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Lesson 11Percentages and Double Number Lines

Let’s use double number lines to represent percentages.

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?”

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.

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.

A double number line for “distance in miles” with 7 evenly spaced tick marks. The top number line has the number 0 on the first tick mark and the remaining tick marks are blank. The bottom number line starting with the first tick mark, 0 percent, 25 percent, 50 percent, 75 percent, 100 percent, 125 percent and 150 percent are labeled

  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?

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?

    A double number line for “weight in pounds” with 2 tick marks. The top number line has the number 0 on the first tick mark and 9 on the second. The bottom number line has 0 percent on the first tick mark and 20 percent on the second.

  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?

    A double number line for “weight in pounds” with 2 tick marks. The top number line has the number 0 on the first tick mark and 9 on the second. The bottom number line has 0 percent on the first tick mark and 30 percent on the second.
  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 Summary

We can use a double number line to solve problems about percentages. For example, what is 30% of 50 pounds? We can draw a double number line like this:

“”

We divide the distance between 0% and 100% and the distance between 0 and 50 pounds into ten equal parts. We label the tick marks on the top line by counting by 5s ( 50 \div 10 = 5 ) and on the bottom line counting by 10% ( 100 \div 10 =10 ). We can then see that 30% of 50 pounds is 15 pounds.

We can also use a table to solve this problem.

A table for weight in pounds: 50, 5, 15, and percentage: 100, 10, 30. Multiply both 50 pounds and 100% by $\frac{1}{10}$ to find 5 pounds is 10%. Multiply 5 pounds and 10% by 3 to find 15 pounds is 30%.

Suppose we know that 140% of an amount is $28. What is 100% of that amount? Let’s use a double number line to find out.

A double number line with 17 evenly spaced tick marks. The top number line is labeled “money, in dollars” and the first tick mark is labeled 0, the eleventh tick mark is labeled with a question mark, and the fifteenth tick mark is labeled 28. The bottom number line is unlabeled and the first tick mark is labeled 0 percent, the eleventh tick mark is labeled 100 percent, and the fifteenth tick mark is labeled 140 percent.

We divide the distance between 0% and 140% and that between $0 and $28 into fourteen equal intervals. We label the tick marks on the top line by counting by 2s and on the bottom line counting by 10%. We would then see that 100% is $20.

Or we can use a table as shown.

A two column table with three rows of data. The first column has the heading “weight, in pounds”. The second column has the heading “percentage.” Row 1; 28, 140. Row 2; 2, 10. Row 3; 20, 100. Arrows on both sides of the table from row 1 to row 2 are labeled "multiply by one fourteenth." Arrows on both sides of the table from row 2 to row 3 are labeled "multiply by 10."

Lesson 11 Practice Problems

  1. Solve each problem. If you get stuck, consider using the double number lines.

    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?

      A double number line with 7 evenly spaced tick marks. The top number line is labeled “free throws” and the first tick mark is labeled 0. The other tick marks are unlabeled. The bottom number line is not labeled and starting with the first tick mark 0, 25 percent, 50 percent, 75 percent, 100 percent, 125 percent, and 150 percent are labeled.

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

      A double number line with 7 evenly spaced tick marks. The top number line is labeled “free throws” and the first tick mark is labeled 0. The other tick marks are unlabeled. The bottom number line is not labeled and starting with the first tick mark 0, 25 percent, 50 percent, 75 percent, 100 percent, 125 percent, and 150 percent are labeled.

  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?

    A double number line with 6 evenly spaced tick marks. The top number line is labeled “vitamin C, in milligrams” and the first tick mark is labeled 0. The other tick marks are unlabeled. The bottom number line is not labeled and starting with the first tick mark 0, 50 percent, 100 percent, 150 percent, 200 percent, and 250 percent are labeled.
  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
    1. 100 inches equal 254 centimeters. What is the distance each vehicle traveled in centimeters?
    2. 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:

    1. How many pounds of mashed potatoes can they make with 15 pounds of potatoes?
    1. How many pounds of potatoes are needed to make 50 pounds of mashed potatoes?