Unit 3

Representing Proportional Relationships

Linear Relationships

Lesson 3

Expressions and Equations

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Let's graph proportional relationships.

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Unit 3 ● Lesson 3

Learning

Goal

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Multiplication

Unit 3 ● Lesson 3 ● Activity 1

Find the value of each product mentally.

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15 • 2

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15 • 0.5

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15 • 0.25

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15 • (2.25)

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Warm-up: Number Talk

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

Representations of Proportional Relationships

Unit 3 ● Lesson 3 ● Activity 2

1. Here are two ways to represent a situation.

1. Create a table that represents this situation with at least 3 pairs of values.
2. Graph this relationship and label the axes.

• How can you see or calculate the constant of proportionality in each representation? What does it mean?
• Explain how you can tell that the equation, description, graph, and table all represent the same situation.

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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.

Representations of Proportional Relationships

Unit 3 ● Lesson 3 ● Activity 2

2. Here are two ways to represent a situation.

1. Write an equation that represents this situation. (Use c to represent number of cars and use m to represent amount raised in dollars.)
2. Create a graph that represents this situation.

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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.

Representations of Proportional Relationships

Unit 3 ● Lesson 3 ● Activity 2

3. How can you see or calculate the constant of proportionality in each representation? What does it mean?
4. Explain how you can tell that the equation, description, graph, and table all represent the same situation.

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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.

Representations of Proportional Relationships

Unit 3 ● Lesson 3 ● Activity 2

Which representation makes it more difficult (and less difficult) to calculate the constant of proportionality? 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.

Info Gap: Proportional Relationships

Unit 3 ● Lesson 3 ● Activity 3

Do not show or read your card to your partner.

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

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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.

Info Gap: Proportional Relationships

Unit 3 ● Lesson 3 ● Activity 3

• Other than the answer, what information would have been nice to have?
• How did you decide what to label the two axes?
• How did you decide to scale the horizontal axis? The vertical?
• What was the rate of change of grams of honey per cups of flour? Where can you see this on the graph you made?
• What was the rate of change of grams of salt per cups of flour? Where can you see this on the graph you made?

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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.

Representing Proportional Relationships

Unit 3 ● Lesson 3

• The proportional relationship y = 5.5x includes the point (18, 99) on its graph. How could you choose a scale for a pair of axes with a 10 by 10 grid to show this point?
• What are some things you learned about graphing today that you are going to try to remember for later?

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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 3 ● Lesson 3

I can scale and label a coordinate axes in order to graph a proportional relationship.

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Learning

Targets

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Graph the Relationship

Unit 3 ● Lesson 3 ● Activity 4

Sketch a graph that shows the relationship between grams of honey and grams of salt needed for a bakery recipe. Show on the graph how much honey is needed for 70 grams of salt.

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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.

constant of proportionality

Unit 3 ● Lesson 3

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.

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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

rate of change

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Unit 3 ● Lesson 3

The rate of change in a linear relationship is the amount y changes when x increases by 1. The rate of change in a linear relationship is also the slope of its graph.

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In this graph, y increases by 15 dollars when x increases by 1 hour. The rate of change is 15 dollars per hour.

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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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