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This problem is designed to challenge pupils both in number and spatial skills. It provides an opportunity for pupils to consider the properties of multiplication and to test their ideas.
If necessary before approaching the six by six array, present two sheets with a four by four array. Try not to go through it completely, but just try a couple of multiplications and then turn the top sheet over (or around, or both) and see what a few of the multiplications would be then.
The six by six grid can be printed out for pupils to use, and pupils might want to use tracing paper in order to create a see-through version of the grid. The challenge will need to be explained very clearly so as to prevent a lot of unnecessary calculations being made.
Pupils could explore a smaller grid, such as a three by three grid or a two by two grid. The restriction about not being allowed to calculate and add every multiplication can be relaxed on a smaller grid, and pupils can calculate which arrangement would give the highest and the lowest total. Pupils should then be encouraged to explain why they think this has happened, and whether or not they think the solution would be similar with a larger grid size.
Children could have a go at It's Times Again, which encourages children to explore how the problem changes if the numbers are no longer necessarily consecutive.