F. Financial Literacy · Making Change

What Is Change?

F1.1 A1About 35 minutes

Learning goals

I can explain what change is.
I can count up to find the change from $5, $10 or $20 when the price is in whole dollars.
I can use an adding fact to find change.
I can show the change with bills and coins, and check it by adding.

Words to know

price
How much something costs. A book with a price of $7 costs seven dollars.

pay
To give money to buy something.

change
The money you get back when you pay more than the price. If you pay $10 for a $7 book, your change is $3.

cashier
The person at a store who takes your money and gives you your change.

count up
Start at one number and count forward to another number to find how far apart they are.

whole-dollar amount
An amount with dollars and no cents, like $4 or $10.

Remember from Grade 2

In Grade 2 you counted coins and bills up to $200. You found different ways to pay exactly, and you figured out how much more money you needed to buy something.

In Grade 3 you will learn what happens when you pay more than the price. The store gives you money back. That money is called change.

Let's get started!

It is the school book fair. Sam finds a book about hockey. The price is $7.

Sam has only a $10 bill. That is more than $7. Can Sam still buy the book?

Yes! Sam gives the $10 bill to the cashier. The cashier keeps $7 for the book and gives Sam the extra money back. Sam gets back a toonie and a loonie. That is $3. The $3 is Sam's change.

Sam pays with a $10 bill. The book costs $7. Sam gets $3 in change: a toonie ($2) and a loonie ($1).

What is change?

When you pay more than the price, the store gives you back the extra. That is your change.

Change = the money you pay − the price

For Sam: $10 − $7 = $3.

If you pay the exact price, there is no change. If you pay a $5 bill for a $5 toy, you get nothing back.

The big idea

The price and the change always add up to the money you paid.

price + change = money you paid

$7 + $3 = $10. This is how you can check your change.

Strategy 1: Count up like a cashier

Many cashiers find change by counting up. They start at the price and count up to the money you paid.

For Sam's book: start at $7. Count up: $8, $9, $10. That is 3 counts, so the change is $3.

Start at the price, $7. Jump up to the money paid, $10. The jump is 3, so the change is $3.

Worked example

Example 1: Change from $10

A puzzle costs $6. Mila pays with a $10 bill. How much change does she get?

Start at the price: $6.
Count up to $10: $7, $8, $9, $10. That is 4 counts.
Check by adding: $6 + $4 = $10. ✔
The cashier could give 2 toonies ($2, $4).

Mila gets $4 in change.

Worked example

Example 2: Change from $5

A colouring book costs $3. Owen pays with a $5 bill. What is his change?

Start at $3. Count up to $5: $4, $5. That is 2 counts.
Check: $3 + $2 = $5. ✔

Owen gets $2 in change. That could be one toonie.

Strategy 2: Use an adding fact you know

You already know the pairs that make 10: 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5. These pairs are a fast way to find change from a $10 bill.

If the price is $8, ask yourself: "8 plus what makes 10?" 8 + 2 = 10, so the change is $2.

The pairs that make 5 (1 + 4 and 2 + 3) work for change from a $5 bill.

Price	Pay with	Adding fact	Change
$9	$10	9 + 1 = 10	$1
$8	$10	8 + 2 = 10	$2
$7	$10	7 + 3 = 10	$3
$6	$10	6 + 4 = 10	$4
$5	$10	5 + 5 = 10	$5
$4	$10	4 + 6 = 10	$6
$3	$10	3 + 7 = 10	$7
$2	$10	2 + 8 = 10	$8
$1	$10	1 + 9 = 10	$9

Change from a $10 bill. Notice the pattern: when the price goes down by $1, the change goes up by $1.

Worked example

Example 3: Change from $20

A board game costs $14. Ava pays with a $20 bill. How much change does she get?

Count up in two jumps. From $14 to $15 is $1.
From $15 to $20 is $5.
Add the jumps: $1 + $5 = $6.
Check: $14 + $6 = $20. ✔
The cashier could give a $5 bill and a loonie.

Ava gets $6 in change.

Counting up from $14 to $20: a jump of 1 to $15, then a jump of 5 to $20. 1 + 5 = 6.

Jump to a friendly number

When you count up, it helps to jump to a friendly number first, like $5, $10, $15 or $20. Then make one big jump to the money paid.

Be a careful cashier

Good cashiers take their time. They count the change out loud as they hand it over, and they check it. If you are not sure, it is fine to slow down and count again. Being careful is a math skill!

Just for fun

The loonie got its name from the common loon, the bird on the coin. When Canada made a $2 coin, people called it the toonie, a mix of "two" and "loonie". It is a rhyming coin!

Hands-on activity

Open a home store

You need: 6 to 8 small things from home (a toy, a book, a pencil, a box of crayons), sticky notes, and real or play money (some $5 and $10 bills, toonies and loonies). Paper play money works well.

With a grown-up, write a price tag for each thing. Use whole dollars from $1 to $9.
One person is the cashier. The other is the shopper.
The shopper picks one thing and pays with a $10 bill (or a $5 bill if the price is $5 or less).
The cashier finds the change by counting up out loud: "Six dollars... seven, eight, nine, ten." The cashier hands over a coin or bill for each part of the count.
The shopper checks: price + change = money paid.
Switch jobs and play again.

Math talk: "How did you know how much change to give?"

Your turn

A pencil case costs $4. You pay with a $5 bill. What is your change?

A toy car costs $7. You pay with a $10 bill. What is your change?

A comic book costs $2. You pay with a $10 bill. What is your change?

A snack box costs $5. You pay with a $10 bill. What is your change?

A puzzle costs $9. You pay with a $10 bill. What is your change?

A ball costs $6. Kim pays with a $10 bill. The cashier gives her $3 back. Is that right? Check by adding.

Show $6 in change using the fewest bills and coins.

More practice: warm-up

A book costs $8. You pay with a $10 bill. What is your change?

A card costs $3. You pay with a $5 bill. What is your change?

A toy costs $2. You pay with a toonie. What is your change?

Finish the fact: 7 + □ = 10

A sticker sheet costs $1. You pay with a $5 bill. What is your change?

More practice: on your own

Mittens cost $6. Leo pays with a $10 bill. What is his change? Show how you counted.

A toque costs $12. Nadia pays with a $20 bill. What is her change?

Leah buys a $3 bookmark with a $10 bill. Her change is exactly 2 pieces of money. What are they?

A game costs $8. Jon pays with a $10 bill and gets a toonie and a loonie back. Is that right?

Ben paid with a $10 bill and got $6 in change. What did his item cost?

Challenge

Kai buys a kite for $13 with a $20 bill. Show his change with the fewest bills and coins.

A cashier gives Ava change from a $10 bill. Find two different ways to give her $3.

Tom has a $5 bill and a $10 bill. He wants a book that costs $7. Which bill should he use? What is his change?

Check your understanding

Quiz

What is change?

A toy costs $6. You pay with a $10 bill. What is your change?

Which adding fact helps you find the change from $10 for a $7 toy?

A book costs $8. You pay with a $10 bill. Which change is correct?

Nia paid with a $5 bill and got $1 back. What was the price?

How can you check your change?

For parents and teachers

What your child is learning: what change is, and how to find the change for simple purchases with whole-dollar prices (Ontario Grade 3 math, F1.1: estimate and calculate the change required for simple cash transactions). The key strategies are counting up from the price to the amount paid (the way many cashiers do it) and using adding facts they already know, like the pairs that make 10. Checking the answer with price + change = amount paid also builds the link between adding and subtracting.

Common difficulties:

Adding instead of subtracting (saying the change for a $6 toy from $10 is $16). Ask, "Will you get back more money than you gave?"
Counting the starting number. When counting up from $6 to $10, the first count is $7, not $6. Have your child hold up a finger for each count after the price.
Knowing the amount but not how to show it. Practise handing over the change with real or play money.

How to help: Play store at home with whole-dollar prices. When you pay at a store, let your child predict the change, then watch what the cashier gives back. Praise careful, out-loud counting and checking (this lesson also practises the social-emotional skill of staying careful and patient, part of A1).