This activity is very simple to introduce, yet it has the
possibility of opening up 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 chose 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 these examples came
about that are in Bernard's Bag.
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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.
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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.
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If you have a class or a group working collaboratively on
this activity, as I have frequently done with 100 square, 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, but to be 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.
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There are some carpet tiles about 20 cm x 20 cm that are a
very good aid when working with a large group together.
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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.
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Have a good time, and send in any results.
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