Mathematics K–6 · Years 3–4

Dollars and cents: making $1 many ways and weighing coins

Number and algebra

Practical, model not builtLow risk

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The idea

One dollar is 100 cents, so an amount is written in dollars and cents and made from many coin combinations, and because 5c, 10c and 20c coins have a mass in proportion to their value, a dollar of any of them has the same mass.

What you need

real Australian coins for the weighing: 20 × 5c, 10 × 10c, 5 × 20c, 2 × 50c, 2 × $1, 1 × $2
a digital kitchen scale reading to 1 g
paper replicas of a $5 note and a $10 note
a price list of 8 classroom items between $0.45 and $4.95 prepared by the teacher
a recording table with columns: dollars and cents, cents only, coins used, mass

How to do it

Write $1 as 100 cents and $3.45 as 345 cents. Make $3.45 with coins in two different ways and record both.
List every way to make $1 from 5c, 10c, 20c and 50c coins in an organised order: start with two 50c coins, then one 50c coin, then none.
Weigh the 20 × 5c coins, then the 10 × 10c coins, then the 5 × 20c coins. Each pile is worth $1. Record the masses.
Weigh the 2 × 50c coins and one $1 coin and compare with the piles from step 3.
A partner makes a secret mixed handful of 5c, 10c and 20c coins. Estimate its value by weighing, then count it to check.
Buy two items from the price list, paying with the $5 replica note, or with the $10 note when the two prices total more than $5, and find the change by counting on.

What you should see

The three $1 piles weigh 56.6 g (20 × 2.83 g), 56.5 g (10 × 5.65 g) and 56.5 g (5 × 11.3 g) from the Royal Australian Mint specifications, so for coins at their specified mass a scale reading to 1 g shows 56 or 57 g for each; worn coins can read a little less. Two 50c coins weigh 31.1 g and one $1 coin 9.00 g, so equal value no longer means equal mass once these coins are included. A handful of 5c, 10c and 20c coins that weighs 113 g is worth $2.00, and a 1 g error on the scale is worth under 2c, less than the smallest coin. There are 49 ways to make $1 from 5c, 10c, 20c and 50c coins. Two items costing, for example, $1.85 and $2.40 total $4.25, and the change from $5 is 75c.

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.

$3.45 means 3 dollars and 45 coins.
A heavier pile of coins is always worth more.

Safety card

Low riskLearners carry it out

Hazards

hygiene when handling real coins
coins going missing

Controls

wash hands after handling coins
count the coins out and back in

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.

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 MAO-WM-01
Australian Curriculum v9AC9M3M06AC9M3N06AC9M4N08

Sources

The pages the author read to write this activity.

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