Percent Increase and Decrease - pearsoncmg.com

1 Grade 7 Teacher Guide Percent Increase and Decrease LAUNCH (7 MIN) _____ Before What are two ways to compare population growth in the two towns? During Which quantity changed more? Why isn t that enough to make a decision? After With whose opinion do you agree? Why? KEY CONCEPT (4 MIN) _____ Emphasize that you only need to know two quantities to find Percent of change: the original quantity and the amount of change. Why is the equation for Percent Increase the same as the one for Percent Decrease ? PART 1 (7 MIN) _____ Before solving the problem What is meant by Percent Increase ? Does a greater amount of Increase always mean a greater Percent of Increase ? Javier Says (Screen 1) Use the Javier Says button to connect Percent of change to part-to-whole ratios, connecting Percent change to scenarios students are already familiar with.

2 While solving the problem How will you find each boy s Percent of change? After solving the problem Your friend says that Toby s number of push-ups increased by 200%. Explain the error. PART 2 (7 MIN) _____ Before solving the problem How is solving this problem similar to solving the previous problem? How is it different? While solving the problem How can you use Percent of change to show decreases in weight? After solving the equation If the astronaut traveled back from the moon to the Earth and weighs 154 lb again, by what Percent does her weight Increase on the Earth? Why isn t the answer the same as the answer to the Example? PART 3 (7 MIN) _____ Javier Says (Screen 1) Use the Javier Says button to discuss how people often estimate percents of change in real life. Describe a situation in which you might estimate a Percent of change.

3 While solving the problem How can you use an analog clock to help you make visual estimations of percents of change in this game? How can you use compatible numbers to help you make estimates of Percent of change? CLOSE AND CHECK (7 MIN) _____ Describe a plan, prediction, or decision that someone might make based on the Percent of change examples in this lesson. Where else have you seen Percent used to show change in the real world? grade 7 Teacher Guide Percent Increase and Decrease LESSON OBJECTIVES 1. Recognize and represent proportional relationships between quantities. 2. Use proportional relationships to solve multi-step ratio and Percent problems involving Percent Increase and Decrease . FOCUS QUESTION How can you use a Percent to represent change? MATH BACKGROUND In this lesson, the focus is on another key real-world use of percents: Percent change.

4 Students use number sense and their understanding of ratios and proportional relationships to solve problems. They work with both Percent Increase and Percent Decrease . A solid understanding of the concepts of Percent Increase and Decrease is essential for decision makers in businesses of all kinds. Many business decisions rely on percents instead of numbers to make plans and predictions. One very important misconception is that a greater amount of change results in a greater Percent of change. Emphasize that the Percent of change depends on the ratio of the amount of change to the original quantity. This lesson does not deal with negative percents. Answers are expressed as positive percents and labeled as either an Increase or Decrease . A common error that students make is to use the wrong quantities to find the ratio.

5 Students should realize that the new quantity is not involved in the ratio that represents Percent of change. Another common misconception is that a 20% Increase followed by a 20% Decrease results in the original quantity. This misconception will be corrected in the next lesson, Markups and Markdowns. In the following lesson, students will apply the formula for Percent of change in order to solve problems that are at the core of marketing and retail decision-making: determining markups and markdowns. Students will later learn about another application of Percent change, Percent error. LAUNCH (7 MIN) _____ Objective: Compare absolute increases and Percent increases. Author Intent Students compare increases in two quantities by examining which changed more. They can compare quantities, or they can compare ratios.

6 This problem prepares students to find the ratio that reflects the change in a quantity and write it as a Percent . Questions for Understanding Before What are two ways to compare population growth in the two towns? [Sample answer: One way is to find the difference in population for each and compare those differences. Another way is to compare the ratios of the change to the original populations in 2000.] During Which quantity changed more? Why isn t that enough to make a decision? [Little Falls, MN changed more. Since one population is much greater than the other, you need to find the relative change.] Percent Increase and Decrease continued grade 7 Teacher Guide After With whose opinion do you agree? Why? [Sample answer: The friend from Wisconsin; the population of Little Falls, WI increased by a greater Percent of the 2000 population.]

7 ] Solution Notes Some students may only mention the number of people. Challenge these students to consider the large difference in populations between the two towns. Ask students which town they would say grew the most if both towns grew by the same number of people. Other students my use ratios to find the relative change per person. They can express these ratios as fractions and find the greatest fraction. They may have an easier time comparing the ratios in decimal or Percent form. Connect Your Learning Move to the Connect Your Learning screen. In the Launch, students found two ways to compare change in quantities. Use the Focus Question to initiate a discussion about other instances where Percent is regularly used to describe a change, such as clothing sales, pay raises, or sports statistics.

8 KEY CONCEPT (4 MIN) _____ Teaching Tips for the Key Concept The Key Concept shows how to derive the Percent of change formula from the Percent equation. You can call on students to click each radio button, which launches an animation. After you derive the formula, you can compare Percent Increase and Percent Decrease to show that the equations are identical. Emphasize that you only need to know two quantities to find Percent of change: the original quantity and the amount of change. Point out that finding Percent of change often involves writing a fraction as a Percent . Emphasize that knowing the Percent forms of common fractions (halves, thirds, fourths, fifths, eighths, and tenths) can allow you to find Percent change using mental math. Why is the equation for Percent Increase the same as the one for Percent Decrease ?

9 [Each equation shows the ratio of the amount of change to the original quantity. You need to include the word Increase or Decrease in your answer.] Do you have to memorize the formula for Percent of change? [No; you can use the Percent equation as long as you know the original quantity is the whole, and the amount of change is the part. Knowing the formula for Percent of change may be more efficient and may help you avoid using the wrong quantity.] PART 1 (7 MIN) _____ Objective: Use proportional relationships to solve multi-step Percent problems involving Percent Increase . Author Intent Students apply the formula for Percent of change to find Percent Increase . They recognize that the Percent of change can be greater even if the amount of change is smaller. This problem continues the reasoning of the Launch and prepares students for Percent Decrease in Part 2.

10 Percent Increase and Decrease continued grade 7 Teacher Guide Questions for Understanding Before solving the problem What is meant by Percent Increase ? [Sample answer: It is the ratio of the amount of change to the original quantity.] Does a greater amount of Increase always mean a greater Percent of Increase ? [No; the Percent of Increase may be slight if the amount of change is a large number but the original quantity is much, much greater.] Javier Says (Screen 1) Use the Javier Says button to connect Percent of change to part-to-whole ratios, thereby connecting Percent change to scenarios students are already familiar with. While solving the problem How will you find each boy s Percent of change? [Find the Increase in pushups or crunches, and divide that number by the original quantity of pushups or crunches.]