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


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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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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Problem Set

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Target Task


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.

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Lesson 5

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Lesson 7

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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