Lesson 11 | Percent and Scaling | 7th Grade Mathematics

Objective

Solve percent applications involving measurement and percent error.

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

Determine the positive amount of error in a measurement or other situation.
Find the percent error by dividing the amount of error by the actual measurement.
Understand the difference between the amount of error and the percent error, and why it is valuable to consider both.

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 measurement and percent error.

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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

Quiana measures the width of her doorway entrance using a measuring tape. She measures the width as 33 inches. She later finds a better tape measure that measures to the nearest half of an inch. After re-measuring, she determines that the actual measure of the doorway is 32 ½ inches.

a. What is the amount of error from using the first measuring tape?

b. What is the error as a percentage of the actual width?

Guiding Questions

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Problem 2

Paul and Kimberly both estimate the weight of their dogs before bringing them to the vet. The table below shows each of their estimates along with the actual weights of the dogs from the vet’s office.

	Estimate (lbs.)	Actual (lbs.)
Paul's dog	10	11.5
Kimberly's dog	84	82.5

Paul notices that both his and Kimberly’s estimates were only 1.5 pounds off from the actual weights. Paul says that means his estimate was as good as Kimberly’s estimate.

Do you agree with Paul? Find the percent error for each person’s guess of their dog’s weight, and use it in your answer.

Guiding Questions

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Problem 3

In science class, Justine measured a rock sample and found it to be 15 grams. Her teacher told her that the scale is off and the actual weight is 0.3 grams more than her measurement.

What is the percent error? Give your answer to the nearest percent.

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

Greg rounded an answer on his calculator to 20. The exact number on his calculator was 19.72.

What is the percent error of Greg’s rounded answer? Give your answer to the nearest tenth of a percent.

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.

Spiral in questions from Lessons 2–10
Challenge: Have students find the length of their hands (or feet or distance from fingertip to elbow) and then use their hands to estimate the length of different objects in the class (desk, wall, door, etc.). Then find the actual measurements and determine the percent errors in the measurements. Challenge students to refine their measurements and estimations to reduce the percent error.

Open Up Resources Grade 7 Unit 4 Lesson 13 — Practice Problems
Open Up Resources Grade 7 Unit 4 Lesson 14 — Practice Problems
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic B > Lesson 8 — Examples, Exercises, Problem Set; note that these materials use absolute value to determine the positive amount of the error

Lesson 10

Lesson 12

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

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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