Percent and Scaling

Lesson 5

Math

Unit 5

7th Grade

Lesson 5 of 19

Objective


Find a new amount given the original and a 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. Understand a percent increase problem as a situation where an original amount is increased by a certain percentage to result in a new, greater amount.
  2. Understand a percent decrease problem as a situation where an original amount is decreased by a certain percentage to result in a new, lesser amount.
  3. Represent percent increase and decrease situations using visual diagrams. 
  4. Find an amount of increase or decrease in order to find a new amount.
  5. 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 are given the original amount and the percent increase or decrease and must find the new amount. In the following lessons, students will consider different variations of this with different knowns and unknowns. 
  • Students reason quantitatively in this lesson, carefully considering what each quantity means in the context of the problems they see. They distinguish between values that represent a whole, a part, a percent, or an increase or decrease. In addition, they distinguish between a quantity increase or decrease and a percent increase or decrease (MP.2).
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Anchor Problems


Problem 1

Match each situation below to one of the diagrams. Explain your reasoning.

Situation 1: In March, you have $220 in your savings account. By the end of April, your savings have increased by 30%. How much money do you have in your savings account at the end of April?

Situation 2: A television regularly costs $220. Over a holiday weekend, a store offers a discount of 30% off the regular price. How much does the television cost over the holiday weekend?

Guiding Questions

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Problem 2

On Sunday, 1,460 customers shopped at Pine Village Bookstore. On Monday, there were 60% fewer customers at the bookstore. How many customers visited Pine Village Bookstore on Monday? 

Draw a diagram and use it to solve. Explain your reasoning.

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Problem 3

A restaurant raises its prices by 10% to account for rising prices of supplies and ingredients. The restaurant’s signature pasta dish costs $14 before the price increase. What is the new price of the pasta dish? 

a.   Solve this problem using any strategy.

b.   Mariam solves this problem by finding 110% of $14. Explain why Mariam’s strategy is correct. How does this strategy compare to yours? 

Guiding Questions

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Problem Set

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Target Task


Lester’s first draft of his English paper had 1,644 words. After revising his paper, Lester’s second draft had 25% fewer words. How many words did Lester’s second draft of his English paper have? 

Show two different ways 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 4

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Lesson 6

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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