Open-ended math problems are a valuable resource in any math curriculum. Built on a simple premise, they provide a low entry point for all students. But they also are automatically differentiated upward by having high exit points.
The Polyomino Problem asks students to consider the number of shapes that can be made by aligning a given number of squares. For example, the pieces in the game Tetris are 4-ominoes. How many pentominoes (made of 5 squares) can be formed? As students explore this and related questions, they will think geometrically, justify their results, and look for patterns.
The PDF includes a lesson plan, teacher notes, and enough extension questions / handouts to turn this simple question into an entire unit on geometric reasoning.