What you should learn
To solve problems involving percent of increase or decrease To solve problems involving discounts or sales tax NCTM Curriculm Standards 2, 6 - 9
To solve problems involving percent of increase or decrease
To solve problems involving discounts or sales tax
NCTM Curriculm Standards 2, 6 - 9
In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:
Percent of Decrease Percent of Increase
Percent of Decrease
Percent of Increase
Introduction: If you've ever bought a package of marshmallows, you've mostly bought air. That's right, marshmallows are 80% air! The marshmallow was invented in ancient Egypt and made with honey and the sap of the mallow plant that grows in swamps, or marshes.
Today, marshmallows are mass produced and made from cornstarch and gelatin. In 1955, the height of marshmallow making in the United States, there were 30 marshmallow companies. Today there are only a handful.
Let's say there are only six marshmallow companies today. You can write a ratio that ocmpares the amount of decrease in marshmallow companies to the original number of companies in 1955. This ratio can be written as a percent. First, subtract to find the amount of change: 30 - 6 = 24. Then divide by the original number of companies.
The amount of decrease is 80/100 or 80% of the original number of companies. So, we can say that the percent of decrease is 80%.
The percent of increase can be found in a similar way.
Exercise 1: In 1982, the population of the California condor had dwindled to a total of 21, making it the rarest bird in North America. According to the Refuge Department of the U.S. Fish and Wildlife Service, however, there were 64 condors in existence in 1992 and 103 as of October 1995. Find the percent of increase in the population of California condors form 1992 to 1995.
First, subtract to find the amount of change 103 - 64 = 39 amount of increase/original number- 39/64 39/64 = r/100 60.9375 = r The percent of increase is about 61%. The percent of increase is about 61%
First, subtract to find the amount of change
103 - 64 = 39
amount of increase/original number- 39/64
39/64 = r/100
60.9375 = r
The percent of increase is about 61%. The percent of increase is about 61%
Sometimes an increase or decrease is given as a percent, rather than an amount. Two applications of percent of change are discounts and sales tax.
Exercise 2: Ayita received a coupon in the mail offering her a 20% discount on the price of a pair of jeans at Jean Express. Ayita visited the store and found a pair of jeans she wants to buy that cost $48. What will be the discounted price?
Explore The original price is $48.00, and the discount is 20%. A discount of 20% means that the price is decreased by 20%. Plan You want to find the amount of discount, then subtract that amount from $48.00. The result is the discounted price. Solve 20% of $48.00 = (0.2)(48.00) = 9.60 Subtract this amount from the original price 48.00 - 9.60 = 38.40 The discounted price will be $38.40 Examine Solve the problem another way. The discount was 20%, so the discounted price will be 80% of the original price. Find 80% of $48.00 ------ 0.80(48.00) = 38.40 This method produces the same discounted price, $38.40.
Explore
The original price is $48.00, and the discount is 20%. A discount of 20% means that the price is decreased by 20%.
Plan
You want to find the amount of discount, then subtract that amount from $48.00. The result is the discounted price.
Solve
20% of $48.00 = (0.2)(48.00) = 9.60 Subtract this amount from the original price 48.00 - 9.60 = 38.40 The discounted price will be $38.40
20% of $48.00 = (0.2)(48.00) = 9.60
Subtract this amount from the original price
48.00 - 9.60 = 38.40
The discounted price will be $38.40
Examine
Solve the problem another way. The discount was 20%, so the discounted price will be 80% of the original price. Find 80% of $48.00 ------ 0.80(48.00) = 38.40 This method produces the same discounted price, $38.40.
Solve the problem another way. The discount was 20%, so the discounted price will be 80% of the original price.
Find 80% of $48.00 ------ 0.80(48.00) = 38.40
This method produces the same discounted price, $38.40.
Exercise 3: Katie Danko, a sophomore at Westerville North High School, is ordering a class ring. The ring she has chosen costs $169.99. She also needs to pay a sales tax of 5 3/4%. What is the total price?
Activity: Exploration: Programming
Suppose a newspaper ad states that a discount store's microwave ovens are discounted 20% form the manufacturer's suggested retail price (MSRP). The store is running a special sale that says all kitchen appliances have been discounted an additional 15%. What is the final sales price of a microwave oven whose MSRP is $250?
There are two ways you might interpret the ad in the paper. The discounts can be successive. That is 20% is taken off the MSRP and then 15% is taken off the resulting price. The discounts can be combined. So the price is 35% off the MSRP.
There are two ways you might interpret the ad in the paper.
The discounts can be successive. That is 20% is taken off the MSRP and then 15% is taken off the resulting price.
The discounts can be combined. So the price is 35% off the MSRP.
Your Turn
Copy the following table and use the program to complete it. (a - d)
e. What is the relationship between the sale price using successive discounts and the sale price using combined discounts? Which one is usually used in stores?
Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.
Homework: The homework to be assigned for tonight would be: 13 - 39 odd, 40 - 46
Alternative Homework: Enriched: 12 - 30 even, 31 - 46
Extra Practice: Students book page 765 Lesson 4-5
Extra Practice Worksheet: Click Here.
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