What are area models?
An area model is a visual strategy to divide using a rectangle picture or model. Larger numbers are broken down by place value to make it easier to divide, and then the quotients are added back together to get the final product. Check out this video here:
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 divide. 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 division, but before you move on to standard algorithms or long division. It shows students the relationship between place value and the division of large numbers. I suggest teaching students how to multiply large numbers in this order:
Basic division concepts and facts
Dividing using an area model
Partial Quotients with or without the help of an area model
Standard Long Division
What are some common misconceptions or mistakes students make with area models?
Problems with Place Value- The first common mistake is students not breaking down numbers properly by place value. For example, if they were dividing 245 by 5, 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!
Not Properly Lining Up Partial Quotients- Students sometimes struggle to line up their partial quotients 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.
Losing their place- Students sometimes forget what numbers they have already divided. 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.
Partial quotients and area models support which math standards?
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Where can I find additional resources on area models?
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.
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