Practical models | Year 5 | Ascent Library

01 / LEARN

The idea, step by step

Build a small model

A mathematical model is a useful, simplified picture of a situation. For a purchase, list how many items you need, the price for one item, and any single extra charge. A table keeps different costs separate.

Multiply to find the cost of several equal-priced items. Add a booking fee once if it is for the whole order. Label the answer in dollars or cents so you know what it means.

Check what the answer means

Read the question again after calculating. Total cost and change from a payment are different answers. Estimate first so that a misplaced digit is easier to notice.

A model uses assumptions. A trip calculation may assume that every child pays the same fare and there are no extra charges. If the situation changes, change the calculation and check the new answer.

A common trap

Multiply a single booking or delivery fee by the number of items.

Instead: Check whether the fee is per item or for the whole order. A one-off charge is added once.

02 / WORKED EXAMPLES

See the thinking

Example 1

One fee for the group

Six students pay 4 dollars each to enter a garden. There is one 5-dollar group booking fee. Find the total.

Tickets: $6 \times 4 = 24$ dollars.
Add the group fee once: $24 + 5 = 29$ .
Assume all six tickets have the same price.

29 dollars

Example 2

Find the change

Buy 3 packs of pencils at 7 dollars each and pay with 30 dollars. Find the change.

Cost: $3 \times 7 = 21$ dollars.
Change: $30 - 21 = 9$ dollars.
Check: $21 + 9 = 30$ .

9 dollars

Check your understanding

Four bags cost 6 dollars each. Delivery for the whole order is 3 dollars. Find the total.

Show answer

27 dollars

Bags: $4 \times 6 = 24$ dollars. Add one delivery charge: $24 + 3 = 27$ dollars.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Five notebooks cost 3 dollars each. Find the cost.
2 marks
Three tickets cost 8 dollars each. Add one 4-dollar booking fee.
2 marks
An order costs 37 dollars. Pay with 50 dollars. Find the change.
2 marks
Use the prices to find the total for 4 brushes and 2 trays.
3 marks
Art-shop prices
Item One costs (dollars)
Brush 4
Paint tray 5
A trip model is $8 \times 5 + 6$ dollars. The 8 means eight students. Explain what the 5 and 6 could mean.
2 marks
Mina says 9 tickets at 4 dollars each cost 396 dollars. Give a quick check that shows this is unreasonable.
3 marks

Art-shop prices
Item	One costs (dollars)
Brush	4
Paint tray	5

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Five notebooks cost 3 dollars each. Find the cost.
2 marks
$5 \times 3 = 15$ .
15 dollars
Three tickets cost 8 dollars each. Add one 4-dollar booking fee.
2 marks
Tickets: $3 \times 8 = 24$ .
$24 + 4 = 28$ .
28 dollars
An order costs 37 dollars. Pay with 50 dollars. Find the change.
2 marks
$50 - 37 = 13$ .
Check: $37 + 13 = 50$ .
13 dollars
Use the prices to find the total for 4 brushes and 2 trays.
3 marks
Art-shop prices
Item One costs (dollars)
Brush 4
Paint tray 5
Brushes: $4 \times 4 = 16$ dollars.
Trays: $2 \times 5 = 10$ dollars.
$16 + 10 = 26$ .
26 dollars
A trip model is $8 \times 5 + 6$ dollars. The 8 means eight students. Explain what the 5 and 6 could mean.
2 marks
$8 \times 5$ represents eight equal fares.
The 6 is added once, so it can represent a group fee.
Accept another consistent explanation.
Each student pays 5 dollars and the group pays one 6-dollar extra charge.
Mina says 9 tickets at 4 dollars each cost 396 dollars. Give a quick check that shows this is unreasonable.
3 marks
$10 \times 4 = 40$ .
$9 \times 4 = 36$ .
396 is far larger than the estimate.
Ten tickets cost 40 dollars, so nine must cost less than 40 dollars. The exact cost is 36 dollars.

Art-shop prices
Item	One costs (dollars)
Brush	4
Paint tray	5

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics 2026

Practical models; immediate/future financial plans; consumer goals; ethical/sustainable choices.

Official curriculum source ↗

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