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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings | 1: Scale Drawings Last updated Save as PDF Page ID 34976 Illustrative Mathematics OpenUp Resources 1.1: Scaled Copies 1.1.2: Corresponding Parts and Scale Factors 1.1.3: Making Scaled Copies 1.1.4: Scaled Relationships 1.1.5: The Size of the Scale Factor 1.1.6: Scaling and Area 1.2: Scale Drawings 1.2.1: Scale Drawings... | libretexts | 2025-03-17T19:52:06.516389 | 2020-01-25T01:41:07 | {
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"book_url": "https://commons.libretexts.org/book/math-34975",
"title": "1: Scale Draw... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page | 1.1: Scaled Copies Last updated Save as PDF Page ID 34977 Illustrative Mathematics OpenUp Resources 1.1.2: Corresponding Parts and Scale Factors 1.1.3: Making Scaled Copies 1.1.4: Scaled Relationships 1.1.5: The Size of the Scale Factor 1.1.6: Scaling and Area | libretexts | 2025-03-17T19:52:06.602898 | 2020-01-25T01:41:08 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.01%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"title... |
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 | 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... | libretexts | 2025-03-17T19:52:06.686630 | 2020-03-29T00:12:19 | {
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"url": "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",
"book_url": "https://co... |
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 | 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 \(... | libretexts | 2025-03-17T19:52:06.853249 | 2020-03-29T00:11:44 | {
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"url": "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",
"book_url": "https://commons.libretexts.... |
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 | 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... | libretexts | 2025-03-17T19:52:06.931135 | 2020-03-29T00:11:05 | {
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"url": "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",
"book_url": "https://commons.libretexts.... |
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 | 1.1.5: The Size of the Scale Factor
Lesson
Let's look at the effects of different scale factors.
Exercise \(\PageIndex{1}\): Number Talk: Missing Factor
Solve each equation mentally.
\(16x=176\)
\(16x=8\)
\(16x=1\)
\(\frac{1}{5}x=1\)
\(\frac{2}{5}x=1\)
Exercise \(\PageIndex{2}\): Card Sort: Scaled Copies
Your teacher w... | libretexts | 2025-03-17T19:52:07.006025 | 2020-03-29T00:10:19 | {
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"url": "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",
"book_url": "https://commons.lib... |
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 | 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... | libretexts | 2025-03-17T19:52:07.089832 | 2020-03-29T00:09:25 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "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",
"book_url": "https://commons.libretexts.org/... |
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Text Col... | libretexts | 2025-03-17T19:52:07.165657 | 2020-01-25T01:41:09 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"title... |
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 | 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... | libretexts | 2025-03-17T19:52:07.239507 | 2020-03-29T00:16:39 | {
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"url": "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",
"book_url": "https://commons.libretexts.org/bo... |
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 | 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... | libretexts | 2025-03-17T19:52:07.305243 | 2020-03-29T00:16:15 | {
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"url": "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",
"book_url": "https://commons.libretex... |
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 | 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{... | libretexts | 2025-03-17T19:52:07.377150 | 2020-03-29T00:15:24 | {
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"url": "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",
"book_url": "https://commons.libretex... |
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 | 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... | libretexts | 2025-03-17T19:52:07.447485 | 2020-03-29T00:14:58 | {
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"url": "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",
"book_url": "https://common... |
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 | 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... | libretexts | 2025-03-17T19:52:07.521709 | 2020-03-29T00:14:27 | {
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"url": "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",
"book_url": "https://commons.libretexts.... |
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 | 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... | libretexts | 2025-03-17T19:52:07.603062 | 2020-03-29T00:13:56 | {
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"url": "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",
"book_url": "https://commons.libretex... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.03%3A_New_Page | 1.3: Let's Put It to Work Last updated Save as PDF Page ID 34979 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:07.675360 | 2020-01-25T01:41:10 | {
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"book_url": "https://commons.libretexts.org/book/math-34975",
"title... |
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 | 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 \(\... | libretexts | 2025-03-17T19:52:07.735280 | 2020-03-29T00:18:23 | {
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"url": "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",
"book_url": "https://commons.libretexts.org/... |
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 | 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... | libretexts | 2025-03-17T19:52:07.830525 | 2020-03-29T00:12:54 | {
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"url": "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",
"book_url": "https://commons.libretexts.o... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships | 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... | libretexts | 2025-03-17T19:52:07.918730 | 2020-01-25T01:41:13 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships",
"book_url": "https://commons.libretexts.org/book/math-34975",
... |
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: Representing Proportional Relationships with Tables Last updated Save as PDF Page ID 34984 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:08.065367 | 2020-01-25T01:41:14 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.01%3A_New_Page",
"book_url": "https://commons.libretexts.org/bo... |
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 | 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.... | libretexts | 2025-03-17T19:52:08.139659 | 2020-04-02T19:44:05 | {
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"url": "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_Other... |
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 | 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... | libretexts | 2025-03-17T19:52:08.233119 | 2020-04-02T19:42:56 | {
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"url": "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_wi... |
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 | 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}{... | libretexts | 2025-03-17T19:52:08.328475 | 2020-04-02T19:42:09 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "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",
... |
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: Representing Proportional Relationships with Equations Last updated Save as PDF Page ID 34985 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:08.399780 | 2020-01-25T01:41:15 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/02%3A_Introducing_Proportional_Relationships/2.02%3A_New_Page",
"book_url": "https://commons.libretexts.org/bo... |
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 | 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... | libretexts | 2025-03-17T19:52:08.499000 | 2020-04-02T19:46:03 | {
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"url": "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"... |
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 | 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... | libretexts | 2025-03-17T19:52:08.582223 | 2020-04-02T19:45:31 | {
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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 | 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.... | libretexts | 2025-03-17T19:52:08.658891 | 2020-04-02T19:44:47 | {
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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: Comparing Proportional and Nonproportional Relationships Last updated Save as PDF Page ID 34986 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:08.734755 | 2020-01-25T01:41:15 | {
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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 | 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 ... | libretexts | 2025-03-17T19:52:08.836316 | 2020-04-02T19:47:52 | {
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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 | 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 \(... | libretexts | 2025-03-17T19:52:08.925037 | 2020-04-02T19:47:21 | {
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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 | 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 ... | libretexts | 2025-03-17T19:52:08.998613 | 2020-04-02T19:46:49 | {
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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: Representing Proportional Relationships with Graphs Last updated Save as PDF Page ID 34987 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:09.071520 | 2020-01-25T01:41:16 | {
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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 | 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... | libretexts | 2025-03-17T19:52:09.153171 | 2020-04-02T19:50:21 | {
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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 | 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... | libretexts | 2025-03-17T19:52:09.312624 | 2020-04-02T19:49:44 | {
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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 | 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{... | libretexts | 2025-03-17T19:52:09.389276 | 2020-04-02T19:49:12 | {
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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 | 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... | libretexts | 2025-03-17T19:52:09.467455 | 2020-04-02T19:48:40 | {
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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: Let's Put it to Work Last updated Save as PDF Page ID 38102 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:09.538728 | 2020-04-02T19:39:09 | {
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"book_url": "https://commons.libret... |
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 | 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... | libretexts | 2025-03-17T19:52:09.608321 | 2020-04-02T19:51:36 | {
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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 | 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... | libretexts | 2025-03-17T19:52:09.665504 | 2020-04-02T19:51:06 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3 | 3: Measuring Circles Last updated Save as PDF Page ID 34990 Illustrative Mathematics OpenUp Resources 3.1: Circumference of a Circle 3.1.1: How Well Can You Measure? 3.1.2: Exploring Circles 3.1.3: Exploring Circumference 3.1.4: Applying Circumference 3.1.5: Circumference and Wheels 3.2: Area of a Circle 3.2.1: Estimat... | libretexts | 2025-03-17T19:52:09.748094 | 2020-01-25T01:41:19 | {
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"title": "3: Measur... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page | 3.1: Circumference of a Circle Last updated Save as PDF Page ID 34991 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:09.818128 | 2020-01-25T01:41:20 | {
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"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.1%3A_How_Well_Can_You_Measure | 3.1.1: How Well Can You Measure?
Lesson
Let's see how accurately we can measure.
Exercise \(\PageIndex{1}\): Estimating a Percentage
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?
- ... | libretexts | 2025-03-17T19:52:09.900282 | 2020-04-07T20:02:45 | {
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"book_url": "https://commons.lib... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.2%3A_Exploring_Circles | 3.1.2: Exploring Circles
Lesson
Let's explore circles.
Exercise \(\PageIndex{1}\): How Do You Figure?
Here are two figures.
Figure C looks more like Figure A than Figure B. Sketch what Figure C might look like. Explain your reasoning.
Exercise \(\PageIndex{2}\): Sorting Round Objects
Your teacher will give you some pic... | libretexts | 2025-03-17T19:52:09.973438 | 2020-04-07T20:02:15 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.3%3A_Exploring_Circumference | 3.1.3: Exploring Circumference
Lesson
Let's explore the circumference of circles.
Exercise \(\PageIndex{1}\): Which is Greater?
Clare wonders if the height of the toilet paper tube or the distance around the tube is greater. What information would she need in order to solve the problem? How could she find this out?
Exe... | libretexts | 2025-03-17T19:52:10.053935 | 2020-04-07T20:01:17 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.4%3A_Applying_Circumference | 3.1.4: Applying Circumference
Lesson
Let's use \(\pi\) to solve problems.
Exercise \(\PageIndex{1}\): What Do We Know? What Can we Estimate?
Here are some pictures of circular objects, with measurement tools shown. The measurement tool on each picture reads as follows:
- Wagon wheel: 3 feet
- Plane propeller: 24 inches... | libretexts | 2025-03-17T19:52:10.130939 | 2020-04-07T20:00:37 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.5%3A_Circumference_and_Wheels | 3.1.5: Circumference and Wheels
Lesson
Let's explore how far different wheels roll.
Exercise \(\PageIndex{1}\): A Rope and a Wheel
Han says that you can wrap a 5-foot rope around a wheel with a 2-foot diameter because \(\frac{5}{2}\) is less than pi. Do you agree with Han? Explain your reasoning.
Exercise \(\PageIndex{... | libretexts | 2025-03-17T19:52:10.211945 | 2020-04-07T20:00:10 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page | 3.2: Area of a Circle Last updated Save as PDF Page ID 34992 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:10.284851 | 2020-01-25T01:41:21 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.1%3A_Estimating_Areas | 3.2.1: Estimating Areas
Lesson
Let's estimate the areas of weird shapes.
Exercise \(\PageIndex{1}\): Mental Calculations
Find a strategy to make each calculatoin mentally:
\(599+87\)
\(254-88\)
\(99\cdot 75\)
Exercise \(\PageIndex{2}\): House Floorplan
Here is a floor plan of a house. Approximate lengths of the walls a... | libretexts | 2025-03-17T19:52:10.349638 | 2020-04-07T20:05:16 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.2%3A_Exploring_the_Area_of_a_Circle | 3.2.2: Exploring the Area of a Circle
Lesson
Let's investigate the areas of circles.
Exercise \(\PageIndex{1}\): Estimating Areas
Your teacher will show you some figures. Decide which figure has the largest area. Be prepared to explain your reasoning.
Exercise \(\PageIndex{2}\): Estimating Areas of Circles
Your teacher... | libretexts | 2025-03-17T19:52:10.417425 | 2020-04-07T20:04:47 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.3%3A_Relating_Area_to_Circumference | 3.2.3: Relating Area to Circumference
Lesson
Let's rearrange circles to calculate their areas.
Exercise \(\PageIndex{1}\): Irrigating a Field
A circular field is set into a square with an 800 m side length. Estimate the field's area.
- About \(5,000\text{m}^{2}\)
- About \(50,000\text{m}^{2}\)
- About \(500,000\text{m}... | libretexts | 2025-03-17T19:52:10.566712 | 2020-04-07T20:04:23 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.02%3A_New_Page/3.2.4%3A_Applying_Area_of_Circles | 3.2.4: Applying Area of Circles
Lesson
Lets's find the areas of shapes made up of circles.
Exercise \(\PageIndex{1}\): Still Irrigating the Field
The area of this field is about 500,000 m 2 . What is the field’s area to the nearest square meter? Assume that the side lengths of the square are exactly 800 m.
- \(502,400\... | libretexts | 2025-03-17T19:52:10.642792 | 2020-04-07T20:03:52 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.03%3A_New_Page | 3.3: Let's Put it to Work Last updated Save as PDF Page ID 34993 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:10.718297 | 2020-01-25T01:41:22 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.03%3A_New_Page/3.3.1%3A_Distinguishing_Circumference_and_Area | 3.3.1: Distinguishing Circumference and Area
Lesson
Let's contrast circumference and area.
Exercise \(\PageIndex{1}\): Filling the Plate
About how many cheese puffs can fit on the plate in a single layer? Be prepared to explain your reasoning.
Exercise \(\PageIndex{2}\): Cart Sort: Circle Problems
Your teacher will giv... | libretexts | 2025-03-17T19:52:10.793276 | 2020-04-07T20:06:39 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/03%3A_Untitled_Chapter_3/3.03%3A_New_Page/3.3.2%3A_Stained-Glass_Windows | 3.3.2: Stained-Glass Windows
Lesson
Let's use circumference and area to design stained-glass windows.
Exercise \(\PageIndex{1}\): Cost of a Stained-Glass Window
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 de... | libretexts | 2025-03-17T19:52:10.849509 | 2020-04-07T20:06:10 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4 | 4: Proportional Relationships and Percentages Last updated Save as PDF Page ID 34997 Illustrative Mathematics OpenUp Resources 4.1: Proportional Relationships with Fractions 4.1.1: Lots of Flags 4.1.2: Ratios and Rates With Fractions 4.1.3: Revisiting Proportional Relationships 4.1.4: Half as Much Again 4.1.5: Say It w... | libretexts | 2025-03-17T19:52:10.934776 | 2020-01-25T01:41:25 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page | 4.1: Proportional Relationships with Fractions Last updated Save as PDF Page ID 34998 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:11.005985 | 2020-01-25T01:41:26 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.1%3A_Lots_of_Flags | 4.1.1: Lots of Flags
Lesson
Let's explore the U.S. flag.
Exercise \(\PageIndex{1}\): Scaled or Not?
1. Which of the geometric objects are scaled versions of each other?
2. Pick two of the objects that are scaled copies and find the scale factor.
Exercise \(\PageIndex{2}\): Flags are Many Sizes
One standard size for the... | libretexts | 2025-03-17T19:52:11.076158 | 2020-04-11T21:39:38 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.2%3A_Ratios_and_Rates_With_Fractions | 4.1.2: Ratios and Rates With Fractions
Lesson
Let's calculate some rates with fractions.
Exercise \(\PageIndex{1}\): Number Talk: Division
Find each quotient mentally.
\(5\div\frac{1}{3}\)
\(2\div\frac{1}{3}\)
\(\frac{1}{2}\div\frac{1}{3}\)
\(2\frac{1}{2}\div\frac{1}{3}\)
Exercise \(\PageIndex{2}\): A Train is Travelin... | libretexts | 2025-03-17T19:52:11.149088 | 2020-04-11T21:39:09 | {
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"book_url": "https://comm... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.3%3A_Revisiting_Proportional_Relationships | 4.1.3: Revisiting Proportional Relationships
Lesson
Let's use constants of proportionality to solve more problems.
Exercise \(\PageIndex{1}\): Recipe Ratios
A recipe calls for \(\frac{1}{2}\) cup sugar and 1 cup flour. Complete the table to show how much sugar and flour to use in different numbers of batches of the rec... | libretexts | 2025-03-17T19:52:11.228957 | 2020-04-11T21:38:45 | {
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"book_url": "https:... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.4%3A_Half_as_Much_Again | 4.1.4: Half as Much Again
Lesson
Let's use fractions to describe increases and decreases.
Exercise \(\PageIndex{1}\): Notice and Wonder: TApe Diagrams
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): Walking Half as Much Again
-
Complete the table to show the total distance walked in each case.
- Jad... | libretexts | 2025-03-17T19:52:11.309369 | 2020-04-11T21:38:17 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.01%3A_New_Page/4.1.5%3A_Say_It_with_Decimals | 4.1.5: Say It with Decimals
Lesson
Let's use decimals to describe increases and decreases.
Exercise \(\PageIndex{1}\): Notice and Wonder: Fractions to Decimals
A calculator gives the following decimal representations for some unit fractions:
\(\begin{array}{lcl}{\frac{1}{2}=0.5}&{\qquad}&{\frac{1}{7}=0.142857143}\\{\fr... | libretexts | 2025-03-17T19:52:11.387021 | 2020-04-11T21:37:50 | {
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"book_url": "https://commons.librete... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page | 4.2: Percent Increase and Decrease Last updated Save as PDF Page ID 34999 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:11.458983 | 2020-01-25T01:41:27 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
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"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.1%3A_Increasing_and_Decreasing | 4.2.1: Increasing and Decreasing
Lesson
Let's use percentages to describe increases and decreases.
Exercise \(\PageIndex{1}\): Improving Their Game
Here are the scores from 3 different sports teams from their last 2 games.
| sports team | total points in game 1 | total points in game 2 |
|---|---|---|
| football team |... | libretexts | 2025-03-17T19:52:11.534989 | 2020-04-11T21:42:41 | {
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"book_url": "https://commons.li... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.2%3A_One_Hundred_Percent | 4.2.2: One Hundred Percent
Lesson
Let's solve more problems about percent increase and percent decrease.
Exercise \(\PageIndex{1}\): Notice and Wonder: Double Number Line
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): Double Number Lines
For each problem, complete the double number line diagram to ... | libretexts | 2025-03-17T19:52:11.611401 | 2020-04-11T21:42:16 | {
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"book_url": "https://commons.libretex... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.3%3A_Percent_Increase_and_Decrease_with_Equations | 4.2.3: Percent Increase and Decrease with Equations
Lesson
Let's use equations to represent increases and decreases.
Exercise \(\PageIndex{1}\): Number Talk: From 100 to 106
How do you get from one number to the next using multiplication or division?
From 100 to 106
From 100 to 90
From 90 to 100
From 106 to 100
Exercis... | libretexts | 2025-03-17T19:52:11.684648 | 2020-04-11T21:41:51 | {
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"book_url": ... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.02%3A_New_Page/4.2.4%3A_More_and_Less_than_1_Percent | 4.2.4: More and Less than 1 Percent
Lesson
Let's explore percentages smaller than 1%.
Exercise \(\PageIndex{1}\): Number Talk: What Percentage?
Determine the percentage mentally.
10 is what percentage of 50?
5 is what percentage of 50?
1 is what percentage of 50?
17 is what percentage of 50?
Exercise \(\PageIndex{2}\):... | libretexts | 2025-03-17T19:52:11.761177 | 2020-04-11T21:40:23 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page | 4.3: Applying Percentages Last updated Save as PDF Page ID 35000 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:11.923208 | 2020-01-25T01:41:27 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.1%3A_Tax_and_Tip | 4.3.1: Tax and Tip
Lesson
Let's learn about sales tax and tips.
Exercise \(\PageIndex{1}\): Notice and Wonder: The Price of SUnglasses
You are on vacation and want to buy a pair of sunglasses for $10 or less. You find a pair with a price tag of $10. The cashier says the total cost will be $10.45.
What do you notice? Wh... | libretexts | 2025-03-17T19:52:12.012874 | 2020-04-11T21:45:38 | {
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"book_url": "https://commons.libretexts.org/b... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.2%3A_Percentage_Contexts | 4.3.2: Percentage Contexts
Lesson
Let's learn about more situations that involve percentages.
Exercise \(\PageIndex{1}\): Leaving a Tip
Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?
\(15\cdot 20\)
\(20+0.15\cdot 20\)
\(1.15\cdot 20\)
\(\frac{15}{100}\cdot 20\)
Exercise \(... | libretexts | 2025-03-17T19:52:12.086288 | 2020-04-11T21:45:08 | {
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"book_url": "https://commons.libretex... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.3%3A_Finding_the_Percentage | 4.3.3: Finding the Percentage
Lesson
Let's find unknown percentages.
Exercise \(\PageIndex{1}\): Tax, Tip, and Discount
What percentage of the car price is the tax?
What percentage of the food cost is the tip?
What percentage of the shirt cost is the discount?
Exercise \(\PageIndex{2}\): What is the Percentage?
- A sal... | libretexts | 2025-03-17T19:52:12.158101 | 2020-04-11T21:44:43 | {
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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.3%3A_Finding_the_Percentage",
"book_url": "https://commons.libre... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.4%3A_Measurement_Error | 4.3.4: Measurement Error
Lesson
Let's use percentages to describe how accurately we can measure.
Exercise \(\PageIndex{1}\): MEasuring to the Nearest
Your teacher will give you two rulers and three line segments labeled A, B, and C.
- Use the centimeter ruler to measure each line segment to the nearest centimeter. Reco... | libretexts | 2025-03-17T19:52:12.238226 | 2020-04-11T21:44:18 | {
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"book_url": "https://commons.libretexts... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.5%3A_Percent_Error | 4.3.5: Percent Error
Lesson
Let's use percentages to describe other situations that involve error.
Exercise \(\PageIndex{1}\): Number Talk: Estimating a Percentage of a Number
Estimate.
25% of 15.8
9% of 38
1.2% of 127
0.53% of 6
0.06% of 202
Exercise \(\PageIndex{2}\): Plants, Bicycles, and Crowds
- Instructions to ca... | libretexts | 2025-03-17T19:52:12.308168 | 2020-04-11T21:43:55 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.03%3A_New_Page/4.3.6%3A_Error_Intervals | 4.3.6: Error Intervals
Lesson
Let's solve more problems about percent error.
Exercise \(\PageIndex{1}\): A Lot of Iron Ore
An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. What is a possible reading on the scale if you put 500 kilograms of iron ore on it?
Exercise \(\Pag... | libretexts | 2025-03-17T19:52:12.380706 | 2020-04-11T21:43:31 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.04%3A_New_Page | 4.4: Let's Put it to Work Last updated Save as PDF Page ID 35001 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:12.451145 | 2020-01-25T01:41:28 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.04%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/04%3A_Untitled_Chapter_4/4.04%3A_New_Page/4.4.1%3A_Posing_Percentage_Problems | 4.4.1: Posing Percentage Problems
Lesson
Let's explore how percentages are used in the news.
Exercise \(\PageIndex{1}\): Sorting the News
Your teacher will give you a variety of news clippings that include percentages.
- Sort the clippings into two piles: those that are about increases and those that are about decrease... | libretexts | 2025-03-17T19:52:12.511249 | 2020-04-11T21:46:22 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5 | 5: Rational Number Arithmetic Last updated Save as PDF Page ID 35004 Illustrative Mathematics OpenUp Resources 5.1: Interpreting Negative Numbers 5.1.1: Interpreting Negative Numbers 5.2: Adding and Subtracting Rational Numbers 5.2.1: Changing Temperatures 5.2.2: Changing Elevation 5.2.3: Money and Debts 5.2.4: Represe... | libretexts | 2025-03-17T19:52:12.599526 | 2020-01-25T01:41:31 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.01%3A_New_Page | 5.1: Interpreting Negative Numbers Last updated Save as PDF Page ID 35005 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:12.670532 | 2020-01-25T01:41:32 | {
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Lesson
Let's review what we know about signed numbers.
Exercise \(\PageIndex{1}\): Using the Thermometer
Here is a weather thermometer. Three of the numbers have been left off.
- What numbers go in the boxes?
- What temperature does the thermometer show?
Exercise \(\PageIndex{2}\): ... | libretexts | 2025-03-17T19:52:12.744154 | 2020-04-12T02:54:06 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page | 5.2: Adding and Subtracting Rational Numbers Last updated Save as PDF Page ID 35006 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:12.815845 | 2020-01-25T01:41:32 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.1%3A_Changing_Temperatures | 5.2.1: Changing Temperatures
Lesson
Let's add signed numbers.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Arrows
Which pair of arrows doesn't belong?
1.
2.
3.
4.
Exercise \(\PageIndex{2}\): Warmer and Colder
1. Complete the table and draw a number line diagram for each situation.
| start (\(^{\circ}\)C) | cha... | libretexts | 2025-03-17T19:52:12.902722 | 2020-04-12T02:57:30 | {
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Lesson
Let's solve problems about adding signed numbers.
Exercise \(\PageIndex{1}\): That's the Opposite
1. Draw arrows on a number line to represents these situations:
a. The temperature was -5 degrees. Then the temperature rose 5 degrees.
b. A climber was 30 feet above sea level. Then she de... | libretexts | 2025-03-17T19:52:12.992478 | 2020-04-12T02:57:04 | {
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Lesson
Let's apply what we know about signed numbers to money.
Exercise \(\PageIndex{1}\): Concert Tickets
Priya wants to buy three tickets for a concert. She has earned $135 and each ticket costs $50. She borrows the rest of the money she needs from a bank and buys the tickets.
- How can you rep... | libretexts | 2025-03-17T19:52:13.144964 | 2020-04-12T02:56:34 | {
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Lesson
Let's subtract signed numbers.
Exercise \(\PageIndex{1}\): Equivalent Equations
Consider the equation \(2+3=5\). Here are some more equations, using the same numbers, that express the same relationship in a different way:
\(3+2=5\qquad\qquad 5-3=2\qquad\qquad 5-2=3\)
For each equa... | libretexts | 2025-03-17T19:52:13.235460 | 2020-04-12T02:56:12 | {
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Lesson
Let's bring addition and subtraction together.
Exercise \(\PageIndex{1}\): Number Talk: Missing Addend
Solve each equation mentally. Rewrite each addition equation as a subtraction equation.
\(247+c=458\)
\(c+43.87=58.92\)
\(\frac{15}{8}+c=\frac{51}{8}\)
Exercise \(\PageIndex{... | libretexts | 2025-03-17T19:52:13.324908 | 2020-04-12T02:55:50 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.02%3A_New_Page/5.2.6%3A_Adding_and_Subtracting_to_Solve_Problems | 5.2.6: Adding and Subtracting to Solve Problems
Lesson
Let's apply what we know about signed numbers to different situations.
Exercise \(\PageIndex{1}\): Positive or Negative?
Without computing:
- Is the solution to \(-2.7+x=-3.5\) positive or negative?
-
Select
all
the expressions that are solutions to \(-2.7+x=-3.5\)... | libretexts | 2025-03-17T19:52:13.412279 | 2020-04-12T02:55:20 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page | 5.3: Multiplying and Dividing Rational Numbers Last updated Save as PDF Page ID 35007 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:13.484157 | 2020-01-25T01:41:33 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.1%3A_Position_Speed_and_Direction | 5.3.1: Position, Speed, and Direction
Lesson
Let's use signed numbers to represent movement.
Exercise \(\PageIndex{1}\): Distance, Rate, Time
- An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?
- A train moves at constant speed and travels 6 miles in 4 minutes. What is its spe... | libretexts | 2025-03-17T19:52:13.569084 | 2020-04-12T03:00:44 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.03%3A_New_Page/5.3.2%3A_Multiplying_Rational_Numbers | 5.3.2: Multiplying Rational Numbers
Lesson
Let's multiply signed numbers.
Exercise \(\PageIndex{1}\): Before and After
Where was the girl:
- 5 seconds after this picture was taken? Mark her approximate location on the picture.
- 5 seconds before this picture was taken? Mark her approximate location on the picture.
Exer... | libretexts | 2025-03-17T19:52:13.659304 | 2020-04-12T03:00:15 | {
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Lesson
Let's get more practice multiplying signed numbers.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Expressions
Which expression doesn't belong?
\(\begin{array}{lcl}{7.9x}&{\qquad}&{-7.9+x}\\{7.9\cdot (-10)}&{\qquad}&{-79}\end{array}\)
Exercise \(\PageIndex{2}\): Card Sort: Matching Expres... | libretexts | 2025-03-17T19:52:13.730532 | 2020-04-12T02:59:43 | {
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Lesson
Let's divide signed numbers.
Exercise \(\PageIndex{1}\): Tell Me Your Sign
Consider the equation: \(-27x=-35\)
Without computing:
- Is the solution to this equation positive or negative?
- Are either of these two number solutions to the equation?
\(\frac{35}{27}\qquad\qquad -\fra... | libretexts | 2025-03-17T19:52:13.815345 | 2020-04-12T02:59:21 | {
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Lesson
Let's apply what we know about signed numbers.
Exercise \(\PageIndex{1}\): Graper per Minute
- If you eat 5 grapes per minute for 8 minutes, how many grapes will you eat?
- If you hear 9 new songs per day for 3 days, how many new songs will you hear?
- If you run 15 laps per practice, how m... | libretexts | 2025-03-17T19:52:13.888190 | 2020-04-12T02:58:53 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.04%3A_New_Page | 5.4: Four Operations with Rational Numbers Last updated Save as PDF Page ID 35008 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:13.963534 | 2020-01-25T01:41:34 | {
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Lesson
Let's develop our signed number sense.
Exercise \(\PageIndex{1}\): True or False: Rational Numbers
Decide if each statement is true or false. Be prepared to explain your reasoning.
- \((-38.76)(-15.6)\) is negative
- \(10,000-99,999<0\)
- \(\left(\frac{3}{4}\right)\left(-... | libretexts | 2025-03-17T19:52:14.041611 | 2020-04-12T03:02:38 | {
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Lesson
Let's use all four operations with signed numbers to solve problems.
Exercise \(\PageIndex{1}\): Which One Doesn't Belong? Equations
Which equation doesn't belong?
\(\begin{array}{llll}{\frac{1}{2}x=-50}&{\qquad}&{\qquad}&{x+90=-100}\\{-60t=30}&{\qquad}&{\qquad}&{-0.... | libretexts | 2025-03-17T19:52:14.124241 | 2020-04-12T03:02:10 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.05%3A_New_Page | 5.5: Solving Equations When There Are Negative Numbers Last updated Save as PDF Page ID 35009 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:14.195990 | 2020-01-25T01:41:35 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.05%3A_New_Page/5.5.1%3A_Solving_Equations_with_Rational_Numbers | 5.5.1: Solving Equations with Rational Numbers
Lesson
Let's solve equations that include negative values.
Exercise \(\PageIndex{1}\): Number Talk: Opposites and Reciprocals
The variables \(a\) through \(h\) all represent different numbers. Mentally find numbers that make each equation true.
\(\frac{3}{5}\cdot\frac{5}{3... | libretexts | 2025-03-17T19:52:14.271010 | 2020-04-12T03:03:59 | {
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Lesson
Let's write equations that represent situations.
Exercise \(\PageIndex{1}\): Don't Solve It
Is the solution positive or negative?
\((-8.7)(1.4)=a\)
\(-8.7b=1.4\)
\(-8.7+c=-1.4\)
\(-8.7-d=-1.4\)
Exercise \(\PageIndex{2}\): Warmer or Colder than Before?
For each situatio... | libretexts | 2025-03-17T19:52:14.440373 | 2020-04-12T03:03:31 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.06%3A_New_Page | 5.6: Let's Put It to Work Last updated Save as PDF Page ID 35010 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:14.511919 | 2020-01-25T01:41:36 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/05%3A_Untitled_Chapter_5/5.06%3A_New_Page/5.6.1%3A_The_Stock_Market | 5.6.1: The Stock Market
Lesson
Let's learn about the stock market.
Exercise \(\PageIndex{1}\): Revisiting Interest and Depreciation
- Lin deposited $300 in a savings account that has a 2% interest rate per year. How much is in her account after 1 year? After 2 years?
- Diego wants to sell his bicycle. It cost $150 when... | libretexts | 2025-03-17T19:52:14.582952 | 2020-04-12T03:04:36 | {
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https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6 | 6: Expressions, Equations, and Inequalities
-
- 6.1: Representing Situations of the Form px+q=r and p(x+q)=r
-
- 6.1.1: Relationships between Quantities
- 6.1.2: Reasoning about Contexts with Tape Diagrams
- 6.1.3: Reasoning about Equations with Tape Diagrams
- 6.1.4: Reasoning about Equations and Tape Diagrams (Part 1... | libretexts | 2025-03-17T19:52:14.650871 | 2020-01-25T01:41:36 | {
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"book_url": "https://commons.libretexts.org/book/math-34975",
"title": "6: Expres... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page | 6.1: Representing Situations of the Form px+q=r and p(x+q)=r Last updated Save as PDF Page ID 35012 Illustrative Mathematics OpenUp Resources | libretexts | 2025-03-17T19:52:14.722218 | 2020-01-25T01:41:37 | {
"license": "Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/",
"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/06%3A_Untitled_Chapter_6/6.01%3A_New_Page",
"book_url": "https://commons.libretexts.org/book/math-34975",
"t... |
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