F. Financial Literacy · Making Change

Estimating Change

F1.1 A1About 35 minutes

Learning goals

I can estimate change before I find the exact amount.
I can use friendly numbers like 25¢, 50¢, 75¢, $5 and $10 to estimate.
I can tell if the change will be more or less than half of the money I paid.
I can use an estimate to decide if change makes sense.

Words to know

estimate
A close guess that uses numbers that are easy to work with. "About 25¢" is an estimate.

exact
The amount that is exactly right. The exact change for a 70¢ snack paid with a loonie is 30¢.

friendly number
A number that is easy to work with, like 25, 50, 75 and 100, or $5 and $10.

half
One of two equal parts. Half of $1 is 50¢. Half of $10 is $5.

reasonable
Makes sense. An answer is reasonable if it is close to your estimate.

Let's get started!

Jai buys a 70¢ juice at the corner store. He pays with a loonie. The store is busy, and the cashier quickly gives him 3 quarters.

Jai thinks, "Hmm, 3 quarters is 75¢. That seems like a lot of change."

Jai is right to wonder. He did not need to find the exact answer to notice. He made an estimate.

What is an estimate?

An estimate is a close guess. To estimate change, move the price to a friendly number that is close by.

Friendly numbers for cents: 25¢, 50¢, 75¢, 100¢.

Friendly numbers for dollars: $5, $10, $20.

Jai's juice costs 70¢. 70 is close to 75. And 75 + 25 = 100. So the change is about 25¢. 75¢ is much too much!

70 is close to the friendly number 75. From 75 to 100 is 25, so the change is about 25¢. (Exact: 30¢.)

Worked example

Example 1: Estimate, then find the exact change

A cookie costs 45¢. You pay with a loonie. Estimate the change, then find the exact change.

Estimate: 45 is close to 50. 50 + 50 = 100. The change is about 50¢.
Exact: 45 to 50 is 5. 50 to 100 is 50. 5 + 50 = 55.
Compare: 55¢ is close to 50¢. The answer makes sense.

About 50¢. Exactly 55¢.

Is the change more or less than half?

Half of a loonie is 50¢. Half of a $10 bill is $5.

If the price is less than half, you get more than half back.
If the price is more than half, you get less than half back.
If the price is exactly half, you get half back.

This is a quick way to see if change makes sense.

The dashed line shows half of a loonie. The 35¢ sticker ends before the line, so the change (65¢) is longer than half.

Worked example

Example 2: More or less than half?

A sticker costs 35¢. You pay with a loonie. Will the change be more or less than 50¢?

35¢ is less than 50¢ (half a dollar).
So the change will be more than 50¢.
Exact: 35 to 40 is 5, 40 to 100 is 60. 5 + 60 = 65¢. Yes, 65¢ is more than 50¢. ✔

More than 50¢. The exact change is 65¢.

Price	Close friendly number	Estimated change from $1	Exact change
20¢	25¢	about 75¢	80¢
45¢	50¢	about 50¢	55¢
70¢	75¢	about 25¢	30¢
80¢	75¢	about 25¢	20¢
95¢	100¢	a very small amount	5¢

Estimates are close to the exact change, but not always the same.

Worked example

Example 3: Whole dollars

A book costs $8. Mia pays with a $10 bill. The cashier gives her a $5 bill and a toonie. Does that make sense?

Estimate: $8 is more than half of $10. So the change should be less than $5.
A $5 bill and a toonie are $7. That is more than $5. Something is wrong!
Exact: $8 + $2 = $10. The change should be $2.

No, it does not make sense. Mia should get $2 back. She should politely tell the cashier.

Worked example

Example 4: Catch a mistake

Leo buys a $4 car. He pays with a $10 bill and gets a $5 bill back. Is that the right change?

Estimate: $4 is less than half of $10, so the change should be more than $5.
Leo got exactly $5. That is not more than $5. So it is not right.
Exact: $4 + $6 = $10. The change should be $6.

No. Leo is short by $1. The change should be $6.

Estimate, calculate, compare

Estimate with a friendly number.
Calculate the exact change.
Compare. If the exact answer is far from your estimate, check again!

When change seems wrong

Everyone makes mistakes, even grown-ups and cashiers. If your change does not make sense, stay calm. Say kindly, "Excuse me, could you please check my change?" Then count it together.

Just for fun

Canada stopped making pennies in 2012. That is why cash prices get rounded to the nearest 5¢. The pennies are retired now... maybe relaxing on a beach somewhere!

Hands-on activity

Quick estimate game

You need: 10 small cards or scraps of paper, a pencil, and some coins (real or play).

With a grown-up, write a price on each card. All prices are less than $1 and end in 0 or 5.
Mix up the cards and put them face down.
Turn over a card. Within 5 seconds, say an estimate of the change from a loonie. Use a friendly number: "70¢ is close to 75¢, so about 25¢."
Now find the exact change with coins by counting up.
Was your estimate close? Give yourself a point if it was within 10¢.
Take turns.

Math talk: "Which friendly number did you use? Why?"

Your turn

A pen costs 55¢. You pay with a loonie. Estimate the change. Then find the exact change.

An eraser costs 20¢. You pay with a loonie. Estimate, then find the exact change.

A juice costs 60¢. You pay with a loonie. Will the change be more or less than 50¢?

A toy costs $2. You pay with a $10 bill. Will the change be more or less than $5?

A puzzle costs $9. You pay with a $10 bill. About how much change will you get?

A pencil costs 30¢. Ana pays with a loonie and gets 20¢ back. Is that reasonable? Explain.

A muffin costs 80¢. You pay with a loonie. Estimate, then find the exact change.

More practice: warm-up

Which friendly number is 70 closest to: 50, 75 or 100?

What is half of a loonie (100¢)?

What is half of $10?

Which friendly number is 95 closest to: 50, 75 or 100?

Which friendly number is 30 closest to: 25, 50 or 75?

More practice: on your own

A cookie costs 40¢. You pay with a loonie. Estimate, then find the exact change.

A bookmark costs $7. You pay with a $10 bill. Will the change be more or less than $5? What is the exact change?

Mia buys an 85¢ snack with a loonie. She gets a quarter back. Is that reasonable?

A ball costs $6. Sam pays with a $10 bill and gets $6 back. Is that reasonable?

A snack costs 70¢. Will one quarter be enough change from a loonie? Estimate first.

Challenge

Noor pays with a loonie. She estimates her change is about 50¢. Name two prices her snack could have.

Ben paid with a $10 bill and his change was more than $5. Which could be the price: $3, $6 or $8? Explain.

Ari buys a 35¢ treat with a loonie. The cashier gives back 2 quarters, a dime and a nickel. Estimate first, then check if the change is exactly right.

Check your understanding

Quiz

A cookie costs 45¢. You pay with a loonie. About how much change will you get?

A toy costs $2. You pay with a $10 bill. What can you say about the change?

Which friendly number is 70¢ closest to?

An apple costs 90¢. You pay with a loonie and get 2 quarters back. Is that reasonable?

What is an estimate?

A muffin costs 80¢. You estimate the change from a loonie is about 25¢. What is the exact change?

For parents and teachers

What your child is learning: the estimate part of F1.1 (estimate and calculate the change required for simple cash transactions). Children move a price to a nearby friendly number (25¢, 50¢, 75¢, 100¢, $5, $10) and use "more or less than half" to predict the change, then use the estimate to judge whether exact change is reasonable. They also practise speaking up calmly and politely when something seems wrong (social-emotional learning skills, A1).

Common difficulties:

Thinking an estimate must equal the exact answer. An estimate is close, not exact. Both "about 25¢" and "exactly 30¢" can be correct answers to different questions.
Choosing a far-away friendly number (saying 70 is close to 50). Use a number line from 0 to 100 marked at 25, 50 and 75 to see which mark is nearest.
Mixing up the "half" rule: a cheap price means more change, not less. Act it out: a 10¢ item from a loonie leaves a lot of change.

How to help: Before paying for something small, ask, "About how much change will we get?" After, ask, "Was that close to what you thought?"