Question P6 Repeated identity
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A chocolate factory packs a rectangular crate tightly with 18 identical large chocolate cubes and some identical small chocolate cubes, so that cubes of the same size are stacked directly on top of each other, filling the crate exactly to the brim. The figure shows the first layer of cubes packed in the crate.
Answer
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One length or count, described two ways in the same question.
In this one. The figure alone fixes L : s = 5 : 3 — one edge written in terms of the other — so the crate's height can be counted in layers of either cube long before any volume is known.
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.
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
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