Area Model

The Area Model question type assesses whether learners understand how multi-digit multiplication works—not just the final answer. Learners construct a visual representation of a multiplication expression by decomposing factors, filling in partial products, and completing partial sums.

Ideal for elementary and middle-school math programs where conceptual understanding of arithmetic operations is a core learning objective. Responses are automatically scored with partial credit and cell-level diagnostic feedback.

Try it

Using the arrow buttons, create a model of the appropriate size and fill in the cells to create a model of the given expression. Complete the partial sum using the column grid on the right.

The Scoring Challenge We've Solved

Building a grid widget is straightforward. Scoring learner responses intelligently is not. Our automatic scoring handles the complexity that makes this question type actually useful for assessment:

• Partial credit — Each cell is scored independently, giving learners credit for what they got right
• Multiple valid decompositions — Accept different ways of breaking down factors (e.g., 12 as 10+2 or 6+6)
• Cell-level diagnostics — Pinpoint exactly where a learner's reasoning diverged, not just "incorrect"

Note: The area model question type can be set to provide immediate feedback (as in this demo), delayed feedback through a "Check Answer" button, or no feedback for summative use cases.