given the original amount and the percent of change, how do you find the amount of change and the...

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?

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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?

Page 2: 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

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.

Page 3: 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

Let’s Review

Solving a Proportion

100x = 25 x 36100x = 900

Page 4: 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

Let’s Review

Solving an Equation

100x = 900

x = 9

Page 5: 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

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

Page 6: 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

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%

Page 7: 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

Core Lesson

Last year = 100% = 24Increase =25% of 24 = 6

This year = 125% of 24 24 + 6 = 30

Page 8: 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

Core Lesson

1 Find 25% of 24 using a proportion

2 Add 25% of 24 to 24

Option 2: Use proportions

Page 9: 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

Core Lesson

Creating a percent proportion:

Page 10: 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

Core Lesson

100x = 24 x 25100x = 600

x = 624 + 6 = 30 boys

Page 11: 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

Core Lesson

100x = 24 x 125100x = 3,000x = 30 boys

1 Find 125% of 24using a proportion

Page 12: 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

Core Lesson

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

Page 13: 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

Core Lesson

125% = 1.25

24 x 1.25 = 30 boys

1 Find 125% of 24using an equation

Page 14: 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

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.

Page 15: 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

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?

Page 16: 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

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?

Page 17: 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

Extension Activities

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?

Page 18: 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

Extension Activities

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.

Page 19: 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

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?

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