# Illustrative Mathematics Unit 6.3, Lesson 11: Percentages and Double Number Lines

Learning Targets:

• I can use double number line diagrams to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”

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Illustrative Math

### Lesson 11: Percentages and Double Number Lines

Let’s use double number lines to represent percentages.

Illustrative Math Unit 6.3, Lesson 11 (printable worksheets)

### Lesson 11 Summary

The following diagrams show how to use double number lines or tables to solve problems about percentages.

### Lesson 11.1 Fundraising Goal

Each of three friends—Lin, Jada, and Andre—had the goal of raising \$40. How much money did each person raise? Be prepared to explain your reasoning.

1. Lin raised 100% of her goal.
2. Jada raised 50% of her goal.
3. Andre raised 150% of his goal.

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

#### Lesson 11.2 Three-Day Biking Trip

Elena biked 8 miles on Saturday. Use the double number line to answer the questions. Be prepared to explain your reasoning.

1. What is 100% of her Saturday distance?
2. On Sunday, she biked 75% of her Saturday distance. How far was that?
3. On Monday, she biked 125% of her Saturday distance. How far was that?

#### Lesson 11.3 - Puppies Grow Up

1. Jada has a new puppy that weighs 9 pounds. The vet says that the puppy is now at about 20% of its adult weight. What will be the adult weight of the puppy?
2. Andre also has a puppy that weighs 9 pounds. The vet says that this puppy is now at about 30% of its adult weight. What will be the adult weight of Andre’s puppy?
3. What is the same about Jada and Andre’s puppies? What is different?

#### Are you ready for more?

A loaf of bread costs \$3.00 today. The same size loaf cost 20 cents in 1955.

1. What percentage of today’s price did someone in 1955 pay for bread?
2. A job pays \$10.00 an hour today. If the same percentage applies to income as well, how much would that job have paid in 1955?

#### Lesson 11 Practice Problems

1. Solve each problem. If you get stuck, consider using the double number lines.
a. During a basketball practice, Mai attempted 40 free throws and was successful on 25% of them. How many successful free throws did she make?

b. Yesterday, Priya successfully made 12 free throws. Today, she made 150% as many. How many successful free throws did Priya make today?

2. A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?

3. At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 100 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school? Explain or show your reasoning.
4. Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can along a straight, level path.
 vehicle distance traveled skateboard 90 feet scooter 1,020 inches bike 4,800 centimeters go-cart 0.03 kilometers
a. 100 inches equal 254 centimeters. What is the distance each vehicle traveled in centimeters?
b. Rank the vehicles in order from fastest to slowest.
5. It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:
a. How many pounds of mashed potatoes can they make with 15 pounds of potatoes?
b. How many pounds of potatoes are needed to make 50 pounds of mashed potatoes?

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.