My kids both loved Don't Break The Ice at that age....and actually still do at 4-1/2 and almost 7. It's such a pain to set up, but it is a cool game. We also liked Cootie, and will Nth the recommendation for Hullabaloo, that's a really good one.  We also had Elefun, which is another battery operated one (which I normally also am not a fan of, someone else bought both of those games for us and they turned out great so I'm a changed person regarding it!Â
)Â where there's an elephant trunk made of some kind of plastic, and you put these nylon butterflies in the base of it, turn it on, and the trunk inflates and shoots the butterflies out of its trunk, and as they flutter down you try to catch as many as you can.Â
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Shortly after 4 something clicked with both my kids and now we're loving playing things like Monopoly Jr, Sequence, Clue Jr, and Sorry. I'm loving it, because I love board games. I just broke out the Twister a couple months ago and the kids are having a BALL with it.