Lesson 15 | Proportional Relationships | 7th Grade Mathematics

Objective

Solve ratio and rate problems by setting up a proportion.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Ratios and Proportional Relationships

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 <sup>1/2</sup>/<sub>1/4</sub> 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.

Ratios and Proportional Relationships

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

The foundational standards covered in this lesson

6.RP.A.3

Ratios and Proportional Relationships

6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

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?

a. Solve this by using equivalent ratios.

b. Solve this by using a unit rate.

c. Solve this by using an equation.

d. 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

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

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

Kuta Software Free Pre-Algebra Worksheets Proportions and Percents — Proportion Word Problems
Inside Mathematics Performance Assessment Tasks Grades 3-High School Cereal
Khan Academy Writing & Solving Proportions
Algebra By Example 3.5 Solving Proportions
Algebra By Example 3.4 Writing Proportions
Illustrative Mathematics Perfect Purple Paint II

Lesson 14

Lesson 16

Lesson Map

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

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

7.RP.A.1 7.RP.A.2

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

7.RP.A.2 7.RP.A.2.B

Determine the constant of proportionality in tables, and use it to find missing values.

7.RP.A.2.A 7.RP.A.2.B

Write equations for proportional relationships presented in tables.

7.RP.A.2.B 7.RP.A.2.C

Write equations for proportional relationships from word problems.

7.RP.A.2 7.RP.A.2.C

Represent proportional relationships in graphs.

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D

Interpret proportional relationships represented in graphs.

7.RP.A.2 7.RP.A.2.D

Topic B: Non-Proportional Relationships

Compare proportional and non-proportional relationships.

7.RP.A.2.A

Determine if relationships are proportional or non-proportional.

7.RP.A.2.A

Topic C: Connecting Everything Together

Make connections between the four representations of proportional relationships (Part 1).

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Make connections between the four representations of proportional relationships (Part 2).

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Use different strategies to represent and recognize proportional relationships.

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Topic D: Solving Ratio & Rate Problems with Fractions

Find the unit rate of ratios involving fractions.

7.RP.A.1

Find the unit rate and use it to solve problems.

7.RP.A.1 7.RP.A.3

Solve ratio and rate problems by setting up a proportion.

7.RP.A.1 7.RP.A.3

Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.

7.RP.A.1 7.RP.A.3

Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.

7.RP.A.3

Use proportional reasoning to solve real-world, multi-step problems.

7.RP.A.1 7.RP.A.2 7.RP.A.3

Proportional Relationships

Objective

Common Core Standards

Core Standards

Ratios and Proportional Relationships

Ratios and Proportional Relationships

Foundational Standards

Ratios and Proportional Relationships

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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