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

Area Method

If you have Cuisenaire rods then you can model multiplication. This type of handson 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
10  4  
10  4  
5  
5 x 10 = 5 x 4 = 
50 20 
70 
10  4  
5  50  20 
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

2 x 35

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.
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 1digit x 2digit 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.
In the examples above, only one factor was decomposed to its base 10 values. When multiplying 2digit by 2digit numbers, both numbers are decomposed and we use four rectangles as shown in the two examples below.
Examples 

18 x 22

25 x 42

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


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

Standard Algorithm

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