Lesson 6: Increasing and Decreasing
Let’s use percentages to describe increases and decreases.
Illustrative Math Unit 7.4, Lesson 6 (printable worksheets)
Lesson 6 Summary
The following diagram shows how to find the percentage increase or decrease using a tape diagram.
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.
Lesson 6.1 Improving Their Game
Here are the scores from 3 different sports teams from their last 2 games.
- What do you notice about the teams’ scores? What do you wonder?
- Which team improved the most? Explain your reasoning.
Lesson 6.2 More Cereal and a Discounted Shirt
- 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?
- 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?
Lesson 6.3 Using Tape Diagrams
- Match each situation to a diagram. Be prepared to explain your reasoning.
a. Compared with last year’s strawberry harvest, this year’s strawberry harvest is a 25% increase.
b. This year’s blueberry harvest is 75% of last year’s.
c. Compared with last year, this year’s peach harvest decreased 25%.
d. This year’s plum harvest is 125% of last year’s plum harvest.
- Draw a diagram to represent these situations.
a. The number of ducks living at the pond increased by 40%.
b. 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.
If there is a 100% decrease in a quantity, it means that the quantity is now 0.
If an item has a 100% decrease in a price, it means that the item is now free.
Lesson 6.4 Card Sort: 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 6 Practice Problems
- For each diagram, decide if y is an increase or a decrease relative to x. Then determine the percent increase or decrease.
- Draw diagrams to represent the following situations.
a. The amount of flour that the bakery used this month was a 40% increase relative to last month.
b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.
- Write each percent increase or decrease as a percentage of the initial amount. The first one is done for you.
a. This year, there was 40% more snow than last year.
The amount of snow this year is 140% of the amount of snow last year.
b. This year, there were 25% fewer sunny days than last year.
c. Compared to last month, there was a 50% increase in the number of houses sold this month.
d. The runner’s time to complete this marathon was 10% less than the time to complete the last marathon.
- The graph shows the relationship between the diameter and the circumference of a circle with the point (1,π) shown. Find 3 more points that are on the line.
- Priya bought x grams of flour. Clare bought 3/8 more than that. Select all equations that represent the relationship between the amount of flour that Priya bought, x, and the amount of flour that Clare bought, y.
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