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

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

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Tangram Paradox

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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 - 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 interactivity, you may like to print off some dotty paper.

Full Screen and Mobile Version

Why do this problem?

This activity can give pupils the opportunity to extend their understanding of squares. It may help pupils who have got used to calling tilted squares "diamond shapes". When using a larger grid they can see a variety of "tilts" that a square can have on such a grid.

Possible approach.

It would be good to have some practical experiences like using pegboards, or perhaps the playground with dots marked in a similar way and the children deciding where 4 pupils could stand to make a square, etc. while listening to each other's statements about what makes a square. When you then give them access to the interactive game it is helpful to ask them to work in two's and encourage discussion about good and bad moves. 

Key Questions.

How have you decided where to put your mark?
Are there some ways of always winning?
What is the change when playing with more dots on the screen?

Possible extension.

These three further activities can be useful as an extension, Eight Hidden Squares , Ten Hidden Squares  and  Square Corners

Possible support.

If the pupil does not seem ready to approach this interactive game then it may be worthwhile looking at Complete the Square  first.