Why do this problem?
This is an engaging activity
that involves both computational skills and organisational skills. I have found that quite young children (6-8 year olds) really enjoy it and do a great deal of work in performing many calculations without really realising it. Quite a few of the children use pentagons and hexagons to vary
it a bit.
Doing a "demonstration" square with the class, making suggestions along the way, works well.
Having some pre-printed sheets available is helpful for some pupils, although just seeing the final shape on inner squares can be very confusing for some.
Tell me about anything you have noticed.
What numbers did you start with?
Do you have any ideas about the number you might end up with in the middle?
You can reverse the process and see if children can come up with what the starting numbers could be to produce a certain specified result in the middle. Asking them how they would work this out leads to some interesting insights into children's methods of thinking through addition and subtraction. Older children (10-11 year olds) could try the reverse when it is addition taking place. The
other thing is to try to predict the result in the middle when you have certain prescribed starting numbers.
With some pupils it is useful to have an adult (more mature thinker) who can keep two fingers at the two places holding the numbers that the pupil is considering at that time.