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A crate of chocolate cubes — large and small
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.
- (a) How many small chocolate cubes are there?
- (b) The volume of the crate is 5625 cm³. The total volume of the 18 large cubes is of the volume of the crate. What is the length of one edge of the small cube?
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The pattern behind it: Repeated identity
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.
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
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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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