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Jim and Ken — sweets and chocolates
Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates becomes 1:7 and the ratio of Ken’s sweets to chocolates becomes 1:4. How many sweets did Ken buy?
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The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. Halving and swapping leaves both boys holding identical amounts, so every difference between them afterwards comes only from what they ate — which lets one quantity (the chocolates) be counted two ways and pin the unit.
How to spot it
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Common mistake
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Try one like it
Standard Water — poured into a second container A rectangular tank measures 30 cm by 20 cm by 25 cm. It is 3/5 full of water. All the water is poured into a second rectangular co…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.
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