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8TB of public domain and openly licensed text • 30 items • Updated • 22
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value | added stringdate 2025-03-17 19:52:06 2025-03-17 22:27:57 | created timestamp[s]date 2013-05-16 21:27:22 2025-03-14 14:40:33 | metadata dict |
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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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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings",
"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 | {
"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",
"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 | {
"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/1.1.3%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 | {
"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/1.1.4%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 | {
"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/1.1.5%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/... |
https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.02%3A_New_Page | Skip to main content
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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 | {
"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/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 | {
"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/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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"url": "https://math.libretexts.org/Bookshelves/PreAlgebra/Pre-Algebra_I_(Illustrative_Mathematics_-_Grade_7)/01%3A_Scale_Drawings/1.03%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/1.03%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 | {
"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/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 | {
"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/2.1.1%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 | {
"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/2.1.2%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 | {
"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/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 | {
"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/2.2.2%3A_Two_Equations_for_Each_Relationship",
"... |
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 | {
"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/2.2.3%3A_Using_Equations_to_Solve_Problems",
"bo... |
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 | {
"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/2.03%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/2.03%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 | {
"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/2.03%3A_New_Page/2.3.1%3A_Comparing_Relationships_with_Tables",
"... |
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 | {
"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/2.03%3A_New_Page/2.3.2%3A_Comparing_Relationships_with_Equations",
... |
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 | {
"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/2.03%3A_New_Page/2.3.3%3A_Solving_Problems_about_Proportional_Relat... |
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 | {
"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/2.04%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/2.04%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 | {
"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/2.04%3A_New_Page/2.4.1%3A_Introducing_Graphs_of_Proportional_Relati... |
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 | {
"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/2.04%3A_New_Page/2.4.2%3A_Interpreting_Graphs_of_Proportional_Relat... |
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 | {
"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/2.04%3A_New_Page/2.4.3%3A_Using_Graphs_to_Compare_Relationships",
... |
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 | {
"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/2.04%3A_New_Page/2.4.4%3A_Two_Graphs_for_Each_Relationship",
"boo... |
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 | {
"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/2.5%3A_Let's_Put_it_to_Work",
"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 | {
"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/2.5%3A_Let's_Put_it_to_Work/2.5.1%3A_Four_Representations",
"book... |
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 | {
"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/2.5%3A_Let's_Put_it_to_Work/2.5.2%3A_Using_Water_Efficiently",
"b... |
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 | {
"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)/03%3A_Untitled_Chapter_3",
"book_url": "https://commons.libretexts.org/book/math-34975",
"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 | {
"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)/03%3A_Untitled_Chapter_3/3.01%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)/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 | {
"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)/03%3A_Untitled_Chapter_3/3.01%3A_New_Page/3.1.1%3A_How_Well_Can_You_Measure",
"book_url": "https://commons.lib... |
End of preview. Expand in Data Studio
LibreTexts
Description
LibreTexts is an online platform that provides a catalog of over 3,000 open-access textbooks.
To collect openly licensed content from LibreTexts we gather links to all textbooks in the catalog and check each each textbook section for a license statement indicating that it is in the public domain or under a CC BY, CC BY-SA, or the GNU Free Documentation License.
We extract plaintext from these textbook sections directly from the HTML pages hosted on the LibreTexts website.
Per-document license information is available in the license entry of the metadata field of each example.
Code for collecting, processing, and preparing this dataset is available in the common-pile GitHub repo.
Dataset Statistics
| Documents | UTF-8 GB |
|---|---|
| 62,269 | 5.3 |
License Issues
While we aim to produce datasets with completely accurate licensing information, license laundering and inaccurate metadata can cause us to erroneously assign the incorrect license to some documents (for further discussion of this limitation, please see our paper). If you believe you have found an instance of incorrect licensing in this dataset, please start a discussion on this repository.
Other Versions
This is the "raw" version of the LibreTexts dataset. If you are looking for the filtered version used to train Comma v0.1, you can find it here.
Citation
If you use this dataset, please cite:
@article{kandpal2025common,
title={{The Common Pile v0.1: An 8TB Dataset of Public Domain and Openly Licensed Text}},
author={Nikhil Kandpal and Brian Lester and Colin Raffel and Sebastian Majstorovic and Stella Biderman and Baber Abbasi and Luca Soldaini and Enrico Shippole and A. Feder Cooper and Aviya Skowron and Shayne Longpre and Lintang Sutawika and Alon Albalak and Zhenlin Xu and Guilherme Penedo and Loubna Ben and Elie Bakouch and John David and Honglu Fan and Dashiell Stander and Guangyu Song and Aaron Gokaslan and John Kirchenbauer and Tom Goldstein and Brian R and Bhavya Kailkhura and Tyler Murray},
journal={arXiv preprint},
year={2025}
}
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