Curriculum  /  Math  /  7th Grade  /  Unit 5: Percent and Scaling  /  Lesson 6

Percent and Scaling

Lesson 6

Math

Unit 5

7th Grade

Lesson 6 of 19

Objective

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

Common Core Standards

Core Standards

  • 7.EE.A.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
  • 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

  • 6.RP.A.3.C

Criteria for Success

  1. Represent percent increase and decrease situations using visual diagrams. 
  2. Find an original amount given a new amount and the percent increase or decrease.
  3. Understand that an increase of $$x$$% is equivalent to ($$100+x$$)% of the original amount and a decrease of $$x$$% is equivalent to ($$100-x$$)% of the original amount.

Tips for Teachers

  • Lessons 5–8 address percent increase and decrease problems. In this lesson, students look to find the original amount, or the value that represents 100%, when they are given a new amount after a percent increase or decrease. 
  • Students continue to reason abstractly, making meaning of the quantities in the problems to understand their relationships before doing any calculations (MP.2).
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Anchor Problems

25-30 minutes

Problem 1

Read each situation below and then answer the questions that follow. 

Situation A: In the spring, an animal shelter had 216 animals. By the end of the summer, this number decreased by 8%. How many animals were at the shelter at the end of summer? 

Situation B: After advertising for adoptions on local television, an animal shelter decreased the number of animals at the shelter by 8%. There are now 216 animals. How many animals were at the shelter before the advertising? 

a.   Sketch a visual diagram to represent each situation. 

b.   How are the two situations similar?

c.   How are the two situations different? 

Guiding Questions

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Student Response

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Problem 2

A store sells backpacks in two sizes: small and large. The large backpacks sell for 20% more than the smaller backpacks. If a large backpack costs $75, how much does the small size cost? 

Draw a visual representation of the situation, and then use an equation to solve. 

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

A supersize laundry detergent has 60% more detergent than the regular size. The supersize detergent has 144 ounces. How many ounces of detergent are in the regular size?

Draw a visual representation of the situation, and then use an equation to solve.

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.

Next

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

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Percent, Part, and Whole

Topic B: Percent Increase and Decrease

Topic C: Percent Applications

Topic D: Scale Drawings

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