Illustrative Mathematics Unit 6.3, Lesson 13: Benchmark Percentages

Learning Targets:

  • When I read or hear that something is 10%, 25%, 50%, or 75% of an amount, I know what fraction of that amount they are referring to.

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Illustrative Math
Grade 6

Lesson 13: Benchmark Percentages

Let’s contrast percentages and fractions.

Illustrative Math Unit 6.3, Lesson 13 (printable worksheets)

Lesson 13 Summary

The following diagram shows some examples of benchmark percentages.
benchmark percentages

Lesson 13.1 What Percentage Is Shaded?

What percentage of each diagram is shaded?

Lesson 13.2 Liters, Meters, and Hours

  1. What percentage of each diagram is shaded? a. How much is 50% of 10 liters of milk?
    b. How far is 50% of a 2,000-kilometer trip?
    c. How long is 50% of a 24-hour day?
    d, How can you find 50% of any number?
  2. a. How far is 10% of a 2,000-kilometer trip?
    b. How much is 10% of 10 liters of milk?
    c. How long is 10% of a 24-hour day?
    d. How can you find 10% of any number?
  3. a. How long is 75% of a 24-hour day?
    b. How far is 75% of a 2,000-kilometer trip?
    c. How much is 75% of 10 liters of milk?
    d. How can you find 75% of any number?

Lesson 13.3 - Nine is . . .

Explain how you can calculate each value mentally.

  1. 9 is 50% of what number?
  2. 9 is 25% of what number?
  3. 9 is 10% of what number?
  4. 9 is 75% of what number?
  5. 9 is 150% of what number?

13.4 Matching the Percentage

Match the percentage that describes the relationship between each pair of numbers. One percentage will be left over. Be prepared to explain your reasoning.

Are you ready for more?

  • What percentage of the world’s current population is under the age of 14?
  • How many people is that?
  • How many people are 14 or older?

Lesson 13 Practice Problems

  1. a.How can you find 50% of a number quickly in your head?
    b. Andre lives 1.6 km from school. What is 50% of 1.6 km?
    c. Diego lives ½ mile from school. What is 50% of ½ mile?
  2. There is a 10% off sale on laptop computers. If someone saves $35 on a laptop, what was its original cost? If you get stuck, consider using the table.
savings (dollars) percentage
3. Explain how to calculate these mentally.
a. 15 is what percentage of 30?
b. 3 is what percentage of 12?
c. 6 is what percentage of 10?
4. Noah says that to find 20% of a number he divides the number by 5. For example, 20% of 60 is 12, because 60 ÷ 5 = 12. Does Noah’s method always work? Explain why or why not.
5. Diego has 75% of $10. Noah has 25% of $30. Diego thinks he has more money than Noah, but Noah thinks they have an equal amount of money. Who is right? Explain your reasoning.
6. Lin and Andre start walking toward each other at the same time from opposite ends of 22-mile walking trail. Lin walks at a speed of 2.5 miles per hour. Andre walks at a speed of 3 miles per hour.
Here is a table showing the distances traveled and how far apart Lin and Andre were over time. Use the table to find how much time passes before they meet.
elapsed time (hour) Lin’s distance (miles) Andre’s distance (miles) distance apart (miles)

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.
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