The Area Model for Multiplication

The algorithm for multiplication, I'm sure most adults today can remember learning. And I'm sure a few even understand and appreciate why it works. I personally like it and find it kind of cool. However, there are other methods that are more intuitive and explain how multi-digit multiplication works.

The Traditional Method
It begins with you stacking your two numbers on top of each other. You then proceed to multiple the first number on the bottom to each of the numbers on the top. You then put down a zero and proceeded to the second digit putting that product below the first one. Once you did this to each number you then found the sums of each of those products.


Common misunderstandings/confusions with the traditional method:

• Why do you "carry" when the product is more than 9?
• Why do you add what you "carry"
• Why do you add the products at the end
• Why do you add a zero each time you move onto the next number?

The Area Model 
With this method you begin by breaking the numbers into their hundreds, tens and units parts. You then label each side of a rectangle with those parts, creating smaller rectangles. You then find the product for each smaller rectangle and add them together. Below is an example of 286*43.


Benefits of this Model:

• Relates to the study of Area and Perimeter
• Reinforces the base-ten system
• Easily extended to Algebra concepts like Distribution and Factoring
• Students understand why they are adding each of the products together