# 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).

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## 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.

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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.

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### 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?

#### Guiding Questions

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## Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

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?

## Target Task

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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.

### Mastery Response

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