In lesson 15, we introduce algebraic reasoning using the envelope technique. In this method, students treat unknown quantities as if they are hidden inside envelopes. Instead of introducing variables right away, each envelope represents a value they do not yet know—but can reason about. For example, if two envelopes together total 20, students understand that each envelope must hold 10.

There is no formal algebra yet. But the thinking is the same: students assign meaning to unknowns, track how quantities relate, and work step by step toward a solution using tools like the “envelope” technique. They are not yet writing equations. But they are thinking in exactly the same way: representing unknowns and balancing relationships.

While students see them as fun logic puzzles, these exercises build a strong foundation for early algebra and problem-solving using variables.