In 5th grade Common Core, students are expected to be able to divide using a variety of strategies. One of those strategies is using division area models. I remember the first time I tried to figure this out…it was a disaster. But now, after many years of teaching this division strategy, I feel like I really “get it.”
I love using both anchor charts and interactive notebooks when I teach math. The notebooks act as a personal reference for my students (since our textbook is a joke when it comes to Common Core), and the anchor charts are up in the room as a visual reference for all students to refer to.
Division Area Models Steps
Step 1: Draw a rectangle.
Step 2: Write the divisor on the left side (or top) of the rectangle.
Step 3: Find an “easy multiple” of the divisor; write it in the rectangle and the number you multiplied by on top. *I explain that an “easy multiple” is one that is easy for the students to find using mental math. Such as the divisor times 2, 5, 10 or 100.
Step 4: Keep track of the remaining area by subtracting the multiple from the dividend off to the side.
Step 5: Repeat steps 3&4 until all the multiples together equal the dividend.
Step 6: To find the quotient, add the numbers on top of the rectangle.
Math Notebook Guide
Division Area Models Anchor Charts
Common Student Errors
As with all math topics, there are some errors that are commonly made by students.
Subtraction
By 5th grade, we expect our students to be able to fluently subtract with regrouping, but they often struggle with this. If students are having difficulty with subtraction, consider pulling a small group to work on just their subtraction, allowing those students to use a calculator for just the subtraction portion of the problem, or giving extra subtraction homework before or during division work.
Not Following the Step Order
I frequently have students who will get carried away with the subtracting, and forget to keep track of the portions of the rectangle. Encourage students to slow down and add to their rectangle every time they subtract out a multiple of the divisor so they don’t skip any portions.
Multiplying Endlessly to Find the Exact Answer
This problem can be an exasperating one. Occasionally we have those students who just insist on finding only the exact, precise answer on the first try. So far, my best solution for this is to time the student to show them just how long this is taking and then time myself or another student using the strategy correctly to show that the student would finish more quickly by just getting started with the “easy multiples.”
Resources
In my Teachers Pay Teachers store, I have a bundle that helps address all of the components of performing the operations with whole numbers and decimals, (division with area models included). Check it out here.
2 thoughts on “Steps for Teaching Division with Area Models”
From what I see this works with numbers that do not have decimal answers. Can it be used with decimal answers?
Yes, it can. It does require a bit of decimal place value background knowledge by the student, however. Here is a very simple example, just for illustration. Say you are dividing 5 by 2. In the first box, you would put 4, and put a 2 on the quotient part. Then, you have 1 left which needs to be divided into 2 equal parts. You would put the .5 on the quotient part because 2 groups of .5 equals 1. You have a total of 5 for the dividend inside the area model, and 2.5 for the total quotient. Obviously this becomes more complicated as you work into the hundredths, but for the basic concept, the area model can still work. As the numbers become smaller, using base ten blocks or hundredths squares can help support the students as they work out the quotients. I really hope this explanation helps make it more clear. Please let me know if I can be of further assistance!
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