ACARA v9 CONTENT DESCRIPTION “use mathematical modelling to solve practical problems involving additive situations including simple money transactions; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem”
Mathematical modelling is the curriculum’s grand name for something children do naturally: taking a messy real situation and turning it into a sum they can handle. The cycle is always the same — read the story, draw the picture, choose a strategy, find the answer, then carry the answer back against the story to see if it fits. Every story problem in this unit is a part-part-whole picture wearing a story, and money is the friendliest place to practise, because Australian coins turn invisible numbers into things a child can hold, stack and hand over the tuckshop counter.
From story to picture
Story, picture, strategy, answer, check — the modelling cycle in four presses.
Mia has 8 shells. Tom gives her 5 more. How many shells now?
A story is just numbers wearing clothes. First, undress it into a picture.
The translation move
The hardest part of a word problem is not the arithmetic; it is the translation. A bar diagram strips the shells, cockatoos and stickers away and leaves the bones: two parts and a whole, with one of the three hiding. Once the picture exists, the child can see which strategy fits — count on, make ten, find the missing part — instead of guessing. Drawing the diagram is not a detour on the way to the answer; it is the understanding itself.
The tuckshop
Two things on the counter is a join story: part, part, whole.
Pick any two things from the menu.
Money you can hold
Simple money transactions are join stories with dollar signs. Two items on the counter are two parts; the total is the whole; and Australian one- and two-dollar coins let children build that whole in their hands. Keeping prices small and friendly matters more than realism at this age — the goal is the structure of the transaction, and the quiet thrill that the same part-part-whole bar from the last unit now buys a sausage roll.
Three stories, one picture
The word more appears in all three — but the question mark keeps moving.
Zoe has 9 stickers. She gets 4 more. How many now?
The whole is hiding: 9 + 4 = 13. Three stories — one picture. Only the question mark moves.
Beware the word trap
Children are often taught keyword tricks: more means add, left means subtract. The tricks betray them quickly. Zoe gets more stickers in two of our three stories, yet one of them needs a subtraction to solve. The cure is to draw before deciding: the same diagram serves all three stories, and only the position of the question mark changes. A child who locates the question mark has understood the problem; a child hunting keywords has only skimmed it.
Change at the tuckshop
Shopkeepers do not subtract — they count up from the price to the money.
Count up one dollar at a time until you reach the money paid.
Change, the shopkeeper’s way
Nobody behind a counter subtracts to give change — they count up. From a seven-dollar pie towards a ten-dollar note: eight, nine, ten, and three dollars sit in your palm. This is the missing-part strategy from the last unit wearing a coin costume, and it gives children a method that feels like the real world because it is exactly what the real world does.
Check it back
An answer is not finished until it has faced the story again.
8 shells and 5 more shells. Sam says 12.
Trust your nose first: does the claim smell right?
The step everyone skips
The modelling cycle only closes when the answer faces the story again. Does thirteen shells make sense if Mia started with eight and got more? Can Ben spend money and end up richer? Checking back catches slips that no amount of careful adding will, because it asks a different question: not is the sum right, but is the answer sensible. Children who build this habit in Year 1 keep it for life. Send the habit home, too: checking the change at the milk bar, recounting the shells in the bucket — every small transaction is a chance to ask whether the answer makes sense.
Quick self-check
1. Jo had 8 marbles. After lunch she has 13. How many did she find?
2. A pie costs $6 and a juice costs $3. Together they cost...
3. An icy pole costs $2. You pay with $5. Your change is...
4. Thirteen kids are on the bus and 5 get off. In the picture, 13 is...
5. Ben had $12 and spent $4. He says he has $16 left. Is that sensible?