Ring a Ring of Numbers , the interactivity allows pupils to
enter their numbers into the boxes and displays the differences
between the two boxes. This means that the focus of the pupils'
activity is on the process of generalising about what is going on,
rather than working out the answers. The generalisations that we
are looking for here are about the sums and differences of odd and
even numbers: an odd plus an odd makes an even, the difference
between two odd numbers is even and so on. We are not asking for a
proof as such but seeking to observe the general rules: the proof
could follow later and might in fact be an appropriate extension to
the question for slightly older children.
problem that links with this is
Make 37 which was published in October 2003. Once again there
is no request for a proof but that is the natural solution of the
problem. We have used this with a number of groups of children, and
of adults, and the initial response is usually the same: people get
stuck in and have a go. We would hate to spoil your enjoyment of
the problem so we won't give the game away - do try it yourself
before we proceed.
To start with we have an investigation
based on ideas about parallel lines and we move quickly into
collecting data. How do we know that we have found all the
possibilities for each number of sticks? We will need arguments
based on the systems we have adopted for finding them and this will
require data handling skills as well as being organised and
systematic in our approach. The third paragraph moves into higher
numbers and eventually into general number and algebra so should be
a challenge to a lot of children even though the initial setting
will be accessible to most.
This article also appears in
Primary Mathematics, a journal published by The
Mathematical Association .