Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

Two by One

Two by One

In Tom's house there are tiles on the floor. Each tile is twice as long as it is wide so they each look like this:

How do you think they fit together to cover the floor? Use squared paper to help you to draw your pattern.

Can you find any other patterns?

How many different patterns can you find?

Why do this problem?

This open-ended activity may well appeal to those children who find number work difficult. It will allow all children to work at their own level and encourage creativity, and this can be a good assessment opportunity for you. Squared paper will be useful.

Key questions

Are you sure your patterns are different?
What shapes will you need at the edges of the floor?
Have you chosen a particular size floor?

Possible extension

Children could focus on repeating patterns and attempt to find all possible ones for a stated floor size.

Possible support

Learners will find the problem more manageable if a certain size of floor is suggested. They could use dominoes to represent the tiles.