I'll give my standard suggestion which is: hard problems, solvable using techniques your kids already know, are FAR FAR more valuable to mathematical development than learning new techniques (i.e., doing the next chunk of curriculum). That's what I'd be pushing for. Fortunately there are lots and lots of options including some free ones out there, at lots of different levels so it should be possible to find something that's challenging without being impossible. Look at (or get the school teachers to look at) the various Olympiads and maths competitions for questions. Ah yes, here's a thread with various suggestions that might be relevant, including the ones that I suggested 5 posts down in it (saves me retyping!)


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