### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

### Square Areas

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

# 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.