Proportional Relationships

Lesson 1

Objective

Solve ratio and rate problems using double number lines, tables, and unit rate.

Common Core Standards

Core Standards

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  • 7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

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

Foundational Standards

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  • 6.RP.A.1

  • 6.RP.A.2

  • 6.RP.A.3

Criteria for Success

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  1. Understand the concept of equivalent ratios in real-world context. 
  2. Define equivalent ratios: The ratio of $${A:B }$$ is equivalent to $${c \times A:c \times B}$$ for a non-zero number $$c$$.
  3. Identify the unit rate for a ratio $${a:b}$$ as $$a/b$$ or $$b/a$$.
  4. Know that equivalent ratios have the same unit rate, and that the unit rate represents the multiplicative factor across columns in a ratio table. 

Tips for Teachers

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  • This lesson approaches standards 7.RP.1 and 7.RP.2 by reviewing concepts and skills from 6th grade standards in the Ratios and Proportions domain. These standards are foundational to this 7th grade unit, and will support students in later lessons. 
  • In terms of pacing, this lesson may be skipped or extended an additional day, depending on the needs of your students.

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Anchor Problems

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Problem 1

Jack mixes yellow and blue paint to make a green paint that he will use to paint his basement. He uses a ratio of 3 pints of yellow paint for every 2 pints of blue paint. Jack pours 18 pints of yellow paint into a bucket. 

  1. How many pints of blue paint should Jack add to the bucket?
  2. Jack's friend Kyle wants to help paint. Kyle said he has a green paint that is 9 parts yellow paint to 4 parts blue paint. Is Kyle's paint the same shade green as Jack's? Explain why or why not.

Guiding Questions

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Problem 2

Terrance bikes 3.6 miles to school in 18 minutes. Jaqueline bikes 5.4 miles to school in 30 minutes. Assuming each student rode at a constant speed, who is traveling at a faster speed? 

Guiding Questions

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Problem 3

At the corner market, you can buy rice by the pound. The table below shows some weights and their corresponding costs.

Rice (lbs.) Cost ($)
2 11
10 55
13 ?
? 88

 

  1. How much does 13 pounds of rice cost?
  2. How many pounds of rice can you buy with $88?

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 that incorporate a review of 6th grade ratio and rate concepts, using double number lines and tables, and finding unit rate

Target Task

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The distance and time traveled for 4 toy cars is shown in the table below.

Car Time (seconds) Distance (meters)
A 4 10
B 6 12
C 9 22.5
D 16 42

Which two cars are traveling at the same constant speed? Show or explain how you determined your answer.

Mastery Response

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