What's your level of math and science knowledge? Can we recommend that you teach the kids group theory?
Also, what's the goal for the kids? You'll want to teach different things depending on whether they want to keep up with schoolwork, skip ahead in schoolwork (and hopefully proceed to skip grades), or just learn more about math and science. Fir the first two you'll need to cover a known curriculum, for the latter you need to avoid that curriculum like the plague of boredom.
For math resource, you might check out Vi Hart's videos and A Mathematician's Lament.
For science resources, check out museums :P Also, I highly recommend pH paper as a powerful experimental tool an 8 year old can use. Lots of cool chemistry experiments out there. For biology, growing plants and growing germs on agar and taking nature walks with a book about trees and making Punnett squares are good activities. Kid physics is mostly like engineering - making telescopes from lenses and water bottle rockets and freezing rubber bands on dry ice and having a competition over who can make something out of paper and tape that will catch dropped eggs from the highest height.
By the time I'll be teaching I'll have finished my Maths and Further Maths A-Levels and I would also have studied a fair amount of higher material.
Those are all good suggestions. One thing troubling me is that I want to help kids develop their problem-solving skills. Ideally I'd introduce some new puzzle and give them a few hints and they would work it out, but from my limited experience with my 9 year old cousin (who is fairly bright), it either ends up with me giving too little help (so he gets stuck and gives up in frustration) or too much help (so he's just following along with what I'm saying rather than discovering something for himself). How can I best strike the balance?
In about eight months or so, I will be one of those (hopefully not starving) students. I'll be moving out to London to live with my aunt and uncle in a rather nice middle-class neighbourhood, while I study and work to prepare for university the following year. They know a lot of the parents around there and suggested that I begin teaching small groups of 8-to-12 year old children for maybe an hour or two regularly, and charge their parents/guardians a reasonable sum per child. I would be teaching them math and science in all likelihood. Apparently word will get around quickly if I'm competent so I might have a substantial number of customers within a few months.
My questions: