Teaching Division with Area Models

In 5th grade Common Core, students are expected to be able to divide using a variety of strategies.  One of those strategies is using 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.

The steps I teach my students to follow are:

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.

Here are some pictures of my math notebook from this topic:

   
   
Here are the anchor charts I have posted in my room for Division Using Area Models:

  
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.

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