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# Equations and Inequalities

## Objective

Solve percent problems using equations.

## Common Core Standards

### Core Standards

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• 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.

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• 6.RP.A.1

• 6.RP.A.2

## Criteria for Success

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1. Determine, through repeated reasoning, an equation to represent the relationship between percent, whole, and part: percent x 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

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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).

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (can be done independently) and Anchor Problem 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### 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.

### 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.

### Problem 3

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

1. 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?
2. 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?

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used 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?