Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Fencing

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Transformations on a Pegboard

How would you move the bands on the pegboard to alter these shapes?

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.