Illustrative Mathematics Unit 6.3, Lesson 10: What Are Percentages?

Learning Targets:

  • I can create a double number line with percentages on one line and dollar amounts on the other line.
  • I can explain the meaning of percentages using dollars and cents as an example.

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Illustrative Math
Grade 6

Lesson 10: What Are Percentages?

Let’s learn about percentages.

Illustrative Math Unit 6.3, Lesson 10 (printable worksheets)

Lesson 10 Summary

The following diagram shows how to find percentages using a double number line.

Lesson 10.1 Dollars and Cents

Find each answer mentally.

  1. A sticker costs 25 cents. How many dollars is that?
  2. A pen costs 1.50 dollars. How many cents is that?
  3. How many cents are in one dollar?
  4. How many dollars are in one cent?

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

Lesson 10.2 Coins

  1. Complete the table to show the values of these U.S. coins.
coin penny nickel dime quarter half-dollar dollar
The value of a quarter is 25% of the value of a dollar because there are 25 cents for every 100 cents.
2. Write the name of the coin that matches each expression.
a. 25% of a dollar
b. 5% of a dollar
c. 1% of a dollar
d. 100% of a dollar
e. 10% of a dollar
f. 50% of a dollar
3. The value of 6 dimes is what percent of the value of a dollar? 4. The value of 6 quarters is what percent of the value of a dollar?

Are you ready for more?

Find two different sets of coins that each make 120% of a dollar, where no type of coin is in both sets.

  • Show Answer

    120% of a dollar = $1.20
    Possible solution:
    Set 1 = 12 dimes or 1 dollar and 2 dimes
    Set 2 = 4 quarters and 4 nickels

Lesson 10.3 - Coins on a Number Line.

A $1 coin is worth 100% of the value of a dollar. Here is a double number line that shows this.

  1. The coins in Jada’s pocket are worth 75% of a dollar. How much are they worth (in dollars)?
  2. The coins in Diego’s pocket are worth 150% of a dollar. How much are they worth (in dollars)?
  3. Elena has 3 quarters and 5 dimes. What percentage of a dollar does she have?

Glossary Terms

The word percent means “for each 100.” The symbol for percent is %.
For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.

Lesson 10 Practice Problems

  1. What percentage of a dollar is the value of each coin combination?
    a. 4 dimes
    b. 1 nickel and 3 pennies
    c. 5 quarters and 1 dime
  2. a. List three different combinations of coins, each with a value of 30% of a dollar.
    b. List two different combinations of coins, each with a value of 140% of a dollar.
  3. The United States government used to make coins of many different values. For each coin, state its worth as a percentage of $1.
    a. ½ cent
    b. 3 cents
    c. 20 cents
    d. $2½
    e. $5
  4. Complete the double number to line show percentages of $50.

  5. Elena bought 8 tokens for $4.40. At this rate:
    a. How many tokens could she buy with $6.05?
    b. How much do 19 tokens cost?
  6. A snail travels 10 cm in 4 minutes. At this rate:
    a. How long will it take the snail to travel 24 cm?
    b. How far does the snail travel in 6 minutes?
  7. a. 3 tacos cost $18. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate.
    b. If you buy t tacos for c dollars, what is the unit rate?
number of tacos cost in dollars rate in dollars per taco

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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