Proportional Relationships

Lesson 9

Objective

Determine if relationships are proportional or non-proportional.

Common Core Standards

Core Standards

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  • 7.RP.A.2.A — Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Foundational Standards

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  • 6.RP.A.3

Criteria for Success

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  1. Determine if two quantities are in a proportional relationship by creating and analyzing tables, graphs, and equations of the relationship.
  2. Justify, with tables, equations, graphs, or explanations, why two quantities are or are not in a proportional relationship.
  3. Understand that quantities with the same unit rate are in a proportional relationship (MP.3).
  4. Understand that perimeter and side length of regular polygons are in a proportional relationship.

Tips for Teachers

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This Lesson extends on Lesson 8 by having students make the determination if a relationship is proportional or non-proportional, and to justify their reasoning.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion) and Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

Is the perimeter of a square proportional to the side length of a square? 
Is the area of a square proportional to the side length of a square? 

Justify your answer to each question using tables, graphs, and/or equations.

Guiding Questions

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Problem 2

At Sunny’s Market, soda water costs $2.55 for 3 liters. 

Which stores below sell soda water at the same price per liter as Sunny’s Market? 

 

Guiding Questions

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Problem 3

Ahmed hiked at a constant speed for 6 hours and covered 21 miles. This is represented in the coordinate plane below.

Which coordinate points, when graphed on the plane above, would be in a proportional relationship to Ahmed’s hike? Select all that apply.

a.  (0, 3.5)

b.  (1, 3.5)

c.  (2, 7)

d.  (3, 14)

e.  (4, 15)

f.  (5, 17.5)

g.  (8, 28)

 

 

Guiding Questions

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Problem Set

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Target Task

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Is the perimeter of an equilateral triangle proportional to the side length of the triangle? For any regular polygon, is the perimeter of the polygon proportional to the side length of the polygon? Explain your reasoning. 

Mastery Response

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