Question P6 Repeated identity
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9 identical rectangles form a large rectangle ABCD (2 lying down on top, 7 standing up below). The perimeter of ABCD is 138 cm. Find the area of ABCD.
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One length or count, described two ways in the same question.
In this one. The top edge AB can be read two ways — 2 long sides (top row) or 7 short sides (bottom row) — and one length read two ways is an equation: 2 long = 7 short.
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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