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2025-03-17T19:52:06.686630 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.2%3A_Corresponding_Parts_and_Scale_Factors | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:1",
"title": "1.1.2: Corresponding Parts and Scale Factors",
"url": "https:... | libretexts | 1.1.2: Corresponding Parts and Scale Factors
Lesson
Let's describe features of scaled copies.
Exercise \(\PageIndex{1}\): Number Talk: Multiplying by a Unit Fraction
Find each product mentally.
\(\frac{1}{4}\cdot 32\)
\((7.2)\cdot\frac{1}{9}\)
\(\frac{1}{4}\cdot (5.6)\)
Exercise \(\PageIndex{2}\): Corresponding Parts
O... |
2025-03-17T19:52:06.853249 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.3%3A_Making_Scaled_Copies | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:2",
"title": "1.1.3: Making Scaled Copies",
"url": "https://math.libretexts... | libretexts | 1.1.3: Making Scaled Copies
Lesson
Let's draw scaled copies.
Exercise \(\PageIndex{1}\): More or Less?
For each problem, select the answer from the two choices.
-
The value of \(25\cdot (8.5)\) is:
- More than 205
- Less than 205
-
The value of \((9.93)\cdot (0.984)\) is:
- More than 10
- Less than 10
-
The value of \(... |
2025-03-17T19:52:06.931135 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.4%3A_Scaled_Relationships | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:3",
"title": "1.1.4: Scaled Relationships",
"url": "https://math.libretexts... | libretexts | 1.1.4: Scaled Relationships
Lesson
Let's find relationships between scaled copies.
Exercise \(\PageIndex{1}\): Three Quadrilaterals (Part 1)
Each of these polygons is a scaled copy of the others.
- Name two pairs of corresponding angles. What can you say about the sizes of these angles?
- Check your prediction by measu... |
2025-03-17T19:52:07.006025 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.5%3A_The_Size_of_the_Scale_Factor | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:4",
"title": "1.1.5: The Size of the Scale Factor",
"url": "https://math.li... | libretexts | 1.1.5: The Size of the Scale Factor
Lesson
Let's look at the effects of different scale factors.
On each card, Figure A is the original and Figure B is a scaled copy.
- Sort the cards based on their scale factors. Be prepared to explain your reasoning.
- Examine cards 10 and 13 more closely. What do you notice about t... |
2025-03-17T19:52:07.089832 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page/1.1.6%3A_Scaling_and_Area | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:5",
"title": "1.1.6: Scaling and Area",
"url": "https://math.libretexts.org... | libretexts | 1.1.6: Scaling and Area
Lesson
Let's build scaled shapes and investigate their areas.
Exercise \(\PageIndex{1}\): Scaling a Pattern Block
Use the applets to explore the pattern blocks. Work with your group to build the scaled copies described in each question.
-
How many blue rhombus blocks does it take to build a scal... |
2025-03-17T19:52:07.239507 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.1%3A_Scale_Drawings | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:6",
"title": "1.2.1: Scale Drawings",
"url": "https://math.libretexts.org/B... | libretexts | 1.2.1: Scale Drawings
Lesson
Let's explore scale drawings.
Exercise \(\PageIndex{1}\): What is a Scale Drawing?
Here are some drawings of a school bus, a quarter, and the subway lines around Boston, Massachusetts. The first three drawings are scale drawings of these objects.
The next three drawings are not scale drawin... |
2025-03-17T19:52:07.305243 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.2%3A_Scale_Drawings_and_Maps | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:7",
"title": "1.2.2: Scale Drawings and Maps",
"url": "https://math.librete... | libretexts | 1.2.2: Scale Drawings and Maps
Lesson
Let's use scale drawings to solve problems.
Exercise \(\PageIndex{1}\): A Train And a Car
Two cities are 243 miles apart.
- It takes a train 4 hours to travel between the two cities at a constant speed.
- A car travels between the two cities at a constant speed of 65 miles per hour... |
2025-03-17T19:52:07.377150 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.3%3A_Creating_Scale_Drawings | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:8",
"title": "1.2.3: Creating Scale Drawings",
"url": "https://math.librete... | libretexts | 1.2.3: Creating Scale Drawings
Lesson
Let's create our own scale drawings.
Exercise \(\PageIndex{1}\): Number Talk: Which is Greater?
Without calculating, decide which quotient is larger.
\(11\div 23\) or \(7\div 13\)
\(0.63\div 2\) or \(0.55\div 3\)
\(15\div\frac{1}{3}\) or \(15\div\frac{1}{4}\)
Exercise \(\PageIndex{... |
2025-03-17T19:52:07.447485 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.4%3A_Changing_Scales_in_Scale_Drawings | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:9",
"title": "1.2.4: Changing Scales in Scale Drawings",
"url": "https://ma... | libretexts | 1.2.4: Changing Scales in Scale Drawings
Lesson
Let's explore different scale drawings of the same actual thing.
Exercise \(\PageIndex{1}\): Appropriate Measurements
1. If a student uses a ruler like this to measure the length of their foot, which choices would be appropriate measurements? Select all that apply. Be pre... |
2025-03-17T19:52:07.521709 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.5%3A_Scales_without_Units | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:10",
"title": "1.2.5: Scales without Units",
"url": "https://math.libretext... | libretexts | 1.2.5: Scales without Units
Lesson
Let's explore a different way to express scales.
Exercise \(\PageIndex{1}\): One to One Hundred
A map of a park says its scale is 1 to 100.
- What do you think that means?
- Give an example of how this scale could tell us about measurements in the park.
Exercise \(\PageIndex{2}\): Apo... |
2025-03-17T19:52:07.603062 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page/1.2.6%3A_Units_in_Scale_Drawings | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:11",
"title": "1.2.6: Units in Scale Drawings",
"url": "https://math.libret... | libretexts | 1.2.6: Units in Scale Drawings
Lesson
Let's use different scales to describe the same drawing.
Exercise \(\PageIndex{1}\): Centimeters in a Mile
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? Explain your reasoning.
- \(\frac{2.54... |
2025-03-17T19:52:07.735280 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.03%3A_New_Page/1.3.1%3A_Draw_It_to_Scale | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:12",
"title": "1.3.1: Draw It to Scale",
"url": "https://math.libretexts.or... | libretexts | 1.3.1: Draw It to Scale
Lesson
Let's draw a floor plan.
Exercise \(\PageIndex{1}\): Which Measurements Matter?
Which measurements would you need in order to draw a scale floor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specific as possible.
Exercise \(\... |
2025-03-17T19:52:07.830525 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/101%3A_New_Page/111%3A_What_are_Scaled_Copies | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:13",
"title": "1.1.1: What are Scaled Copies?",
"url": "https://math.libret... | libretexts | 1.1.1: What are Scaled Copies?
Lesson
Let's explore scaled copies.
Exercise \(\PageIndex{1}\): Printing Portraits
Here is a portrait of a student. Move the slider under each image, A–E, to see it change.
- How is each one the same as or different from the original portrait of the student?
- Some of the sliders make sca... |
2025-03-17T19:52:07.918730 | 1,579 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:14",
"title": "2: Introducing Proportional Relationships",
"url": "https://... | libretexts | 2: Introducing Proportional Relationships Last updated Save as PDF Page ID 34983 Illustrative Mathematics OpenUp Resources 2.1: Representing Proportional Relationships with Tables 2.1.1: One of These Things is Not Like the Others 2.1.2: Introducing Proportional Relationships with Tables 2.1.3: More about Constant of Pr... |
2025-03-17T19:52:08.139659 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page/2.1.1%3A_One_of_These_Things_is_Not_Like_the_Others | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:15",
"title": "2.1.1: One of These Things is Not Like the Others",
"url": "... | libretexts | 2.1.1: One of These Things is Not Like the Others
Lesson
Let's remember what equivalent ratios are.
Exercise \(\PageIndex{1}\): Remembering Double Number Lines
1. Complete the double number line diagram with the missing numbers.
2. What could each of the number lines represent? Invent a situation and label the diagram.... |
2025-03-17T19:52:08.233119 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page/2.1.2%3A_Introducing_Proportional_Relationships_with_Tables | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:16",
"title": "2.1.2: Introducing Proportional Relationships with Tables",
... | libretexts | 2.1.2: Introducing Proportional Relationships with Tables
Lesson
Let's solve problems involving proportional relationships using tables.
Exercise \(\PageIndex{1}\): NOtice and Wonder: Paper Towels by The Case
Here is a table that shows how many rolls of paper towels a store receives when they order different numbers of... |
2025-03-17T19:52:08.328475 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page/2.1.3%3A_More_about_Constant_of_Proportionality | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:17",
"title": "2.1.3: More about Constant of Proportionality",
"url": "http... | libretexts | 2.1.3: More about Constant of Proportionality
Lesson
Let's solve more problems involving proportional relationships using tables.
Exercise \(\PageIndex{1}\): Equal Measures
Use the numbers and units from the list to find as many equivalent measurements as you can. For example, you might write “30 minutes is \(\frac{1}{... |
2025-03-17T19:52:08.499000 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page/2.2.1%3A_Proportional_Relationships_and_Equations | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:18",
"title": "2.2.1: Proportional Relationships and Equations",
"url": "ht... | libretexts | 2.2.1: Proportional Relationships and Equations
Lesson
Let's write equations describing proportional relationships.
Exercise \(\PageIndex{1}\): NUmber Talk: Division
Find each quotient mentally.
\(645\div 100\)
\(645\div 50\)
\(48.6\div 30\)
\(48.6\div x\)
Exercise \(\PageIndex{2}\): Feeding a Crowd, Revisited
1. A rec... |
2025-03-17T19:52:08.582223 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page/2.2.2%3A_Two_Equations_for_Each_Relationship | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:19",
"title": "2.2.2: Two Equations for Each Relationship",
"url": "https:/... | libretexts | 2.2.2: Two Equations for Each Relationship
Lesson
Let's investigate the equations that represent proportional relationships.
Exercise \(\PageIndex{1}\): Missing Figures
Here are the second and fourth figures in a pattern.
- What do you think the first and third figures in the pattern look like?
- Describe the 10th figu... |
2025-03-17T19:52:08.658891 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page/2.2.3%3A_Using_Equations_to_Solve_Problems | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:20",
"title": "2.2.3: Using Equations to Solve Problems",
"url": "https://m... | libretexts | 2.2.3: Using Equations to Solve Problems
Lesson
Let's use equations to solve problems involving proportional relationships.
Exercise \(\PageIndex{1}\): Number Talk: Quotients with Decimal Points
Without calculating, order the quotients of these expressions from least to greatest.
\(42.6\div 0.07\)
\(42.6\div 70\)
\(42.... |
2025-03-17T19:52:08.836316 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.03%3A_New_Page/2.3.1%3A_Comparing_Relationships_with_Tables | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:21",
"title": "2.3.1: Comparing Relationships with Tables",
"url": "https:/... | libretexts | 2.3.1: Comparing Relationships with Tables
Lesson
Let's explore how proportional relationships are different from other relationships.
Exercise \(\PageIndex{1}\): Adjusting a Recipe
A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.
Invent four new versions of this lemonade ... |
2025-03-17T19:52:08.925037 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.03%3A_New_Page/2.3.2%3A_Comparing_Relationships_with_Equations | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:22",
"title": "2.3.2: Comparing Relationships with Equations",
"url": "http... | libretexts | 2.3.2: Comparing Relationships with Equations
Lesson
Let's develop methods for deciding if a relationship is proportional.
Exercise \(\PageIndex{1}\): Notice and Wonder: Patterns with Rectangles
Do you see a pattern? What predictions can you make about future rectangles in the set if your pattern continues?
Exercise \(... |
2025-03-17T19:52:08.998613 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.03%3A_New_Page/2.3.3%3A_Solving_Problems_about_Proportional_Relationships | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:23",
"title": "2.3.3: Solving Problems about Proportional Relationships",
"... | libretexts | 2.3.3: Solving Problems about Proportional Relationships
Lesson
Let's solve problems about proportional relationships.
Exercise \(\PageIndex{1}\): What Do You Want to Know?
Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race?
What information would you need ... |
2025-03-17T19:52:09.153171 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.1%3A_Introducing_Graphs_of_Proportional_Relationships | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:24",
"title": "2.4.1: Introducing Graphs of Proportional Relationships",
"u... | libretexts | 2.4.1: Introducing Graphs of Proportional Relationships
Lesson
Let's see how graphs of proportional relationships differ from graphs of other relationships.
Exercise \(\PageIndex{1}\): Notice These Points
- Plot the points \((0,10), (1,8), (2,6), (3,4), (4,2)\).
- What do you notice about the graph?
Exercise \(\PageInd... |
2025-03-17T19:52:09.312624 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.2%3A_Interpreting_Graphs_of_Proportional_Relationships | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:25",
"title": "2.4.2: Interpreting Graphs of Proportional Relationships",
"... | libretexts | 2.4.2: Interpreting Graphs of Proportional Relationships
Lesson
Let's read stories from the graphs of proportional relationships.
Exercise \(\PageIndex{1}\): What Could the Graph Represent?
Here is a graph that represents a proportional relationship.
- Invent a situation that could be represented by this graph.
- Label... |
2025-03-17T19:52:09.389276 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.3%3A_Using_Graphs_to_Compare_Relationships | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:26",
"title": "2.4.3: Using Graphs to Compare Relationships",
"url": "https... | libretexts | 2.4.3: Using Graphs to Compare Relationships
Lesson
Let's graph more than one relationship on the same grid.
Exercise \(\PageIndex{1}\): Number Talk: Fraction Multiplication and Division
Find each product or quotient mentally.
\(\frac{2}{3}\cdot\frac{1}{2}\)
\(\frac{4}{3}\cdot\frac{1}{4}\)
\(4\div\frac{1}{5}\)
\(\frac{... |
2025-03-17T19:52:09.467455 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.04%3A_New_Page/2.4.4%3A_Two_Graphs_for_Each_Relationship | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:27",
"title": "2.4.4: Two Graphs for Each Relationship",
"url": "https://ma... | libretexts | 2.4.4: Two Graphs for Each Relationship
Lesson
Let's use tables, equations, and graphs to answer questions about proportional relationships.
Exercise \(\PageIndex{1}\): True or False: Fractions and Decimals
Decice whether each equation is true or false. Be prepared to explain your reasoning.
- \(\frac{3}{2}\cdot 16=3\c... |
2025-03-17T19:52:09.608321 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.5%3A_Let's_Put_it_to_Work/2.5.1%3A_Four_Representations | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:28",
"title": "2.5.1: Four Representations",
"url": "https://math.libretext... | libretexts | 2.5.1: Four Representations
Lesson
Let's contrast relationships that are and are not proportional in four different ways.
Exercise \(\PageIndex{1}\): Which is the Bluest?
1. Which group of blocks is the bluest?
2. Order the groups of blocks from least blue to bluest.
Exercise \(\PageIndex{2}\): One Scenario, Four Repre... |
2025-03-17T19:52:09.665504 | 1,585 | https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.5%3A_Let's_Put_it_to_Work/2.5.2%3A_Using_Water_Efficiently | {
"author": "Illustrative Mathematics",
"book_url": "https://commons.libretexts.org/book/math-34975",
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"provenance": "libretexts-0000.json.gz:29",
"title": "2.5.2: Using Water Efficiently",
"url": "https://math.libret... | libretexts | 2.5.2: Using Water Efficiently
Lesson
Let's investigate saving water.
Exercise \(\PageIndex{1}\): Comparing Baths and Showers
Some people say that it uses more water to take a bath than a shower. Others disagree.
- What information would you collect in order to answer the question?
- Estimate some reasonable values for... |
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