Math 7 · Unit 2, Lesson 5
Percent Increase and Decrease
How much it grew or shrank, compared to the start.
I say it the way your test says it.
And I say it the way you would say it to a friend. Same idea, two ways.
Write it down. Do every step on paper, one line per step. Percent problems go wrong in your head, not on the page. If you changed something, it should be on the paper.
Go in order. Each tile has a short explanation, then a "Let me try a few" button.
When you have finished
At the end of each tile you will find a review form to give us feedback.
NC standards: NC.7.RP.3.
Words we use
| Word | Plain English | What you do |
|---|---|---|
| Percent increase | How much it grew, as a percent of where it started. | Change divided by the original, then to a percent. |
| Percent decrease | How much it shrank, as a percent of where it started. | Same division, and say decrease. |
| Original | The starting amount. | Always the thing you divide by. |
| Change | New minus original, or original minus new. | Find it first. |
The big idea
A proportional relationship always multiplies by the same number, the unit rate.
Percent means out of 100. A percent is a unit rate for 100 instead of for 1: 30 percent means 30 for every 100.
This lesson added change over time. Percent change compares the change to the original amount, so the same jump is a bigger percent when you start smaller: Town A and Town B both added 3,000 people, but that is 60 percent of 5,000 and 50 percent of 6,000. To find a percent change, find the change and divide by the original, never the new amount. To find a new amount, use one multiplier: more than 1 to grow, less than 1 to shrink.
Exit ticket
On paper or an index card. Use the math word and the plain-English word.
- A plant grows from 40 centimeters to 50 centimeters. What is the percent increase?
- A company with 70 employees grows by 10 percent. How many now?
- Two towns each added 3,000 people, one starting at 5,000 and one at 6,000. Which grew by a bigger percent?
Check your exit ticket
- 25 percent.
- 77.
- The one that started at 5,000: 60 percent against 50 percent.
Printables
A one-page study guide with Elle and Finn, the two big-idea sentences, Town A and Town B, the divide-by-the-original rule, and the growth and shrink multipliers. Plus a worksheet with an answer key and a lesson plan that walks a parent or tutor through the three tiles.
Where this goes next
NC Grade 7 standards in this lesson: NC.7.RP.3.