Mathematics K–6 · Years 1–2

Class shop: paying and giving change with Australian coins

Number and algebra

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

A coin stands for a value rather than a count of one, so the same amount can be made with different coins, and change is found by counting on from the price to the amount paid.

Safety card

Low riskAn adult supervises

Hazards

coins are a choking hazard for young children
hygiene when handling real coins

Controls

keep coins on the mat and count them back at the end
wash hands after handling real coins

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

What you need

Australian coins per pair (real or classroom replicas): 10 × 5c, 10 × 10c, 5 × 20c, 4 × 50c, 3 × $1, 2 × $2
10 shop items (fruit, stationery) with price tags from 5c to $2 in steps of 5c
a coin-sorting mat and a recording sheet

How to do it

Sort the coins by value and put them in order from 5c to $2. Compare the order of value with the order of size.
Make 50c in as many ways as possible from 5c, 10c and 20c coins and record each way in a table.
Buy an item priced 35c with a 50c coin. The shopkeeper counts on from 35c: a 5c coin makes 40c and a 10c coin makes 50c. Record the change.
Take turns as buyer and shopkeeper for 8 purchases, paying with the fewest coins possible and checking the change by counting on.
Year 2: buy two items whose prices total $2 or less, find the total, pay with a $2 coin and count on to find the change.

What you should see

The order of size does not follow the order of value: the $2 coin (20.50 mm) is smaller than the 10c coin (23.60 mm), and the 50c coin (31.65 mm across the flats) is the largest. 50c can be made in 12 ways from 5c, 10c and 20c coins, or 13 counting a single 50c coin. The change from 50c for a 35c item is 15c, given as a 10c and a 5c coin. Items totalling $1.35 paid with $2 give 65c change, and the fewest coins for 65c are 3 (50c, 10c and 5c). In every purchase the price plus the change equals the amount paid.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A bigger coin is always worth more.
Five coins are always worth more than two coins.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-AR-01 MA2-AR-02 MAO-WM-01
Australian Curriculum v9AC9M1N05AC9M2N06

Sources

The pages the author read to write this activity.

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