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Age 11 to 14
Challenge Level Yellow star
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Why do this problem?

This problem requires learners to work logically with numbers and shapes at the same time. The best ways of finding a solution include using a letter to represent the length of the side of the square.

Key questions

What sort of number of tiles must you use to make a square?
What sort of number of tile edges will make up the perimeter of the square?
Have you thought of using a letter to represent the length of the side of the square?

Possible extension

Learners could try to arrange the tiles so that touching edges are all the same colour. They could also try Painting Cubes which is a similar problem.

Possible support

Suggest making a list of possible square numbers. Then using squared paper and colouring the edges of the small squares within a suitably sized larger square and finding the answer by trial and improve.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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