Lesson 7.3 Ratios, Rates, and Percents

# Solve Proportions

#### Materials

• CCB Mathematics pages 224 - 229

#### Standards

• Analyze proportional relationships and use them to solve real-world and mathematical problems.

#### Objectives

• Understand and write proportions

• Solve proportions

#### Key Concept

• Understand how to use proportions to solve problems.

#### Vocabulary

Tier 2 EquivalentProportionvalue cross-multiplication

## Before Lesson

In this lesson, students learn to solve proportions. To determine their readiness, organize students into pairs. Assign the pairs the fractions 3/4 and 1/12. Ask students to determine whether or not they are equivalent. Ask students to tell you how they know. Then have them write equivalent fractions for both fractions. Provide more practice problems, if necessary.

## Background

A proportion is a statement of the equality of two ratios. Present a real-life example of a proportion to students. Say: 36 slices of bread will make 12 club sandwiches. How many slices of bread do I need to make 8 club sandwiches? Tell students that they don’t have to solve the problem now, but after completing this lesson, they will be able to write and solve a proportion to find the answer. Revisit the problem at the end of the lesson, and invite a volunteer to write a proportion and solve the problem.

## Guided Practice

• Understand Proportions
• Solve Proportions

## Core Skill

Represent Real-World Problems: Have students read the first paragraph and identify the proportion in the problem width/length=10/19. Then organize students into pairs. Have pairs work together to read the problem, and write and solve the proportion. Afterward, ask one student from each pair to write the proportion and its solution on the board. Compare solutions and resolve any discrepancies that may occur.

Build Solution Pathways: Read the first paragraph to students. Invite students to share solution strategies they like to use most often, such as creating visuals or listing steps. Work with students to help them solve Example 4 in the two ways the text suggests. Have students discuss in small groups which method they prefer, and why. Then have them choose a method to complete the sidebar activity.

## Extension

Restate Examples: Invite students to select an example from the lesson to explain to the class, to a group, or to a partner. Afterward, have the partner or a student in the group or class restate or explain the solution process in his or her own words, using simple vocabulary to explain the more complicated processes.

Interpret Information: Have students go online to find examples of architectural house or room plans. Have student locate the scales used to create the plans. Then have them use proportions to recreate a plan to double the size of the house or room.