### Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

### Dissect

What is the minimum number of squares a 13 by 13 square can be dissected into?

### 2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

# Coloured Edges

### 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.