Area Model Multiplication Generator Area Models
Create clean, labeled area model diagrams in seconds. Split factors by place value into tens and ones, fill each box with its partial product, and sum them to the answer. Free for teachers, parents, and students.
Area Model Multiplication Generator
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Area Model Examples
Browse area models made with Figviz, or generate your own above
2-Digit by 1-Digit Area Model
A 2-digit by 1-digit area model that splits the larger factor into tens and ones, giving two partial products that sum to the answer.
2-Digit by 2-Digit Area Model
A 2-digit by 2-digit area model with four boxes, one partial product per box, summed to the final answer to teach the standard method visually.
Area Model for Division
An area model for division that breaks the dividend into place-value chunks, finding each part of the quotient above the boxes.
Area Model Multiplying Fractions
An area model for fractions that partitions a unit square in two directions, with the overlapping shaded region showing the product.
Blank Area Model Template
A blank area model template with empty boxes and label slots along the edges, ready for students to fill in factors and partial products.
Area Model Worksheet
A printable area model multiplication worksheet with several blank diagrams and problems for students to split, label, and total.
What is an area model?
An area model is a box model that turns multiplication into the area of a rectangle. Each factor is split by place value, so a number like 23 becomes 20 and 3, and the rectangle is partitioned into smaller boxes for every combination. The area of each box is a partial product, and adding the partial products gives the final answer. Because the work is laid out visually, students can see exactly where every number comes from, which makes the area model a clear bridge between concrete arrays and the standard algorithm. The same idea extends to area model division and to multiplying fractions, so one mental model supports many topics.
How to make an area model for multiplication
Area model for division
The area model also makes division visual by running the multiplication idea in reverse. You start with the dividend as the total area and the divisor as one known side of the rectangle, then find the missing side piece by piece. For 156 divided by 12, place 12 on the left and ask how many groups fit: ten groups give an area of 120, leaving 36, and three more groups give 36 exactly. The partial quotients written above the boxes, 10 and 3, add to the answer of 13. This place-value approach keeps the numbers friendly, connects directly to the multiplication model students already know, and prepares them for long division with understanding rather than memorized steps.
Area model for fractions
To multiply fractions with an area model, start with a single unit square and partition it in two directions. For two thirds times three fourths, divide the square into thirds going one way and fourths going the other way, creating a grid of twelve equal cells. Shade two of the three columns to show two thirds, then shade three of the four rows to show three fourths. The region where the two shadings overlap covers six of the twelve cells, which is the product six twelfths, or one half in simplest form. This overlapping-area picture explains why you multiply numerators and denominators, turning an abstract rule into something students can see and reason about.
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