Mathematics K–6 · Years 5–6
Balance puzzles: finding an unknown mass
Number and algebra
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The idea
When a balance is level, both sides hold the same mass, so removing equal amounts from each side keeps it level and reveals an unknown.
What you need
- an equal-arm balance
- 64 identical metal washers: 40 loose as unit masses and 24 sealed by the teacher in the filled canisters
- 6 small opaque film canisters, each filled by the teacher with the same number of washers (the unknown; 4 each for the puzzle cards), and 4 empty canisters of the same kind
- puzzle cards written as balance pictures and as number sentences: 3 bags + 2 = 14, 2 bags + 5 = bag + 9, 4 x (bag + 1) = 20
How to do it
- Put 3 bags and 2 washers on the left and 14 washers with 3 empty canisters on the right (the empty canisters cancel the canisters' own mass). Check the balance is level. Remove 2 washers from each side and confirm it stays level.
- With 3 bags against 12 washers, share the washers into three equal piles, one per bag. Open a bag and count to check.
- Set up 2 bags + 5 against 1 bag + 9, with 1 empty canister added on the right. Remove one bag from each side, then 5 washers from each side, and read the mass of a bag.
- Set up 4 bags + 4 washers against 20 washers and 4 empty canisters. Group the left side into four equal groups of one bag and one washer and find what one group balances.
- Write each step as a number sentence with a symbol for the bag, and check the value by opening a bag.
What you should see
For 3 bags + 2 = 14 the balance stays level after removing 2 from each side (3 bags against 12), and sharing gives 4 washers per bag, which opening a bag confirms. For 2 bags + 5 = 1 bag + 9, removing a bag and then 5 from each side gives 1 bag against 4, so a bag holds 4. For 4 groups of (bag + 1) against 20, one group balances 5, so a bag holds 4. Removing from one side only tips the balance at once, which shows why both sides must change together.
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.
- Taking washers off one side of a level balance keeps it level.
- The bag must hold the number written on the right side of the sentence.
Safety card
Hazards
- washers dropped on feet
- pinching at the pivot
Controls
- work over the table; keep fingers clear of the pivot
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.
Sources
The pages the author read to write this activity.