When it comes to children and puzzles pieces always end up missing. So in our classroom we have included dollar store baskets in our puzzle area.
Each puzzle has a basket with it, so as the children choose a puzzle they also get a basket.
The children place the pieces in the basket and then pull pieces from the basket to put the puzzle together.
If a child is having a hard time putting the puzzle together or just does not want to finish it because something else has caught their attention then the child places the puzzle and the basket of pieces on the shelf together so that if another child wants that puzzle all the piece are together.
This has helped with the missing piece problem.