### 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?

# The Dice Train

##### Stage: 2 Challenge Level:

This dice model represents an old blue steam train with a white funnel on the engine at the front. The dice that make up the train are joined using three rules.

RULE 1: Faces that touch each other have the same number.
So, underneath the white dice is a $3$ touching a $3$ on the blue dice.
The blue dice has a $6$ on the face that touches the $6$ on the middle blue dice.
The middle blue dice has a $1$ that touches the $1$ on the last dice.

RULE 2: The number on the top of the funnel must equal the total of the numbers showing on top of the remaining dice (carriages) that can be seen.
So, the $4$ on top of the funnel equals the two $2$'s on top of the blue carriages.

RULE 3: Always use four or more dice – so you have at least two 'carriage numbers' to add up.