### Geoboards

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

### Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

### 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?

# Triangle Island

## Triangle Island

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle? You must obey the following rules:

You can only move one peg (corner) at a time.

Pegs (corners) must stay on the island.

The area of your tent (the triangle) must always stay the same but the sides may stretch.

### Why do this problem?

This problem will challenge children to find areas of triangles on a square grid.  They do not need to know a 'formula' as they could use the area of surrounding rectangles to help.

### Key questions

What is the area of the tent?
How could you find the area of this triangle?
How could you draw a rectangle around the triangle to help?

### Possible extension

Some children might like to draw their own island on squared paper and 'pitch' their own tents.