Proportional Relationships

Lesson 15

Objective

Solve ratio and rate problems by setting up a proportion.

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.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Foundational Standards

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  • 6.RP.A.3

Criteria for Success

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  1. Understand a proportion as two equivalent ratios written as an equation.
  2. Write a proportion of two equivalent ratios.
  3. Attend to precision with units when setting up a proportion (MP.6).
  4. Solve a proportion using the relationship across the numerators, the relationship between the numerator and the denominator, or cross multiplication. 
  5. Understand the connections between different strategies to solve a ratio problem. 

Tips for Teachers

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  • This lesson introduces students to the strategy of using a proportion and cross multiplication to solve problems. From 6th grade, and from earlier in this unit, students have learned numerous strategies to solve ratio and rate problems. Solving a proportion of two equivalent ratios is often an efficient method. 
  • Ensure that students are shown a demonstration of why the act of cross multiplication works. One explanation is shown in the notes for Anchor Problem 1. This site  explains cross multiplication from the perspective of comparing fractions.

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Anchor Problems

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Problem 1

A movie theater has reduced ticket prices for the early afternoon show. A group of 4 students go to the movies and pay $24. At this rate, how much would 20 students pay for the movie?

  1. Solve this by using equivalent ratios.
  2. Solve this by using a unit rate.
  3. Solve this by using an equation.
  4. Solve this by setting up a proportion.

Guiding Questions

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Problem 2

A recipe for sweet potato pie calls for 3 tsp of cinnamon for every 2 cups of sweet potato. How many cups of sweet potato should you add to 11 tsp of cinnamon?

Solve using a proportion, and then choose one other method to check your answer.

Guiding Questions

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Problem Set

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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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The ratio of boys to girls at a soccer camp is 3:5. If there are 51 boys at the camp, then how many of the campers are girls?

Solve using a proportion, and then choose one other method to check your answer.

Mastery Response

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