Unit 4

Revisiting Proportional Relationships

Proportional Relationships and Percentages

Lesson 3

Expressions and Equations

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Let’s use constants of proportionality to solve more problems.

Unit 4 ● Lesson 3

Learning

Goal

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Recipe Ratios

Unit 4 ● Lesson 3 ● Activity 1

A recipe calls for ½ 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 recipe.

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

The Price of Rope

Unit 4 ● Lesson 3 ● Activity 2

Two students are solving the same problem: At a hardware store, they can cut a length of rope off of a big roll, so you can buy any length you like. The cost for 6 feet of rope is $7.50. How much would you pay for 50 feet of rope, at this rate?

1. Kiran knows he can solve the problem this way.

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What would be Kiran’s answer?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

The Price of Rope

Unit 4 ● Lesson 3 ● Activity 2

2. Kiran wants to know if there is a more efficient way of solving the problem. Priya says she can solve the problem with only 2 rows in the table.

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What do you think Priya’s method is?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

The Price of Rope

Unit 4 ● Lesson 3 ● Activity 2

• How did you find the scale factor?
• How did you find the constant of proportionality?
• What does the constant of proportionality (1.25) mean in this context?
• Which method is your preference to use? Why?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

The Price of Rope

Unit 4 ● Lesson 3 ● Activity 2

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Swimming, Manufacturing, and Painting

Unit 4 ● Lesson 3 ● Activity 3

1. Tyler swims at a constant speed, 5 meters every 4 seconds. How long does it take him to swim 114 meters?

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• A factory produces 3 bottles of sparkling water for every 8 bottles of plain water. How many bottles of sparkling water does the company produce when it produces 600 bottles of plain water?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Swimming, Manufacturing, and Painting

Unit 4 ● Lesson 3 ● Activity 3

3. A certain shade of light blue paint is made by mixing 1½ quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint?
4. For each of the previous three situations, write an equation to represent the proportional relationship.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Swimming, Manufacturing, and Painting

Unit 4 ● Lesson 3 ● Activity 3

• Does it matter which heading goes in which column?
• Do you get a different answer if you switch them? Why or why not?
• Would your strategy change if you switched them? Why or why not?
• If you got stuck, what helped you to move through the hard parts?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Finishing the Race and More Orange Juice

Unit 4 ● Lesson 3 ● Activity 4

1. Lin runs miles in of an hour. Tyler runs miles in of an hour. How long does it take each of them to run 10 miles at that rate?
2. Priya mixes cups of water with cup of orange juice concentrate. Diego mixes cups of water with cup orange juice concentrate. How much concentrate should each of them mix with 100 cups of water to make juice that tastes the same as their original recipe? Explain or show your reasoning.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Revisiting Proportional Relationships

Unit 4 ● Lesson 3

How can we use a table that only has two rows to solve a problem about a proportional relationship?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 4 ● Lesson 3

• I can use a table with 2 rows and 2 columns to find an unknown value in a proportional relationship.
• When there is a constant rate, I can identify the two quantities that are in a proportional relationship.

Learning

Targets

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Walnuts in Bulk

Unit 4 ● Lesson 3 ● Activity 5

It costs $3.45 to buy ¾ lb of chopped walnuts. How much would it cost to purchase 7.5 lbs of walnuts? Explain or show your reasoning.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

percentage

Unit 4 ● Lesson 3

A percentage is a rate per 100.

For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

unit rate

Unit 4 ● Lesson 3

A unit rate is a rate per 1.

For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because 12 ÷ 2 = 6. The other unit rate is of a pie per person, because 2 ÷ 12 = .

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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