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Teacher Guide: Making Change

Learn how to calculate the correct change when paying for items with cash.

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Printable worksheet

All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Money Basics. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Calculate change by subtracting the purchase price from the amount paid
  • Use the counting up method to find change
  • Identify appropriate coin and bill combinations for change
  • Verify change received in real transactions
Prerequisites
  • • Recognizing coins and bills and their values
  • • Adding and subtracting money amounts
  • • Understanding decimal notation for money
Discussion Starters
  • 1. Have you ever received the wrong change? What did you do?
  • 2. Why is it important to know how to make change even though we have calculators?
  • 3. What is the fewest number of coins you need to make 99 cents?
  • 4. If you were a cashier, how would you count back change for a 7.50 dollar purchase paid with a 20 dollar bill?
Common Misconceptions

Thinking bigger digit means more money (37 cents is more than 3.70 dollars)

Remediation: Remind students that dollars are worth more than cents. 3.70 dollars equals 370 cents, which is much more than 37 cents.

Subtracting dollars and cents separately without borrowing

Remediation: Use place value charts. Show that 5.00 - 2.75 is NOT 3.25 (5-2=3, 0-75 is impossible). Practice borrowing from the dollar column.

Differentiation Ideas

For Struggling Students:

  • • Use physical play money to model each problem
  • • Start with whole dollar amounts only (no cents)
  • • Provide coin value charts as reference

For On-Level Students:

  • • Calculate change with dollars and cents
  • • Practice both subtraction and counting up methods
  • • Solve word problems involving multiple items

For Advanced Students:

  • • Determine the minimum number of coins and bills for any amount
  • • Calculate change in different currencies
  • • Solve multi-step problems involving discounts and taxes
Standards Alignment
  • 2.MD.C.8 (CCSS.MATH.CONTENT.2.MD.C.8)

    Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and cent symbols appropriately

  • 3.NBT.A.2 (CCSS.MATH.CONTENT.3.NBT.A.2)

    Fluently add and subtract within 1000 using strategies and algorithms

Lesson Resources
  • visualInteractive Cash Register

    Students practice making change with virtual money

  • activityStore Simulation

    Role-play buying and selling with play money

  • worksheetMaking Change Practice

    Word problems with various purchase amounts

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Making change means calculating how much money to give back when someone pays more than the purchase price.
The basic formula is:
Change=Amount Paid−Purchase Price\text{Change} = \text{Amount Paid} - \text{Purchase Price}
For example, if you buy something for 3 dollars and 50 cents and pay with a 5 dollar bill:
Change=5.00−3.50=1.50\text{Change} = 5.00 - 3.50 = 1.50
You should receive 1 dollar and 50 cents back!

Worked Examples

You buy a book for 7 dollars and pay with a 10 dollar bill. How much change do you get?
1

Identify the amounts

Purchase price: 7 dollars. Amount paid: 10 dollars → 7 and 10
2

Subtract to find change

10.00−7.00=3.0010.00 - 7.00 = 3.00 → 3 dollars
3

Count the bills

Three 1 dollar bills make 3 dollars → 3 one-dollar bills

Common Mistakes

Forgetting to borrow when subtracting cents

Why it's wrong: When the cents you are subtracting is larger than the cents you have, you need to borrow from the dollars.

Correct: If subtracting 75 cents from 50 cents, borrow 1 dollar (100 cents) first: 150 - 75 = 75 cents, then subtract the borrowed dollar from the dollars.

Confusing the price and amount paid

Why it's wrong: Change should always be positive! If you get a negative answer, you probably subtracted in the wrong order.

Correct: Always subtract: Amount Paid - Purchase Price. The larger number (what you gave) minus the smaller (what it costs).

Giving wrong coin combinations

Why it's wrong: There are often multiple ways to make the same amount, but some are more efficient.

Correct: Use the fewest coins possible. For 75 cents, use 3 quarters instead of 7 dimes and 1 nickel.

Why It Matters

Making change is a life skill you will use almost every day:
  • Shopping: Verify that cashiers give you the correct change
  • Working: Many jobs involve handling cash and making change for customers
  • Selling: At garage sales, lemonade stands, or fundraisers
  • Budgeting: Understanding exactly how much money you have left after purchases
Knowing how to make change helps you manage your money wisely and catch mistakes!

Real World Applications

Working as a Cashier

Cashiers must quickly calculate change for every cash transaction to keep lines moving and customers happy.

Example:

A customer buys items totaling 23.47 dollars and pays with 30 dollars. The cashier gives back 6.53 dollars: one 5 dollar bill, one 1 dollar bill, two quarters, and 3 pennies.

1Try It Yourself

A customer buys a meal for 8.75 dollars and pays with a 10 dollar bill.

What change should you give?

Step 1: Write the mathematical expression

Calculate: 10.00−8.7510.00 - 8.75

Garage Sale

Running a garage sale means making change all day long for different items at various prices.

Example:

You sell a game for 4 dollars. The buyer gives you a 20 dollar bill. You need to count back 16 dollars in change.

2Try It Yourself

Someone buys three items: a book for 2 dollars, a toy for 3.50 dollars, and a puzzle for 1.75 dollars. They pay with a 10 dollar bill.

How much change do you give?

Step 1: Write the mathematical expression

First add: 2+3.50+1.752 + 3.50 + 1.75, then subtract from 10

Checking Your Change

Always count your change to make sure you received the correct amount. Mistakes happen!

Example:

You buy a drink for 2.50 dollars and pay with a 5 dollar bill. You should get 2.50 dollars back. If the cashier only gives you 2 dollars, speak up politely!

3Try It Yourself

You buy a sandwich for 6.25 dollars and pay with a 20 dollar bill. The cashier gives you 13.25 dollars in change.

Is this correct? If not, how much should you have received?

Step 1: Write the mathematical expression

Calculate: 20.00−6.2520.00 - 6.25

Key Takeaways

  • 1Change equals the amount paid minus the purchase price
  • 2The counting up method: start at the price and count up to the amount paid
  • 3Use the fewest bills and coins possible for efficient change
  • 4Always double-check your change to catch any mistakes

Frequently Asked Questions

What is the counting up method?

Instead of subtracting, you start at the purchase price and count up to the amount paid. For example, from 3.67 to 5.00 dollars: add 3 cents to get 3.70, add 30 cents to get 4.00, add 1 dollar to get 5.00. Your change is 1.33 dollars.

Why do cashiers count change back to you?

Counting change back helps both the cashier and customer verify the correct amount. It also helps catch mistakes before the customer leaves.

What if I do not have exact change?

Pay with a larger bill or coin combination, and the cashier will give you the difference back. For example, pay for a 3.25 dollar item with a 5 dollar bill and get 1.75 dollars back.

Glossary

Change
The money returned to you when you pay more than the purchase price
Purchase price
The cost of the item or items you are buying
Counting up
A method of finding change by adding from the price to the amount paid
Denomination
The value printed on a bill or coin (1 dollar, 5 dollars, 25 cents, etc.)

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