Now we can open the question out and see where our imagination takes us. 4's and 7's - what else could we try? What borders of rectangles can we make?
It's really a matter of having a grasp that the doing and exploring for the child is as - if not more - important than just getting an answer to a question. For this to work well the pupils need to have been shown in every way that they are allowed 'to think', not simply 'to remember'. So much value has to have been put on to the speaking and listening of the teacher - as
well as the pupil.
Asking, "Tell me what you notice about 4, 6, 6 and 8?" may provoke answers such as:
1. "They're all even" - so maybe the response then is "Could we do the same kind of thing with all odd, OR with a mixture?". For some children you could ask, "What effects do you notice when using evens only, as apposed to a mixture of odds and evens?"
Such things are possible when teachers are confident enough to take little risks and to let the children do so too. Enjoy!!
This article also appears in Primary Mathematics, a journal published by The Mathematical Association .