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Make a cube out of straws and have a go at this practical challenge.


Reasoning about the number of matches needed to build squares that share their sides.

Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Seeing Squares

Age 5 to 11
Challenge Level

Seeing Squares

This game can be played against a friend or against the computer.

Players take it in turns to click on a dot on the grid - the first player's dots will be blue and the second player's (or computer's) will be red.
If you choose to play with a friend rather than the computer click '2 player'. (Click '1 player' if you choose to play the computer.)
The winner is the first to have four dots that are shown joined by straight lines to form a square.

Squares can be any size, anywhere and can be tilted.

For a further challenge, why not increase the size of the grid using the arrow buttons?

If you are not using the interactive game, you may like to print off some dotty paper.

Full Screen and Mobile Version

You may be interested in the other problems in our Strategy Games Feature.

Why do this problem?

This activity will help pupils deepen their understanding of squares. It is also a useful context in which to challenge pupils who have got used to calling tilted squares 'diamonds'. As they play the game, learners will have plenty of opportunities to practise visualising squares and to develop systematic ways of working in order to beat an opponent.

Possible approach

This game featured in an NRICH Primary webinar in November 2021.

Introduce the game on the interactive whiteboard, either with you playing against a pair of pupils, or the whole class playing against the computer. If the winning square is 'tilted' use this opportunity to talk about what makes a square a square, and encourage learners to explain how they know that the shape drawn is indeed a square.

Once everyone has understood how to play, encourage learners to play in pairs against another pair. You could do this on tablets or computers using the interactivity, or using dotty paper, or using sets of differently coloured counters with a printed (and laminated) copy of this grid

If a tilted square was not made in the demonstration game, watch out for one during the pupils' own games and use it as an opportunity to bring the class together to discuss how we know that a square is a square. 

Allow time for learners to play several games and as they play, listen out for those pairs who are thinking strategically. They may, for example, be looking at where the best place to start could be. They may be thinking ahead and considering consequences of their possible moves. They may be focusing on what their opponents are doing too, trying to block them where possible. They may be trying to set up a situation in which they can create two different squares on the next turn, meaning that their opponents cannot block both in a single turn, so ensuring a win.

You could encourage learners to share their various strategies in a mini plenary, then encourage everyone to try to make use of what they have heard as they play more games.

The final plenary might involve the whole class playing against the computer, putting into practice the strategies that have been discussed. If that game is lost, help the class to analyse what went wrong and what they could have done differently, and how this might help them win in a future game.

Key questions

How are you deciding where to go?
Where is a good place to start? Why?
Are there any ways of always winning?


Possible support

It may be worthwhile looking at Complete the Square before playing this game.

Possible extension

These three activities can be useful follow-up to this game: Eight Hidden Squares, Ten Hidden Squares and Square Corners.