Why do this problem?
, I have found to be very enjoyable for pupils, because it opens up a new world for most of them - that they can create their own number patterns and explore them! It's a healthy change for many of them to feel that they are not just being handed something that the teacher already knows an awful lot about. So
if these thoughts encourage you then present it to your pupils.
I've found it valuable to use this with the whole class and focus on an introduction where they're meeting the usual number patterns. As they look at some familiar patterns, I note down for all to see the comments that pupils are making. I've usually numbered their findings and got to at least number six for each one! This then leads into the idea of them creating their own, to explore in
Tell me about your rules.
Do you notice anything that you want to tell me about?
See the 'Then choose' suggestions at the end of the problem
Calculators are useful here so that the pupils are free to explore rather than getting tied down by the calculations.
For more extension work
The pupils could go to Become a Maths Detective which is an interactive version of this activity. They can then explore much further and do some powerful comparisons of results. Further ideas relating to that later activity can be found by following the link in Become a Maths Detective for the NRICH Projects site
where other pupils' ideas can be viewed and commented on once you have registered.
The patterns that are generated can be very exciting. I find it useful if the children have already met things like the patterns that are evident in the nine times table to take things a bit further and investigate Digital Roots
. I have also found that following the a, b, c, d, e parts as suggested in this activity,
writing what they notice, changing something slightly and repeating etc. to be a very good investigational process for the youngsters to get used to. Caleb Gattegno in the 1960s said; "Mathematics is the study of the invariances under a set of transformation". Or if you prefer it, in my words now; "Doing mathematics is taking something, changing it in some way and observing what is the same and
what is different."
BE WARNED it may be hard to stop some children once they get going!