This racing-chasing game is guaranteed fun for ducks and geese alike. It also adapts readily to any party theme.
Play "Drop the Hanky." Instead of sitting down, the players stand in a circle facing each other. Another person walks outside the circle, and drops a handkerchief (or piece of cloth) at the feet of one of the players. That player then picks it up and chases the hanky dropper, who races around the circle and tries to capture the other person's space without getting tagged.
All of the children except one sit in a circle facing each other. The remaining person goes around the circle, tapping each child gently on the head and saying "duck."
When the tapper says "goose," the child whose head was just touched jumps up and chases the tapper around the circle.
The tapper in turn tries to get all the way back to the goose's spot without getting tagged by the goose. If the tapper succeeds, the goose becomes the new tapper and the game continues. But if the goose catches the tapper, the tapper continues his or her walk around the circle.