Making change

What is this skill?

Making change is the everyday skill of working out how much money comes back after you pay. A pencil costs 35 cents and you pay with 50 cents, so you get 15 cents back. Third graders learn to count coins, add prices and subtract from the amount they handed over, and many learn the shopkeeper's trick of counting up: start at the price and add coins until you reach what was paid.

In this practice a child reads coin pictures and says how much money they show, such as a quarter, a dime and a nickel (40 cents), or a dollar, a quarter and a dime ($1.35). Many questions are typed: "A sticker costs 20¢. You pay with 25¢. How much change?" or "A toy costs $3.50. You pay with $5." Later ones add two prices, such as juice for $1.20 and a muffin for $2.30, or two pens at $1.25 each paid with $5. Some questions ask which coins make exactly 30¢, or which coins could be change from $1 for a 65¢ snack. A true-or-false question confirms that four quarters make one dollar. The printable worksheet has coin pictures and answer lines for the typed questions.

Why it matters

Money is the place where third grade math meets real life. A child who can add decimals and subtract from a dollar is practicing the same skills that appear in school math, but with a reason to care about the answer.

It builds confidence in shops. A child who can check their change is less likely to be rushed or confused at a counter, and the skill is a base for the budgeting they will learn in the upper grades.

Counting up also strengthens number sense. Going from 35 to 40 to 50 shows that subtraction can be done by adding, which is one of the most useful mental math ideas.

Common mistakes

• Adding the price and the payment, not subtracting. Ask "Which is more, what I paid or what it cost?" The change is the difference.
• Mixing up the values of coins. A nickel is bigger than a dime but worth less. Practice with real coins and say the values aloud.
• Losing track of the decimal point, for example writing $1.5 for $1.50. In money, always show two places after the point, so $1.50 means one dollar and fifty cents.
• Mixing cents and dollars in one problem, such as paying with $1 for a 45¢ item and subtracting 45 from 1. Change the dollar to 100 cents first, or count up from 45¢ to $1.

How to help at home

• Set up a pretend store with a few items priced in cents and a jar of coins. Let your child be the cashier and give change.
• Count up out loud at the real checkout. Say "The total is 3.50 and I paid 5. Fifty cents more makes 4, then one more dollar makes 5," and let your child try next time.
• Let your child count the coins in a pocket jar and write the total with the cent or dollar sign.
• Ask "Which coins make 30 cents?" at random times. There is more than one right answer, and finding two is a good challenge.

Worked examples

These are real questions from the Tutorsaurus making change practice, with the answers worked out.

1. Example 1

   How much money is this?

   25¢

   10¢

   5¢

   Choices: 35¢, 40¢, 45¢

   Answer: 40¢. 25¢ + 10¢ + 5¢ = 40¢.

2. Example 2

   A toy costs $3.50. You pay with $5. How much change?

   Answer: 1.50 $. $5.00 − $3.50 = $1.50. From $3.50 to $4 is 50¢, then $4 to $5 is $1. Total $1.50.

3. Example 3

   Maya pays for a 65¢ snack with $1. Which coins could be her change?

   Choices: A quarter and a dime, A dime and a nickel, Two quarters

   Answer: A quarter and a dime. 100¢ − 65¢ = 35¢. A quarter and a dime make 25¢ + 10¢ = 35¢.

Printable worksheet (PDF) — one page of questions from this practice that work on paper, easier ones first, with an answer key on page 2. Free to print, no sign-up.