WebMaths

Grades 3 to 5

Area Model

Multiply or divide with a rectangle split by place value. Each box holds one partial product and the boxes add up to the answer. Hide the boxes to practice, or print a page of area model problems.

Type a number to split it by place value, or type it as a sum, like 20+3, to choose the parts yourself.

Ways to use it in class

Printing area model worksheets

Press Worksheet for six problems of the kind chosen under Practice, with the sides labeled and the boxes empty, then press Print. For one model on the board, choose what to hide and print that.

Questions teachers ask

What is the area model for multiplication?
A rectangle whose sides are the two factors, cut into smaller boxes by place value. For 23 × 14 one side is 20 and 3, the other 10 and 4. Each box holds one partial product (200, 30, 80 and 12), and the boxes add up to the answer, 322. It shows why multiplication works, not just the steps.
Is the area model the same as the box method and partial products?
They are one idea. The box method is the area model drawn as a grid that is not to scale, and partial products is the list of the box values written in a column and added. Students often draw the boxes first and move to the written list later, then to the standard algorithm.
How does the area model work for division?
The divisor is one side of the rectangle and the quotient is the side you are looking for. Take away the biggest easy chunk first: for 875 ÷ 7, seven hundreds make 700 and leave 175, seven twenties make 140 and leave 35, and seven fives make 35. The side lengths 100, 20 and 5 add up to the quotient, 125.
Can I split a number my own way?
Yes. Type the factor as a sum, like 20+5 or 10+10+5, and the rectangle uses those parts. Choosing a friendly split, such as 25 as 20 and 5, is part of what the area model teaches.
How do I print area model worksheets?
Choose the kind of problem under Practice, press Worksheet for six empty area models, and press Print. Press Worksheet again for a new set.

More classroom tools

Number LineGrades K to 8

Whole numbers, fractions, decimals and negatives. Mark points and draw jumps for adding and subtracting.

Hundreds ChartGrades K to 3

Color squares, hide numbers to fill in, and light up skip counting by any number.

Place Value ChartGrades 1 to 6

Type a number and see each digit's value, expanded form, word form and base ten blocks.

Ten FrameGrades K to 2

One or two frames with two-color counters, for counting, making ten and quick looks.

RekenrekGrades K to 2

A number rack of red and white beads in 1, 2 or 10 rows. Slide beads in one push to see fives and tens, doubles and near doubles.

Multiplication ChartGrades 2 to 5

Up to 12 x 12 or 20 x 20. Tap a product to light up its row and column, hide answers to practice, and print.

Fraction StripsGrades 2 to 6

A fraction wall from wholes to twelfths. Shade pieces to compare fractions and find equivalent ones.

Number BondsGrades K to 2

A whole and its two parts. Build bonds, practice the missing part, and print a worksheet.

Base Ten BlocksGrades K to 5

Build any number to 9,999 with ones, rods, flats and cubes. Ten trade up for one, and a block breaks back into ten, to show regrouping.

Graph PaperGrades 1 to 8

Printable square grid, dot grid, coordinate axes and isometric dots, in the square size you choose.

Analog ClockGrades K to 3

Drag the hands, read the time in digits and words, and practice with random times from the hour to the minute.

GeoboardGrades 2 to 8

Tap pegs to stretch a rubber band into shapes, then read the area and perimeter. Boards from 5 x 5 to 11 x 11.

Pattern BlocksGrades K to 5

The six classic blocks to drag and turn: make pictures and patterns, tile shapes and explore fractions of a hexagon.

Algebra TilesGrades 6 to 9

Build expressions from x squared, x and 1 tiles, flip them negative, and use them to combine terms, multiply and factor.

Coordinate PlaneGrades 5 to 8

One or four quadrants. Tap to plot points, join them into shapes, and print blank grids.