Divisibility rules explained

As James Tanton points out, many students (and teachers!) use the divisibility rules, but can't explain why they work. That is unfortunate, because the explanations are a great stepping stone to modular arithmetic. The video above explains the divisibility rules for 3 and 9. (Double-click on it to see it full screen!)

Here's his explanation for the divisibility rule for 11.

And here's his explanation for the divisibility rule for 7. After viewing this one, you should have ideas about how to create your own divisibility rules for numbers like 13, 17, 47, etc.