~ 4.6 ~

Increasing and Decreasing

Learning Targets

  • I can draw a tape diagram that represents a percent increase or decrease.

  • When I know a starting amount and the percent increase or decrease, I can find the new amount.

Notes

Imagine that it takes Andre ¾ more than the time it takes Jada to get to school. Then we know that Andre’s time is 1 ¾ or 1.75 times Jada’s time. We can also describe this in terms of percentages:

We say that Andre’s time is 75% more than Jada’s time. We can also see that Andre’s time is 175% of Jada’s time. In general, the terms percent increase and percent decrease describe an increase or decrease in a quantity as a percentage of the starting amount.

For example, if there were 500 grams of cereal in the original package, then “20% more” means that 20% of 500 grams has been added to the initial amount, 500 + (0.2) ⋅ 500 = 600, so there are 600 grams of cereal in the new package.

We can see that the new amount is 120% of the initial amount because

500 + (0.2) ⋅ 500 = (1+0.2) 500

Vocabulary

percentage increase: Given an initial amount, and a final amount which is larger than the initial amount, the percentage increase is the difference (final amount minus initial amount) expressed as a percentage of the initial amount.

percentage decrease: Given an initial amount, and a final amount which is smaller than the initial amount, the percentage decrease is the difference (initial amount minus final amount) expressed as a percentage of the initial amount.

Activities

6.2 More Cereal and a Discounted Shirt

  1. ​​A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?

  2. The price of a shirt is $18.50, but you have a coupon that lowers the price by 20%. What is the price of the shirt after using the coupon?


Questions to Ponder before answering:

  • Did the number of ounces of cereal in the box (or price of the shirt) increase or decrease?

  • What percentage of the original amount of cereal (original price of the shirt) is the new amount of cereal?

Add to Your Notes

  • 100% always corresponds to the original amount before the change.

Cereal Box

  • A cereal box says that it now contains 20% more.

  • This is an example of a percent increase.

Shirt

  • The price of a shirt lowers the price by 20%.

  • This is an example of a percent decrease.

6.3 Using Tape Diagrams

  1. Match each situation to a diagram on the right. Be prepared to explain your reasoning.

    • Compared with last year’s strawberry harvest, this year’s strawberry harvest is a 25% increase.

    • This year’s blueberry harvest is 75% of last year’s.

    • Compared with last year, this year’s peach harvest decreased 25%.

    • This year’s plum harvest is 125% of last year’s plum harvest.

  2. Draw a diagram to represent these situations.

    • The number of ducks living at the pond increased by 40%.

    • The number of mosquitoes decreased by 80%.

Add to Your Notes

What is another way to describe a 25% increase or decrease?

    • percent increase → 100% + 25% = 125%

    • percent decrease → 100% - 25% = 75%

When a quantity is increased or decreased, what percent describes the original or starting value?

    • The original/starting value is 100%.

What strategies have we used to help us calculate percent increase and decrease?

    • table, equation, tape diagram, double number line

Summary

Assignment

Check Google Classroom!