Teaching Grammar! Starting with the basics: Der, Die, Das!

The one thing I've struggled with as I've raised my children in my non-native German is teaching them correct grammar. My own grammar is faulty and I often see them making the same mistakes that I make. One of the most difficult obstacles for us is learning the correct gender of nouns. Even I struggle with this on a regular basis. It's one of those things for which you develop a "feel." And when you don't live in a German speaking country, surrounded by German speaking people, it can be much more difficult to develop that "feel" for the language.
German has three genders: Masculine, feminine and neuter. And unless you know the correct gender for any given noun, you will never pull off a grammatically correct sentence in which that noun is used! So, before we learn much else, we need to work on genders!
I came up with a gender game for the kids. I have a bunch of small flash cards with pictures one side and the noun (along with the gender) on the other. For example: On one side of the card is a drawing of a cow and written on the opposite side is "Die Kuh." (the cow).

I laid all the cards on the floor with the picture side up. If one of the kids picked the picture of the cow and (without turning the card over and checking) guessed that it was "die" (feminine), then they got to sort the card with all the other feminine nouns. If they got it wrong, they put it back in the pile. I really enjoyed this game, because it really gave me a feel for what words they know and which they don't. I was glad to see that they got more right answers than wrong answers. I'm anxious to play this game with them on a regular basis. I think I'll change it up. Instead of putting the wrong answers back in the pile, I'll have them each keep their own pile of wrong answers. At the end of the game, we can review the cards that they got wrong.