Peter-
Though I don't know the specifics of what you have in mind, one fun "family" activity is to play Set. It is a card game though an online "daily puzzle" can be found at http://www.setgame.com. There is a description on that site of the mathematics involved with the game. Though I can't be sure, my guess is that a second grade student who likes games would enjoy this and develop the beginnings of a sense of sets and "making sets" according to given criteria.

Good luck!
OSUMathEdGuy.