Lesson 3Increasing and Decreasing

Learning Goal

Let’s use percentages to describe increases and decreases.

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.

Lesson Terms

percentage decrease
percentage increase

Warm Up: Improving Their Game

Here are the scores from 3 different sports teams from their last 2 games.

sports team	total points in game 1	total points in game 2
football team	$22$	$30$
basketball team	$100$	$108$
baseball team	$4$	$12$

What do you notice about the teams’ scores? What do you wonder?
Which team improved the most? Explain your reasoning.

Activity 1: More Cereal and a Discounted Shirt

Problem 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?

Picture of a cereal box with the label "20% more free" on the box.

Problem 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?

A picture of a shirt with a label "20% off"

Activity 2: Using Tape Diagrams

Problem 1

Match each situation to a diagram. Be prepared to explain your reasoning.

Tape diagram A-with "last year" and "this year". Last year is one segment labeled 100%. This year is 2 segments-a white one the same length as last year and a blue one labeled 25%.

Tape diagram B- is the same as A except both segments together are 100% (same as last year)

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.

Problem 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%.

Are you ready for more?

What could it mean to say there is a 100% decrease in a quantity? Give an example of a quantity where this makes sense.

Activity 3: Agree or Disagree: Percentages

Do you agree or disagree with each statement? Explain your reasoning.

Employee A gets a pay raise of 50%. Employee B gets a pay raise of 45%. So Employee A gets the bigger pay raise.
Shirts are on sale for 20% off. You buy two of them. As you pay, the cashier says, “20% off of each shirt means 40% off of the total price.”

Lesson Summary

Imagine that it takes Andre $\frac{3}{4}$ more than the time it takes Jada to get to school. Then we know that Andre’s time is $1 \frac{3}{4}$ or 1.75 times Jada’s time. We can also describe this in terms of percentages:

Tape diagrams of Jada's and Andre's time. Jada has 4 segments labeled 100%. Andre has the 4 white segments and 3 blue segments all together labeled 175%

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, $500 + (0.2) \times 500 = 600$ , so there are 600 grams of cereal in the new package.

$500 + (0.2) \cdot 500 = (1 + 0.2) 500$

A tape diagram with 5 white segments labeled 100% and 1 blue segment labeled 20%. The entire diagram is labeled 120%