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P6 Repeated identity

Today’s problem — free all day, every step. Every day has one.

Two flower beds — the length of BC

In a park, ABDF and BCEF are two rectangular flower beds, and CDE is a straight edging path. AB = 9 m, AF = 12 m and BF = 15 m. Find the length of BC.

One step of the worked solution to Two flower beds — the length of BC, drawn in pencil.
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The pattern behind it: Repeated identity

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

In this one. Triangle BDF has one fixed area but two usable bases — measure it from AB, then re-read it from BF, and the unknown BC turns from a side into a height.

the same edge, measured twicelong tilesshort tilesboth rows end level, so 3 long = 5 short

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…
All 19 with this pattern →

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.

A PDF, and a note when new solutions go up.