Area models come from the basic idea of solving for area. They are a wonderful tool for younger students to do multi-digit multiplication problems (for example 14 x 17). They develop student understanding of multiplication, place value, and the distributive property that is later used in Algebra.
I did not learn area models in school but I swear by them with my students and can’t wait for my children to do them!
Let’s review the basic idea of area. If I want to put tile down in my bathroom and it measures 5ft by 6ft. We multiply 5 x 6 and 30 total square feet.
Here is the model of this situation. It shows 6 feet extended across and 5 feet extended down. When they overlap they create 30 squares that are a foot by a foot. This example is an area model.
Here is an examples of a double-digit multiplication problem solved with an area model. This example can be done by students starting in 3rd grade. I know it is not the fastest way but it teaches students understanding and skills they can use when problems get more difficult. By 6th grade they will learn to do it the traditional method, which yes, is more efficient.
Let’s solve 14 x 17.
First, setup a square just like real life area problems.
Take each number, 14 and 17, and break them down by place value. 14 becomes 10 and 4 and 17 becomes 10 and 7.
Just like with the bathroom floor problem, we are going to extend each number and draw 4 boxes. Inside each box will be the answer of the over lapping multiplication problem.
We first solve 10 x 7 and write 70. Then multiply 10 by 10 to get 100. (This idea represents an Algebra concept called distribution. We have distributed the 10 to 7 and 10.)
Next we are going to multiply 4 by 7 to get 28 and 4 by 10 to get 40. Answers go in each box.
Lastly! We add up all the answers we got from multiplying. These answers are called products.
238 is the same answer we would get if we did it the traditional way.