Proportional Relationships

Lesson 2

Objective

Represent proportional relationships in tables, and define the constant of proportionality.

Common Core Standards

Core Standards

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  • 7.RP.A.2 — Recognize and represent proportional relationships between quantities.

  • 7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Foundational Standards

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  • 6.RP.A.2

  • 6.RP.A.3

Criteria for Success

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  1. Understand a proportional relationship between two quantities as a collection of equivalent ratios of those quantities.
  2. Understand the constant of proportionality as the constant value that tells how much of the second quantity is per 1 of the first quantity; the constant of proportionality is a constant multiplier between the two quantities.
  3. Describe a proportional relationship between two quantities shown in a table.
  4. Use unit rate and constant of proportionality to find missing values.

Tips for Teachers

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  • The terms proportional relationships and constant of proportionality are introduced in this lesson. These terms will be used throughout the rest of the unit and students will have many more opportunities to understand and internalize their meanings. In this lesson, encourage students to make connections between these terms and their prior understandings of unit rate and equivalent ratios. 
  • In this lesson, students analyze tables as a way to understand the relationship between two quantities. They identify a numerical pattern (the unit rate or constant of proportionality) in the table (MP.8) and then contextualize that value to understand what it means about the two units involved (MP.2).

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 2 (benefits from discussion). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

A self-serve frozen yogurt store sells yogurt at a price based on weight. Each member of Isabelle’s family weighed his or her dish to determine the cost of their yogurt, as shown in the table below.

Weight (ounces) Cost ($)
12 6
5 2.50
8 4
6 3

Is the cost of the yogurt proportional to the weight of the yogurt?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic A > Lesson 2Example 1

Grade 7 Mathematics > Module 1 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

The table below relates the number of gallons to number of quarts.

Gallons Quarts
5 20
3 12
8 32
12 48
  1. Describe the relationship between gallons and quarts.
  2. What is the constant of proportionality for this relationship?

Guiding Questions

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Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include problems where students practice using the new vocabulary, describing proportional relationships
  • Include problems similar to Anchor Problem 2

Target Task

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A family took a road trip down the East coast. On average, they traveled at a constant speed, represented in miles and hours in the table below.

Number of Hours Number of Miles
$$\frac{1}{2}$$ $$30$$
$$2$$ $$120$$
$$5\frac{1}{2}$$ $$330$$
$$7\frac{1}{2}$$ $$450$$
$$9$$ $$540$$
  1. Describe the relationship between hours and miles.
  2. How fast is the family driving?
  3. What is the constant of proportionality? Explain what it means in this situation.

Mastery Response

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