Split and conquer big numbers
Watch 12×13 fracture along the tens place into four colored regions: 10×10, 2×10, 10×3, and 2×3. Each region's area is a partial product — add them up for the total.
Multi-digit multiplication is just a rectangle cut by place value. The area model splits 12 × 13 into four regions — (10 + 2) × (10 + 3) — so the distributive property becomes a picture instead of a memorized algorithm.
Aligned with CCSS 4.NBT.B.5 (multiply using place value strategies).
Watch 12 × 13 split into four partial products that sum to 156.
Press Split to see the distributive property in action
Multiplication model
Area Model Multiplication is built for students who can recite facts but need to understand the array, area, or partial-product structure. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Area Model Multiplication helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
Learning goals
How to play
Continue with guided practice
A rectangle whose sides are the two factors. Splitting each side at place values cuts the rectangle into smaller rectangles whose areas (partial products) sum to the answer.
(10 + 2) × (10 + 3) = 100 + 30 + 20 + 6 = 156. Each term is one of the four sub-rectangles.
The same four-rectangle split powers (x + 2)(x + 3) = x² + 5x + 6 in middle-school algebra. Place value is just a number-line version of variables.
Grades 3–5, aligned with CCSS 4.NBT.B.5. Strong bridge from multiplication facts to two-digit multiplication.
