### 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

##### Stage: 2 Challenge Level:

Hugo sent us pictures of his solution. Well done, Hugo!

I know that the area of a triangle is given by the forumula $\frac{1}{2} \times base \times height.$ The original triangle has base $1$ and height $1$, so as long as each triangle on the way also has base $1$ and height $1$ the area will stay the same".