Teaching Kids Philosophy

I recently volunteered for a mentoring program which paired me up with a gifted 10-year old who is interested in philosophy. The idea is that we meet for an hour a week and pursue these interests that he wouldn't be able to learn about in the usual school curriculum. We've just had a couple of sessions so far, and it's been quite fun, just chatting about various philosophical topics. The kid is very intelligent, which certainly helps. Anyway, I was wondering if people have any advice about teaching philosophy to (or, rather, discussing philosophy with) children.

I've found some useful sites already: the Stanford encyclopedia has some interesting background; Philosophy for kids offers some "story" resources one could use as a basis for discussion; and NorthWestern describes some group activities that sound really fun.

But most of this stuff is directed towards classroom or group discussions, and is not always so easy to apply in a 1-on-1 context. I'm not sure that kids have the capacity - or the attention spans - to go into great depth on a philosophical topic. But that doesn't matter so much in groups, because the diversity of voices provides plenty of breadth in its place.

What I really need is a way to keep a topic 'open' and interesting when there's just one student. So far, we tend to exhaust the surface of a topic fairly quickly, but I'm not sure I could go into more detail without confusing or boring the student. As a result, we've just discussed a little bit of a great many topics (e.g. skepticism, ethics, free will, logical paradoxes, whether time began, etc.). But I'm going to run out of topics soon, so really I need some way to be allow him to pursue some of these in more depth. Any ideas?

Ideas for activities would be especially appreciated. Discussions are all well and good, but they can get tiring, and a bit more variety would go down well, I think. Can anyone think of some sort of "project" that the kid might enjoy working on - something that would involve a more in-depth study of a philosophical issue, perhaps, all the while remaining accessible to a 10-year old (bearing in mind that he is exceptionally bright)?

Also, are there any discussion topics you would particularly recommend as being of interest to someone that age? The kid himself expressed some interest in time, and in logical paradoxes (say, I should combine them and discuss time-travel paradoxes - those are always fun!), and he is a huge fan of skepticism. In fact, he's convinced that he doesn't know he has hands -- which is kind of amusing, but I think I probably ought to discuss some responses to skepticism with him. (After all, dogmatic skepticism is no more enlightening than dogmatic anything-else.) It might help if I focused on questions of justification rather than knowledge, to avoid any infallibalist intuitions. And of course we'll need to examine some of his underlying relativistic assumptions (though he may be not quite so bad as most in this respect). Any other suggestions?