ACARA v9 CONTENT DESCRIPTION “use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation”
Mathematical modelling sounds grand, but at Year 2 it is a simple loop: read a real situation, draw or write what is going on, pick a strategy from the toolbox, work the numbers, then carry the result back to the situation that asked. Money is the natural arena because every child already trades in it — and because Australian money has personality: no 1c or 2c coins since 1992, gold coins worth more than silver giants, and prices that love round numbers. The fete stall below runs on all of it.
Coins of the realm
Australia put $2 on its smallest gold coin and 50c on its biggest silver one. On purpose, probably.
Two Australian coins, drawn to size. Which one buys more?
Read the face, not the footprint
Every Australian child meets the same paradox in the coin jar: the tiny gold $2 outranks the enormous silver 50c. It is worth a slow minute, because the paradox carries the deepest idea in money — value is a label agreed by everyone, not a property you can weigh. Once that lands, coins become numbers wearing metal, and a handful of change becomes an addition problem. Raid the real coin jar at home and sort it twice: once by size, once by worth. The two orders disagree, and the disagreement is the lesson.
Make the amount
The stall float is empty. Build the exact amount, then ask the shopkeeper question: fewer coins?
Build $3.50 from the coins below. There is more than one way.
Many ways to the same amount
One amount, many recipes: $3.50 is a $2 with a $1 and a 50c, or seven 50c pieces, or a pocketful of 20c and 10c if patience allows. Making amounts several ways is renaming again, wearing a coin costume, and the tray-full moment teaches the shopkeeper instinct: bigger coins first, small coins to finish. Ask the follow-up every time the target is hit — could you do it in fewer coins? That little question is a child's first taste of an efficient solution beating a merely correct one.
The change counter
Watch a shopkeeper: seven... eight, ten. Change is counted up, never taken away.
Hand coins back until the price plus the change reaches the note.
Change is a climb, not a takeaway
Watch any shopkeeper make change: seven... eight, ten. Nobody subtracts; they count up from the price to the note, exactly the chase strategy from the addition unit, now earning its keep at a cash tin. The coins handed over are the working, said out loud. This is also where children learn that a subtraction sentence can be solved without subtracting — the sentence states the gap, and climbing measures it. When the climb lands on the note exactly, the change is simply the coins in the customer's hand.
Which operation?
Every stall problem hides one of four moves. The story decides which; the picture confirms it.
Lamington drive: 4 boxes, 6 lamingtons in each. How many lamingtons?
The words choose the operation
Each, altogether, left over, shared between — the words choose the operation, and learning to hear them is half of modelling. But word-spotting alone is a trap: a sly problem can say each and still want addition. The protection is the picture. Boxes of lamingtons become an array, spent money becomes a shortened bar, shared toffees become plates — and the picture either agrees with the chosen sentence or refuses to. Draw first, choose second, and the operation almost picks itself.
Answer the question asked
The hardest step is the last one: making the number face the question again.
Pies are $4. Nila buys 3 and pays with a $20 note. What is her change?
Walk the number home
The last step of modelling is the one tests punish and life demands: the answer must walk back into the story. Nila's 12 was perfect arithmetic and the wrong answer, because the question asked for change; a bare number is only half an answer until it wears its units and faces its question. This habit — answer in boxes, in drinks, in dollars of change — closes the Year 2 Number strand. Six units, from numbers to 1000 down to the coins in a pocket; next door, Algebra is waiting with patterns and the addition facts.
Quick self-check
1. Which Australian coin is worth the most?
2. A snag costs $3. Ari pays with a $5 note. The change is...
3. Stickers cost $2 each. 4 stickers cost...
4. Which story matches 15 ÷ 3?
5. Drinks cost $2 each. Mia has $9. How many can she buy?