MathBrush

The pattern

Repeated identity

One length or count, described two ways in the same question.

Repeated identity illustrated in pencil.
The key insight from Water — poured into a second container, drawn in pencil.
The key step, from Water — poured into a second container
the same edge, measured twicelong tilesshort tilesboth rows end level, so 3 long = 5 short

The same length, area or count turns up twice in one figure, described a different way each time. Write down both descriptions and they become two expressions for a single value, which can be set equal. It might be a triangle's area seen from two bases, or one edge measured along two rows of different sized tiles.

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.

23 worked solutions

Standard

Challenging

Very challenging

All the problem patterns →

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.