### 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.

### Multilink Cubes

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

# Counters

##### Age 7 to 11Challenge Level

To play this game, you'll need a friend and twelve counters.

The aim of the game is to be the player who takes the last counter or counters.

How to play:

Lay out the counters in an array like this:

The first player chooses a counter and removes it from the array, and also removes all the counters that touch it.

The second player also chooses a counter and removes it from the array, and also removes all the counters that touch it.

Play continues like this with players taking it in turns, until one of the players removes the last counter (or counters). That player is the winner!

Here is an example, where the first player has chosen the counter with the black cross. This means that all the counters coloured red in the picture below are removed:

So, now the counters left look like this:

Player two then decides to choose the bottom left counter, so all the counters coloured blue in the picture below are removed:

So now there are just these counters left:

Player one then chooses the top left counter, and removes it with the one that is touching it:

Player two now decides to choose the bottom right counter and removes it:

So player two takes the last counter and is the winner!

Play the game a few times with a friend.

Now begin to think about your strategy, in other words, how you can make sure you win.
If the first player takes the middle counter from the first column on the left, how could the second player make sure he or she wins?
If the first player removes the middle counter in the second column to start with, what should the second player do to win the game?

Do you think it is better to be the first player or the second player? Why? Try to explain your reasoning by giving some examples.