Lesson 17 | Proportional Relationships | 7th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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

5.NF.B.6

Number and Operations—Fractions

5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
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

Find a fractional amount of a quantity and reason about what to do with the value using the context of the problem.
Find an original value when given either a discount or a markup and a fractional rate.
Use different strategies to solve price increase, decrease, commission, and fee problems, including tape diagrams, proportions, equations, and other proportional reasoning.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In terms of pacing, this lesson may be extended over more than one day depending on the amount of practice and/or exposure to different variations of problems students need. The Target Task includes 2 problems which could be split over 2 days.
The Anchor Problems specifically cover the topics of price increase and price decrease. The other topics of commissions and fees should be included in the problem set.
Percent problems are not included in this lesson; all problems involve fractional amounts rather than percentages. In Unit 5, students will revisit this topic, but with percentages.

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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

Peter’s Pants Palace advertises the following sale:

a. If a pair of shoes originally costs $40, what is the sale price?

b. A pair of pants usually sells for $33. What is the sale price of the pants?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 14 — Example 1

Grade 7 Mathematics > Module 1 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

A phone case was on sale for $${{1\over3}}$$ off the original price. Terry purchased the phone case at this discounted price for $24. What was the original price of the phone case?

Guiding Questions

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Problem 3

An autographed baseball card of Pedro Martinez was originally worth $240. In 2015, when the retired player was inducted into the Baseball Hall of Fame, the value of the card increased in value by $$\frac{1}{5}$$ its original value. What is the new value of the card?

Guiding Questions

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Problem 4

A motorcycle dealer paid a certain price for a motorcycle and marked it up by $${{1\over5}}$$ of the price he paid. Later, he sold it for $14,000. What is the original price?

Solve this using two different strategies.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 14 — Example 4

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

Problem 1

A furniture store offers a deal to new customers. On your first purchase, you can use a $$\frac{1}{4}$$ discount on the price of any table.

Brian is a new customer at the store and wants to buy a table that originally costs $$$96$$. What discounted price would Brian pay for the table?

Problem 2

A washing machine is on sale, and its price is marked down by $$\frac{1}{5}$$ of its original price. The sale price of the washing machine is $$$304$$. What is the original price of the washing machine before the discount?

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.

Include problems similar to each anchor problem, asking students to find both the prices after the markup or markdown, and the prices before the markup or markdown.
Include problems about commission.
Include problems that involve fractional fees, such as late fees, registration fees, tax fees, etc.

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 14 — Examples 2-3, Problem Set

Lesson 16

Lesson 18

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

Foundational Standards

Number and Operations—Fractions

Ratios and Proportional Relationships

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem 4

Guiding Questions

References

Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Lesson Map

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