Planning party games for the 2-year-old set can be a bit of a challenge. At this age, most children are not competitive with each other and, in fact, you're more likely to see parallel play than kids playing with each other. Look for games that you play as a group to keep the 2-year-olds entertained.
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This game works when you have allowed the parents to stay at the party. Print out two sets of three cards that include images of a kangaroo, a koala and a penguin on each one. Two mom and toddler teams will race each other. Each team picks a card from one of the sets. If it's a koala, mom has to carry the child on her back; if it's a kangaroo, mom carries the child in the front; if it's a penguin, mom must walk with her child standing on her feet.
Balls in the Umbrella
Play this game outside. Open up an umbrella and turn it upside down and hold it just high enough to be out of reach of the children. Kids have one minute to throw as many small plastic balls into the umbrella as they can. Once the minute is up, you can count the balls together to see how many they threw in. Repeat the game, challenging them to get more balls in the next time.
Play music and allow all children to dance. When the music stops, children must form a statue, staying completely still. If a child moves, he has to sit out the next round, but can continue after that. Give each child a chance to control the music and look for the "statues" that are moving.
Take the children on a pretend journey to hunt a bear. Act animated as you do steps like pushing the forest leaves out of the way, climbing up a tree and running away from a lion. The children must copy all of your actions.
Touch the Colors
Challenge children to see who knows the colors. Start in the middle of the room with all children touching your arm or hand. Call out a color. Children must run to find something in the room that color. If a child touches that color, she is "safe," but if she's not touching it, you can give her a tickle.