Money and Modelling
Mathematics as a model of a real situation
Mathematical modelling means using numbers to stand for a real situation so that a question about it can be answered. In Year 3 there are three steps. First, formulate: read the situation and write it as a number sentence. Second, solve: choose a way to work the number sentence out. Third, interpret: check that the answer makes sense in the situation and say it in words. The situations can be about anything children meet, and many of them are about money: what things cost, how much is left, and how many can be bought.
Formulate: write the number sentence
The first step is deciding what kind of situation it is. If more are joining a group, it is adding; if some are taken away or spent, it is subtracting. If there are equal groups of the same size, such as 4 packs of 6 juice boxes, it is multiplying; if a total is shared out equally, it is dividing. Once the kind is clear, the number sentence writes itself: 4 packs of 6 becomes 4 × 6. A quick picture, a bar for adding and taking away or boxes for equal groups, helps children see which kind they are looking at.
Solve: choose a strategy
There is often more than one way to work a number sentence out. Five sausage rolls at $3 each can be found by adding $3 again and again, 3, 6, 9, 12, 15, or by knowing that 5 × 3 = 15. Both are correct; the multiplication is quicker once the facts are known, and the repeated addition shows why it works. Encouraging children to choose a strategy, and to check one way with another, is part of what the curriculum means by choosing calculation strategies.
Totalling a purchase
A shopping basket is an adding situation: the total cost is the sum of the prices of the items bought. Adding 80 cents, $2.50 and $1.20 gives the basket total, using the same addition as earlier units but now on money. Keeping the dollars and cents lined up, like keeping place-value columns aligned, makes the adding reliable.
Working out the change
Change is a taking-away situation: the amount handed back when you pay with more than the cost is what you pay take away what it costs, so paying $5 for a $4.50 item gives 50 cents change. Writing the number sentence first, $5.00 − $4.50, makes the step clear, and a child who can calculate change can check they have not been short-changed.
A purchase from start to finish
A complete purchase is a model with two steps: add to find the total, then subtract to find the change. Buying a 95-cent pencil and a 55-cent eraser comes to $1.50; paying with $2 gives 50 cents change. Writing both number sentences shows the whole plan before any working out begins.
Interpret: does the answer make sense?
The last step is to read the answer back into the situation. Twenty children each want one slice and a pizza has 8 slices: two pizzas give only 16 slices, and nobody sells half a pizza, so the answer that works is 3 pizzas, with 4 slices spare. With $18 and tickets at $4, four tickets cost $16 and five would cost $20, so the answer is 4 tickets with $2 left. The same sum can need rounding up or rounding down depending on the situation, which is why modelling always ends by saying the answer in words that fit the story.