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'Walking the Squares' printed from http://nrich.maths.org/

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Why do this problem?

This activity gives pupils an opportunity to explore a scenario and gradually start using a strategy while learning to overcome problems or difficults - all the atmosphere of a kind of game.

Possible approach

It would be good to give pupils a sheet of several copies of the square (See here for doc or pdf).
The pupils can then work on the first one and if and when they come to a stop because they realise it is going wrong they do not rub it out but write about what they are thinking they did do and what they should now do - on the right and start again underneath.
Here is a page (doc,  pdf) that gives you an opportunity to print out four different sizes.

Key questions

Tell me about what happened here that made you start again.
You seen to be using a system (if it looks like it!) can you tell me about it?
Is there anything you would like to change about the way that you did it?
Have you covered as many pairs as possible?
 

Possible extension

Here is a page (doc, pdf) that gives you an opportunity to print out four different sizes of squares for the pupil to do and compare and maybe come to some predictions.

Possible support

Some pupils might want to use some drawing software.