( + mc_problems[['problem_id', 'answer_options', 'correct_answers', 'n_choices']], + on='problem_id', + how='left' + ) + + # Analyze each problem + results = [] + + for problem_id in mc_problems['problem_id'].unique(): + problem_data = mc_interactions[mc_interactions['problem_id'] == problem_id] + + if len(problem_data) < 10: # Skip problems with too few responses + continue + + problem_info = mc_problems[mc_problems['problem_id'] == problem_id].iloc[0] + answer_options = problem_info['answer_options'] + correct_answers = problem_info['Fill-in Answers'] + + # Normalize correct answers for comparison + correct_normalized = set(normalize_answer(a) for a in correct_answers) + + # Count responses for each option + option_counts = Counter() + total_responses = 0 + + for _, row in problem_data.iterrows(): + student_answer = row['answer_text'] + if pd.isna(student_answer): + continue + + # Normalize student answer + student_normalized = normalize_answer(student_answer) + + # Match to options + for opt in answer_options: + opt_normalized = normalize_answer(opt) + if student_normalized == opt_normalized or student_normalized in opt_normalized or opt_normalized in student_normalized: + option_counts[opt] += 1 + total_responses += 1 + break + + if total_responses < 10: + continue + + # Separate correct and incorrect options + distractors = {} + correct_count = 0 + + for opt in answer_options: + opt_normalized = normalize_answer(opt) + count = option_counts.get(opt, 0) + + if opt_normalized in correct_normalized or any(normalize_answer(c) in opt_normalized or opt_normalized in normalize_answer(c) for c in correct_answers): + correct_count = count + else: + distractors[opt] = count + + if not distractors: + continue + + # Find most/least common distractor + sorted_distractors = sorted(distractors.items(), key=lambda x: x[1], reverse=True) + most_common = sorted_distractors[0] + least_common = sorted_distractors[-1] + + # Compute frequencies + distractor_freqs = {opt: count / total_responses for opt, count in distractors.items()} + + results.append({ + 'problem_id': int(problem_id), + 'n_choices': int(problem_info['n_choices']), + 'total_responses': int(total_responses), + 'correct_count': int(correct_count), + 'correct_rate': correct_count / total_responses, + 'distractors': {opt: int(count) for opt, count in distractors.items()}, + 'distractor_frequencies': distractor_freqs, + 'most_common_distractor': most_common[0], + 'most_common_distractor_freq': most_common[1] / total_responses, + 'least_common_distractor': least_common[0], + 'least_common_distractor_freq': least_common[1] / total_responses, + }) + + print(f"Problems with sufficient data: {len(results)}") + + return results + + +def print_summary(results): + """Print summary statistics.""" + print("\n--- Summary Statistics ---") + + correct_rates = [r['correct_rate'] for r in results] + most_common_freqs = [r['most_common_distractor_freq'] for r in results] + least_common_freqs = [r['least_common_distractor_freq'] for r in results] + + print(f"\nCorrect Answer Rate:") + print(f" Mean: {np.mean(correct_rates):.1%}") + print(f" Median: {np.median(correct_rates):.1%}") + print(f" Min: {np.min(correct_rates):.1%}") + print(f" Max: {np.max(correct_rates):.1%}") + + print(f"\nMost Common Distractor Frequency:") + print(f" Mean: {np.mean(most_common_freqs):.1%}") + print(f" Median: {np.median(most_common_freqs):.1%}") + + print(f"\nLeast Common Distractor Frequency:") + print(f" Mean: {np.mean(least_common_freqs):.1%}") + print(f" Median: {np.median(least_common_freqs):.1%}") + + # Count problems where least common distractor is never chosen + never_chosen = sum(1 for r in results if r['least_common_distractor_freq'] == 0) + print(f"\nProblems with ineffective distractor (0 selections): {never_chosen} ({100*never_chosen/len(results):.1f}%)") + + +def save_results(results, output_dir): + """Save results to JSON.""" + os.makedirs(output_dir, exist_ok=True) + output_path = os.path.join(output_dir, 'distractor_stats.json') + + with open(output_path, 'w') as f: + json.dump(results, f, indent=2) + + print(f"\nSaved: {output_path}") + + +def plot_results(results, output_dir): + """Generate plots.""" + os.makedirs(output_dir, exist_ok=True) + + fig, axes = plt.subplots(1, 3, figsize=(15, 5)) + + # Plot 1: Correct rate distribution + correct_rates = [r['correct_rate'] for r in results] + axes[0].hist(correct_rates, bins=20, edgecolor='black', alpha=0.7) + axes[0].set_xlabel('Correct Answer Rate') + axes[0].set_ylabel('Number of Problems') + axes[0].set_title('Distribution of Correct Answer Rates') + axes[0].axvline(np.mean(correct_rates), color='red', linestyle='--', label=f'Mean: {np.mean(correct_rates):.1%}') + axes[0].legend() + + # Plot 2: Most common distractor frequency + most_common_freqs = [r['most_common_distractor_freq'] for r in results] + axes[1].hist(most_common_freqs, bins=20, edgecolor='black', alpha=0.7, color='orange') + axes[1].set_xlabel('Most Common Distractor Frequency') + axes[1].set_ylabel('Number of Problems') + axes[1].set_title('Distribution of Most Common Distractor') + axes[1].axvline(np.mean(most_common_freqs), color='red', linestyle='--', label=f'Mean: {np.mean(most_common_freqs):.1%}') + axes[1].legend() + + # Plot 3: Least common distractor frequency + least_common_freqs = [r['least_common_distractor_freq'] for r in results] + axes[2].hist(least_common_freqs, bins=20, edgecolor='black', alpha=0.7, color='green') + axes[2].set_xlabel('Least Common Distractor Frequency') + axes[2].set_ylabel('Number of Problems') + axes[2].set_title('Distribution of Least Common Distractor') + axes[2].axvline(np.mean(least_common_freqs), color='red', linestyle='--', label=f'Mean: {np.mean(least_common_freqs):.1%}') + axes[2].legend() + + plt.tight_layout() + plot_path = os.path.join(output_dir, 'distractor_analysis.png') + plt.savefig(plot_path, dpi=150) + plt.close() + + print(f"Saved: {plot_path}") + + +def main(): + args = parse_args() + + # Load data + student_df, problems_df = load_data(args.data_dir) + + # Analyze distractors + results = analyze_distractors(student_df, problems_df) + + # Print summary + print_summary(results) + + # Save results + save_results(results, args.output_dir) + + # Plot + if not args.no_plots: + plot_results(results, args.output_dir) + + print("\nDone!") + + +if __name__ == "__main__": + main() diff --git a/Results/pedagogical_grounding/evaluate_pedagogical.py b/Results/pedagogical_grounding/evaluate_pedagogical.py new file mode 100644 index 0000000000000000000000000000000000000000..71077c6e56ec043cff780bc01a0a7959159d32ab --- /dev/null +++ b/Results/pedagogical_grounding/evaluate_pedagogical.py @@ -0,0 +1,285 @@ +""" +Evaluation script for Pedagogical Grounding LLM Benchmark. + +Computes accuracy metrics for: +1. Difficulty comparison task +2. Discrimination comparison task +3. Most common distractor prediction +4. Least common distractor prediction + +Usage: + python evaluate_pedagogical.py --input results.jsonl + python evaluate_pedagogical.py --input results.jsonl --output metrics.json +""" + +import argparse +import json +from collections import defaultdict +from typing import Dict, List, Optional + + +def load_results(jsonl_path: str) -> List[Dict]: + """Load results from JSONL file.""" + results = [] + with open(jsonl_path, 'r') as f: + for line in f: + if line.strip(): + results.append(json.loads(line)) + return results + + +def evaluate_comparison_task(results: List[Dict], task_name: str) -> Dict: + """Evaluate a comparison task (difficulty or discrimination).""" + task_results = [r for r in results if r.get('task') == task_name] + + if not task_results: + return {'error': f'No results found for task: {task_name}'} + + total = len(task_results) + correct = sum(1 for r in task_results if r.get('is_correct', False)) + accuracy = correct / total if total > 0 else 0 + + # Breakdown by stratum + stratum_stats = defaultdict(lambda: {'correct': 0, 'total': 0}) + for r in task_results: + stratum = r.get('stratum', 'unknown') + stratum_stats[stratum]['total'] += 1 + if r.get('is_correct', False): + stratum_stats[stratum]['correct'] += 1 + + stratum_accuracy = {} + for stratum, stats in stratum_stats.items(): + if stats['total'] > 0: + stratum_accuracy[stratum] = { + 'accuracy': stats['correct'] / stats['total'], + 'correct': stats['correct'], + 'total': stats['total'] + } + + # Breakdown by difficulty difference bins + diff_bins = [ + ('very_small', 0, 0.2), + ('small', 0.2, 0.5), + ('medium', 0.5, 1.0), + ('large', 1.0, float('inf')) + ] + + diff_stats = defaultdict(lambda: {'correct': 0, 'total': 0}) + for r in task_results: + diff = r.get('difference', 0) + for bin_name, low, high in diff_bins: + if low <= diff < high: + diff_stats[bin_name]['total'] += 1 + if r.get('is_correct', False): + diff_stats[bin_name]['correct'] += 1 + break + + diff_accuracy = {} + for bin_name, stats in diff_stats.items(): + if stats['total'] > 0: + diff_accuracy[bin_name] = { + 'accuracy': stats['correct'] / stats['total'], + 'correct': stats['correct'], + 'total': stats['total'] + } + + return { + 'task': task_name, + 'total': total, + 'correct': correct, + 'accuracy': accuracy, + 'baseline_random': 0.5, # Random guess for binary choice + 'lift_over_random': accuracy - 0.5, + 'by_stratum': dict(stratum_accuracy), + 'by_difference': dict(diff_accuracy) + } + + +def evaluate_distractor_task(results: List[Dict], task_name: str) -> Dict: + """Evaluate a distractor task (most or least common).""" + task_results = [r for r in results if r.get('task') == task_name] + + if not task_results: + return {'error': f'No results found for task: {task_name}'} + + total = len(task_results) + correct = sum(1 for r in task_results if r.get('is_correct', False)) + accuracy = correct / total if total > 0 else 0 + + # Breakdown by number of choices + choices_stats = defaultdict(lambda: {'correct': 0, 'total': 0}) + for r in task_results: + n_choices = r.get('n_choices', 0) + # Number of distractors = n_choices - 1 (excluding correct answer) + n_distractors = n_choices - 1 if n_choices > 1 else 1 + choices_stats[n_distractors]['total'] += 1 + if r.get('is_correct', False): + choices_stats[n_distractors]['correct'] += 1 + + choices_accuracy = {} + baseline_by_choices = {} + for n_distractors, stats in sorted(choices_stats.items()): + if stats['total'] > 0: + acc = stats['correct'] / stats['total'] + baseline = 1.0 / n_distractors if n_distractors > 0 else 0 + choices_accuracy[f'{n_distractors}_distractors'] = { + 'accuracy': acc, + 'correct': stats['correct'], + 'total': stats['total'], + 'baseline_random': baseline, + 'lift_over_random': acc - baseline + } + baseline_by_choices[n_distractors] = baseline + + # Compute weighted average baseline + total_weighted_baseline = 0 + for r in task_results: + n_choices = r.get('n_choices', 0) + n_distractors = n_choices - 1 if n_choices > 1 else 1 + if n_distractors > 0: + total_weighted_baseline += 1.0 / n_distractors + avg_baseline = total_weighted_baseline / total if total > 0 else 0 + + # Breakdown by ground truth frequency + freq_bins = [ + ('very_rare', 0, 0.05), + ('rare', 0.05, 0.10), + ('moderate', 0.10, 0.20), + ('common', 0.20, 0.30), + ('very_common', 0.30, 1.0) + ] + + freq_stats = defaultdict(lambda: {'correct': 0, 'total': 0}) + for r in task_results: + freq = r.get('ground_truth_freq', 0) + for bin_name, low, high in freq_bins: + if low <= freq < high: + freq_stats[bin_name]['total'] += 1 + if r.get('is_correct', False): + freq_stats[bin_name]['correct'] += 1 + break + + freq_accuracy = {} + for bin_name, stats in freq_stats.items(): + if stats['total'] > 0: + freq_accuracy[bin_name] = { + 'accuracy': stats['correct'] / stats['total'], + 'correct': stats['correct'], + 'total': stats['total'] + } + + return { + 'task': task_name, + 'total': total, + 'correct': correct, + 'accuracy': accuracy, + 'baseline_random_avg': avg_baseline, + 'lift_over_random': accuracy - avg_baseline, + 'by_num_distractors': dict(choices_accuracy), + 'by_ground_truth_freq': dict(freq_accuracy) + } + + +def print_comparison_results(metrics: Dict) -> None: + """Print comparison task results.""" + print(f"\n{'='*60}") + print(f"Task: {metrics['task'].upper()}") + print(f"{'='*60}") + + print(f"\nOverall Accuracy: {metrics['accuracy']:.1%} ({metrics['correct']}/{metrics['total']})") + print(f"Random Baseline: {metrics['baseline_random']:.1%}") + print(f"Lift over Random: {metrics['lift_over_random']:+.1%}") + + if metrics.get('by_stratum'): + print(f"\nBy Sampling Stratum:") + for stratum, stats in sorted(metrics['by_stratum'].items()): + print(f" {stratum:12}: {stats['accuracy']:.1%} ({stats['correct']}/{stats['total']})") + + if metrics.get('by_difference'): + print(f"\nBy Value Difference:") + for bin_name, stats in metrics['by_difference'].items(): + print(f" {bin_name:12}: {stats['accuracy']:.1%} ({stats['correct']}/{stats['total']})") + + +def print_distractor_results(metrics: Dict) -> None: + """Print distractor task results.""" + print(f"\n{'='*60}") + print(f"Task: {metrics['task'].upper()}") + print(f"{'='*60}") + + print(f"\nOverall Accuracy: {metrics['accuracy']:.1%} ({metrics['correct']}/{metrics['total']})") + print(f"Random Baseline: {metrics['baseline_random_avg']:.1%} (weighted avg)") + print(f"Lift over Random: {metrics['lift_over_random']:+.1%}") + + if metrics.get('by_num_distractors'): + print(f"\nBy Number of Distractors:") + for key, stats in sorted(metrics['by_num_distractors'].items()): + print(f" {key:15}: {stats['accuracy']:.1%} ({stats['correct']}/{stats['total']}) " + f"[baseline: {stats['baseline_random']:.1%}, lift: {stats['lift_over_random']:+.1%}]") + + if metrics.get('by_ground_truth_freq'): + print(f"\nBy Ground Truth Frequency:") + for bin_name, stats in metrics['by_ground_truth_freq'].items(): + print(f" {bin_name:12}: {stats['accuracy']:.1%} ({stats['correct']}/{stats['total']})") + + +def main(): + parser = argparse.ArgumentParser( + description="Evaluate Pedagogical Grounding Benchmark Results" + ) + parser.add_argument( + "--input", "-i", + type=str, + required=True, + help="Input JSONL file with predictions" + ) + parser.add_argument( + "--output", "-o", + type=str, + default=None, + help="Output JSON file for metrics (optional)" + ) + args = parser.parse_args() + + print(f"Loading results from {args.input}...") + results = load_results(args.input) + print(f"Loaded {len(results)} predictions") + + # Identify tasks in results + tasks = set(r.get('task') for r in results if r.get('task')) + print(f"Tasks found: {tasks}") + + all_metrics = {} + + # Evaluate each task + for task in sorted(tasks): + if task in ['difficulty', 'discrimination']: + metrics = evaluate_comparison_task(results, task) + print_comparison_results(metrics) + elif task in ['distractor_most', 'distractor_least']: + metrics = evaluate_distractor_task(results, task) + print_distractor_results(metrics) + else: + print(f"Unknown task: {task}") + continue + + all_metrics[task] = metrics + + # Summary + print(f"\n{'='*60}") + print("SUMMARY") + print(f"{'='*60}") + for task, metrics in all_metrics.items(): + if 'error' not in metrics: + print(f"{task:20}: {metrics['accuracy']:.1%} accuracy " + f"({metrics['lift_over_random']:+.1%} vs random)") + + # Save metrics if output specified + if args.output: + with open(args.output, 'w') as f: + json.dump(all_metrics, f, indent=2) + print(f"\nMetrics saved to {args.output}") + + +if __name__ == "__main__": + main() diff --git a/Results/pedagogical_grounding/gptoss120b_pedagogical.py b/Results/pedagogical_grounding/gptoss120b_pedagogical.py new file mode 100644 index 0000000000000000000000000000000000000000..f61984fe519860bf8ad691d6a48d4727c26250a7 --- /dev/null +++ b/Results/pedagogical_grounding/gptoss120b_pedagogical.py @@ -0,0 +1,57 @@ +""" +Pedagogical Grounding benchmark with GPT-OSS-120B model. + +Usage: + # Run difficulty comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python gptoss120b_pedagogical.py \ + --task difficulty \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 \ + --sampling-mode stratified \ + --cache-dir /data1/ + + # Run discrimination comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python gptoss120b_pedagogical.py \ + --task discrimination \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 + + # Run most common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python gptoss120b_pedagogical.py \ + --task distractor_most \ + --data-dir . \ + --num-gpus 4 + + # Run least common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python gptoss120b_pedagogical.py \ + --task distractor_least \ + --data-dir . \ + --num-gpus 4 + + # Run all tasks + CUDA_VISIBLE_DEVICES=0,1,2,3 python gptoss120b_pedagogical.py \ + --task all \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 500 +""" + +from pedagogical_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "openai/gpt-oss-120b", + "gen_configs": { + "temperature": 0.7, + "top_p": 0.95, + "top_k": 20, + "max_tokens": 1024, # Shorter responses expected for this task + "repetition_penalty": 1.0, + }, + "output_prefix": "gptoss120b", + "system_prompt_prefix": "Reasoning: medium\n\n", +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Results/pedagogical_grounding/irt_parameters.py b/Results/pedagogical_grounding/irt_parameters.py new file mode 100644 index 0000000000000000000000000000000000000000..12d7846627dd104c5a2992edd80f7c6bdb049b02 --- /dev/null +++ b/Results/pedagogical_grounding/irt_parameters.py @@ -0,0 +1,384 @@ +""" +IRT Parameter Estimation for Pedagogical Grounding + +Computes Item Response Theory parameters (1PL, 2PL) from student response data +using py-irt (Bayesian inference with Pyro, native sparse data support). +""" + +import argparse +import os +import json +import pandas as pd +import numpy as np +import matplotlib.pyplot as plt +import torch +import pyro + +from py_irt.models.one_param_logistic import OneParamLog +from py_irt.models.two_param_logistic import TwoParamLog + +# Configuration +DEFAULT_DATA_DIR = "foundationalktdataset" +STUDENT_FILE = "Interactions.csv" +PROBLEMS_FILE = "Problems.csv" + + +def parse_args(): + parser = argparse.ArgumentParser(description="Compute IRT parameters using py-irt") + parser.add_argument( + "--data-dir", "-d", + type=str, + default=DEFAULT_DATA_DIR, + help=f"Directory containing input CSV files (default: {DEFAULT_DATA_DIR})" + ) + parser.add_argument( + "--output-dir", "-o", + type=str, + default="pedagogical_grounding/output", + help="Directory to save output (default: pedagogical_grounding/output)" + ) + parser.add_argument( + "--min-responses", + type=int, + default=50, + help="Minimum responses per problem to include (default: 50)" + ) + parser.add_argument( + "--epochs", + type=int, + default=500, + help="Number of training epochs (default: 500)" + ) + parser.add_argument( + "--device", + type=str, + default="cpu", + choices=["cpu", "gpu"], + help="Device for training (default: cpu)" + ) + parser.add_argument( + "--no-plots", + action="store_true", + help="Skip generating plots" + ) + return parser.parse_args() + + +def load_data(data_dir): + """Load student and problem data.""" + print(f"Loading data from {data_dir}...") + + student_df = pd.read_csv(os.path.join(data_dir, STUDENT_FILE)) + problems_df = pd.read_csv(os.path.join(data_dir, PROBLEMS_FILE)) + + print(f" Loaded {len(student_df):,} student interactions") + print(f" Loaded {len(problems_df):,} problems") + + return student_df, problems_df + + +def prepare_sparse_data(student_df, min_responses=50): + """Prepare data in sparse format for py-irt (no imputation needed).""" + print("\nPreparing sparse data for IRT...") + + # Use discrete_score as binary response (0/1) + responses = student_df[['user_id', 'problem_id', 'discrete_score']].copy() + + # Remove NaN responses + responses = responses.dropna(subset=['discrete_score']) + + # Handle duplicate (student, problem) pairs - take first attempt + responses = responses.drop_duplicates(subset=['user_id', 'problem_id'], keep='first') + print(f" Unique (student, problem) pairs: {len(responses):,}") + + # Filter problems with enough responses + problem_counts = responses.groupby('problem_id').size() + valid_problems = problem_counts[problem_counts >= min_responses].index + responses = responses[responses['problem_id'].isin(valid_problems)] + print(f" Problems with >= {min_responses} responses: {len(valid_problems):,}") + + # Create mappings + unique_students = responses['user_id'].unique() + unique_problems = responses['problem_id'].unique() + + student_to_idx = {s: i for i, s in enumerate(unique_students)} + problem_to_idx = {p: i for i, p in enumerate(unique_problems)} + idx_to_problem = {i: p for p, i in problem_to_idx.items()} + + # Convert to indices + student_indices = responses['user_id'].map(student_to_idx).values + problem_indices = responses['problem_id'].map(problem_to_idx).values + response_values = responses['discrete_score'].values + + print(f" Students: {len(unique_students):,}") + print(f" Problems: {len(unique_problems):,}") + print(f" Observations: {len(responses):,}") + + return (student_indices, problem_indices, response_values, + len(unique_students), len(unique_problems), idx_to_problem) + + +def compute_simple_difficulty(student_df, min_responses=50): + """Compute simple difficulty as -logit(percent_correct) for all problems.""" + print("\nComputing simple difficulty estimates...") + + responses = student_df[['problem_id', 'discrete_score']].copy() + + # Compute percent correct per problem + problem_stats = responses.groupby('problem_id').agg( + n_responses=('discrete_score', 'count'), + percent_correct=('discrete_score', 'mean') + ).reset_index() + + # Filter by min responses + problem_stats = problem_stats[problem_stats['n_responses'] >= min_responses] + + # Compute IRT-scale difficulty: -logit(p) = log((1-p)/p) + # Clamp to avoid log(0) + p = problem_stats['percent_correct'].clip(0.001, 0.999) + problem_stats['difficulty_simple'] = np.log((1 - p) / p) + + print(f" Problems with simple difficulty: {len(problem_stats):,}") + + return problem_stats + + +def fit_irt_models(student_indices, problem_indices, response_values, + num_students, num_problems, epochs, device): + """Fit 1PL and 2PL IRT models using py-irt.""" + print(f"\nFitting IRT models ({epochs} epochs, device={device})...") + + # Convert to tensors + device_torch = torch.device('cuda' if device == 'gpu' else 'cpu') + models = torch.tensor(student_indices, dtype=torch.long, device=device_torch) + items = torch.tensor(problem_indices, dtype=torch.long, device=device_torch) + # Ensure responses are 0/1 integers, then convert to float for Bernoulli + response_int = np.round(response_values).astype(int).clip(0, 1) + obs = torch.tensor(response_int, dtype=torch.float, device=device_torch) + + results = {} + + # Fit 1PL + print(" Fitting 1PL (Rasch)...") + try: + pyro.clear_param_store() + model_1pl = OneParamLog( + priors='vague', + device=device, + num_items=num_problems, + num_models=num_students, + verbose=False + ) + model_1pl.fit(models, items, obs, num_epochs=epochs) + + # Extract parameters + difficulty_1pl = pyro.param('loc_diff').detach().cpu().numpy() + results['1PL'] = { + 'difficulty': difficulty_1pl.tolist() + } + print(f" Difficulty range: [{difficulty_1pl.min():.2f}, {difficulty_1pl.max():.2f}]") + except Exception as e: + print(f" 1PL failed: {e}") + results['1PL'] = None + + # Fit 2PL + print(" Fitting 2PL...") + try: + pyro.clear_param_store() + model_2pl = TwoParamLog( + priors='vague', + device=device, + num_items=num_problems, + num_models=num_students, + verbose=False + ) + model_2pl.fit(models, items, obs, num_epochs=epochs) + + # Extract parameters + difficulty_2pl = pyro.param('loc_diff').detach().cpu().numpy() + discrimination_2pl = pyro.param('loc_slope').detach().cpu().numpy() + + results['2PL'] = { + 'difficulty': difficulty_2pl.tolist(), + 'discrimination': discrimination_2pl.tolist() + } + print(f" Difficulty range: [{difficulty_2pl.min():.2f}, {difficulty_2pl.max():.2f}]") + print(f" Discrimination range: [{discrimination_2pl.min():.2f}, {discrimination_2pl.max():.2f}]") + except Exception as e: + print(f" 2PL failed: {e}") + results['2PL'] = None + + return results + + +def format_results(irt_results, idx_to_problem, simple_stats): + """Format results as per-problem dictionary.""" + formatted = [] + + # Get IRT problems + irt_problem_ids = set(idx_to_problem.values()) + + # Process IRT results + for idx, problem_id in idx_to_problem.items(): + item = {'problem_id': int(problem_id)} + + if irt_results['1PL']: + item['difficulty_1pl'] = float(irt_results['1PL']['difficulty'][idx]) + + if irt_results['2PL']: + item['difficulty_2pl'] = float(irt_results['2PL']['difficulty'][idx]) + item['discrimination_2pl'] = float(irt_results['2PL']['discrimination'][idx]) + + # Add simple difficulty + simple_row = simple_stats[simple_stats['problem_id'] == problem_id] + if len(simple_row) > 0: + item['difficulty_simple'] = float(simple_row['difficulty_simple'].iloc[0]) + item['percent_correct'] = float(simple_row['percent_correct'].iloc[0]) + item['n_responses'] = int(simple_row['n_responses'].iloc[0]) + + formatted.append(item) + + # Add problems not in IRT but in simple stats + for _, row in simple_stats.iterrows(): + if row['problem_id'] not in irt_problem_ids: + formatted.append({ + 'problem_id': int(row['problem_id']), + 'difficulty_simple': float(row['difficulty_simple']), + 'percent_correct': float(row['percent_correct']), + 'n_responses': int(row['n_responses']) + }) + + return formatted + + +def print_summary(irt_results, simple_stats): + """Print summary statistics.""" + print("\n--- Summary Statistics ---") + + print(f"\nSimple Difficulty (all {len(simple_stats)} problems):") + print(f" Mean: {simple_stats['difficulty_simple'].mean():.2f}") + print(f" Std: {simple_stats['difficulty_simple'].std():.2f}") + print(f" Range: [{simple_stats['difficulty_simple'].min():.2f}, {simple_stats['difficulty_simple'].max():.2f}]") + + if irt_results['2PL']: + difficulties = irt_results['2PL']['difficulty'] + discriminations = irt_results['2PL']['discrimination'] + + print(f"\n2PL Difficulty (b):") + print(f" Mean: {np.mean(difficulties):.2f}") + print(f" Std: {np.std(difficulties):.2f}") + print(f" Range: [{np.min(difficulties):.2f}, {np.max(difficulties):.2f}]") + + print(f"\n2PL Discrimination (a):") + print(f" Mean: {np.mean(discriminations):.2f}") + print(f" Std: {np.std(discriminations):.2f}") + print(f" Range: [{np.min(discriminations):.2f}, {np.max(discriminations):.2f}]") + + # Categorize difficulty + easy = sum(1 for d in difficulties if d < -1) + medium = sum(1 for d in difficulties if -1 <= d <= 1) + hard = sum(1 for d in difficulties if d > 1) + print(f"\nDifficulty Categories:") + print(f" Easy (b < -1): {easy} ({100*easy/len(difficulties):.1f}%)") + print(f" Medium (-1 <= b <= 1): {medium} ({100*medium/len(difficulties):.1f}%)") + print(f" Hard (b > 1): {hard} ({100*hard/len(difficulties):.1f}%)") + + +def save_results(formatted_results, output_dir): + """Save results to JSON.""" + os.makedirs(output_dir, exist_ok=True) + + output_path = os.path.join(output_dir, 'irt_parameters.json') + with open(output_path, 'w') as f: + json.dump(formatted_results, f, indent=2) + print(f"\nSaved: {output_path}") + print(f" Total problems: {len(formatted_results)}") + + +def plot_results(irt_results, simple_stats, output_dir): + """Generate plots.""" + os.makedirs(output_dir, exist_ok=True) + + fig, axes = plt.subplots(2, 2, figsize=(12, 10)) + + # Plot 1: Simple difficulty distribution (all problems) + axes[0, 0].hist(simple_stats['difficulty_simple'], bins=30, edgecolor='black', alpha=0.7, color='steelblue') + axes[0, 0].set_xlabel('Difficulty (logit scale)') + axes[0, 0].set_ylabel('Number of Problems') + axes[0, 0].set_title(f'Simple Difficulty Distribution (n={len(simple_stats)})') + axes[0, 0].axvline(0, color='red', linestyle='--', alpha=0.5) + + if irt_results['2PL']: + difficulties = irt_results['2PL']['difficulty'] + discriminations = irt_results['2PL']['discrimination'] + + # Plot 2: 2PL Difficulty + axes[0, 1].hist(difficulties, bins=30, edgecolor='black', alpha=0.7, color='orange') + axes[0, 1].set_xlabel('Difficulty (b)') + axes[0, 1].set_ylabel('Number of Problems') + axes[0, 1].set_title(f'2PL Difficulty Distribution (n={len(difficulties)})') + axes[0, 1].axvline(0, color='red', linestyle='--', alpha=0.5) + + # Plot 3: 2PL Discrimination + axes[1, 0].hist(discriminations, bins=30, edgecolor='black', alpha=0.7, color='green') + axes[1, 0].set_xlabel('Discrimination (a)') + axes[1, 0].set_ylabel('Number of Problems') + axes[1, 0].set_title('2PL Discrimination Distribution') + axes[1, 0].axvline(1, color='red', linestyle='--', alpha=0.5) + + # Plot 4: Difficulty vs Discrimination scatter + axes[1, 1].scatter(difficulties, discriminations, alpha=0.5) + axes[1, 1].set_xlabel('Difficulty (b)') + axes[1, 1].set_ylabel('Discrimination (a)') + axes[1, 1].set_title('Difficulty vs Discrimination') + axes[1, 1].axhline(1, color='red', linestyle='--', alpha=0.3) + axes[1, 1].axvline(0, color='red', linestyle='--', alpha=0.3) + else: + for ax in [axes[0, 1], axes[1, 0], axes[1, 1]]: + ax.text(0.5, 0.5, '2PL not fitted', ha='center', va='center', transform=ax.transAxes) + + plt.tight_layout() + plot_path = os.path.join(output_dir, 'irt_parameters.png') + plt.savefig(plot_path, dpi=150) + plt.close() + + print(f"Saved: {plot_path}") + + +def main(): + args = parse_args() + + # Load data + student_df, problems_df = load_data(args.data_dir) + + # Compute simple difficulty for ALL problems + simple_stats = compute_simple_difficulty(student_df, args.min_responses) + + # Prepare sparse data for IRT (no imputation!) + (student_indices, problem_indices, response_values, + num_students, num_problems, idx_to_problem) = prepare_sparse_data( + student_df, args.min_responses + ) + + # Fit IRT models + irt_results = fit_irt_models( + student_indices, problem_indices, response_values, + num_students, num_problems, args.epochs, args.device + ) + + # Print summary + print_summary(irt_results, simple_stats) + + # Format and save results + formatted = format_results(irt_results, idx_to_problem, simple_stats) + save_results(formatted, args.output_dir) + + # Plot + if not args.no_plots: + plot_results(irt_results, simple_stats, args.output_dir) + + print("\nDone!") + + +if __name__ == "__main__": + main() diff --git a/Results/pedagogical_grounding/llama33_70b_instruct_pedagogical.py b/Results/pedagogical_grounding/llama33_70b_instruct_pedagogical.py new file mode 100644 index 0000000000000000000000000000000000000000..c16936bdbe1ccc9552d9898c23f08c7ee84b06c4 --- /dev/null +++ b/Results/pedagogical_grounding/llama33_70b_instruct_pedagogical.py @@ -0,0 +1,56 @@ +""" +Pedagogical Grounding benchmark with Llama-3.3-70B-Instruct model. + +Usage: + # Run difficulty comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/llama33_70b_instruct_pedagogical.py \ + --task difficulty \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 \ + --sampling-mode stratified \ + --cache-dir /data1/ + + # Run discrimination comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/llama33_70b_instruct_pedagogical.py \ + --task discrimination \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 + + # Run most common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/llama33_70b_instruct_pedagogical.py \ + --task distractor_most \ + --data-dir . \ + --num-gpus 4 + + # Run least common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/llama33_70b_instruct_pedagogical.py \ + --task distractor_least \ + --data-dir . \ + --num-gpus 4 + + # Run all tasks + CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/llama33_70b_instruct_pedagogical.py \ + --task all \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 500 +""" + +from pedagogical_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "meta-llama/Llama-3.3-70B-Instruct", + "gen_configs": { + "temperature": 0.7, + "top_p": 0.9, + "max_tokens": 1024, + "repetition_penalty": 1.0, + }, + "output_prefix": "llama33_70b_instruct", + "system_prompt_prefix": "", +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Results/pedagogical_grounding/output/distractor_analysis.png b/Results/pedagogical_grounding/output/distractor_analysis.png new file mode 100644 index 0000000000000000000000000000000000000000..b640df9dff0c64ac767e13599ff9463d55ce5846 Binary files /dev/null and b/Results/pedagogical_grounding/output/distractor_analysis.png differ diff --git a/Results/pedagogical_grounding/output/distractor_stats.json b/Results/pedagogical_grounding/output/distractor_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..99ad2ad7fdf9e919e81b1bf6ae93e9767204a7b0 --- /dev/null +++ b/Results/pedagogical_grounding/output/distractor_stats.json @@ -0,0 +1,4844 @@ +[ + { + "problem_id": 74236, + "n_choices": 4, + "total_responses": 256, + "correct_count": 140, + "correct_rate": 0.546875, + "distractors": { + "Han is correct": 29, + "Elena is correct": 53, + "Neither is correct": 34 + }, + "distractor_frequencies": { + "Han is correct": 0.11328125, + "Elena is correct": 0.20703125, + "Neither is correct": 0.1328125 + }, + "most_common_distractor": "Elena is correct", + "most_common_distractor_freq": 0.20703125, + "least_common_distractor": "Han is correct", + "least_common_distractor_freq": 0.11328125 + }, + { + "problem_id": 97579, + "n_choices": 4, + "total_responses": 309, + "correct_count": 222, + "correct_rate": 0.7184466019417476, + "distractors": { + "Agree with both": 52, + "Agree with Jada": 35, + "Disagree with both": 0 + }, + "distractor_frequencies": { + "Agree with both": 0.16828478964401294, + "Agree with Jada": 0.11326860841423948, + "Disagree with both": 0.0 + }, + "most_common_distractor": "Agree with both", + "most_common_distractor_freq": 0.16828478964401294, + "least_common_distractor": "Disagree with both", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 78469, + "n_choices": 4, + "total_responses": 237, + "correct_count": 104, + "correct_rate": 0.4388185654008439, + "distractors": { + "I agree with Jada": 58, + "I agree with both of them": 63, + "I agree with neither of them": 12 + }, + "distractor_frequencies": { + "I agree with Jada": 0.24472573839662448, + "I agree with both of them": 0.26582278481012656, + "I agree with neither of them": 0.05063291139240506 + }, + 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15,795 cm³

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": 31, + "

B

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C

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Reflect over line p, then reflect over line p again.

": 16, + "Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.": 2 + }, + "distractor_frequencies": { + "Translate 3 units up, then 3 units down.": 0.7534246575342466, + "

Reflect over line p, then reflect over line p again.

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7.57

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21

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75.7

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Multiply 12 by 3, then divide by 8.

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Multiply 3 by 8, then divide by 12.

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Multiply 12 by 18, then multiply by 3.

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Multiply 12 by 3, then divide by 8.

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Multiply 12 by 18, then multiply by 3.

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Multiply 12 by 3, then divide by 8.

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Multiply 12 by 18, then multiply by 3.

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$9.60

": 86, + "

$10.60

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$5.90

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18 mile per hour

": 0, + "

18 hours per mile

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8 hours per mile

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18 mile per hour

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18 hours per mile

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8 hours per mile

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18 hours per mile

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(-5, -2)

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(-5, -2)

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(-5, -2)

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A rectangle that is 3.25 inches wide and 6.1 inches long.

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A parallelogram with a base of 5.875 inches and a height of 3.5 inches.

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A triangle with a base of 7.18 inches and a height of 5.4 inches.

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A rectangle that is 3.25 inches wide and 6.1 inches long.

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A parallelogram with a base of 5.875 inches and a height of 3.5 inches.

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A triangle with a base of 7.18 inches and a height of 5.4 inches.

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A triangle with a base of 7.18 inches and a height of 5.4 inches.

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A rectangle that is 3.25 inches wide and 6.1 inches long.

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0.171 grams

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1.71 grams

": 64, + "

171 grams

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0.171 grams

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1.71 grams

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171 grams

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0.171 grams

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171 grams

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95 grams

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7 grams

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95 grams

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7 grams

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7 grams

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95 grams

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2

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1

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43

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2

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1

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2

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43

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8.8

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"most_common_distractor_freq": 0.26194690265486725, + "least_common_distractor": "Yes", + "least_common_distractor_freq": 0.26194690265486725 + }, + { + "problem_id": 178083, + "n_choices": 4, + "total_responses": 454, + "correct_count": 209, + "correct_rate": 0.460352422907489, + "distractors": { + "About 100 in\u00b2": 36, + "About 300 in\u00b2": 43, + "About 900 in\u00b2": 166 + }, + "distractor_frequencies": { + "About 100 in\u00b2": 0.07929515418502203, + "About 300 in\u00b2": 0.0947136563876652, + "About 900 in\u00b2": 0.3656387665198238 + }, + "most_common_distractor": "About 900 in\u00b2", + "most_common_distractor_freq": 0.3656387665198238, + "least_common_distractor": "About 100 in\u00b2", + "least_common_distractor_freq": 0.07929515418502203 + }, + { + "problem_id": 116435, + "n_choices": 3, + "total_responses": 19, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "4": 2 + }, + "distractor_frequencies": { + "4": 0.10526315789473684 + }, + "most_common_distractor": "4", + "most_common_distractor_freq": 0.10526315789473684, + "least_common_distractor": "4", + "least_common_distractor_freq": 0.10526315789473684 + }, + { + "problem_id": 636346, + "n_choices": 4, + "total_responses": 41, + "correct_count": 19, + "correct_rate": 0.4634146341463415, + "distractors": { + "33": 5, + "85": 11, + "107": 6 + }, + "distractor_frequencies": { + "33": 0.12195121951219512, + "85": 0.2682926829268293, + "107": 0.14634146341463414 + }, + "most_common_distractor": "85", + "most_common_distractor_freq": 0.2682926829268293, + "least_common_distractor": "33", + "least_common_distractor_freq": 0.12195121951219512 + }, + { + "problem_id": 375982, + "n_choices": 4, + "total_responses": 1138, + "correct_count": 736, + "correct_rate": 0.6467486818980668, + "distractors": { + "6 units": 132, + "4.8 units": 95, + "5 units": 175 + }, + "distractor_frequencies": { + "6 units": 0.11599297012302284, + "4.8 units": 0.08347978910369068, + "5 units": 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"Day 3": 0.0 + }, + "most_common_distractor": "Day 2", + "most_common_distractor_freq": 0.0, + "least_common_distractor": "Day 3", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 362327, + "n_choices": 4, + "total_responses": 339, + "correct_count": 265, + "correct_rate": 0.7817109144542773, + "distractors": { + "Jada": 36, + "Andre": 20, + "Neither": 18 + }, + "distractor_frequencies": { + "Jada": 0.10619469026548672, + "Andre": 0.058997050147492625, + "Neither": 0.05309734513274336 + }, + "most_common_distractor": "Jada", + "most_common_distractor_freq": 0.10619469026548672, + "least_common_distractor": "Neither", + "least_common_distractor_freq": 0.05309734513274336 + }, + { + "problem_id": 55545, + "n_choices": 4, + "total_responses": 221, + "correct_count": 89, + "correct_rate": 0.40271493212669685, + "distractors": { + "P\u2019s surface area is less than Q\u2019s surface area.": 30, + "P\u2019s surface area is equal to Q\u2019s surface area.": 88, + "There is not enough information given to compare their surface areas.": 14 + }, + "distractor_frequencies": { + "P\u2019s surface area is less than Q\u2019s surface area.": 0.13574660633484162, + "P\u2019s surface area is equal to Q\u2019s surface area.": 0.39819004524886875, + "There is not enough information given to compare their surface areas.": 0.06334841628959276 + }, + "most_common_distractor": "P\u2019s surface area is equal to Q\u2019s surface area.", + "most_common_distractor_freq": 0.39819004524886875, + "least_common_distractor": "There is not enough information given to compare their surface areas.", + "least_common_distractor_freq": 0.06334841628959276 + }, + { + "problem_id": 196678, + "n_choices": 4, + "total_responses": 28, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "True for all triangles": 28, + "True for some right triangles": 0, + "Never true": 0 + }, + "distractor_frequencies": { + "True for all triangles": 1.0, + "True for some right triangles": 0.0, + 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Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds each and wait 6 months for the plants to grow and count the fraction of groups that produce flowers.

": 50, + "

Roll a standard number cube 5 times. Each time a 6 appears, it represents a plant producing flowers. Repeat this process 30 times and count the fraction of times at least one number 6 appears.

": 40, + "

Create a spinner with 10 equal sections and mark one of them “flowers.” Spin the spinner 5 times to represent the 5 seeds. Repeat this process 30 times and count the fraction of times that at least 1 “flower” was spun.

": 0 + }, + "distractor_frequencies": { + "

Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds each and wait 6 months for the plants to grow and count the fraction of groups that produce flowers.

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Roll a standard number cube 5 times. Each time a 6 appears, it represents a plant producing flowers. Repeat this process 30 times and count the fraction of times at least one number 6 appears.

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Create a spinner with 10 equal sections and mark one of them “flowers.” Spin the spinner 5 times to represent the 5 seeds. Repeat this process 30 times and count the fraction of times that at least 1 “flower” was spun.

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Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds each and wait 6 months for the plants to grow and count the fraction of groups that produce flowers.

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Create a spinner with 10 equal sections and mark one of them “flowers.” Spin the spinner 5 times to represent the 5 seeds. Repeat this process 30 times and count the fraction of times that at least 1 “flower” was spun.

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b=29f

": 186, + "

b=52f

": 0, + "

b=92f

": 0 + }, + "distractor_frequencies": { + "

b=29f

": 1.0, + "

b=52f

": 0.0, + "

b=92f

": 0.0 + }, + "most_common_distractor": "

b=29f

", + "most_common_distractor_freq": 1.0, + "least_common_distractor": "

b=92f

", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 590738, + "n_choices": 4, + "total_responses": 51, + "correct_count": 49, + "correct_rate": 0.9607843137254902, + "distractors": { + "210.975 km": 1, + "21.0975 km": 0, + "0.8439 km": 1 + }, + "distractor_frequencies": { + "210.975 km": 0.0196078431372549, + "21.0975 km": 0.0, + "0.8439 km": 0.0196078431372549 + }, + "most_common_distractor": "210.975 km", + "most_common_distractor_freq": 0.0196078431372549, + "least_common_distractor": "21.0975 km", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 444018, + "n_choices": 4, + "total_responses": 23, + "correct_count": 11, + "correct_rate": 0.4782608695652174, + "distractors": { + "274,963": 2, + "244,905": 6, + "1,997": 4 + }, + "distractor_frequencies": { + "274,963": 0.08695652173913043, + "244,905": 0.2608695652173913, + "1,997": 0.17391304347826086 + }, + "most_common_distractor": "244,905", + "most_common_distractor_freq": 0.2608695652173913, + "least_common_distractor": "274,963", + "least_common_distractor_freq": 0.08695652173913043 + }, + { + "problem_id": 42091, + "n_choices": 5, + "total_responses": 33, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "impossible": 0, + "certain": 3 + }, + "distractor_frequencies": { + "impossible": 0.0, + "certain": 0.09090909090909091 + }, + "most_common_distractor": "certain", + "most_common_distractor_freq": 0.09090909090909091, + "least_common_distractor": "impossible", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 42491, + "n_choices": 5, + "total_responses": 33, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "impossible": 0, + "unlikely": 6, + "certain": 0 + }, + "distractor_frequencies": { + "impossible": 0.0, + "unlikely": 0.18181818181818182, + "certain": 0.0 + }, + "most_common_distractor": "unlikely", + "most_common_distractor_freq": 0.18181818181818182, + "least_common_distractor": "certain", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 97961, + "n_choices": 4, + "total_responses": 37, + "correct_count": 19, + "correct_rate": 0.5135135135135135, + "distractors": { + "107.1%": 3, + "93.3%": 7, + "7.1%": 8 + }, + "distractor_frequencies": { + "107.1%": 0.08108108108108109, + "93.3%": 0.1891891891891892, + "7.1%": 0.21621621621621623 + }, + "most_common_distractor": "7.1%", + "most_common_distractor_freq": 0.21621621621621623, + "least_common_distractor": "107.1%", + "least_common_distractor_freq": 0.08108108108108109 + }, + { + "problem_id": 347917, + "n_choices": 4, + "total_responses": 1129, + "correct_count": 626, + "correct_rate": 0.5544729849424269, + "distractors": { + "

I agree with Mai.

": 266, + "

I agree with both.

": 151, + "

I agree with neither.

": 86 + }, + "distractor_frequencies": { + "

I agree with Mai.

": 0.23560673162090345, + "

I agree with both.

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I agree with neither.

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I agree with Mai.

", + "most_common_distractor_freq": 0.23560673162090345, + "least_common_distractor": "

I agree with neither.

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A trapezoidal prism

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A rectangular pyramid

": 42, + "

A triangular prism

": 135 + }, + "distractor_frequencies": { + "

A trapezoidal prism

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A rectangular pyramid

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A triangular prism

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A triangular prism

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A trapezoidal prism

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125 square feet

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1,250 feet

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1,250 square feet

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125 square feet

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1,250 feet

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1,250 square feet

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125 square feet

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1,250 square feet

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41\u00b0

": 70, + "

123\u00b0

": 30, + "

164\u00b0

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41\u00b0

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123\u00b0

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164\u00b0

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164\u00b0

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123\u00b0

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60 hours

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6 hours

": 9, + "

223 hours

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60 hours

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6 hours

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223 hours

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6 hours

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223 hours

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4.5

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9.92

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4,500

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4.5

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412 batches

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338 batches

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16 of a batch

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412 batches

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338 batches

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16 of a batch

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412 batches

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16 of a batch

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23 times as far

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94 times as far

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2438 times as far

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23 times as far

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94 times as far

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2438 times as far

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23 times as far

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2438 times as far

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(-3,-2)

": 66, + "

(-3,2)

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(3,2)

": 98 + }, + "distractor_frequencies": { + "

(-3,-2)

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(-3,2)

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(3,2)

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(-3,2)

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(-3,-2)

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PQ = 3P'Q'

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P'Q' = 13PQ

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PQ = 3P'Q'

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P'Q' = 13PQ

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PQ = 3P'Q'

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P'Q' = 13PQ

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125 feet

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125 square feet

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1,250 feet

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125 feet

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125 square feet

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1,250 feet

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125 square feet

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125 feet

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20

": 550, + "

200

": 0, + "

20,000

": 0 + }, + "distractor_frequencies": { + "

20

": 1.0, + "

200

": 0.0, + "

20,000

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20

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20,000

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5,000

": 81, + "

50,000

": 66, + "

5,000,000

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5,000

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50,000

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5,000,000

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5,000

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5,000,000

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x \u00b7 x \u00b7 x = 1 \u00b7 1 \u00b7 1 \u00b7 1

": 14, + "

x = 34

": 0, + "

x + 1 = 4

": 4 + }, + "distractor_frequencies": { + "

x \u00b7 x \u00b7 x = 1 \u00b7 1 \u00b7 1 \u00b7 1

": 0.2413793103448276, + "

x = 34

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x + 1 = 4

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x \u00b7 x \u00b7 x = 1 \u00b7 1 \u00b7 1 \u00b7 1

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x = 34

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Negative

": 115, + "

Zero

": 9 + }, + "distractor_frequencies": { + "

Negative

": 0.31420765027322406, + "

Zero

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Negative

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Zero

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1 inch to 1 foot

": 150, + "

1  inch to 100 feet

": 0, + "

1  inch to 1 mile

": 0, + "

1  centimeter to 1 meter

": 0, + "

1  centimeter to 1 kilometer

": 0 + }, + "distractor_frequencies": { + "

1 inch to 1 foot

": 0.21067415730337077, + "

1  inch to 100 feet

": 0.0, + "

1  inch to 1 mile

": 0.0, + "

1  centimeter to 1 meter

": 0.0, + "

1  centimeter to 1 kilometer

": 0.0 + }, + "most_common_distractor": "

1 inch to 1 foot

", + "most_common_distractor_freq": 0.21067415730337077, + "least_common_distractor": "

1  centimeter to 1 kilometer

", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 275383, + "n_choices": 4, + "total_responses": 57, + "correct_count": 46, + "correct_rate": 0.8070175438596491, + "distractors": { + "Pair 1": 6, + "Pair 2": 3, + "Pair 4": 2 + }, + "distractor_frequencies": { + "Pair 1": 0.10526315789473684, + "Pair 2": 0.05263157894736842, + "Pair 4": 0.03508771929824561 + }, + "most_common_distractor": "Pair 1", + "most_common_distractor_freq": 0.10526315789473684, + "least_common_distractor": "Pair 4", + "least_common_distractor_freq": 0.03508771929824561 + }, + { + "problem_id": 2433, + "n_choices": 4, + "total_responses": 57, + "correct_count": 29, + "correct_rate": 0.5087719298245614, + "distractors": { + "24 teaspoons": 9, + "22 teaspoons": 15, + "12 teaspoons": 4 + }, + "distractor_frequencies": { + "24 teaspoons": 0.15789473684210525, + "22 teaspoons": 0.2631578947368421, + "12 teaspoons": 0.07017543859649122 + }, + "most_common_distractor": "22 teaspoons", + "most_common_distractor_freq": 0.2631578947368421, + "least_common_distractor": "12 teaspoons", + "least_common_distractor_freq": 0.07017543859649122 + }, + { + "problem_id": 7396, + "n_choices": 5, + "total_responses": 50, + "correct_count": 7, + "correct_rate": 0.14, + "distractors": { + "About 5,000 m\u00b2": 41, + "About 50,000 m\u00b2": 2, + "About 5,000,000 m\u00b2": 0, + "About 50,000,000 m\u00b2": 0 + }, + "distractor_frequencies": { + "About 5,000 m\u00b2": 0.82, + "About 50,000 m\u00b2": 0.04, + "About 5,000,000 m\u00b2": 0.0, + "About 50,000,000 m\u00b2": 0.0 + }, + "most_common_distractor": "About 5,000 m\u00b2", + "most_common_distractor_freq": 0.82, + "least_common_distractor": "About 50,000,000 m\u00b2", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 228072, + "n_choices": 3, + "total_responses": 968, + "correct_count": 853, + "correct_rate": 0.881198347107438, + "distractors": { + "Definitely True": 62, + "Possibly True": 53 + }, + 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the new figure is greater.": 73, + "The area of the original square is greater.": 72, + "We don't know because neither the side length nor the area of the original square is known.": 67 + }, + "distractor_frequencies": { + "The area of the new figure is greater.": 0.060380479735318446, + "The area of the original square is greater.": 0.05955334987593052, + "We don't know because neither the side length nor the area of the original square is known.": 0.055417700578990904 + }, + "most_common_distractor": "The area of the new figure is greater.", + "most_common_distractor_freq": 0.060380479735318446, + "least_common_distractor": "We don't know because neither the side length nor the area of the original square is known.", + "least_common_distractor_freq": 0.055417700578990904 + }, + { + "problem_id": 24916, + "n_choices": 4, + "total_responses": 699, + "correct_count": 578, + "correct_rate": 0.82689556509299, + "distractors": { + "40\u00b0, 50\u00b0, 60\u00b0": 47, + "60\u00b0, 70\u00b0, 80\u00b0": 34, + "70\u00b0, 80\u00b0, 90\u00b0": 40 + }, + "distractor_frequencies": { + "40\u00b0, 50\u00b0, 60\u00b0": 0.06723891273247497, + "60\u00b0, 70\u00b0, 80\u00b0": 0.04864091559370529, + "70\u00b0, 80\u00b0, 90\u00b0": 0.05722460658082976 + }, + "most_common_distractor": "40\u00b0, 50\u00b0, 60\u00b0", + "most_common_distractor_freq": 0.06723891273247497, + "least_common_distractor": "60\u00b0, 70\u00b0, 80\u00b0", + "least_common_distractor_freq": 0.04864091559370529 + }, + { + "problem_id": 42186, + "n_choices": 5, + "total_responses": 33, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "impossible": 1, + "unlikely": 3, + "certain": 0 + }, + "distractor_frequencies": { + "impossible": 0.030303030303030304, + "unlikely": 0.09090909090909091, + "certain": 0.0 + }, + "most_common_distractor": "unlikely", + "most_common_distractor_freq": 0.09090909090909091, + "least_common_distractor": "certain", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 518599, + "n_choices": 7, + "total_responses": 537, + "correct_count": 474, + "correct_rate": 0.88268156424581, + "distractors": { + "

7

": 13, + "

12

": 0, + "

-0.8

": 32, + "

0.8

": 0, + "

-110

": 0, + "

-2

": 18 + }, + "distractor_frequencies": { + "

7

": 0.024208566108007448, + "

12

": 0.0, + "

-0.8

": 0.0595903165735568, + "

0.8

": 0.0, + "

-110

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-2

": 0.0335195530726257 + }, + "most_common_distractor": "

-0.8

", + "most_common_distractor_freq": 0.0595903165735568, + "least_common_distractor": "

-110

", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 63205, + "n_choices": 4, + "total_responses": 733, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "Quadrant IV": 0 + }, + "distractor_frequencies": { + "Quadrant IV": 0.0 + }, + "most_common_distractor": "Quadrant IV", + "most_common_distractor_freq": 0.0, + "least_common_distractor": "Quadrant IV", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 112678, + "n_choices": 5, + "total_responses": 1038, + "correct_count": 688, + "correct_rate": 0.6628131021194605, + "distractors": { + "2": 67, + "3": 25, + "7": 239, + "n": 19 + }, + "distractor_frequencies": { + "2": 0.06454720616570328, + "3": 0.024084778420038536, + "7": 0.2302504816955684, + "n": 0.018304431599229287 + }, + "most_common_distractor": "7", + "most_common_distractor_freq": 0.2302504816955684, + "least_common_distractor": "n", + "least_common_distractor_freq": 0.018304431599229287 + }, + { + "problem_id": 30522, + "n_choices": 3, + "total_responses": 806, + "correct_count": 0, + "correct_rate": 0.0, + "distractors": { + "Yes": 146 + }, + "distractor_frequencies": { + "Yes": 0.18114143920595532 + }, + "most_common_distractor": "Yes", + "most_common_distractor_freq": 0.18114143920595532, + "least_common_distractor": "Yes", + "least_common_distractor_freq": 0.18114143920595532 + }, + { + "problem_id": 228382, + "n_choices": 3, + "total_responses": 970, + "correct_count": 691, + "correct_rate": 0.7123711340206186, + "distractors": { + "Definitely True": 118, + "Definitely Not True": 161 + }, + "distractor_frequencies": { + "Definitely True": 0.12164948453608247, + "Definitely Not True": 0.16597938144329896 + }, + "most_common_distractor": "Definitely Not True", + "most_common_distractor_freq": 0.16597938144329896, + "least_common_distractor": "Definitely True", + "least_common_distractor_freq": 0.12164948453608247 + }, + { + "problem_id": 503038, + "n_choices": 4, + "total_responses": 10, + "correct_count": 6, + "correct_rate": 0.6, + "distractors": { + "The length of 3 cubes lined up, in inches": 2, + "The cube\u2019s surface area in square inches": 2, + "The total volume of 3 cubes, in cubic inches": 0 + }, + "distractor_frequencies": { + "The length of 3 cubes lined up, in inches": 0.2, + "The cube\u2019s surface area in square inches": 0.2, + "The total volume of 3 cubes, in cubic inches": 0.0 + }, + "most_common_distractor": "The length of 3 cubes lined up, in inches", + "most_common_distractor_freq": 0.2, + "least_common_distractor": "The total volume of 3 cubes, in cubic inches", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 478570, + "n_choices": 4, + "total_responses": 96, + "correct_count": 69, + "correct_rate": 0.71875, + "distractors": { + "Agree with Clare": 12, + "Agree with Both": 5, + "Agree with Neither": 10 + }, + "distractor_frequencies": { + "Agree with Clare": 0.125, + "Agree with Both": 0.052083333333333336, + "Agree with Neither": 0.10416666666666667 + }, + "most_common_distractor": "Agree with Clare", + "most_common_distractor_freq": 0.125, + "least_common_distractor": "Agree with Both", + "least_common_distractor_freq": 0.052083333333333336 + }, + { + "problem_id": 90063, + "n_choices": 4, + "total_responses": 85, + "correct_count": 73, + "correct_rate": 0.8588235294117647, + "distractors": { + "

7

": 7, + "

5

": 5, + "

2012

": 0 + }, + "distractor_frequencies": { + "

7

": 0.08235294117647059, + "

5

": 0.058823529411764705, + "

2012

": 0.0 + }, + "most_common_distractor": "

7

", + "most_common_distractor_freq": 0.08235294117647059, + "least_common_distractor": "

2012

", + "least_common_distractor_freq": 0.0 + }, + { + "problem_id": 3852, + "n_choices": 4, + "total_responses": 159, + "correct_count": 120, + "correct_rate": 0.7547169811320755, + "distractors": { + "48 miles": 16, + "30 miles": 10, + "18 miles": 13 + }, + "distractor_frequencies": { + "48 miles": 0.10062893081761007, + "30 miles": 0.06289308176100629, + "18 miles": 0.08176100628930817 + }, + "most_common_distractor": "48 miles", + "most_common_distractor_freq": 0.10062893081761007, + "least_common_distractor": "30 miles", + "least_common_distractor_freq": 0.06289308176100629 + }, + { + "problem_id": 14654, + "n_choices": 3, + "total_responses": 27, + "correct_count": 19, + "correct_rate": 0.7037037037037037, + "distractors": { + "City A": 7, + "Neither": 1 + }, + "distractor_frequencies": { + "City A": 0.25925925925925924, + "Neither": 0.037037037037037035 + }, + "most_common_distractor": "City A", + "most_common_distractor_freq": 0.25925925925925924, + "least_common_distractor": "Neither", + "least_common_distractor_freq": 0.037037037037037035 + }, + { + "problem_id": 28051, + "n_choices": 3, + "total_responses": 1736, + "correct_count": 1287, + "correct_rate": 0.7413594470046083, + "distractors": { + "

Store X: 4 cans for $2.48

": 148, + "

Store Y: 5 cans for $3.00

": 301 + }, + "distractor_frequencies": { + "

Store X: 4 cans for $2.48

": 0.08525345622119816, + "

Store Y: 5 cans for $3.00

": 0.17338709677419356 + }, + "most_common_distractor": "

Store Y: 5 cans for $3.00

", + "most_common_distractor_freq": 0.17338709677419356, + "least_common_distractor": "

Store X: 4 cans for $2.48

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5 12 \u00d7 4 14

": 16, + "

4 \u00d7 3

": 0, + "

5 \u00d7 4

": 0 + }, + "distractor_frequencies": { + "

5 12 \u00d7 4 14

": 1.0, + "

4 \u00d7 3

": 0.0, + "

5 \u00d7 4

": 0.0 + }, + "most_common_distractor": "

5 12 \u00d7 4 14

", + "most_common_distractor_freq": 1.0, + "least_common_distractor": "

5 \u00d7 4

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-3

": 35, + "

12

": 0, + "

-0.8

": 23, + "

0.8

": 0, + "

-110

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-2

": 7 + }, + "distractor_frequencies": { + "

-3

": 0.06352087114337568, + "

12

": 0.0, + "

-0.8

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0.8

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-3

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-110

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medium

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large

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medium

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large

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medium

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large

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white, blue, white, white, red

": 7 + }, + "distractor_frequencies": { + "

white, blue, white, white, red

": 0.3888888888888889 + }, + "most_common_distractor": "

white, blue, white, white, red

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white, blue, white, white, red

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b=4, h=3.5

": 111, + "

b=6, h=2.25

": 159, + "

b=10, h=1.4

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b=4, h=3.5

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b=6, h=2.25

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b=10, h=1.4

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b=6, h=2.25

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b=10, h=1.4

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270

": 90, + "

338

": 0 + }, + "distractor_frequencies": { + "

270

": 0.1565217391304348, + "

338

": 0.0 + }, + "most_common_distractor": "

270

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338

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0.04x - 25

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0.04x - 25.04

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0.04x - 25

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0.04x - 25.04

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0.04x - 25

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0.04x - 25.04

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(-1,-4)

": 43, + "

(-1,4)

": 111, + "

(4,1)

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(-1,-4)

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(-1,4)

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(4,1)

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(4,1)

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(-1,-4)

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x - y

": 60, + "

x \u2022 y

": 31, + "

xy

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x - y

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x \u2022 y

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xy

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x - y

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xy

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-10 is irrational because it is not rational.

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- 10 is irrational because it is less than zero.

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-10 is irrational because it is not a whole number.

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-10 is irrational because it is not rational.

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- 10 is irrational because it is less than zero.

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-10 is irrational because it is not a whole number.

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-10 is irrational because it is not rational.

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-10 is irrational because it is not a whole number.

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012
26
33
40
\n

 

": 0, + "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
06
212
315
418
\n

 

": 0, + "

 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
00
24
39
416
\n

 

": 0 + }, + "distractor_frequencies": { + "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
012
26
33
40
\n

 

": 0.0, + "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
06
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315
418
\n

 

": 0.0, + "

 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
00
24
39
416
\n

 

": 0.0 + }, + "most_common_distractor": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
012
26
33
40
\n

 

", + "most_common_distractor_freq": 0.0, + "least_common_distractor": "

 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
00
24
39
416
\n

 

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18

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18

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diff --git a/Results/pedagogical_grounding/pedagogical_inference_base.py b/Results/pedagogical_grounding/pedagogical_inference_base.py new file mode 100644 index 0000000000000000000000000000000000000000..5668b371b50fc29120a5ce8511392f845e183f6f --- /dev/null +++ b/Results/pedagogical_grounding/pedagogical_inference_base.py @@ -0,0 +1,1137 @@ +""" +Base module for Pedagogical Grounding LLM Benchmark. + +This module benchmarks LLMs on 4 pedagogical reasoning tasks: +1. Difficulty comparison: Which of two questions has higher IRT difficulty? +2. Discrimination comparison: Which of two questions has higher discrimination? +3. Most common distractor: Which wrong answer is most commonly chosen? +4. Least common distractor: Which wrong answer is least commonly chosen? + +================================================================================ +INPUT FILES (relative to --data-dir): +================================================================================ +- pedagogical_grounding/output/irt_parameters.json + Source: Pre-computed IRT parameters (~2,548 problems) + Used by: difficulty, discrimination tasks + Fields: problem_id, difficulty_2pl, discrimination_2pl, percent_correct + +- pedagogical_grounding/output/distractor_stats.json + Source: Pre-computed distractor analysis (~236 MC problems) + Used by: distractor_most, distractor_least tasks + Fields: problem_id, most_common_distractor, least_common_distractor, distractors + +- foundationalktdataset/Problems.csv + Source: Problem text and answer options + Used by: All tasks (merged by problem_id to get question text) + +================================================================================ +OUTPUT FORMAT (JSONL): +================================================================================ +Each line is a JSON object with: +- prediction_id: Unique identifier (e.g., "difficulty_405080_448452") +- task: Task name ("difficulty", "discrimination", "distractor_most", "distractor_least") +- ground_truth: Correct answer from IRT/distractor data +- predicted_answer: LLM's prediction +- is_correct: Boolean indicating if prediction matches ground truth +- full_response: Raw LLM output text + +Output filename pattern: {model_prefix}_pedagogical_{task}_n{samples}_{mode}_mindiff_dot{X}.jsonl +Example: gptoss120b_pedagogical_difficulty_n1000_stratified_mindiff_dot2.jsonl + +================================================================================ +EVALUATION: +================================================================================ +Run separately after inference: + + python evaluate_pedagogical.py --input + python evaluate_pedagogical.py --input --output metrics.json + +Metrics computed: +- Overall accuracy vs random baseline (50% for comparison, ~33% for distractors) +- Accuracy by stratum (small/medium/large difference) for comparison tasks +- Accuracy by number of distractors for distractor tasks + +================================================================================ +SAMPLING MODES (--sampling-mode): +================================================================================ +For comparison tasks (difficulty, discrimination): + +- "random": Randomly pair any two questions + May include trivial pairs with nearly identical values + +- "stratified" (default): Ensure meaningful differences between pairs + Samples equally from 3 strata: + - Small: 0.2 - 0.5 difference (hard comparisons) + - Medium: 0.5 - 1.0 difference (moderate comparisons) + - Large: > 1.0 difference (easy comparisons) + +================================================================================ +CLI ARGUMENTS: +================================================================================ +Required: + --task, -t Task to run (see below) + +Sampling: + --sampling-mode, -s Pair sampling: "random" or "stratified" (default: stratified) + --num-samples, -n Number of pairs/problems to sample (default: 1000) + --min-difference Min difference for stratified sampling (default: 0.2) + --seed Random seed for reproducibility (default: 42) + +Output: + --output, -o Output JSONL file path (overrides auto-generated name) + --output-dir Output directory for results (default: current directory) + --data-dir, -d Base directory containing data files (default: .) + +vLLM Configuration: + --batch-size, -b Batch size for inference (default: 500) + --num-gpus GPUs for tensor parallelism (default: 1) + --cache-dir, -c Directory for model cache (vLLM download_dir) + --max-num-seqs Max sequences per batch + --max-model-len Max sequence length in tokens + --gpu-memory-utilization Fraction of GPU memory (default: 0.9) + --reasoning-level For models that support it: none/low/medium/high + +================================================================================ +TASK SELECTION (--task, REQUIRED): +================================================================================ +- "difficulty": Compare IRT difficulty between question pairs +- "discrimination": Compare IRT discrimination between question pairs +- "distractor_most": Predict most commonly chosen wrong answer +- "distractor_least": Predict least commonly chosen wrong answer +- "all": Run all 4 tasks sequentially + +================================================================================ +USAGE EXAMPLES: +================================================================================ +# Run from project root directory: + +# Run difficulty comparison with stratified sampling (1000 pairs) +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \\ + --task difficulty \\ + --num-samples 1000 \\ + --sampling-mode stratified \\ + --num-gpus 4 + +# Run all tasks with 500 samples each +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \\ + --task all \\ + --num-samples 500 \\ + --num-gpus 4 + +# Run distractor task (uses all 236 available MC problems) +CUDA_VISIBLE_DEVICES=0,1,2,3 python pedagogical_grounding/gptoss120b_pedagogical.py \\ + --task distractor_most \\ + --num-gpus 4 + +================================================================================ +CREATING MODEL CONFIGS: +================================================================================ + from pedagogical_inference_base import run_inference + + MODEL_CONFIG = { + "model_id": "model/name", + "gen_configs": { + "temperature": 0.3, + "max_tokens": 1024, + }, + "output_prefix": "prefix", + "system_prompt_prefix": "", # e.g., "Reasoning: medium\\n\\n" for GPT-OSS + } + + if __name__ == "__main__": + run_inference(MODEL_CONFIG) +""" + +import argparse +import contextlib +import os +import sys +import json +import re +import gc +from typing import List, Dict, Optional, Tuple, Set + +import numpy as np +import pandas as pd +import torch +from tqdm import tqdm +from vllm import LLM, SamplingParams +from vllm.distributed.parallel_state import ( + destroy_model_parallel, + destroy_distributed_environment, +) + +# Add parent directory to path for clean_utils import +sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) +from clean_utils import clean_problem_body + + +class NumpyEncoder(json.JSONEncoder): + """Custom JSON encoder that handles numpy types.""" + def default(self, obj): + if isinstance(obj, np.integer): + return int(obj) + if isinstance(obj, np.floating): + return float(obj) + if isinstance(obj, np.ndarray): + return obj.tolist() + return super().default(obj) + + +# Default configuration +DEFAULT_NUM_SAMPLES = 1000 +DEFAULT_BATCH_SIZE = 500 +DEFAULT_MIN_DIFFERENCE = 0.2 + +# Input file paths (relative to data_dir) +IRT_PARAMS_FILE = "pedagogical_grounding/output/irt_parameters.json" +DISTRACTOR_STATS_FILE = "pedagogical_grounding/output/distractor_stats.json" +PROBLEMS_FILE = "foundationalktdataset/Problems.csv" + +# Task types +TASK_DIFFICULTY = "difficulty" +TASK_DISCRIMINATION = "discrimination" +TASK_DISTRACTOR_MOST = "distractor_most" +TASK_DISTRACTOR_LEAST = "distractor_least" +TASK_ALL = "all" + +COMPARISON_TASKS = [TASK_DIFFICULTY, TASK_DISCRIMINATION] +DISTRACTOR_TASKS = [TASK_DISTRACTOR_MOST, TASK_DISTRACTOR_LEAST] + +# System prompts +SYSTEM_PROMPT_DIFFICULTY = """You are an expert educator evaluating mathematics problems for instructional design. + +Your task is to compare two problems and determine which one is MORE DIFFICULT. + +A problem is MORE DIFFICULT if: +- It requires more prerequisite knowledge or skills +- It involves more complex reasoning steps +- It has higher cognitive load +- Students are more likely to make errors +- It requires synthesizing multiple concepts + +Instructions: +1. Carefully read both Problem A and Problem B +2. Consider factors like conceptual complexity, prerequisite knowledge, cognitive load, and potential for errors +3. Make your judgment based solely on the problem content +4. Respond with exactly "A" or "B" + +Output Format: +Respond with a single JSON object: +{"answer": "A"} or {"answer": "B"} +""" + +SYSTEM_PROMPT_DISCRIMINATION = """You are an expert educator evaluating mathematics problems for instructional design. + +Your task is to compare two problems and determine which one has HIGHER DISCRIMINATION. + +A problem has HIGHER DISCRIMINATION if: +- It better distinguishes between students who understand the material vs. those who don't +- Correct answers strongly indicate mastery +- Incorrect answers are unlikely for knowledgeable students +- The problem tests specific, well-defined skills rather than general guessing +- It avoids ambiguity that could confuse strong students + +Instructions: +1. Carefully read both Problem A and Problem B +2. Consider how well each problem separates students by ability level +3. Make your judgment based solely on the problem content +4. Respond with exactly "A" or "B" + +Output Format: +Respond with a single JSON object: +{"answer": "A"} or {"answer": "B"} +""" + +SYSTEM_PROMPT_DISTRACTOR_MOST = """You are an expert educator analyzing student misconceptions in mathematics. + +Your task is to predict which incorrect answer option (distractor) is MOST COMMONLY CHOSEN by students. + +The MOST COMMON distractor is the wrong answer that students choose most frequently. +Common reasons include: +- It represents a predictable computational error +- It matches a common misconception +- It seems plausible but contains a subtle flaw +- It results from a partial understanding of the concept +- It's what you get if you make a typical arithmetic mistake + +Instructions: +1. Read the problem carefully +2. Identify the correct answer +3. Consider common student misconceptions and errors for this type of problem +4. Analyze each incorrect answer option +5. Predict which distractor students would most often choose +6. Respond with the letter of that distractor (A, B, C, etc.) + +Output Format: +Respond with a single JSON object: +{"answer": "X"} where X is the letter of the most common distractor +""" + +SYSTEM_PROMPT_DISTRACTOR_LEAST = """You are an expert educator analyzing student misconceptions in mathematics. + +Your task is to predict which incorrect answer option (distractor) is LEAST COMMONLY CHOSEN by students. + +The LEAST COMMON distractor is the wrong answer that students rarely choose. +Common reasons include: +- It is obviously incorrect to most students +- It doesn't correspond to any common error pattern +- It requires a very unusual misconception +- It is far from the correct answer conceptually +- It looks implausible compared to other options + +Instructions: +1. Read the problem carefully +2. Identify the correct answer +3. Consider which wrong answer would seem most obviously incorrect +4. Analyze each incorrect answer option +5. Predict which distractor students would rarely choose +6. Respond with the letter of that distractor (A, B, C, etc.) + +Output Format: +Respond with a single JSON object: +{"answer": "X"} where X is the letter of the least common distractor +""" + + +def parse_args(default_output_jsonl: str) -> argparse.Namespace: + """Parse command line arguments.""" + parser = argparse.ArgumentParser( + description="Pedagogical Grounding LLM Benchmark" + ) + + # Task selection + parser.add_argument( + "--task", "-t", + type=str, + required=True, + choices=[TASK_DIFFICULTY, TASK_DISCRIMINATION, + TASK_DISTRACTOR_MOST, TASK_DISTRACTOR_LEAST, TASK_ALL], + help="Task to run: difficulty, discrimination, distractor_most, distractor_least, or all" + ) + + # Sampling configuration + parser.add_argument( + "--sampling-mode", "-s", + type=str, + default="stratified", + choices=["random", "stratified"], + help="Pair sampling mode: random or stratified (default: stratified)" + ) + parser.add_argument( + "--num-samples", "-n", + type=int, + default=DEFAULT_NUM_SAMPLES, + help=f"Number of pairs/problems to sample (default: {DEFAULT_NUM_SAMPLES})" + ) + parser.add_argument( + "--min-difference", + type=float, + default=DEFAULT_MIN_DIFFERENCE, + help=f"Minimum difference for stratified sampling (default: {DEFAULT_MIN_DIFFERENCE})" + ) + + # Output + parser.add_argument( + "--output", "-o", + type=str, + default=None, + help="Output JSONL file path (overrides auto-generated name)" + ) + parser.add_argument( + "--output-dir", + type=str, + default=".", + help="Output directory for results (default: current directory)" + ) + parser.add_argument( + "--data-dir", "-d", + type=str, + default=".", + help="Base directory containing data files (default: current directory)" + ) + + # vLLM configuration + parser.add_argument( + "--batch-size", "-b", + type=int, + default=DEFAULT_BATCH_SIZE, + help=f"Batch size for LLM inference (default: {DEFAULT_BATCH_SIZE})" + ) + parser.add_argument( + "--cache-dir", "-c", + type=str, + default=None, + help="Directory for vLLM model cache" + ) + parser.add_argument( + "--num-gpus", + type=int, + default=1, + help="Number of GPUs for tensor parallelism (default: 1)" + ) + parser.add_argument( + "--max-num-seqs", + type=int, + default=None, + help="Maximum number of sequences to process in a batch" + ) + parser.add_argument( + "--max-model-len", + type=int, + default=None, + help="Maximum sequence length in tokens" + ) + parser.add_argument( + "--gpu-memory-utilization", + type=float, + default=0.9, + help="Fraction of GPU memory to use (default: 0.9)" + ) + parser.add_argument( + "--reasoning-level", + type=str, + choices=["none", "low", "medium", "high"], + default=None, + help="Reasoning level for models that support it" + ) + + # Reproducibility + parser.add_argument( + "--seed", + type=int, + default=42, + help="Random seed for reproducibility (default: 42)" + ) + + return parser.parse_args() + + +def load_irt_parameters(data_dir: str) -> pd.DataFrame: + """Load IRT parameters and merge with problem text.""" + irt_path = os.path.join(data_dir, IRT_PARAMS_FILE) + problems_path = os.path.join(data_dir, PROBLEMS_FILE) + + print(f"Loading IRT parameters from {irt_path}...") + with open(irt_path, 'r') as f: + irt_data = json.load(f) + + print(f"Loading problem text from {problems_path}...") + problems_df = pd.read_csv(problems_path) + problems_df['cleaned_body'] = problems_df['Problem Body'].apply(clean_problem_body) + + # Merge on problem_id + irt_df = pd.DataFrame(irt_data) + merged = irt_df.merge( + problems_df[['problem_id', 'cleaned_body', 'Multiple Choice Options', 'Problem Type']], + on='problem_id', + how='inner' + ) + + # Filter to problems with valid 2PL parameters + merged = merged.dropna(subset=['difficulty_2pl', 'discrimination_2pl']) + + print(f"Loaded {len(merged)} problems with IRT parameters") + return merged + + +def load_distractor_stats(data_dir: str) -> pd.DataFrame: + """Load distractor stats and merge with problem text.""" + distractor_path = os.path.join(data_dir, DISTRACTOR_STATS_FILE) + problems_path = os.path.join(data_dir, PROBLEMS_FILE) + + print(f"Loading distractor stats from {distractor_path}...") + with open(distractor_path, 'r') as f: + distractor_data = json.load(f) + + print(f"Loading problem text from {problems_path}...") + problems_df = pd.read_csv(problems_path) + problems_df['cleaned_body'] = problems_df['Problem Body'].apply(clean_problem_body) + + # Convert to DataFrame and merge + distractor_df = pd.DataFrame(distractor_data) + merged = distractor_df.merge( + problems_df[['problem_id', 'cleaned_body', 'Multiple Choice Options', + 'Multiple Choice Answers']], + on='problem_id', + how='inner' + ) + + print(f"Loaded {len(merged)} problems with distractor stats") + return merged + + +def sample_pairs_random( + df: pd.DataFrame, + param_col: str, + num_samples: int, + seed: int = 42 +) -> List[Dict]: + """Random sampling of problem pairs.""" + np.random.seed(seed) + + problem_ids = df['problem_id'].values + n = len(problem_ids) + + pairs = [] + sampled = set() + max_attempts = num_samples * 10 + attempts = 0 + + while len(pairs) < num_samples and attempts < max_attempts: + attempts += 1 + i, j = np.random.choice(n, size=2, replace=False) + + # Ensure we don't duplicate pairs + pair_key = tuple(sorted([problem_ids[i], problem_ids[j]])) + if pair_key in sampled: + continue + sampled.add(pair_key) + + row_a = df.iloc[i] + row_b = df.iloc[j] + + # Skip if values are too close (tie) + val_a = row_a[param_col] + val_b = row_b[param_col] + if abs(val_a - val_b) < 0.01: + continue + + # Determine ground truth + ground_truth = "A" if val_a > val_b else "B" + + pairs.append({ + 'problem_id_a': int(row_a['problem_id']), + 'problem_id_b': int(row_b['problem_id']), + 'text_a': row_a['cleaned_body'], + 'text_b': row_b['cleaned_body'], + 'value_a': float(val_a), + 'value_b': float(val_b), + 'difference': float(abs(val_a - val_b)), + 'ground_truth': ground_truth, + 'stratum': 'random' + }) + + print(f"Sampled {len(pairs)} random pairs") + return pairs + + +def sample_pairs_stratified( + df: pd.DataFrame, + param_col: str, + num_samples: int, + min_difference: float = 0.2, + seed: int = 42 +) -> List[Dict]: + """Stratified sampling to ensure meaningful differences.""" + np.random.seed(seed) + + values = df[param_col].values + problem_ids = df['problem_id'].values + n = len(problem_ids) + + # Define strata + strata = [ + ('small', min_difference, 0.5), + ('medium', 0.5, 1.0), + ('large', 1.0, float('inf')) + ] + + samples_per_stratum = num_samples // len(strata) + + pairs = [] + sampled = set() + + for stratum_name, low, high in strata: + stratum_pairs = [] + attempts = 0 + max_attempts = samples_per_stratum * 100 + + while len(stratum_pairs) < samples_per_stratum and attempts < max_attempts: + attempts += 1 + i = np.random.randint(0, n) + j = np.random.randint(0, n) + + if i == j: + continue + + diff = abs(values[i] - values[j]) + if not (low <= diff < high): + continue + + pair_key = tuple(sorted([problem_ids[i], problem_ids[j]])) + if pair_key in sampled: + continue + sampled.add(pair_key) + + row_a = df.iloc[i] + row_b = df.iloc[j] + ground_truth = "A" if row_a[param_col] > row_b[param_col] else "B" + + stratum_pairs.append({ + 'problem_id_a': int(row_a['problem_id']), + 'problem_id_b': int(row_b['problem_id']), + 'text_a': row_a['cleaned_body'], + 'text_b': row_b['cleaned_body'], + 'value_a': float(row_a[param_col]), + 'value_b': float(row_b[param_col]), + 'difference': float(diff), + 'ground_truth': ground_truth, + 'stratum': stratum_name + }) + + pairs.extend(stratum_pairs) + print(f" Stratum '{stratum_name}' ({low:.1f}-{high:.1f}): {len(stratum_pairs)} pairs") + + print(f"Total stratified pairs: {len(pairs)}") + return pairs + + +def sample_distractor_problems( + df: pd.DataFrame, + num_samples: Optional[int] = None, + seed: int = 42 +) -> List[Dict]: + """Sample distractor problems (or use all if num_samples > available).""" + np.random.seed(seed) + + if num_samples is None or num_samples >= len(df): + sampled = df + print(f"Using all {len(df)} distractor problems") + else: + sampled = df.sample(n=num_samples, random_state=seed) + print(f"Sampled {num_samples} distractor problems from {len(df)}") + + return sampled.to_dict('records') + + +def format_answer_options(answer_string: str) -> Tuple[str, Dict[str, str]]: + """Format pipe-delimited answers for display. + + Returns: + formatted_text: String like "A) Option1\nB) Option2..." + letter_map: Dict mapping letters to option text + """ + if pd.isna(answer_string) or answer_string == '': + return "", {} + + options = [opt.strip() for opt in answer_string.split('||')] + letters = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'] + + letter_map = {} + lines = [] + for i, opt in enumerate(options): + if i < len(letters): + letter_map[letters[i]] = opt + lines.append(f"{letters[i]}) {opt}") + + return '\n'.join(lines), letter_map + + +def get_correct_letter(correct_answer: str, letter_map: Dict[str, str]) -> Optional[str]: + """Find the letter corresponding to the correct answer.""" + if pd.isna(correct_answer): + return None + + correct_answer = correct_answer.strip() + for letter, text in letter_map.items(): + if text.strip() == correct_answer: + return letter + return None + + +def get_distractor_letter(distractor_text: str, letter_map: Dict[str, str]) -> Optional[str]: + """Find the letter corresponding to a distractor.""" + if pd.isna(distractor_text): + return None + + distractor_text = distractor_text.strip() + for letter, text in letter_map.items(): + if text.strip() == distractor_text: + return letter + return None + + +def create_comparison_prompt(text_a: str, text_b: str, task_type: str) -> str: + """Create user prompt for difficulty/discrimination comparison.""" + if task_type == TASK_DIFFICULTY: + comparison_type = "more difficult" + else: + comparison_type = "more discriminating (better at distinguishing student ability levels)" + + return f"""Compare the following two problems and determine which is {comparison_type}. + +**Problem A:** +{text_a} + +**Problem B:** +{text_b} + +Which problem is {comparison_type}? Respond with {{"answer": "A"}} or {{"answer": "B"}}.""" + + +def create_distractor_prompt( + problem_text: str, + options_formatted: str, + correct_letter: str, + task_type: str +) -> str: + """Create user prompt for distractor prediction.""" + if task_type == TASK_DISTRACTOR_MOST: + distractor_type = "MOST COMMONLY" + behavior = "most often" + else: + distractor_type = "LEAST COMMONLY" + behavior = "least often" + + return f"""Analyze this multiple-choice problem and predict which distractor (wrong answer) is {distractor_type} chosen by students. + +**Problem:** +{problem_text} + +**Answer Options:** +{options_formatted} + +**Correct Answer:** {correct_letter} + +Which incorrect answer option do students choose {behavior}? Respond with {{"answer": "X"}} where X is the letter of the distractor.""" + + +def extract_json_prediction(response_text: str) -> Optional[Dict]: + """Extract the JSON prediction from the model's response.""" + json_matches = re.findall(r'\{[^{}]*\}', response_text) + + if json_matches: + # Take the last JSON object + json_str = json_matches[-1] + try: + return json.loads(json_str) + except json.JSONDecodeError: + pass + return None + + +def extract_answer(response_text: str) -> Optional[str]: + """Extract answer (A/B or letter) from response.""" + prediction = extract_json_prediction(response_text) + if prediction and 'answer' in prediction: + return str(prediction['answer']).strip().upper() + + # Fallback: look for standalone A or B + match = re.search(r'\b([A-H])\b', response_text) + if match: + return match.group(1) + + return None + + +def load_completed_predictions(output_jsonl: str) -> Set[str]: + """Load already-completed prediction IDs from JSONL file.""" + completed = set() + if os.path.exists(output_jsonl): + with open(output_jsonl, 'r') as f: + for line in f: + if line.strip(): + result = json.loads(line) + completed.add(result['prediction_id']) + print(f"Loaded {len(completed)} completed predictions from {output_jsonl}") + return completed + + +def append_results_jsonl(results: List[Dict], output_jsonl: str) -> None: + """Append batch results to JSONL file.""" + with open(output_jsonl, 'a') as f: + for result in results: + f.write(json.dumps(result, cls=NumpyEncoder) + '\n') + + +def prepare_comparison_batch( + samples: List[Dict], + task_type: str, + system_prompt: str, + completed_ids: Set[str] +) -> Tuple[List[str], List[Dict]]: + """Prepare prompts and metadata for comparison task.""" + prompts = [] + metadata = [] + + for i, sample in enumerate(samples): + pred_id = f"{task_type}_{sample['problem_id_a']}_{sample['problem_id_b']}" + + if pred_id in completed_ids: + continue + + user_prompt = create_comparison_prompt( + sample['text_a'], + sample['text_b'], + task_type + ) + full_prompt = system_prompt + "\n\n" + user_prompt + + prompts.append(full_prompt) + metadata.append({ + 'prediction_id': pred_id, + 'task': task_type, + 'problem_id_a': sample['problem_id_a'], + 'problem_id_b': sample['problem_id_b'], + 'value_a': sample['value_a'], + 'value_b': sample['value_b'], + 'difference': sample['difference'], + 'ground_truth': sample['ground_truth'], + 'stratum': sample.get('stratum', 'unknown'), + 'prompt': full_prompt + }) + + return prompts, metadata + + +def prepare_distractor_batch( + samples: List[Dict], + task_type: str, + system_prompt: str, + completed_ids: Set[str] +) -> Tuple[List[str], List[Dict]]: + """Prepare prompts and metadata for distractor task.""" + prompts = [] + metadata = [] + + for sample in samples: + pred_id = f"{task_type}_{sample['problem_id']}" + + if pred_id in completed_ids: + continue + + # Format answer options + options_formatted, letter_map = format_answer_options( + sample['Multiple Choice Options'] + ) + + if not options_formatted: + continue + + # Get correct answer letter + correct_letter = get_correct_letter( + sample.get('Multiple Choice Answers', ''), + letter_map + ) + + if not correct_letter: + # Try to infer from distractor data + distractors = sample.get('distractors', {}) + all_letters = set(letter_map.keys()) + distractor_letters = set() + for d_text in distractors.keys(): + d_letter = get_distractor_letter(d_text, letter_map) + if d_letter: + distractor_letters.add(d_letter) + correct_letters = all_letters - distractor_letters + if len(correct_letters) == 1: + correct_letter = list(correct_letters)[0] + else: + continue # Skip if we can't determine correct answer + + # Get ground truth distractor letter + if task_type == TASK_DISTRACTOR_MOST: + ground_truth_text = sample.get('most_common_distractor', '') + ground_truth_freq = sample.get('most_common_distractor_freq', 0) + else: + ground_truth_text = sample.get('least_common_distractor', '') + ground_truth_freq = sample.get('least_common_distractor_freq', 0) + + ground_truth_letter = get_distractor_letter(ground_truth_text, letter_map) + if not ground_truth_letter: + continue # Skip if we can't map ground truth + + user_prompt = create_distractor_prompt( + sample['cleaned_body'], + options_formatted, + correct_letter, + task_type + ) + full_prompt = system_prompt + "\n\n" + user_prompt + + prompts.append(full_prompt) + metadata.append({ + 'prediction_id': pred_id, + 'task': task_type, + 'problem_id': sample['problem_id'], + 'n_choices': sample.get('n_choices', len(letter_map)), + 'correct_letter': correct_letter, + 'ground_truth_letter': ground_truth_letter, + 'ground_truth_text': ground_truth_text, + 'ground_truth_freq': ground_truth_freq, + 'distractors': sample.get('distractors', {}), + 'letter_map': letter_map, + 'prompt': full_prompt + }) + + return prompts, metadata + + +def process_comparison_results( + metadata: List[Dict], + responses: List[str] +) -> List[Dict]: + """Process comparison task results.""" + results = [] + + for meta, response in zip(metadata, responses): + predicted = extract_answer(response) + is_correct = predicted == meta['ground_truth'] if predicted else False + + results.append({ + 'prediction_id': meta['prediction_id'], + 'task': meta['task'], + 'problem_id_a': meta['problem_id_a'], + 'problem_id_b': meta['problem_id_b'], + 'value_a': meta['value_a'], + 'value_b': meta['value_b'], + 'difference': meta['difference'], + 'stratum': meta['stratum'], + 'ground_truth': meta['ground_truth'], + 'predicted_answer': predicted, + 'is_correct': is_correct, + 'full_response': response + }) + + return results + + +def process_distractor_results( + metadata: List[Dict], + responses: List[str] +) -> List[Dict]: + """Process distractor task results.""" + results = [] + + for meta, response in zip(metadata, responses): + predicted = extract_answer(response) + is_correct = predicted == meta['ground_truth_letter'] if predicted else False + + results.append({ + 'prediction_id': meta['prediction_id'], + 'task': meta['task'], + 'problem_id': meta['problem_id'], + 'n_choices': meta['n_choices'], + 'correct_letter': meta['correct_letter'], + 'ground_truth_letter': meta['ground_truth_letter'], + 'ground_truth_text': meta['ground_truth_text'], + 'ground_truth_freq': meta['ground_truth_freq'], + 'predicted_answer': predicted, + 'is_correct': is_correct, + 'full_response': response + }) + + return results + + +def get_system_prompt(task_type: str, prefix: str = "") -> str: + """Get the system prompt for a task type.""" + prompts = { + TASK_DIFFICULTY: SYSTEM_PROMPT_DIFFICULTY, + TASK_DISCRIMINATION: SYSTEM_PROMPT_DISCRIMINATION, + TASK_DISTRACTOR_MOST: SYSTEM_PROMPT_DISTRACTOR_MOST, + TASK_DISTRACTOR_LEAST: SYSTEM_PROMPT_DISTRACTOR_LEAST, + } + return prefix + prompts[task_type] + + +def run_inference(config: Dict) -> None: + """Main inference function that runs pedagogical grounding benchmark. + + Args: + config: Dict with keys: + - model_id: HuggingFace model ID + - gen_configs: Dict of generation parameters + - output_prefix: Prefix for output filename + - system_prompt_prefix: Optional prefix for system prompt + """ + model_id = config["model_id"] + gen_configs = config["gen_configs"] + output_prefix = config["output_prefix"] + + # Parse arguments + default_output_jsonl = f"{output_prefix}_pedagogical.jsonl" + args = parse_args(default_output_jsonl) + + # Determine system prompt prefix + if args.reasoning_level is not None: + if args.reasoning_level == "none": + system_prompt_prefix = "" + else: + system_prompt_prefix = f"Reasoning: {args.reasoning_level}\n\n" + else: + system_prompt_prefix = config.get("system_prompt_prefix", "") + + # Determine tasks to run + if args.task == TASK_ALL: + tasks = COMPARISON_TASKS + DISTRACTOR_TASKS + else: + tasks = [args.task] + + # Generate output filename + task_str = args.task + # Format min_difference as "dot1" for 0.1, "dot2" for 0.2, etc. + mindiff_str = f"_mindiff_dot{str(args.min_difference).replace('0.', '')}" + params_suffix = f"_{task_str}_n{args.num_samples}_{args.sampling_mode}{mindiff_str}" + + if args.output: + # Use explicit output path + output_jsonl = args.output + else: + # Auto-generate filename in output directory + filename = f"{output_prefix}_pedagogical{params_suffix}.jsonl" + output_jsonl = os.path.join(args.output_dir, filename) + + print(f"Model: {model_id}") + print(f"Tasks: {tasks}") + print(f"Sampling mode: {args.sampling_mode}") + print(f"Num samples: {args.num_samples}") + print(f"Output: {output_jsonl}") + print(f"Data directory: {args.data_dir}") + + # Load data + irt_df = None + distractor_df = None + + if any(t in COMPARISON_TASKS for t in tasks): + irt_df = load_irt_parameters(args.data_dir) + + if any(t in DISTRACTOR_TASKS for t in tasks): + distractor_df = load_distractor_stats(args.data_dir) + + # Load completed predictions for resume support + completed_ids = load_completed_predictions(output_jsonl) + + # Prepare all prompts and metadata + all_prompts = [] + all_metadata = [] + task_info = [] # Track which task each prompt belongs to + + for task_type in tasks: + print(f"\nPreparing {task_type} task...") + + if task_type in COMPARISON_TASKS: + param_col = 'difficulty_2pl' if task_type == TASK_DIFFICULTY else 'discrimination_2pl' + + if args.sampling_mode == 'stratified': + samples = sample_pairs_stratified( + irt_df, param_col, args.num_samples, + args.min_difference, args.seed + ) + else: + samples = sample_pairs_random( + irt_df, param_col, args.num_samples, args.seed + ) + + system_prompt = get_system_prompt(task_type, system_prompt_prefix) + prompts, metadata = prepare_comparison_batch( + samples, task_type, system_prompt, completed_ids + ) + + all_prompts.extend(prompts) + all_metadata.extend(metadata) + task_info.extend([task_type] * len(prompts)) + + else: # Distractor tasks + samples = sample_distractor_problems( + distractor_df, args.num_samples, args.seed + ) + + system_prompt = get_system_prompt(task_type, system_prompt_prefix) + prompts, metadata = prepare_distractor_batch( + samples, task_type, system_prompt, completed_ids + ) + + all_prompts.extend(prompts) + all_metadata.extend(metadata) + task_info.extend([task_type] * len(prompts)) + + print(f"\nTotal predictions to make: {len(all_prompts)}") + print(f"Already completed: {len(completed_ids)}") + + if not all_prompts: + print("All predictions already completed!") + return + + # Initialize vLLM engine + print("\nInitializing vLLM engine...") + sampling_params = SamplingParams(**gen_configs) + llm_kwargs = { + "model": model_id, + "tensor_parallel_size": args.num_gpus, + "trust_remote_code": True, + "gpu_memory_utilization": args.gpu_memory_utilization, + "enable_prefix_caching": True, + } + if args.max_num_seqs is not None: + llm_kwargs["max_num_seqs"] = args.max_num_seqs + if args.max_model_len is not None: + llm_kwargs["max_model_len"] = args.max_model_len + if args.cache_dir: + llm_kwargs["download_dir"] = args.cache_dir + + llm = LLM(**llm_kwargs) + + # Process in batches + batch_size = args.batch_size + num_batches = (len(all_prompts) + batch_size - 1) // batch_size + total_results = 0 + + for batch_idx in range(num_batches): + batch_start = batch_idx * batch_size + batch_end = min(batch_start + batch_size, len(all_prompts)) + + batch_prompts = all_prompts[batch_start:batch_end] + batch_metadata = all_metadata[batch_start:batch_end] + batch_tasks = task_info[batch_start:batch_end] + + print(f"\n{'='*80}") + print(f"Processing batch {batch_idx + 1}/{num_batches}") + print(f"Items: {batch_start} to {batch_end} ({len(batch_prompts)} prompts)") + print(f"{'='*80}") + + try: + outputs = llm.generate(batch_prompts, sampling_params) + response_texts = [o.outputs[0].text.strip() for o in outputs] + + # Process results based on task type + batch_results = [] + for meta, response, task_type in zip(batch_metadata, response_texts, batch_tasks): + if task_type in COMPARISON_TASKS: + result = process_comparison_results([meta], [response])[0] + else: + result = process_distractor_results([meta], [response])[0] + batch_results.append(result) + + # Save results + append_results_jsonl(batch_results, output_jsonl) + total_results += len(batch_results) + + # Print batch summary + correct = sum(1 for r in batch_results if r.get('is_correct', False)) + print(f"Batch accuracy: {correct}/{len(batch_results)} ({100*correct/len(batch_results):.1f}%)") + print(f"Total results so far: {total_results}") + + except Exception as e: + print(f"\nERROR processing batch {batch_idx + 1}: {str(e)}") + print(f"Progress saved in {output_jsonl} - restart to resume") + raise + + print(f"\n{'='*80}") + print("All batches processed successfully!") + print(f"{'='*80}") + print(f"Results saved to: {output_jsonl}") + print(f"Total predictions: {total_results}") + + # Cleanup + print("\nCleaning up...") + destroy_model_parallel() + destroy_distributed_environment() + del llm + with contextlib.suppress(AssertionError): + torch.distributed.destroy_process_group() + gc.collect() + torch.cuda.empty_cache() + + print("\nDone!") diff --git a/Results/pedagogical_grounding/qwen3next80b_instruct_pedagogical.py b/Results/pedagogical_grounding/qwen3next80b_instruct_pedagogical.py new file mode 100644 index 0000000000000000000000000000000000000000..9c7037723d3fe64aa5f0189c9a71e6db5dac3133 --- /dev/null +++ b/Results/pedagogical_grounding/qwen3next80b_instruct_pedagogical.py @@ -0,0 +1,61 @@ +""" +Pedagogical Grounding benchmark with Qwen3-Next-80B-A3B-Instruct model. + +This is the standard instruction-following model (no thinking blocks). +Recommended sampling: temperature=0.7, top_p=0.8, top_k=20, min_p=0 + +Usage: + # Run difficulty comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_pedagogical.py \ + --task difficulty \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 \ + --sampling-mode stratified \ + --cache-dir /data1/ + + # Run discrimination comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_pedagogical.py \ + --task discrimination \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 + + # Run most common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_pedagogical.py \ + --task distractor_most \ + --data-dir . \ + --num-gpus 4 + + # Run least common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_pedagogical.py \ + --task distractor_least \ + --data-dir . \ + --num-gpus 4 + + # Run all tasks + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_pedagogical.py \ + --task all \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 500 +""" + +from pedagogical_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "Qwen/Qwen3-Next-80B-A3B-Instruct", + "gen_configs": { + "temperature": 0.7, + "top_p": 0.8, + "top_k": 20, + "min_p": 0.0, + "max_tokens": 1024, # Shorter responses expected for this task + "repetition_penalty": 1.0, + }, + "output_prefix": "qwen3next80b", + "system_prompt_prefix": "", # No prefix - standard instruct model +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Results/pedagogical_grounding/qwen3next80b_thinking_pedagogical.py b/Results/pedagogical_grounding/qwen3next80b_thinking_pedagogical.py new file mode 100644 index 0000000000000000000000000000000000000000..7b7d0b817e62f06581d464fe510a9e381621981d --- /dev/null +++ b/Results/pedagogical_grounding/qwen3next80b_thinking_pedagogical.py @@ -0,0 +1,61 @@ +""" +Pedagogical Grounding benchmark with Qwen3-Next-80B-A3B-Thinking model. + +This model has native thinking mode - it automatically generates ... blocks. +Recommended sampling: temperature=0.6, top_p=0.95, top_k=20, min_p=0 + +Usage: + # Run difficulty comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_thinking_pedagogical.py \ + --task difficulty \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 \ + --sampling-mode stratified \ + --cache-dir /data1/ + + # Run discrimination comparison task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_thinking_pedagogical.py \ + --task discrimination \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 1000 + + # Run most common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_thinking_pedagogical.py \ + --task distractor_most \ + --data-dir . \ + --num-gpus 4 + + # Run least common distractor task + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_thinking_pedagogical.py \ + --task distractor_least \ + --data-dir . \ + --num-gpus 4 + + # Run all tasks + CUDA_VISIBLE_DEVICES=0,1,2,3 python qwen3next80b_thinking_pedagogical.py \ + --task all \ + --data-dir . \ + --num-gpus 4 \ + --num-samples 500 +""" + +from pedagogical_inference_base import run_inference + +MODEL_CONFIG = { + "model_id": "Qwen/Qwen3-Next-80B-A3B-Thinking", + "gen_configs": { + "temperature": 0.6, + "top_p": 0.95, + "top_k": 20, + "min_p": 0.0, + "max_tokens": 4096, # Longer for thinking blocks + response + "repetition_penalty": 1.0, + }, + "output_prefix": "qwen3next80bthinking", + "system_prompt_prefix": "", # No prefix - model has native thinking +} + +if __name__ == "__main__": + run_inference(MODEL_CONFIG) diff --git a/Results/similar_node_code_conflicts.csv b/Results/similar_node_code_conflicts.csv new file mode 100644 index 0000000000000000000000000000000000000000..d46d6ad1d5868f9f1848222381bc3cde5a448dbe --- /dev/null +++ b/Results/similar_node_code_conflicts.csv @@ -0,0 +1,33 @@ +conflict_type,compact_node_code,canonical_node_codes,raw_node_codes,skill_ids,node_names,problem_count,mapping_count,n_skill_ids +normalized_match,8FB4,8.F.B.4,8.F.B.4,"267,268,269,270,271,273,274,275,277",Use Functions to Model Relationships Between Quantities,57,58,9 +normalized_match,5NBTB7,5.NBT.B.7,5.NBT.B.7,"91,1131,1132,1133",Compute Decimal Problems Involving All 4 Operations,34,36,4 +normalized_match,6GA1,6.G.A.1,6.G.A.1,"170,171,172,173","Find the Area of Triangles, Quadrilaterals & Polygons",111,112,4 +normalized_match,6NSB3,6.NS.B.3,6.NS.B.3,"137,138,139,140","Add, Subtract, Multiply & Divide Multi-Digit Decimals",126,136,4 +normalized_match,6SPB5C,6.SP.B.5C,6.SP.B.5c,"188,189,190,191",Give & Describe Quantitative Measures of Center & Variability,62,69,4 +normalized_match,7GB6,7.G.B.6,7.G.B.6,"228,229,230,2281","Find Area, Volume & Surface Area of 2D/3D Objects",64,76,4 +normalized_match,6NSB4,6.NS.B.4,6.NS.B.4,"141,142,144",Find Common Factors & Multiples,29,30,3 +normalized_match,6RPA3C,6.RP.A.3C,6.RP.A.3c,"131,132,133",Solve Problems Involving Percents,147,152,3 +normalized_match,6SPB4,6.SP.B.4,6.SP.B.4,"181,183,2277","Display Numerical Data Using Dot Plots, Histograms & Box Plots",26,30,3 +normalized_match,7GB4,7.G.B.4,7.G.B.4,"222,223,224",Solve Problems Involving Area & Circumference of Circles,105,115,3 +normalized_match,7GB5,7.G.B.5,7.G.B.5,"225,227,2279",Use Facts About Angles to Write & Solve Equations,44,44,3 +normalized_match,7NSA1D,7.NS.A.1D,7.NS.A.1d,"203,204,205",Apply Properties of Operations to Add/Subtract Rational Numbers,41,41,3 +normalized_match,7NSA2C,7.NS.A.2C,7.NS.A.2c,"208,209,210",Apply Properties of Operations to Multiply/Divide Rational Numbers,47,51,3 +normalized_match,8EEA1,8.EE.A.1,8.EE.A.1,"249,250,251",Know & Apply Properties of Exponents,29,31,3 +normalized_match,8GA3,8.G.A.3,8.G.A.3,"284,286,2283",Describe the Effect of Transformations on 2D Figures,14,14,3 +normalized_match,8GA5,8.G.A.5,8.G.A.5,"288,289,2284",Use Informal Arguments to Establish Facts about Angles for Similar Triangles,10,10,3 +normalized_match,8GC9,8.G.C.9,8.G.C.9,"293,294,295",Know & Use Volume Formulas,92,102,3 +normalized_match,4GA1,4.G.A.1,4.G.A.1,"76,77",Draw & Identify Types of Lines and Angles,8,8,2 +normalized_match,4MDA3,4.MD.A.3,4.MD.A.3,"68,69",Apply Area & Perimeter Formulas for Rectangles,12,13,2 +normalized_match,5GB4,5.G.B.4,5.G.B.4,"124,125",Classify 2D Figures Based on Properties,3,3,2 +normalized_match,5NBTA2,5.NBT.A.2,5.NBT.A.2,"84,1129",Explain Patterns when Multiplying & Dividing Powers of 10,2,2,2 +normalized_match,5NFA1,5.NF.A.1,5.NF.A.1,"94,95",Add & Subtract Fractions with Unlike Denominators,3,3,2 +normalized_match,5NFB4A,5.NF.B.4A,5.NF.B.4a,"99,1134",Interpret & Compute Products of Fractions and Whole Numbers,10,10,2 +normalized_match,6EEA2C,6.EE.A.2C,6.EE.A.2c,"160,161",Evaluate Expression in Real-World Context,22,22,2 +normalized_match,6EEC9,6.EE.C.9,6.EE.C.9,"168,169",Write & Analyze Relationships Between Dependent & Independent Variables,18,20,2 +normalized_match,6GA4,6.G.A.4,6.G.A.4,"176,1135",Represent 3D Figures Using Nets to Find Surface Area,43,48,2 +normalized_match,7EEB3,7.EE.B.3,7.EE.B.3,"215,216",Solve Applied Problems Using Numerical and Algebraic Expressions and Equations,25,26,2 +normalized_match,7EEB4A,7.EE.B.4A,7.EE.B.4a,"217,1136",Solve 2-Step Equations,107,108,2 +normalized_match,7EEB4B,7.EE.B.4B,7.EE.B.4b,"218,1137","Solve, Graph & Interpret 2-Step Inequalities",28,28,2 +normalized_match,7SPC8B,7.SP.C.8B,7.SP.C.8b,"243,244",Represent Sample Spaces for Compound Events,21,22,2 +normalized_match,8NSA1,8.NS.A.1,8.NS.A.1,"246,1138",Understand & Approximate Rational & Irrational Numbers,9,9,2 +normalized_match,8NSA2,8.NS.A.2,8.NS.A.2,"247,248",Approximate Irrational Numbers,28,28,2 diff --git a/Results/time_gap_distribution.png b/Results/time_gap_distribution.png new file mode 100644 index 0000000000000000000000000000000000000000..c0a82c8bdbc3e053c8bf842427db78e12a121c50 --- /dev/null +++ b/Results/time_gap_distribution.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a6062e90f5a394191fee6ca17590d532b64d3d6210ebc5c3e386e5c5805a8106 +size 188461 diff --git a/Results/time_gap_distribution_counts.csv b/Results/time_gap_distribution_counts.csv new file mode 100644 index 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