Math Background

Lesson: Comparing Money Amounts
Developing the Concept

In this lesson, students extend their understanding of money to making change.

Materials: play money for each group of students: $20, $10, $5, and $1 bills; half-dollars, quarters, dimes, nickels, pennies

Preparation: Distribute play money to each group.

Prerequisite Skills and Background: Students should know the value of coins and bills and how to write amounts of money. Students should also be able to count by 5s, 10s, 20s, and 25s.

  • Say: Suppose you used a $10 bill to pay for a pen that costs $6.00. Find out how much change you should receive by counting on from $6.00 to $10.00 with $1 bills.
    Have students count aloud $7.00, $8.00, $9.00, $10.00 as they show four $1 bills.
  • Ask: What is the change?
    (four $1 bills or $4.00)
  • Ask: If you paid for the pen with a $20 bill, what would your change be? Count aloud from $6 to $20 with $1 and $5 bills to find out.
    ($7.00, $8.00, $9.00, $10.00, $15.00, $20.00; four $1 bills and two $5 bills)
  • Ask: What is the value of the bills you used to make the change? ($14.00.)
    You may need to remind students that to find the total value of bills, it is easier to count on from the bill with the greatest value.
  • Ask: Are there any other combinations of bills that equal $14.00?
    Some students may say fourteen $1 bills. Others may say four $1 bills and one $10 bill. Have students count on from $6 to $20 as they show four $1 bills and one $10 bill. ($7.00, $8.00, $9.00, $10.00, $20.00)
  • Say: Suppose you used 20¢ to pay for an eraser that costs 17¢. Count on from 17¢ to 20¢ with pennies to find the change you should receive.
    (18¢, 19¢, 20¢)
  • Ask: What is the change? (3 pennies or 3¢)
  • Ask: If you paid for the eraser with a quarter, what would your change be? Count on from 17¢ to 25¢ with pennies and a nickel to find out. (18¢, 19¢, 20¢, 25¢; 8¢)
  • Say: Suppose you used a $20 bill to pay for a T-shirt that costs $14.77. Let's find out how much change you should receive. Count on from $14.77, starting with pennies. Then use coins and bills of increasing value until you reach $20.00.
    Point out to students that there is more than one way to solve this problem.
  • Ask: Who can tell us how they counted on from $14.77?
    Have a volunteer from one group count aloud as you draw each coin and bill on the board. Label pennies P, nickels N, and so on. (one possible answer: $14.78, $14.79, $14.80, $14.90, $15.00, $20.00; three pennies, two dimes, and one $5 bill)
  • Ask: Did anyone count on by using a different combination of coins and bills?
    Have volunteers from other groups explain how they counted on to reach $20.00. If everyone in the class used the same bills and coins, ask students to suggest other combinations. (one possible combination: three pennies, two nickels, one dime, five $1 bills)
  • Ask: What is the total value of the bills and coins you used to make the change? ($5.23)
    You may need to remind students again that to find the total value of coins and bills, it is easier to count on from the bill with the greatest value.
  • Say: Suppose you used a $10 bill to pay for a baseball that costs $3.48. To find the change you should receive, what amount will you count on from? ($3.48) What amount will you count up to? ($10.00)
  • Ask: What is the least number of coins and bills needed to make the change? (three pennies, one half-dollar, one $1 bill, one $5 bill)
    Give students adequate time to try different combinations of coins. Have a volunteer count on as you draw each coin and bill on the board. ($3.49, $3.50, $4.00, $5.00, $10.00)

Wrap-Up and Assessment Hints
Point out to students that when they find change, they count on from the cost of the item to the amount paid by using bills and coins of increasing, not decreasing, value. Remind them to start with smaller values, then progress to greater values. When you assess students, have them explain the strategies they used to find change.


Houghton Mifflin Math Grade 4