Lesson 7.2 Ratios, Rates, and Percents

# Unit Rates and Proportional Relationships

#### Materials

• CCB Mathematics pages 218 - 223

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

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

• Understand the connections between proportional relationships, lines, and linear equations.

#### Objectives

• Use unit rates to solve mathematics problems

• Interpret representations of proportional relationships

#### Key Concept

• A unit rate is a special example of a ratio. When it is expressed in fractional form, the denominator equals one. When expressed verbally, a ratio is an example of a unit rate if the second value being compared is one.

#### Vocabulary

Tier 3 constant of proportionalityproportional relationship

## Before Lesson

This lesson helps students understand the concept of a unit rate, which is a special kind of ratio. To determine student readiness, use words to describe ratios, such as three oranges for every five apples. Have student students translate words into numbers, writing ratios and simplifying them to write them in lowest terms.

## Background

Proportional relationships are related to ratios, which students examined in the previous lesson. Like ratios, unit rates are used to compare two different types of quantities. Write an example of a unit rate in words on the board, such as 33 miles per gallon. Then rewrite the rate in fraction for (33 miles/1 gallon)m.

## Guided Practice

• What Is a Unit Rate?
• Converting Ratios to Unit Rates
• Proportional Relationships
• Apply Proportional Relationships

## Core Skill

Compute Unit Rates: Associated with Ratios of Fractions Have students read the sidebar. You may want to allow student to use calculators to help them calculate the aspect ratios in the example and as they complete the table. Ask: What do all unit rates have in common? Remind students that all unit rates have 1 as a denominator.

Evaluate Reasoning: Give students time to read the text. Then ask volunteers to explain why it is important to include units when writing a ratio. Explain to students that it is helpful to think about whether the answer in the given context is sensible, or reasonable. If they are unsure, they can check the ratio. The correct ratio for this problem is (28 wheelbarrows)/(3 hours):, because the problem asks for wheelbarrows ours per hour. Have students use the correct ratio to find the unit rate.

## Extension

Multiple Meanings: Explain to students that the word proportion has many uses in the English language. Have students use a print or online dictionary to find different uses of the word. For example, guide students toward a discussion of proportion as it applies to art and design. You may want to have students apply what they learn about proportion to draw a human face or animal.

Compare Unit Rates: Have students find examples of ratios in online advertisements or in print media and have them convert the ratios into unit rates. In particular, have them look for the same item in different quantities or from different businesses. Then have students use the unit rates to compare values.