For instance in this kind of problem, 769 divided by 47, I think he uses estimation to come to the answer. He ends up with the correct answer with a remainder more quickly than he could write out the problem and i take nearly the same amount of time to check his answer using traditional long division--but i compute very quickly. I've never computed in my head though.
I guess I'm surprised because this is my verbal kid who finds math concepts exciting but not the computation.
Okay. So it's not that there are tricks or shortcuts to this (like there would be with, say, 2017/125). It's just that it's not hard enough, relative to his mental skills, to force him to pencil and paper. Harder problems will convince him that it's sometimes necessary.
Also there are a couple of later reasons where the concepts are useful, e.g. rewriting x^3/(x+2) as x^2-2x+4-(8/(x+2)), which is analogous to rewriting 769/47 as 16 17/47.
Also, if this is really busywork, which "show your work" can
sometimes become, maybe see if the teacher will accept a couple of "homemade" harder problems in place of writing all the details for the easier ones.
