| There are a few games out there for children that age. I bought a couple of them for my just turned 4 year old grandsons for Christmas. I bought them Uno Moo--a variation of the card game uno with animals.
I also got them Yahtzee JR. again a variation of the origional aimed at 4 year olds.
There is also one called Picture Domino's--played like regular domino's only you match pictures. I have bought them old maid cards with animals, which we played without the old maid and just dealt out 3 cards and turned over the rest on a pile one by one. When a card turned up that matched one in his hand he could put it with his and take another one off the pile. The winner has the most cards, but most times we didn't count the winners or losers. Just look around there is lots out there and what's saying you have to play the way they say. You can make up your own rules to suit playing with your youngster. Something else my grandsons like doing is putting together jig saw puzzles. You can start with 8 or 12 pieces and work your way up to however many pieces you want | 
