1. Given the original amount and the percent of change, how do you find the amount of change and the final amount? For example: A school with 1,500 students grew by 12%. How many more students enrolled and what was the new enrollment?

2. In this lesson you will learn how to find the amount of change and the final amount given the percent of change and the original amount by using diagrams, proportions, and equations.

3. Let’s Review Solving a Proportion 100x = 25 x 36 100x = 900

4. Solving an Equation 100x = 900 x = 9

5. A Common Mistake Percent Increase/Decrease = Amount Change 40% increase/decrease in price means you just add/subtract $40 Amount increase/decrease = Final amount Increase/decrease of $40 means the final amount is $40

6. Core Lesson Last year there were 24 boys in chess club. This year the number of boys increased by 25%. How many boys are in chess club this year? Option 1: Use a diagram 24 = 100% 25% Last Year This Year 24 = 100% 25%

7. Core Lesson 24 6 6 Last year = 100% = 24 Increase =25% of 24 = 6 This year = 125% of 24 24 + 6 = 30

8. Core Lesson 1 Find 25% of 24 using a proportion 2 Add 25% of 24 to 24 Option 2: Use proportions

9. Creating a percent proportion:

10. 100x = 24 x 25 100x = 600 x = 6 24 + 6 = 30 boys

11. 100x = 24 x 125 100x = 3,000 x = 30 boys 1 Find 125% of 24 using a proportion

12. 1 Find 25% of 24 using an equation 2 Add 25% of 24 to 24 25% = 0.25 24 x 0.25 = 6 24 + 6 = 30 boys Option 3: Use equations

13. 125% = 1.25 24 x 1.25 = 30 boys 1 Find 125% of 24 using an equation

14. In this lesson you have learned how to find the amount of change and the final amount given the original amount and the percent of change by using diagrams, proportions, and equations.

15. Guided Practice Last year there were 20 girls on the chess club. This year the number of girls decreased by 10%. Use a diagram, proportion, and equation to find how many girls are on the chess club this year?

16. Extension Activities City regulations require that the sand underneath the swings be 15 inches deep. Currently the sand is only 12 inches deep. The 9 feet by 12 feet area under the small swing set required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will be needed to increase the depth of sand under the large swing set if the length and width are both 50% longer than the length and width under the small swing set?

17. Assume the sales tax rate in your area is 8%. Pretend you want to buy 3 items, a $220 bike, a $15 t-shirt, and $75 sneakers. How much will you pay for tax on each item? How much tax will you pay for all items? What is the total cost of all 3 items after tax?

18. Which of the following offers gives the biggest price reduction? Which gives the smallest price reduction? Explain your reasoning. Two for the price of one. Buy two and get 50% off the second one. Three for the price of two. Buy one and get 25% off the second.

19. Quick Quiz The price of gas yesterday was $4.25. The price has increased 30%. Use a diagram, proportion, and equation to determine the price of gas today? Last week a cellphone was $95. This week it is on sale for 15% off. Use a diagram, proportion, and equaiton to determine how much the cellphone costs this week?