ACARA v9 CONTENT DESCRIPTION “recognise the relationships between dollars and cents, and represent money values in multiple ways; use money to model and solve problems involving purchases and the calculation of change”
Money is where the number skills of Year 3 meet everyday life. This unit covers the relationship between dollars and cents, the different ways the same amount can be shown, and using money to model real problems — totalling a purchase and working out the change. A dollar is a hundred cents, so money is really two units working together, much like the metres and centimetres of measurement. Because every child handles money, it is a context where addition, subtraction and place value suddenly matter, and getting the calculations right has obvious, real consequences.
A dollar is a hundred cents
One dollar equals one hundred cents; this is the key money relationship.
A dollar is built from cents. Add ten-cent blocks until you reach one hundred.
Dollars and cents
The foundation of money is one fixed relationship: one dollar equals one hundred cents. This makes dollars and cents behave like a two-unit measure, with cents the smaller unit and dollars the larger, exactly a hundred to one. Seeing a dollar built from a hundred cents — ten lots of ten, for instance — makes the relationship concrete. It is the same hundreds-and-ones structure as place value, which is why the number work of earlier units transfers straight to money. Knowing this relationship is what lets a child move between cents and dollars with confidence.
Writing money
A money value can be written in cents or in dollars and cents, two ways of the same amount.
How is 135 cents written as a dollar amount?
Two ways to write an amount
The same money value can be written in more than one way: 135 cents is also $1.35, and 5 cents is $0.05. In dollars-and-cents form, the digits before the point are whole dollars and the two digits after are the cents, always two places so that five cents is written $0.05, not $0.5. Representing money in multiple ways, as the descriptor asks, means recognising that the cents form and the dollars form are the same amount. Reading and writing both forms fluently is essential, because prices and change appear in dollars-and- cents but are often reasoned about in cents.
Many ways to make it
The same money value can be represented by different combinations of coins and notes.
Tap coins to build $1.35. There is more than one correct way.
Many coins, one value
A money value can also be represented physically, and usually in several ways: $1.35 might be a dollar coin with a twenty, a ten and a five, or two fifties with a twenty, a ten and a five. There is rarely one correct set of coins, and seeing the different combinations that make the same total deepens the sense of what the value really is. This flexible view of money — many representations of one amount — is part of what the curriculum means by representing values in multiple ways, and it is genuinely useful when paying with whatever coins happen to be in a pocket.
Add up the basket
The cost of a purchase is the sum of the prices of the items bought.
Adding the prices one at a time builds the total. Keep going to total the whole basket.
Totalling a purchase
Modelling a purchase begins with finding its total cost, which is just the sum of the prices of the items bought. Adding 80 cents, $2.50 and $1.20 gives a basket total, using the same addition skills from earlier units but now applied to money. Keeping the dollars and cents lined up, like keeping place-value columns aligned, makes the adding reliable. Using money to model a purchase, exactly as the descriptor states, starts here — turning a list of prices into the single number a shopper needs to hand over.
Counting the change
Change is the amount paid minus the cost of the purchase.
You pay $5.00 for something costing $4.50. What is the change?
Working out the change
The other half of a purchase is the change: the amount handed back when you pay with more than the cost. Change is found by subtraction — what you pay take away what it costs — so paying $5 for a $4.50 item gives 50 cents change. This is the subtraction of earlier units doing a job every shopper needs, and a child who can calculate change can check they have not been short-changed. Calculating change, named directly in the descriptor, is one of the most practical pieces of mathematics in the whole year.
The whole transaction
A complete purchase models the total cost and then the change in one go.
A full shop: first the items, then the total, then what you pay, then the change.
A purchase from start to finish
A complete transaction puts both halves together: total the items, then work out the change from what is paid. Buying a 95-cent pencil and a 55-cent eraser comes to $1.50; paying with $2 gives 50 cents change. Modelling the whole purchase — adding to find the total, then subtracting to find the change — is the goal of the unit, and it uses addition and subtraction together on money that matters. With the dollar-and-cent relationship, multiple representations, totalling and change all in hand, a child can handle the everyday mathematics of buying and being given change, and the Year 3 Number strand turns next to its algorithms and patterns.
Quick self-check
1. How many cents are in one dollar?
2. Which amount is the same as $1.35?
3. How is 5 cents written as a dollar amount?
4. You buy items costing $2.50 and $1.20. What is the total?
5. You pay $5 for something costing $4.50. What change do you get?