Question Repeated identity
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Jack's cubes — large and small in a box
Jack has 8 identical large cubes and some identical small cubes. He packed all the cubes tightly into a rectangular box such that cubes of the same size are stacked on top of each other. The box is filled to its brim exactly. The figure shows the first layer of cubes packed in the box.
- (a) How many small cubes does Jack have?
- (b) The volume of the box is 4032 cm³. The total volume of the 8 large cubes is of the volume of the box. What is the length of one edge of the small cube?
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About this method
One length or count, described two ways in the same question.
In this one. The figure is not decoration — the two blocks span the same box depth, which pins L : s = 3 : 2 and lets the box height be counted in small cubes 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.
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