### Geoboards

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

### Polydron

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

If you had 36 cubes, what different cuboids could you make?

# Open Boxes

##### Stage: 2 Challenge Level:

Here is a small open box made out of little cubes.
It is 5 cubes wide, 5 cubes long and 3 cubes high.
It is just 1 cube thick everywhere.

Challenge 1

Work out how many little cubes were used to make the open box in the picture.

Challenge 2

If you were going to make a bigger box that is 5 cubes wide, 12 cubes long, 3 cubes high and just 1 cube thick, how many little cubes would you need?

Challenge 3

You have 112 little cubes.
Imagine that you are asked to make more open boxes which are 1 cube thick, always with a width between 3 and 5 cubes inclusive, the length between 10 and 20 cubes inclusive and the height of 2 or 3 cubes.
What size open boxes could you make if you have to use all 112 cubes?

Challenge 4

If open boxes have to be 1 cube thick, have a width of 3, 4 or 5 cubes inclusive, the length between 10 and 20 cubes inclusive and the height of 2 or 3 cubes (as in the previous challenge), what sizes use exactly 144, 145, 147 and 148 little cubes?