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An interesting approach to teaching factors (stolen from Graham!), based on techniques used in Primary schools.
..... They use the idea of a "factor bug". The bug's body is drawn and the number (e.g. 12) is written inside the body. Two antennae are then drawn and the "cheeky factors" (1 and 12) and written on the end of the antennae. Since bugs always have two antennae, kids know that these numbers will always be there. They then look for other factors, and realise that for most numbers, they must always come in pairs. So for each factor they find, they draw a leg on the bug and write the factor at the end of the leg (e.g. 3). Since factors come in pairs, they look for the other one and draw another leg (e.g. 4). So they see that they always have an even number of legs. The one scenario this doesn't work for is square numbers, where the factor doesn't come in pairs. In this case, they write the odd factor on a tail.
This helps kids to see different numbers as different bugs. They can look at a bug with 25 on, and see that it's a square number immediately by the fact it has a tail. They can see if a number is prime if the bug has no legs or tail. And so on.
I think this is a really neat way of introducing kids to the idea of factors and can get them used to the different factors that certain numbers have, as well as improving their knowledge of their times tables. The main downside that I see is when prime factorisation is introduced, as the idea cannot really be extended easily to incorporate this concept. Still, I think it's a pretty neat way of writing down factors for younger kids.