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Understanding Unit Rates: Definitions, Applications, and Comparisons

This lesson helps students grasp the concept of unit rates and ratios in real-life contexts. They will learn to identify and calculate unit rates, compare unit prices, and apply these skills in solving practical problems. Through engaging examples and activities, students will gain an understanding of how to represent ratios in various forms. Activities like comparing products based on unit rates will provide essential skills for real-world applications, ensuring students are able to make informed decisions based on mathematical reasoning.

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Understanding Unit Rates: Definitions, Applications, and Comparisons

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  1. Unit Rates Lesson 6.2

  2. CCS: 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations Objectives: • Students will find rates and unit rates • Students will compare unit prices • Students will solve real world problems using unit rates

  3. Check the Skills You’ll Need A drama club has 14 females and 8 males. Write each ratio in three ways: • Males to females • Females to males • Total to females Write each ratio in simplest form: • 8 to 12 • 10:6 8 to 14, 8:14. 8/14 14 to 8, 14:8. 14/8 22 to 14, 22:14, 22/14 2 to 3 5:3

  4. Vocabulary • Arateis a ratio that compares two quantities measured in different units. • The unit rateis the rate for one unit of a given quantity. Unit rates have a denominator of 1. • A unit price is a unit rate that gives the cost per unit

  5. Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute.

  6. Find the Unit Rate Amy can read 88 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?) 88 pages 22 pages / hour 4 hours

  7. Using Unit Rates • You can find the missing terms of equal ratios. • Use the unit rate, and set it equal to another ratio. • Solve for what is missing by dividing or multiplying.

  8. Example Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? x 8 25 miles = Unit Rate 8 gallons 1 gallon x 8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.

  9. Comparing Unit Prices • Use division to find the unit prices of the two products in question. • The unit rate that is smaller (costs less) is the better value.

  10. Example Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 $0.04 per fl.oz. 0.043125 48 fl.oz. $1.64 $0.05 per fl.oz. 0.05125 32 fl.oz. The 48 fl.oz. bottle is the better value.

  11. Classwork: Play this Jeopardy style game with a partner to practice rates and unit rates. Then…Check out this interactive for ratios and unit rates. You can click on lessons, interactives, or applications.Try it at BRAINCAMPHomework Time:pg. 275, 2-38 Even

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