Basketball games for 4-year-olds should be designed for the kids to have fun and learn the basic fundamentals of the game. They should also teach kids teamwork and good sportsmanship. Kids at this age have a limited attention span, so games should have minimal rules to keep them engaged.
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This game is similar to musical chairs. Have the kids line up on the baseline with a basketball. When the whistle is blown the kids drop their balls and run to the other end of the court and back to pick up their ball. While they are running, the coach picks up one ball, leaving the rest on the floor. The kid without a ball is out. The playing area can be reduced as more kids get out.
Bean Bag Dribble
Divide the kids into two teams and put one team on the baseline and the other on center court. Place a pile of bean bags in the circle of the key. When the whistle is blown, one player from each team dribbles to the key and continues dribbling while picking up a bean bag, then dribbles back carrying the bean bag, as fast as possible. Then the ball is given to the next kid in line, repeating the process until all of the bean bags have been picked up. The team with the most bean bags wins.
Have the kids lie on their stomachs with their eyes closed at the half-court line. When the whistle is blown, the ball is thrown into the air. The kids get up and race after the ball. This game teaches the kids how to react quickly to a loose ball.
Red Light, Green Light
Give each kid a ball and have them line up on the baseline. When the coach says "green light," the kids walk and dribble toward the coach. When the coach says "red light," the players stop and pick up their ball. The kid who makes it to the other end of the court first wins.