### 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?

# Broken Toaster

##### Stage: 2 Short Challenge Level:

Erika sent us her very thoughtful solution. Well done!

If there are three slices of bread, there are a total of 6 "sides" to be toasted As we can only toast 2 sides at a time, and toasting two sides takes 2 minutes, it will take at least 6 minutes to toast all the bread. Also, each slice must go in the toaster twice, and we can toast two different slices at once. We can toast all three slices by doing
• 1 and 2
• 3 and 2
• 1 and 3
If there are 4 slices of bread, there are a total of 8 "sides", so it will take 8 minutes to toast all the bread. We can do slices 1 and 2 in the first 4 minutes (turning them over after 2 minutes), and 3 and 4 in the last 4 minutes (turning them over after two minutes). If there are 5 slices it will take 10 minutes.

If there are $n$ slices of bread it will take $2 \times n$ minutes to toast all the bread.