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.
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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.
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.
An area model for division that breaks the dividend into place-value chunks, finding each part of the quotient above the boxes.
An area model for fractions that partitions a unit square in two directions, with the overlapping shaded region showing the product.
A blank area model template with empty boxes and label slots along the edges, ready for students to fill in factors and partial products.
A printable area model multiplication worksheet with several blank diagrams and problems for students to split, label, and total.
Start with one of these examples, then adapt the subject, labels, data, or layout for your own use.
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.
Create an area model for 36 times 4: a rectangle split into two boxes by place value, the top edge labeled 30 and 6 and the left edge labeled 4, each box holding its partial product 120 and 24, with the two products summed to 144 shown below. Crisp evenly spaced straight ruled lines and legible labels. White background.
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.
Create an area model for 23 times 14: a rectangle split into a two by two grid of boxes by place value, the top edge labeled 20 and 3 and the left edge labeled 10 and 4, each of the four boxes holding its partial product 200, 30, 80, and 12, with the four products summed to 322 shown below. Crisp evenly spaced straight ruled lines and legible labels. White background.
An area model for division that breaks the dividend into place-value chunks, finding each part of the quotient above the boxes.
Create an area model for division of 156 divided by 12: a long horizontal rectangle split into two sections by place value, the divisor 12 labeled on the left edge, partial quotients 10 and 3 labeled above the sections, each section holding its area 120 and 36, with the quotient 13 shown to the side. Crisp evenly spaced straight ruled lines and legible labels. White background.
An area model for fractions that partitions a unit square in two directions, with the overlapping shaded region showing the product.
Create an area model for multiplying fractions two thirds times three fourths: a unit square divided into thirds vertically and fourths horizontally, two of the three columns shaded one way and three of the four rows shaded another way, the overlapping region of six out of twelve cells highlighted to show the product six twelfths. Crisp evenly spaced straight ruled lines and legible labels. White background.
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.
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.
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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