### 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?

# Uncanny Triangles

##### Age 7 to 11 Challenge Level:

Thomas, Jane and Anna were drawing right angled triangles on squared paper. Their triangles had two sides which were an exact number of squares long and could not be longer than $15$ squares. These are Jane's triangles:

They were calculating the areas of the triangles.

"I've got one triangle where the area and the sum of the lengths of the two shorter sides come to exactly the same number!" exclaimed Anna, "Look, it's that one!"

Thomas looked at his work. "How uncanny - but so have I! But look at it. It's quite a different shape from yours."

What were the measurements of the triangles they had drawn?