This is pretty straight forward.  It is good to have opportunities to speak with youngsters to discover how they are going about generating new ideas.   If you are doing this with a whole class, [ and its suitable for year 5 upwards and below if drawing skills are not seen as a difficulty ] then I suggest that you do one or two examples all together and perhaps have some pretend tiles ready for use.   When asking about the number of tiles that would be use if instead of 1 by 1 they were 2 by 2 then very often, as you can imagine they say that you would have to use 50 of them and very gradually, pennies begin to drop, realisation of "area increase" develop and they get to grips with the fact that you only need 25.   It is useful to put up a huge chart of square from 1 to 100 for them to sign up when they have used that particular number of tiles in their shopping list for a patio.   This , as a class activity, starts an interesting bit of challenging as they try to get the ones that others have not .   Also arguments occur as some think that certain ones  are impossible whilst others have solved that one.   When " impossible" ones are noted it is interesting to get children to explain why they are impossible.
 

 
<p>I have used this activity on a number of occasions on parents' evening when the school has tried to help parents understand what it is to do a mathematics investigation and the need for discussion and plenty of aids and time become apparent. 
 
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