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

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

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Multilink Cubes

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


Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3


Play the game below 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.

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Why do this problem?

Children will be motivated to work systematically as they play this game because they will want to think ahead.

Key questions

Would it be a good idea to start with a smaller number of counters.  How about four arranged in a square?
How many different ways are there for the first player to begin?
Does the grid have any symmetry that may help you? 

Possible extension

Learners could try with a larger number of counters, or the counters arranged differently.

Possible support

Working with $2$cm squared paper and counters will mean that children can simplify the game easily.