# Illustrative Mathematics Unit 6.3, Lesson 14: Solving Percentage Problems

Learning Targets:

• I can choose and create diagrams to help me solve problems about percentages.

Related Pages
Illustrative Math

### Lesson 14: Solving Percentage Problems

Let’s solve more percentage problems.

Illustrative Math Unit 6.3, Lesson 14 (printable worksheets)

### Lesson 14 Summary

The following diagram shows how to solve a percentage problem with the help of double number lines or tables.

### Lesson 14.1 Number Talk: Multiplication with Decimals

Find the products mentally. 6 · (0.8) · 2
(4.5) · (0.6) · 4

Scroll down the page for the answer to the “Are you ready for more?” section.

### Lesson 14.2 Coupons

Han and Clare go shopping, and they each have a coupon. Answer each question and show your reasoning.

1. Han buys an item with a normal price of \$15, and uses a 10% off coupon. How much does he save by using the coupon?
2. Clare buys an item with a normal price of \$24, but saves \$6 by using a coupon. For what percentage off is this coupon?

#### Are you ready for more?

Clare paid full price for an item. Han bought the same item for 80% of the full price. Clare said, “I can’t believe I paid 125% of what you paid, Han!” Is what she said true? Explain.

Clare paid 100% of the price.
Han paid 80% of the price.
Clare paid 100 ÷ 80 = 1¼ = 125% times more than Han.
So, what Clare said is true.

#### Lesson 14.3 - Info Gap: Music Devices

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:

3. Explain how you are using the information to solve the problem.
If your teacher gives you the data card:
6. Ask your partner “What specific information do you need?” and wait for them to ask for information.
If your partner asks you for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
7. Have them explain “Why do you need that information?” before telling them the information.
8. After your partner solves the problem, ask them to explain their reasoning, even if you understand what they have done.
Both partners should record a solution to the problem.

#### Lesson 14 Practice Problems

1. For each problem, explain or show your reasoning.
a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
2. A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves \$13, what was the original price of her purchase? Explain or show your reasoning.
3. The original price of a scarf was \$16. During a store-closing sale, a shopper saved \$12 on the scarf. What percentage discount did she receive? Explain or show your reasoning.
4. Select all the expressions whose value is larger than 100.
A. 120% of 100
B. 50% of 150
C. 150% of 50
D. 20% of 800
E. 200% of 30
F. 500% of 400
G. 1% of 1,000
5. An ant travels at a constant rate of 30 cm every 2 minutes.
a. At what pace does the ant travel per centimeter?
b. At what speed does the ant travel per minute?
6. Is 3½ cups more or less than 1 liter? Explain or show your reasoning. (Note: 1 cup ≈ 236.6 milliliters)
7. Name a unit of measurement that is about the same size as each object.
a. The distance of a doorknob from the floor is about 1 _____________.
b. The thickness of a fingernail is about 1 _____________.
c. The volume of a drop of honey is about 1 _____________.
d. The weight or mass of a pineapple is about 1 _____________.
e. The thickness of a picture book is about 1 _____________.
f. The weight or mass of a buffalo is about 1 _____________.
g. The volume of a flower vase is about 1 _____________.
h. The weight or mass of 20 staples is about 1 _____________.
i. The volume of a melon is about 1 _____________.
j. The length of a piece of printer paper is about 1 _____________.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.