Patches

Each number sits in a patch of its own. Drag out the rectangle that belongs to it — exactly as many squares as the number says, and the shape the chip is drawn in: wide, tall, square, or a dashed chip when any of them will do. Cover every square and the board is done.

The dashed chips are the ones to leave alone at first. Place every fixed shape you can — the wides, the talls, the squares — and the dashed numbers usually have only one place left to go by the time you reach them. Working a corner first helps too, because a corner square can only belong to a patch that reaches it one way.