Lesson 7.1 Ratios, Rates, and Percents

# Ratios and Rates

#### Materials

• CCB Mathematics pages 212 - 217

#### Standards

• Understand ratio concepts and use ratio reasoning to solve problems.

#### Objectives

• Understand and write ratios

• Understand and find unit rates and unit prices

#### Key Concept

• Understand how to write ratios to understand the meaning of a unit rate.

#### Vocabulary

Tier 2 rateratio unit priceunit rate paraphrase

#### 21st Century Skill

• Critical Thinking and Problem Solving: Explain to students that being a good problem solver means being willing and able to look at a problem in different ways. Ratios describe relationships. They can describe the relationship between a part and the whole or between two (or more) parts. By looking at different parts of a problem, it is often possible to find more information than seemed obvious at first glance. Give students time to analyze the problem and discuss a reasonable answer. Then have students explain their thinking and revise their answers, if necessary.

## Before Lesson

To determine student readiness for this lesson, write a variety of fractions on the board and have students use greatest common factors to simplify them. Observe students as they work, and ask questions to determine if intervention is required.

## Background

Explain to students that they probably use ratios and unit rates regularly. For example, they may use ratios when they follow a recipe. They may pay attention to unit rates when they purchase food in a grocery store, or pump gas at a gas station. Both ratios and unit rates use the word per in their descriptions. For example, a recipe may call for one egg per cup of flour. Gasoline may cost \$3.87 per gallon. Have students suggest other familiar examples of ratios and unit rates.

## Guided Practice

• Understand Ratios
• Restate or Paraphrase Information
• Understand Unit Rates

## Core Skill

Understand Ratio Concepts: Allow students time to read the sidebar. Explain that it is important to read problems carefully to know when two or more steps are needed. Then have them choose partners to complete the activity. Encourage them to talk through the steps they need to take to solve each problem.

Use Ratio and Rate Reasoning: Ask a volunteer to read the sidebar. Point out the example that tells students to calculate the cost of a single shirt by multiplying the numerator and denominator of the fraction. Ask students if they can think of another way to describe how to perform that calculation. Students will probably notice that they would get the same result by dividing by four.

## Extension

Connect to Real-Life: Distribute advertisements from a local grocery s tore or other retail store. Ask students to identify examples of ratios and determine the unit rates for the items they find. Encourage students to use the terms ratios, fractions, and unit rates in their discussion.

Draw Conclusions from Data: Give students an opportunity to conduct research, either independently or collaboratively, to find examples of ratios in different areas. For example, students might examine geographic, economic, medical, manufacturing, consumer, entertainment, and sports data. Have students display and explain the ratios they find.