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You can make all kinds of designs, perhaps pretending that you are making an animal or an alien or designing a house or some futuristic building or in fact, you can just imagine that you are creating rather interesting shapes and are happy with that.
It is quite a good idea to set some sort of rule or rules that you have to follow and see how many models/designs you can make if you follow those rules.
I think a good challenge to start with is;
Now let's say that the cubes have to be joined "properly", that is with no twists, so a that a square face is flat against the next square face.
So the two main rules that will control how we will build are as follows:-
Well, I wonder how many different designs you can discover or forecast?
Unless you have lots and lots, I really mean lots, of these cubes to use you will have to make a record of what you have done each time. This can be useful so that you can check that you have not done the same ones twice.
When you've done a few it would be good to see if there is a "system", or "particular way of working" that you are using or could use to make things easier.
You may be interested in the following talks given by Professor Susan Engels, which focus on encouraging curiosity and are available on YouTube:
The Rise and Fall of Curiosity - the extract from 23.50 to 37.15 on adult encouragement and teacher behaviour is particularly worth viewing
The Hungry Mind: The Origins of Curiosity - the extract from 8.22 to 12.29 on children asking questions is especially useful.
Some pupils :-Make all the possibilities with a base shape, including the overhangs and then see whether there are the same number of arrangements for each different base, when exploring the small 'X' base they are surprised how few there are;