Lesson 10 | Percent and Scaling | 7th Grade Mathematics

Objective

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

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

Find simple interest using the formula $${ I=PRT}$$, where I represents the simple interest, $$P$$ represents the principle amount, $$R$$ represents the interest rate, and $$T$$ represents the time of the investment.
Solve percent application problems involving commissions and fees.

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 simple interest, commission, and fees. Ensure students have an adequate working knowledge of these concepts so that they can access the problems appropriately.

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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

Larry invests $500 in a savings plan. The plan pays 4% interest each year on his $500 account balance. The table below shows the balance of his account after each year for the next 5 years. He did not make any deposits or withdrawals during this time.

Time (in years)	Balance (in dollars)
1	500
2	520
3	540
4	560
5	580

a. How much interest did Larry earn each year? Where do you see this in the table?

b. How is the amount of interest determined?

c. Assuming Larry makes no additional deposits or withdrawals, how much interest will he earn after 8 years?

d. What equation can Larry use to determine the interest he will earn on his account after $$T$$ years?

e. Is there a proportional relationship between the amount of interest earned and the number of years of the investment? If so, what is the constant of proportionality?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic B > Lesson 10 — Example 1

Grade 7 Mathematics > Module 4 > Topic B > Lesson 10 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 2

At a furniture store, the employees earn a 2.5% commission on every sale they make.

a. If Robert made $8,850 in sales one week, how much money in commission did he earn?

b. Francesca made $279 in commission that same week, at the same rate. How much did she sell?

Guiding Questions

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Problem 3

Tyler bought two tickets to a basketball game on the website Game Finder. Each ticket cost $65, and the website charged a convenience fee that was a small percent of the ticket cost.

If Tyler’s total bill came to $132.60, what percent was the convenience fee?

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

Lynn takes out a special loan for college students in the amount of $7,540. She is charged an annual simple interest rate of 6.5%. She does not need to make any payments for $$2\frac{1}{2}$$ years.

How much will Lynn owe on her loan after $$2\frac{1}{2}$$ years?

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.

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic B > Lesson 10 — Examples, Exercises, and Problem Set
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic B > Lesson 11 — Examples, Exercises, and Problem Set
Illustrative Mathematics Lincoln’s Math Problem — calculators recommended

Lesson 9

Lesson 11

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

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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