Equivalent amounts | Year 3

01 / LEARN

Understand the idea.

Different collections, equal value

Equivalent amounts have equal value, even when the coins look different. Two $50$ -cent coins total $100$ cents, just like one dollar. Swapping these collections does not give or take away any money.

Check a swap by adding each collection separately. Name both totals in cents so they are easy to compare. Equal totals mean the collections can pay the same exact price.

Choose coins carefully

Count value, not just coins. Five $10$ -cent coins total only $50$ cents. One $2$ -dollar coin is worth $200$ cents, so the single coin has more value.

Read any extra condition before choosing coins. “Make one dollar” allows several answers, but “use exactly two coins” limits the choices. Check the total value and the number of coins separately.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Two ways to make a dollar

Show 1 dollar using 50-cent coins, then using 20-cent coins.

Worked solution

1
Set the target in cents.
$1 dollar = 100 cents$
Both coin collections must reach this same value.
2
Count in fifties.
$50 + 50 = 100 cents$
Two 50-cent coins reach the target exactly.
3
Count in twenties.
$20 + 20 + 20 + 20 + 20 = 100 cents$
Five 20-cent coins also reach the target exactly.

Answer

Two 50-cent coins or five 20-cent coins.

EXAMPLE 02

Compare collections

Which has more value: three 20-cent coins or one 50-cent coin?

Worked solution

1
Total the three coins.
$3 \times 20 = 60 cents$
Three equal coin values make three groups of 20 cents.
2
Compare with the single coin.
$60 > 50$
The three-coin collection has the greater total value.
3
Find how much greater.
$60 - 50 = 10 cents$
Subtracting the smaller value gives the difference.

Answer

Three 20-cent coins, by 10 cents.

03 / YOUR TURN

Try it yourself.

Check your understanding

Are 50c + 20c + 20c + 10c and 1 dollar equivalent?

Show answer & reasoning

Yes.

The collection totals $50 + 20 + 20 + 10 = 100$ cents. One dollar is also $100$ cents, so the amounts are equivalent.

Keep practising

6 worksheet questions

Open worksheet Worked solutions

Read the questions online

How many 20-cent coins make 1 dollar?
Give two different coin collections worth 40 cents.
Find the total: $1 dollar + 50 cents + 20 cents$ .
Which is worth more: four 10-cent coins or one 50-cent coin?
Make exactly 1 dollar using exactly 2 Australian coins.
A child swaps one 2-dollar coin for five 20-cent coins. Is the value equal?

Read the worked solutions

How many 20-cent coins make 1 dollar?
$5 \times 20 = 100$ cents.
5 coins.
Give two different coin collections worth 40 cents.
$20 + 20 = 40$ and $10 + 10 + 10 + 10 = 40$ . Other valid collections are acceptable.
For example, two 20-cent coins; or four 10-cent coins.
Find the total: $1 dollar + 50 cents + 20 cents$ .
$100 + 50 + 20 = 170$ cents.
1 dollar 70 cents.
Which is worth more: four 10-cent coins or one 50-cent coin?
Four 10-cent coins total 40 cents; $50 - 40 = 10$ .
The 50-cent coin, by 10 cents.
Make exactly 1 dollar using exactly 2 Australian coins.
$50 + 50 = 100$ cents, using 2 coins.
Two 50-cent coins.
A child swaps one 2-dollar coin for five 20-cent coins. Is the value equal?
$5 \times 20 = 100$ cents, but 2 dollars are 200 cents.
No. Five 20-cent coins total only 1 dollar.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Dollars/cents; equivalent amounts; modelling purchases; needs/wants; class enterprise and others' wellbeing.

Official curriculum source ↗

In this lesson

Understand the idea.

Different collections, equal value

Choose coins carefully

See the method in action.

Two ways to make a dollar

Set the target in cents.

Count in fifties.

Count in twenties.

Compare collections

Total the three coins.

Compare with the single coin.

Find how much greater.

Try it yourself.

Check your understanding

Keep practising