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Water — poured into a second container
A rectangular tank measures 30 cm by 20 cm by 25 cm. It is full of water. All the water is poured into a second rectangular container with a base area of 200 cm². What is the height of the water in the second container?
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45 cm.
The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. The water is the quantity that does not change when you pour — 9000 cm³ before and after — so the only thing the second container alters is the base area it is spread over, and therefore the depth.
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
Challenging Eleven planks — the area of PQRS 11 identical wooden planks are nailed together to build a large rectangular fence panel PQRS. 3 planks lie flat along the top and …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.