### Polydron

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

### Tiles on a Patio

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

### My New Patio

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

# Geoboards

##### Stage: 2 Challenge Level:

You may like to use the Geoboard interactivity to investigate this problem. To get a square board, just click the small circle of dots to the left of the letters.

 On a $4$ by $4$ geoboard (say) - how many different sized squares can you make using rubber bands? How could you make a square with NO pins along a side (an edge) and just the 4 pins at the corners (vertices)? The basic unit of measurement is one square unit (as shaded in the diagram). How can you make a square whose area is 2 square units? Can you make a square with an area of 3 square units?