30% Black Friday SALE! Click here to lock in and save 30% now!

Area Method For Multiplication

Grades K-8 Worksheets

Looking for high-quality Math worksheets aligned to Common Core standards for Grades K-8?

Our premium worksheet bundles contain 10 activities and answer key to challenge your students and help them understand each and every topic within their grade level.

Understanding Basic Number Properties of Multiplication Worksheets

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)

Standard Algorithm

2 4
x 5
2 0


1 0 0
1 2 0

Area Method

204
510020

 

100 + 20 = 120

Modeling Multiplication

Activity: Modeling 5 x 14 with Cuisenaire Rods

Start with 14 made up of a 10 and a 4 rod.
 104
 10 cuisenaire rod4 cuisenaire rod
5 times (5x) means we need five (5) 14s.
 104
10 cuisenaire rod4 cuisenaire rod
10 cuisenaire rod4 cuisenaire rod
10 cuisenaire rod4 cuisenaire rod
10 cuisenaire rod4 cuisenaire rod
10 cuisenaire rod4 cuisenaire rod
5 x 14 = (5 x 10) + (5 x 4)
5 x 10 =
5 x 4 =
50
20
 70
The same multiplication can be modeled by sketching boxes without any cuisenaire rods. The partial products are written in the boxes.
 104
5020

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.

Examples

5 x 15

  
   

Click to Show/ Hide Solution

2 x 35

  
   

Click to Show/ Hide Solution

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.

Examples

18 x 22

202
1020020
816016

 

200 + 160 + 20 + 16 = 396

25 x 42

402
2080040
520010

 

800 + 200 + 40 + 10 = 1050

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.

Example

55 x 412

400102
5020000500100
520005010
    
    

 

20000
2000
500
100
50
+ 10
22660

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

Example

Area Method

500201
201000040020
42000804

 

10000+2000+400+80 20+4 = 12504

Standard Algorithm

5 2 1
x 2 4
2 0 8 4

1 0 4 2 0
1 2 5 0 4

Multiplication Worksheets

Use the worksheets below to practice using the area method for multiplication as well as other methods.