We used to play a game using dried peas and straws: each child has a bowl of dried peas in front of them, and a drinking straw. By sucking, they can pick up a pea. See who can transfer most peas in this way to another bowl, say 12 inches away, in a given time. Either everyone can play at once, or they can take turns.
Jigsaw pictures: my dad collected as many big, colourful pictures as he could from magazines - most of them were adverts.
He cut each one in half, usually in a slightly zigzag way.
Before the game, one half of all the pictures would be spread around the house.
To start the game, each child would be given one of the other halves, and they had to go off to search for its missing piece. As soon as they found it, they went back to the organiser, who then gave them another half (at this stage an adult needs to have a list of the names and put a tick against the appropriate one each time that child completes another pair, to see who has found most when there are none left to be found)
You need a lot of pictures, so that each child gets to search for several.
Alternatively, I suppose you could put the children in pairs for this game, and perhaps give each pair a set number of pictures right at the beginning (four, maybe), so that the winner is the first pair to find the corresponding halves of all of their pictures.