### 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?

# Octa Space

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

The trick to this problem was to Work Systematically.

Well done to Jannis and Rohaan from Long Bay Primary did this by counting the number of routes with different numbers of stops, giving an answer of 28:

"We saw there was 4 ways to travel from A inZargon. One way, you have 1 stop, the next you have 2 stops, then 3, and then 4. The first way you would only have 4 different routes, the second this number would double because you now have 2 routes for every letter. For Example, when you went from A toB you could next go to C or E. In the next Category there would still be 8 routes because from a letter (like B) there are only 2 ways to go sideways. This is the same in the next category so 4 + 8 + 8 + 8 = 28. We wrote down all the combinations:

A D Z
A E Z
A B Z
A C Z

and similarly for stopping more times.

Others counted a different way, first looking at where you can go after A-B. Eitherthey went left to E, and then there were four routes that could be taken, or right to C, from where four routes could be taken, or straight to Z. This gives 7 possible routes, and doing the same with A-C, A-D and A-E, gives a total of 28.