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'Coloured Edges' printed from https://nrich.maths.org/
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.