Grades K-8 Worksheets
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The area method, also sometimes called the box method, is an alternative to the standard algorithmic method (see below) for long multiplication. Both these methods use the distributive law for multiplication but they differ in how the partial products are calculated and written.
The standard algorithm is generally a faster method but, unlike the area method, it does not promote understanding or encourage the development of mathematical thinking. It may be best to introduce your children to long multiplication with the area method before using the standard algorithm. The area method also supports the important ability to estimate answers.
5 x 24 = 5 x (20 + 4) = (5 x 20) + (5 x 4)
Activity: Modeling 5 x 14 with Cuisenaire Rods
1-digit x 2-digit Examples
View the examples below with your children. Discuss the steps and calculate then add the partial products. Click the links to show or hide the solutions.
When introducing a new method it is good to start with smaller numbers and multiplication facts that are easier to recall. This means the focus can be on the method and it also helps students who struggle to remember multiplication facts.
Practice Area Method Multiplication
Try this worksheet generator to practice using the area method for multiplication. Set the values of the First Number to less than 10 to practice 1-digit x 2-digit multiplication.
This method of multiplication relies on students' ability to multiply mentally by multiples of 10 and multiples of 100. If your children are not comfortable doing this then you can review multiplication by multiples of 10 with them here.
2-Digit x 2-Digit Multiplication Using Area Method
In the examples above, only one factor was decomposed to its base 10 values. When multiplying 2-digit by 2-digit numbers, both numbers are decomposed and we use four rectangles as shown in the two examples below.
18 x 22
25 x 42
2-Digit x 3-Digit Multiplication Using Area Method
The example below shows how the method can be extended for the multiplication of larger numbers. Note that the area method becomes increasing cumbersome as the number of digits involved increases. In such cases, where understanding has been established, the standard algorithm (or a calculator!) is likely better.
55 x 412
Comparing the Area Method with the Standard Algorithm
Compare the 2 methods Discuss the two methods with your children. Use the example below to show the correlation between the two methods
Use the worksheets below to practice using the area method for multiplication as well as other methods.