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Unit 2

Introducing Proportional Relationships with Tables

Introducing Proportional Relationships

Lesson 2

Expressions and Equations

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Let’s solve problems involving proportional relationships using tables.

Unit 2 ● Lesson 2

Learning

Goal

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Unit 2 ● Lesson 2 ● Activity 1

Here is a table that shows how many rolls of paper towels a store receives when they order different numbers of cases.

What do you notice about the table? What do you wonder?

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Warm-up: Notice and Wonder

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

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Feeding a Crowd

Unit 2 ● Lesson 2 ● 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.

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Feeding a Crowd

Unit 2 ● Lesson 2 ● Activity 2

  1. A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
    1. How many people will 10 cups of rice serve?
    2. How many cups of rice are needed to serve 45 people?
  2. A recipe says that 6 spring rolls will serve 3 people. Complete the table.

number of spring rolls

number of people

6

3

30

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40

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28

cups of rice

number of people

2

6

3

9

10

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45

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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.

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Making Bread Dough

Unit 2 ● Lesson 2 ● Activity 3

A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour. Complete the table as you answer the questions. Be prepared to explain your reasoning.

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  1. How many cups of flour do they use with 20 tablespoons of honey?
  2. How many cups of flour do they use with 13 tablespoons of honey?
  3. How many tablespoons of honey do they use with 20 cups of flour?
  4. What is the proportional relationship represented by this table?

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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.

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Making Bread Dough

Unit 2 ● Lesson 2 ● Activity 3

  • If you only had 1 tbsp of honey, how much flour would you need?
  • Does the relationship between how much flour is needed for each tablespoon of honey remain constant across every row of the table? How would you describe this 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.

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Quarters and Dimes

Unit 2 ● Lesson 2 ● Activity 4

4 quarters are equal in value to 10 dimes.

  1. How many dimes equal the value of 6 quarters?
  2. How many dimes equal the value of 14 quarters?
  3. What value belongs next to the 1 in the table? What does it mean in this context?

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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.

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Introducing Proportional Relationships with Tables

Unit 2 ● Lesson 2

  1. How would you describe a proportional relationship? Can you provide an example from one of today’s activities?
  2. How would you describe the constant of proportionality? Can you provide an example from one of today’s activities?

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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.

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Unit 2 ● Lesson 2

  • I can use a table to reason about two quantities that are in a proportional relationship.
  • I understand the terms proportional relationship and constant of proportionality.

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Learning

Targets

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Green Paint

Unit 2 ● Lesson 2 ● Activity 5

When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.

  1. How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning.
  2. Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green.
  3. What is the proportional relationship represented by this table?
  4. What is the constant of proportionality? What does it represent?

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cups of blue paint

cups of yellow paint

2

1

10

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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.

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constant of proportionality

Unit 2 ● Lesson 2

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.

In this example, the constant of proportionality is 3, because 2 • 3 = 6, 3 • 3 = 9, and 5 • 3 = 15. This means that there are 3 apples for every 1 orange in the fruit salad.

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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.

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equivalent ratios

Unit 2 ● Lesson 2

Two ratios are equivalent if you can multiply each of the numbers in the first ratio by the same factor to get the numbers in the second ratio. For example, 8 : 6 is equivalent to 4 : 3 because 8 • ½ = 4 and 6 • ½ = 3.

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A recipe for lemonade says to use 8 cups of water and 6 lemons. If we use 4 cups of water and 3 lemons, it will make half as much lemonade. Both recipes taste the same, because 8 : 6 and 4 : 3 are equivalent ratios.

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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.

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proportional relationship

Unit 2 ● Lesson 2

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.

For example, in this table every value of� is equal to 4 times the value of on the same row.

We can write this relationship as . This equation shows that is proportional to .

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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.

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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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