In 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.
Another 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 .