Area Model Multiplication
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.
What this game shows · Area Model Multiplication
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.
- Distributive property
- (a + b)(c + d) = ac + ad + bc + bd.
- Partial product
- one of the four sub-rectangles in the split.
- Place-value split
- 12 = 10 + 2; 13 = 10 + 3 — split at the tens.
Aligned with CCSS 4.NBT.B.5 (multiply using place value strategies).
Area Model — Distributive Property
Watch 12 × 13 split into four partial products that sum to 156.
Press Split to see the distributive property in action
Area model, unpacked.
01 What is the area model for multiplication? Visual model
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.
02 Why does 12 × 13 = 156 in the area model? 156
(10 + 2) × (10 + 3) = 100 + 30 + 20 + 6 = 156. Each term is one of the four sub-rectangles.
03 How does this connect to algebra? FOIL preview
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.
04 Which grade is this game for? Grades 3–5
Grades 3–5, aligned with CCSS 4.NBT.B.5. Strong bridge from multiplication facts to two-digit multiplication.