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 Caterpillar Problem describes a simple rule for building a "caterpillar" and then poses a challenge to students. Students will experiment with numbers, generate strategies, and look for patterns. From simple arithmetic to two-variable algebraic equations, this