Lesson 10What Are Percentages?

Learning Goal

Let’s learn about 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.

Lesson Terms

  • percent
  • percentage

Warm Up: Dollars and Cents

Problem 1

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?

Activity 1: Coins

Problem 1

Complete the table to show the values of these U.S. coins.

An image of 6 U.S. coins. A penny, nickel, dime, quarter, half dollar, and dollar coin are presented.

The value of a quarter is 25% of the value of a dollar because there are 25 cents for every 100 cents.

A tape diagram of 1 Quarter and a 25 cent box. The bottom row is 1 Dollar and a 100 cent box.

coin

penny

nickel

dime

quarter

half dollar

dollar

value (cents)

Problem 2

Write the name of the coin that matches each expression.

  1. 25% of a dollar

  2. 5% of a dollar

  3. 1% of a dollar

  4. 100% of a dollar

  5. 10% of a dollar

  6. 50% of a dollar

Problem 3

The value of 6 dimes is what percent of the value of a dollar?

Problem 4

The value of 6 quarters is what percent of the value of a dollar?

Are you ready for more?

Problem 1

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

Activity 2: Coins on a Number Line

Problem 1

An image of a 1 dollar coin.

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

A double number line for “value of coins in dollars” with 7 evenly spaced tick marks. The top number line has the number 0 is on the first tick mark and 1 on the fifth. The remaining tick marks are blank. The bottom number starting with the first tick mark 0 percent, 25 percent, 50 percent, 75 percent, 100 percent, 125 percent and 150 percent are labeled.

  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?

Lesson Summary

A percentage is a rate per 100.

We can find percentages of $10 using a double number line where 10 and 100% are aligned, as shown here:

A double number line for the dollar value of money: 0, 2.50,5.00, 7.50, 10.00, 12.50, 15.00 and percentages: 0, 25, 50, 75, 100, 125, 150.

Looking at the double number line, we can see that $5.00 is 50% of $10.00 and that $12.50 is 125% of $10.00.