ColinsMum, could you recommend some sources of problems in addition to Alcumus. We've almost never had DS7 solving (non-routine) problems at all, yet, as we were just getting him through the basic K-5 maths so he'd have some basic knowledge, but now he desperately needs to be challenged.

Another question, what's your approach to assessing "mathematical maturity" and readiness for certain mathematical activities? For example, I haven't mentioned at all to DS7 about theorems and proofs, since he's not ready for that. He can understand and explain things, but I'm just happy for him to think about things without worrying about rigor at this time. Know what I mean? What other stages of "mathematical maturity" should I be thinking about?

Another question, anyone know of a good resource (especially online) for learning very basic logic (and, or, not, quantifiers) and the same for set theory. These topics are totally absent from the school curriculum, so this void needs to be filled.

Not the person addressed, but thought I'd give the info I have while bumping the question up again.

In addition to the suggestions for sources of non-routine problems already made, you could try

NRICH math. Another resource that could be useful is

IMACS or eIMACS. (Have had (good) experience with IMACS classes, but none with on-line.) This would also be an answer for your question on basic logic and set theory.

Math circles could be good, if there is one locally and it works out for you.

And I'm sure there are things I'm not thinking of right at the minute.

My recollection is that in the past, ColinsMum has recommended

Tarski's world for logic. I'm hoping she'll say more again here since I'm not sure if that is still her recommendation and I'd like to know too.