This girl's traditional Chinese game is similar to Jacks or Knucklebones, and is played with a collection of pebbles.
Gather together a handful of pebbles. Throw them up into the air and let them land.
One child starts by drawing her finger between any two pebbles (to mark the two pebbles she is going to use). The then "snaps" one of the pebbles with her fingers towards the other one. If she hits it, she takes both pebbles and puts them aside, then has another go. If she misses, play passes to the next player.
Obviously the first player has the advantage of being able to choose the closest, or otherwise easiest, pair of pebbles. Each time you start the game again, the first play should pass to a new player.