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Bicycles and tricycles — 58 wheels
A cycling club has 25 vehicles parked outside, a mix of bicycles and tricycles. Bicycles have 2 wheels and tricycles have 3 wheels. Altogether there are 58 wheels. How many tricycles are there?
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The pattern behind it: Suppose and swap
Suppose everything is one kind, then swap one at a time until the total is right.
In this one. Pretend every vehicle is the 2-wheel kind, see how many wheels you fall short by, and divide that shortfall by the 1 wheel each swap adds — the answer is how many tricycles there are.
How to spot it
Two kinds of thing are mixed together with a known total count and a known total of something else, such as legs or sweets, and neither kind's count is given on its own.
Common mistake
Children lose track of whether a swap adds to the total or takes away from it. Compare the starting total with the target first, then swap in the direction that closes the gap.
Try one like it
Standard Car park — cars and motorcycles, counting wheels A car park has 14 vehicles, only cars and motorcycles. Each car has 4 wheels and each motorcycle has 2 wheels. In total there are …The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.