Ep 304: Context, Models, and Strategy for a Better CRA

In this episode of Math is Figure-Out-Able!, Pam and Kim dive into a powerful instructional sequence they co-created with Hand2Mind for teaching multi-digit multiplication through a context-rich, manipulative-based approach. Centered around a 'Willy Wonka'-themed chocolate bar design challenge, the lesson sequence begins with students building physical models using base-10 materials to explore area as composed of unit squares. This concrete experience grounds their understanding before transitioning to closed arrays on grid paper and eventually open arrays—models that represent thinking more efficiently while maintaining connection to the context. The episode emphasizes that the goal isn't to mimic algorithms, but to develop deep conceptual understanding of area and multiplicative reasoning through 'smart partial products' and the 'over strategy' introduced via 'adjust' problems. These problems, where students revise an initial design (e.g., 30×32 → 29×32), prompt them to use known facts and adjust by subtracting a group—introducing the over strategy naturally. The conversation also challenges the myth of a linear CRA (Concrete-Representational-Abstract) progression, arguing instead for a dynamic, interconnected process where students move fluidly between models and strategies while building sophisticated, transferable reasoning. The episode concludes with a call to action to register for an upcoming live webinar with Hand2Mind, reinforcing the mission to make math more figure-outable through meaningful, relationship-based teaching.