Students can learn significant mathematics during play. For example, when playing with tangrams students discover that they must sometimes "flip" a piece over to make it fit into a picture they are creating, while other times they must rotate the piece. Translating a piece from one location to another can change the picture they are creating from one form to another. Students discover that several pieces can be combined to make a larger piece and that the square can be broken up into the seven tangram pieces.
Also, if students are to use a manipulative to discover a mathematical concept, they first need time to play with the manipulative to become familiar with it. The same is true with computer programs, computer games, and calculators. Once familiar with the new tool, they will stay on task longer as teachers introduce guided activities.
