This activity is very simple to introduce, yet it has the possibility of opening up a door in mathematics for the pupils. They are probably very used to a 100 square and finding out things in different ways. Here the pupils are allowed so much more freedom. It's so good to let them have the freedom to choose what shape the 64 should be in. I find that most pupils just need a couple of examples and then told very strongly that these are just examples and they may choose a shape of their own. That's how the examples came about that areon the problem page.
Then there's the choice of how the numbers should go. I was very pleased with the year 5 pupils in Bromley who came up with the examples shown.


You may find it useful to provide cards with the number 1 - 64 on them and let them explore the ways of arranging them. This helps a lot so that they can see whether the 64 fit in well to the shape that they want to achieve.

If you have a class or a group working collaboratively on this activity, it is good to let the pupils try out a shape and ordering of their own invention without the teacher intervening, even though you can foresee a problem with the arrangement. Some triangular arrangements cause problems, butbe brave enough to hand over the problem to the pupils so that they can debate what can be done to get the numbers and shape working well together.

There are some carpet tiles about 20 cm x 20 cm available, that are a very good aid when working with a large group together.

Then the shape of four I feel is quite a good starter as there are not too many possibilities. When the pupils have explored then the trying of the same activity with 3 or 5 squares to make a new frame for enclosing numbers will lead to interesting comparisons.

Have a good time, and send in any results.