Percentages and Double Number Lines

Warmup

Activity #1

Equivalent percentages.

The red arrow is used to show equivalent amounts on the centimeter scale and the inches scale.

• Move the red slider to see equivalent amounts.​
• Check the Number Lines box. As you move the red slider back and forth, you see the changing percentage value as the slider moves along the scale.​
• Check the Tick Marks box. The percentage scale is divided into 4 quarters. As you move the red slider again, you see the changing percentage value as the slider moves along the scale.​
• Change the intervals to 3 and also to 5 and play around with the red slider.​
• The top line has a default reference to 20. Check the Label top line box. And the line is labeled.​
• Play around with the Intervals slider and the red slider to see the percentage value of the number on the top line. ​
• Change the Reference value and continue to practice.

Activity #2

Use the Double Number Line to Solve Percentage Problems.

• Read the problems below carefully and answer them.
• If you get stuck, consider using the double number line below.​

(1.) During a basketball practice, Mai attempted 40 free throws and was successful on 25% of them. How many successful free throws did she make?

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

(3.) 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? You can use the double number line in the applet below.

Activity #3

Application of Double Number Lines to Solve Percentage Problems

• Use the double number line to answer the questions below. Explain your reasoning.

(1.) Elena biked 8 miles on Saturday.

(a.) What is 100% of her Saturday distance?

(b.) On Sunday, she biked 75% of her Saturday distance. How far was that?

(c.) On Monday, she biked 125% of her Saturday distance. How far was that?

• Use the double number line to answer the question below. Explain your reasoning.

(2.) 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?

• Use the double number line to answer the questions below. Explain your reasoning.

(3.) Andre also has a puppy that weighs 9 pounds. The vet says that this puppy is now at about 30% of its adult weight.

(1.) What will be the adult weight of Andre’s puppy?

(2.) What is the same about Jada and Andre’s puppies? What is different?

Challenge #1

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.

(1.) What is the distance each vehicle traveled in centimeters?

(2.) Rank the vehicles in order from fastest to slowest.

Challenge #2

It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

(1.) How many pounds of mashed potatoes can they make with 15 pounds of potatoes?

(2.) How many pounds of potatoes are needed to make 50 pounds of mashed potatoes?

Challenge #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 your reasoning.