Area Method For Multiplication

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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)

Standard Algorithm

2 4
x 5
2 0
1 0 0
1 2 0

Area Method

20 4
5 100 20

 

100 + 20 = 120

 

Modeling Multiplication

If you have Cuisenaire rods then you can model multiplication. This type of hands-on practice with materials greatly helps students to develop an understanding of mathematical concepts and provides a sound basis for the transition to paper and pencil methods. Work with your children using examples, sketches, and explanations similar to those shown below. Be sure to discuss with them what you are doing.

Activity: Modeling 5 x 14 with Cuisenaire Rods

Start with 14 made up of a 10 and a 4 rod.
  10 4
  10 cuisenaire rod 4 cuisenaire rod
5 times (5x) means we need five (5) 14s.
  10 4
10 cuisenaire rod 4 cuisenaire rod
10 cuisenaire rod 4 cuisenaire rod
10 cuisenaire rod 4 cuisenaire rod
10 cuisenaire rod 4 cuisenaire rod
10 cuisenaire rod 4 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.
  10 4
50 20

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

20 2
10 200 20
8 160 16

 

200 + 160 + 20 + 16 = 396

25 x 42

40 2
20 800 40
5 200 10

 

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

400 10 2
50 20000 500 100
5 2000 50 10
       
       

 

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

500 20 1
20 10000 400 20
4 2000 80 4

 

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.