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Nine tiles — the area of WXYZ
9 identical rectangular tiles are used to make a mosaic panel WXYZ for a bathroom wall. 4 tiles are laid flat along the top and 5 tiles are stood upright below them, as shown. The perimeter of WXYZ is 174 cm. Find the area of WXYZ.
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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 edge WX is the same length read two ways — as 4 tile-lengths and as 5 tile-breadths — so 4L = 5B, and that one equation fixes the ratio L : B = 5 : 4 before any number is used.
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
Standard Water — poured into a second container A rectangular tank measures 30 cm by 20 cm by 25 cm. It is 3/5 full of water. All the water is poured into a second rectangular co…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.
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