Lesson 9 | Percent and Scaling | 7th Grade Mathematics

Objective

Solve percent applications involving discount, tax, and tip.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Expressions and Equations

7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

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.C

Ratios and Proportional Relationships

6.RP.A.3.C — Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Criteria for Success

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

Solve percent applications involving more than one percent; for example, finding a restaurant bill including tax and a tip.
Understand that multiple discounts are not additive but are taken sequentially where the order does not matter.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In Lessons 9–11, students apply the strategies and skills they learned so far in this unit to solve real-world percent applications (MP.4). In this lesson, students look at examples involving tax, tips, and price markups and markdowns. Ensure students have an adequate working knowledge of these concepts so they can access the problems appropriately.
In regards to pacing, this lesson may extend over two days if needed.

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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

For Simon’s birthday, he and his family go out to eat at a restaurant.

a. The amount of tax is $3.40, which is 5% of the food bill. How much was the food bill not including the tax?

b. If Simon wants to leave a 20% tip on the amount of the food bill before tax, how much should he leave for a tip?

c. What is Simon’s total bill including tax and tip? What percent of the food bill is this?

Guiding Questions

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Problem 2

Emily has a coupon for 20 percent off of her purchase at the store. She finds a backpack that she likes on the discount rack. Its original price is $60, but everything on the rack comes with a 30 percent discount.

Emily says, “Thirty percent and twenty percent make fifty percent, so it will cost $30.”

Is Emily correct? Explain your reasoning. In your explanation, if you disagree with Emily, find the price she will pay for the backpack.

Guiding Questions

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References

Illustrative Mathematics Double Discounts

Double Discounts, accessed on Dec. 18, 2017, 9:29 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 3

In order to make money, a store marks up its prices by 25% from the warehouse prices. Let $$p$$ represent the price at which the store gets its merchandise from the warehouse, and let $$s$$ represent the price the store sells the merchandise for after the markup.

a. Write an equation to determine the selling price, $$s$$, based on the warehouse purchase price, $$p$$.

b. Create a table showing possible pairs of solutions to the equation.

Warehouse price ($$p$$)	Selling price ($$s$$)

c. Create and label a graph for your table.

d. Interpret the points $$(0, 0)$$ and $$(1, r) $$ from the graph in context of the situation.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic B > Lesson 7 — Exercise 4

Grade 7 Mathematics > Module 4 > Topic B > Lesson 7 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..

Modified by Fishtank Learning, Inc.

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

Lauren and her sister are buying their mom a watch for her birthday. The original price of the watch is $50, but the store is having a 25% off sale on watches. The sales tax in Lauren’s state is 6%.

a. How much will Lauren and her sister pay for the watch including tax?

b. What percent of the original price do Lauren and her sister pay for the watch, after paying tax?

Student Response

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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.

Challenge: Asher paid $100.80 at a restaurant for his family's dinner. His bill included 5% for tax, and he added 20% of the total, including the tax, for the tip. What was the amount of the bill before tax and tip?

Kuta Software Free Pre-Algebra Worksheets Markup, Discount, and Tax (Hard)
Illustrative Mathematics Anna in D.C.
Illustrative Mathematics Tax and Tip
Illustrative Mathematics Buying Protein Bars and Magazines
MARS Summative Assessment Tasks for Middle School 25% Sale — This task addresses the misconception of adding discounts.
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic B > Lesson 7 — Exercises, Examples, and Problem Set
Open Up Resources Grade 7 Unit 4 Practice Problems — Lesson 10
Illustrative Mathematics Discounted Books

Lesson 8

Lesson 10

Lesson Map

Topic A: Percent, Part, and Whole

Define percent and convert between fractions, decimals, and percentages. Solve percent problems mentally with benchmark percentages.

7.RP.A.3

Find percent of a number when given percent and the whole.

7.NS.A.3 7.RP.A.3

Find the whole given a part and percent.

7.NS.A.3 7.RP.A.3

Find the percent given a part and the whole.

7.NS.A.3 7.RP.A.3

Topic B: Percent Increase and Decrease

Find a new amount given the original and a percent increase or decrease.

7.EE.A.2 7.RP.A.3

Find the original amount given a new amount after a given percent increase or decrease.

7.EE.A.2 7.RP.A.3

Find the percent of increase or decrease given the original and new amounts.

7.RP.A.3

Solve percent problems fluently, including percent increase and decrease.

7.EE.A.2 7.RP.A.3

Topic C: Percent Applications

Solve percent applications involving discount, tax, and tip.

7.EE.B.3 7.RP.A.3

Solve percent applications involving simple interest, commissions, and other fees.

7.EE.B.3 7.RP.A.3

Solve percent applications involving measurement and percent error.

7.EE.B.3 7.RP.A.3

Topic D: Scale Drawings

Define and identify scale images.

7.G.A.1

Define and determine scale factor between two scale images. Use scale factor to draw scale images.

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

Use a scale to determine actual measurements.

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

Use scales in maps to find actual distances between locations.

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

Use scales in floor plans to find actual measurements and dimensions.

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

Compute actual areas from scale drawings.

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

Draw scale drawings at different scales.

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

Create a scale floor plan (optional).

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

Percent and Scaling

Objective

Common Core Standards

Core Standards

Expressions and Equations

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

References

Problem 3

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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