Materials-wise, I can't recommend the Murderous Maths books by Kjartan Poskitt enough. They're what got me into maths, and introduce topics at a basic level while leaving the top end open for further development. They've got lots of fun puzzles and activities. I think they're aimed at 10-14 year olds, so would be towards the top of your tutee's age range.
Less paper-based and more free is NRICH (http://nrich.maths.org/), which is run by a group at Cambridge (I've done some holiday work writing questions for them). It contains materials for all ages (pre-school up to sixth form! (4-or-5-ish to 8)) and is intended as simultaneous for teachers and keen students. It's got a good selection of mathematical games as well as themed monthly questions, and keen students can type up their solutions and submit it to them for a chance of being featured on the website. The games in particular will be a good way of introducing lots of mathematical concepts, since that's how they're designed.
In fact, teaching your kids basic game theory is probably a good idea. It teaches you them to think rationally and is easy to motivate (beat all your school friends!). Many rationality concepts and techniques are founded upon the basics of game theory!
pre-school up to sixth form!
Given the international nature of the internet, it would be helpful to provide clarifying definitions for country-specific terms.
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: