Teaching Advice?

I'm doing some part-time tutoring over the holiday break. In particular, I'm teaching maths and science to a couple of intelligent young (about 12 years old) Asian students. I was wondering if anyone has any advice to offer about activities or topics I could cover to make the lessons a bit more interesting than your usual tired curriculum.

In the maths lessons I'd like to do some 'problem solving'-type questions. Does anyone know of a good online resource which offers some examples of these? I think I might also try to explain some basic proofs, e.g. that there is no greatest prime number. (That's pretty advanced for kids so young, I know, but I think they could manage it. There's really just two things I'd need to explain: (1) factorials, which would be easy enough, and (2) why (k*n + 1) is guaranteed to not be a multiple of n. This would be slightly trickier, but not excessively so, I don't think.)

As for science, I think I'd quite like to explore the conceptual side of things in more detail, rather than just doing lots of exercises (which are effectively just applied maths, after all). So again, any resources which might help here would be much appreciated. Also, to give them a taste of the practical aspect, a few "baking soda & vinegar" type experiments would probably be a good idea too.

So... any ideas?