What are area models?
An area model is a visual strategy to multiply using a rectangle picture or model. Larger numbers are broken down by place value to make it easier to multiply, and then the products are added back together to get the final product.
Why are area models useful?
Area models are useful because good mathematicians have multiple tools to solve different math problems. Area models can be used as a tool to solve multiplication and division problems. It allows you to break down larger numbers into smaller equations to make them easier to multiply. It also gives you a great visual representation to show your thinking to others and check your work.
When should I teach area models?
Area models are a great strategy to teach after students have grasped the basic concept of multiplication, but before you move on to standard algorithms. It shows students the relationship between place value and multiplication of large numbers. I suggest teaching students how to multiply large numbers in this order:
Basic multiplication concepts and facts
Multiplying using an area model
Partial products with or without the help of an area model
Standard multiplication algorithm
What are some common misconceptions or mistakes students make with area models?
1. Problems with place value - The first common mistake is students not breaking down numbers properly by place value. For example, if they were multiplying 243 x 6, they might just put 2 down instead of 200. Making sure students fully understand place value and the importance of zero as a placeholder will help!
2. Not properly lining up the partial products to add - Students sometimes struggle to line up their partial products properly to add in order to find their final product. Have students check that they are using the proper standard addition algorithm and that they are adding correctly.
3. Losing their place when multiplying - Students sometimes forget what numbers they have already multiplied. It helps if students write the partial products inside the area model so that they can see which portions they have completed, and which numbers they still need to multiply.
Where can I find additional resources on area models?
Check out this multiplying using an area model video.
Here is my area model clipart set to add to teaching resources and to print out so that students can use it as a template.
Want more information on teaching upper elementary math? Sign up for our email list and get access to our free resource library!
