[9th grade Algebra Class in Computer Lab with Microsoft Excel Software] JOAN GOEBEL

HOW DO WE FIND THE PERCENT OF CHANGE FOR AN INCREASE OR DECREASE?

MOTIVATION: During the summer, a bear’s heart rate is about 60 beats per minute, but it can drop to as low as 8 beats per minute during winter. What is the percent of change in a bear’s heart rate from the summer rate to the winter low rate?

DEVELOPMENT: The percent of change is the ratio of the amount of change to the original amount. Percent increase describes an amount that has grown and percent decrease describes an amount that has been reduced.

PERCENT OF CHANGE = AMOUNT OF INCREASE OR DECREASE

ORIGINAL

To find the percent of decrease in a bear’s heart rate as described above, use the percent of change equation 60 – 8 = 52 = .8666…. Therefore, the percent of decrease is about 86.7%.

60 60

APPLICATION/DRILL:

Example: The population of a village has increased from 1500 to 1800 since the last census. What is the percent of increase in population?

Procedure: 1. We find the increase (change) in population

2.  We find what fractional part of the original population the increase represents

3.  We express this fraction as a percent

Step1 Step 2 Step 3

1800 – 1500 = 300 increase = 300 = 1 1 = .20 = 20%

New – old = increase original 1500 5 5

Example: Last year, Mr. Stone bought a car for $4650. This year his car is worth $3700. Find the percent of decrease in the value of his car.

Step1 Step 2 Step 3

$4650 – 3700 = $950 decrease = 950 = .2043… approx. 20%

Old – new = decrease original 4650

WORK WITH A PARTNER

1.  Jake weighed 200 pounds before he lost 40 pounds on a new diet. Find the percent of change to the nearest whole percent.

2.  Find the percent of change from 96 minutes to 108 minutes.

3.  List at least 5 more examples in real life which have percent increases and percent decreases.

4. DO TECHNOLOGY LAB – PERCENT INCREASE AND DECREASE

SUMMARY QUESTIONS:

How do you determine which value is the original amount?

Can the original amount ever be equal to zero? Explain.

How is finding the result of a percent increase similar to finding the result of a percent decrease? How is it different?

HOMEWORK ASSIGNMENT:

Textbook pages/handout

STUDENT OBJECTIVES: Use common applications of percents. Estimate with percents.

NEW YORK PERFORMANCE INDICATORS:

A.N.5 Solve algebraic problems arising from situations that involve fractions, decimals, percent, and proportionality/direct variation

A.A.25 Solve equations involving fractional expressions

A.CN.6 Recognize and apply mathematics to situations in the outside world

A.R.7 Use mathematics to show and understand social phenomena

ADDITIONAL ACTIVITIES RECOMMENDED

Comparing baseball salaries from year to year

Comparing salesmen and amounts of commission

Census 2010 statistics, populations, etc.

TECHNOLOGY LAB – PERCENT INCREASE AND DECREASE

You can use an Excel spreadsheet to determine the percent increase/decrease of the price of an item.

ACTIVITY 1

Find the percent decrease.

The first column in the table shows the original price for an item in a store. The second column shows the price of the same item after a discount has been applied.

To determine the percent decrease, or in this case the percent of discount, for each amount, enter the formula = ((A2-B2)/A2 into the C2 cell.

Use the FILL Down command from the Edit menu to find the percent decrease for every item in the table.

To convert the values in the C column to percents, highlight the entire C column by clicking on the C cell. Then, go to the Format menu, select Style, and then select Percent.

ACTIVITY 2

Find the percent increase.

The first column in the table shows the original price for an item. The second column shows the price of the same item after a sales tax, or tariff, has been applied.

To determine the percent increase for each amount, enter the formula = ((B2-A2)/B2) into the C2 cell.

Use the Fill Down command from the Edit menu to find the percent increase for every item in the table.

To convert the values in the C column to percents, highlight the entire C column by clicking on the C Cell. Then, go to the Format menu, select Style, and then select Percent.

TRY THIS - Use a spreadsheet to find the percent increase of each item in column A.

What formula do you insert into cell C2 to calculate the percent increase?

What is the percent increase of the item in row 3?

What is the original price of the item that has the largest percent increase?

What is the new price of the item that had the least percent increase?