There's not a lot to say about this. The children in the 1980's were the lowest of achievers and found it quite captivating. I'm quite convinced that with a helper 6 year olds up wards can get into this even if they only use two hoops.

If you use this as some staff inservice, it shows how important it is to do this kind of activity for real and not just do it on paper. The discussions are also very valuable - people do this activity in so many different ways.

I'm pretty certain that the following results are correct for producing 4, 5 & 6 in the hoops:-

using 6 - 2 ways
using 7 - 6 ways
using 8 - 16 ways
using 9 - 21 ways
using 10- 28 ways
using 11- 18 ways
using 12- 8 ways
using 13- 5 ways
using 14- 3 ways
using 15- 1 way

Now there's always something about numbers produced by doing an activity like this. I'm convinced of that and pupils can catch the excitement as you all find different things.

I've not explored the four hoops situation, but those having very enthusiastic pupils at KS2/3 could work on that for me.