How to Do Box Method Multiplication (Area Model), Step by Step
The box method — also called the area model — is a way to multiply larger numbers by breaking them into their place-value parts. Instead of stacking numbers and carrying, you multiply the parts in a simple grid and add them up. It makes multiplication visual and far easier to understand.
Step 1: Split each number by place value
Write each number as the sum of its tens and ones (and hundreds, if needed). For example, to multiply 23 × 14:
- 23 becomes 20 + 3
- 14 becomes 10 + 4
Step 2: Draw the box and label it
Make a grid with one number's parts across the top and the other number's parts down the side. For 23 × 14, you get a 2 × 2 grid with columns 20 and 3, and rows 10 and 4.
Step 3: Multiply each cell
Fill every cell with the product of its row and column. These are called partial products:
3 × 10 = 30
20 × 4 = 80
3 × 4 = 12
Step 4: Add all the partial products
Add every cell together to get the final answer:
So 23 × 14 = 322.
Why the box method works
Each cell is just one piece of the total area of a 23-by-14 rectangle. By splitting the rectangle into smaller, easy pieces and adding them back together, you get the same answer as any other method — but every step is visible, so it's easier to spot and fix mistakes.
Tips for teachers and parents
- Start with 2-digit × 1-digit before moving to 2-digit × 2-digit.
- Have students say each partial product out loud to reinforce place value.
- Use the box method calculator to check work, then try problems by hand.
Frequently asked questions
What is the box method in multiplication?
It breaks each number into place-value parts, multiplies every pair of parts in a grid, and adds the partial products to get the answer.
Is the box method the same as the area model?
Yes — "box method" and "area model" are two names for the same strategy.
Where can I practice it?
Use the free Box Method Multiplication Calculator to see the grid and steps for any numbers, or try the math games for fun fact practice.