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Recently, I've heard from several parents who are curious about why we teach multiplication using different methods than they remember.  I want to talk a bit about the area model for multiplication, and its benefits for the math education of students throughout their math education.

The area model for multiplication is a different algorithm that students can use to multiply large numbers.  Here is an example of multiplying 5 x 18:

Let me explain what's going on in this problem:

• I drew a rectangle, and divided it into two parts.  
  • Since 18 consists of a digit in the 10's place and a digit in the 1's place, the rectangle is split vertically into two pieces. 
  • Since 5 is a single digit, we only need 1 row horizontally.
• The 18 is split into 10 + 8. These are written on the top of the area model, and the 5 is written along the left side.
• Each of the two parts of 18, the 10 and the 8, are multiplied by 5. These are partial products, and each is represented by a section of the rectangular model created. I have written the factors and partial products into each of the two parts of the rectangle, showing the multiplication that students will do in their heads.
• The partial products, 50 and 40, are then added together to create the final product.  I have written this operation to the right of the area model.  
• Here are the pieces demonstrated in this diagram: 5 x 18 = 5 x (10 + 8) = (5 x 10) + (5 x 8) = 50 + 40 = 90.

This is definitely a greater number of steps than the standard algorithm, shown here: 

Most of you are familiar with some form of this algorithm.  The 5 is multiplied by the 8 to get 40, and the 4 is written above the 1 in the 18.  Then the 5 is multiplied by the 1 to get 5, and then add the 4 to get 9.  We write the 9 next to the 0, and get 90 for our final product.  

The standard algorithm is quicker and easier to use to calculate a product.  However, this algorithm doesn't tell us anything about the nature of multiplying numbers.  Here are a list of math concepts that are embedded in each of the two methods:

When I was in high school, my algebra teacher told us that we needed to learn to calculate by hand because we weren't going to be carrying a calculator around in our pockets everywhere we went.  Well, guess what?!  We do!  So the reason for learning to multiply has changed.  Calculating quickly and efficiently isn't as important as understanding the nature of mathematics, which allows students to have flexibility with numbers, and think about their properties in different ways.  It makes sense that since our purpose for teaching mathematics has changed, that our methods have changed as well.