My thought on videotaping the math was that I wanted to "prove" my child was doing the work. I, too, feel uncertain about taping chess. . .
What if you combined short clips of everything (including the chess) into one video, and included it with the written work?
My son isn't a chess champion either, but he was the only six year old that we knew of who could play and win with the correct rules. I was quite surprised, actually, that there weren't other kids (it doesn't seem to me like a game that's too advanced for a six year old, but then again, I only know my own kids).
We'd hear of friend's kids who were learning (they were older), but they never had the same grasp that my son did. Thank heavens for our neighbour's gifted son: he likes chess too and they play together

I think my son loses most of their games (our neighbour's son is two years older)
My point is, though, is that when my son was six, he had NO ONE his age to play chess with. He would have been the youngest member in the school chess club if they had run it that year. So yeah, I'd include the chess
