Equations and Inequalities

Lesson 6

Math

Unit 6

6th Grade

Lesson 6 of 14

Objective


Solve percent problems using equations.

Common Core Standards


Core Standards

  • 6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
  • 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.

Foundational Standards

  • 6.RP.A.1
  • 6.RP.A.2

Criteria for Success


  1. Determine, through repeated reasoning, an equation to represent the relationship between percent, whole, and part: $$percent\times{whole}=part$$ (MP.8).
  2. Write an equation to represent a percent situation when given a part and a percent.
  3. Write and solve equations to find the whole, given the part and percent.

Tips for Teachers


In Unit 2, students solved percent problems by reasoning about diagrams, double number lines, and tables. Now having learned about equations in the form $${px=q}$$, students revisit percent problems to see how they can be modeled and solved efficiently using an equation (MP.4).

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Anchor Problems


Problem 1

What is...

  • 30% of 40?
  • 30% of 120?
  • 30% of 15?

In general, if you’re given a percent and a whole, how can you find the part? Write this as an equation.

Guiding Questions

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Problem 2

30% of what number is 12?

Solve this problem first by drawing a diagram. Then write and solve an equation to verify your solution. 

Guiding Questions

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Problem 3

For each situation below, write and solve an equation to answer the question.

a.   There are 6 liters of water in a bucket, which is 20% of the maximum number of liters the bucket can hold. What is the maximum number of liters the bucket can hold?

b.   A softball team won 18 games, which was 60% of the games they played this season. How many games did the softball team play this season?

Guiding Questions

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Problem Set

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

Target Task


Paula is saving money to buy a tablet. So far, she has saved $54, which is 45% of what she needs to buy the tablet. 

Write and solve an equation to find the price of the tablet. 

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.

  • Challenge: In a choir, there are 28 female singers which is 40% of the choir. How many female singers would have to be added to the group so exactly 50% of the choir were females?
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Lesson 5

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Lesson 7

Lesson Map

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

Topic A: Reasoning About and Solving Equations

Topic B: Reasoning About and Solving Inequalities

Topic C: Representing and Analyzing Quantitative Relationships

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