Proportional Relationships

Lesson 8

Objective

Compare proportional and non-proportional relationships.

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. Identify and explain examples of non-proportional relationships.
  2. Represent non-proportional relationships in tables and graphs and compare to features of proportional relationships.
  3. Determine if a table or graph represents a proportional relationship.

Tips for Teachers

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This lesson is a good opportunity for students to construct arguments and defend their decisions around if a relationship is proportional or not. They may also work in pairs to listen to and critique the arguments of others (MP.3). 

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 3 (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

Syrus is 12 years old and has a younger sister, Samira, who is 6 years old. Syrus says, “Our ages are in a proportional relationship because I am two times as old as my sister.” 

Is Syrus correct? Justify your answer.

Guiding Questions

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Problem 2

At the zoo, you can buy tickets to take a train ride between exhibits. Each ticket costs $0.50; however, there is a deal that if you buy 10 tickets, you only pay $4.00. 

Is the cost of the tickets proportional to the number of tickets you buy? Create a table with some values and plot the points on a coordinate plane.

Guiding Questions

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Problem 3

Four tables and four graphs are shown below. Which tables and graphs represent proportional relationships? Explain your reasoning for each one.

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.

Target Task

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Two ice cream shops are located across the street from one another on a busy street. 

  • At Max’s Ice Cream shop, you can buy a sundae with unlimited toppings for $5 per sundae. 
  • At Mary’s Ice Cream shop, you can buy a sundae by paying $3.50 for the ice cream and then $0.75 for each topping.

At which ice cream shop is the cost of the sundaes (including the toppings), proportional to the number of sundaes purchased? Justify your answer with tables, graphs, or an explanation. 

Mastery Response

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