Well teachers, I have found this to be a really enjoyable activity for youngsters to get their teeth into, if they are relatively confident at mathematics and are not really struggling (perhaps 66% pf the class but of course it really depends on so many factors; younger groups change so much!). It may be the first time that they can really feel that they are exploring something new and not just something handed to them that someone else has already worked out.

The patterns that are generated can be very exciting. I have found it useful if the children have already met things like the patterns that are evident in the 9 x table. When children have seen that 18, 27, 36, 45, 54 etc. have digits that add up to 9, then you can go further. Adding up digits in this way is sometimes called "digitizing". Any number can be digitized. So this current year 1997 would add up to 26 if the digits were summed. The 26 should then be added to give 8. Some further examples would be:-

1564 >16 > 7
225864 > 27> 9
and so on.

If children are happy with this, and they usually are, then introduce this idea, perhaps starting from what they notice about the answers to the 9x table , before starting this challenge, as it adds a new dimension of things that can be studied and enjoyed in the exploration of their Number Patterns.

I also have found that the whole process of doing a, b, c, d, e, ; writing about what they notice; changing something slightly and repeating, etc. to be a very good investigational process for the youngsters to get used to.Caleb Cattegno in the 1960's said:

"Mathematics is the study of the invariances under a set of transformation" or if you prefer it:-

"Doing maths is, take something, change it in some way, seek out what does not change" in very simple terms .

I have found it very hard to stop children when they are working in the activity.

Just as a final comment, it is a useful tool when encouraging children to work together.

You may wish to look at Divisibility Tests - an article in the archive.