Why I love the Division Area Model (and you should, too)! - Ideas By Jivey: For the Classroom

Why I love the Division Area Model (and you should, too)!

I know there is a lot of controversy about the Common Core, and that is not what I'm here to discuss. If you are a teacher, whether you are for or against CCSS, you have to teach the standards! So I am here to (hopefully) make your life a little easier. :)


The division area model can seem difficult to teach because it's NEW to so many, but actually, I found my students to be MUCH more successful with it than the traditional long division algorithm.

>>>Why?<<<

Well, first of all, students have been working on multiplication facts for about a year by the time you get to division in 4th grade (counting third grade practice, and constant practice the first part of fourth grade). This method makes them think in a "multiplication problem with a missing product" kind of way.

Second, the area model breaks down a "hard" division problem into a few easier ones. 

Third, it helps them SEE what they are actually dividing (hundreds, tens, and ones), unlike the traditional algorithm. 

And fourth, it allows them to "check" themselves much easier.

>>>How do I do it?<<<

The size of your model, or number of "boxes" will be determined by your dividend- I will be demonstrating with a 3-digit dividend, but you can absolutely use this (and should!) with 2-digit, 4-digit, and so on. 
Area Models With Ideas by Jivey
First, let's look at what the students will be doing with manipulatives. It's important to start with concrete models first before moving to the more abstract. We are going to divide 834 by 3. We start in the hundreds. We can only put two hundreds into three groups to divide evenly.
Area Models With Ideas by Jivey
That means we need to slide the "remainders" over to the tens place, but we also need to trade those two hundreds for twenty tens to be able to make groups.
Area Models With Ideas by Jivey
Now, we can put seven tens into three groups to divide evenly.
Area Models With Ideas by Jivey
So again, we slide those remainders over, this time to the ones... so those two extra tens should now be traded for twenty ones.
Area Models With Ideas by Jivey
And of course, we can divide 24 into three equal groups by putting eight in each group!
Area Models With Ideas by Jivey
By adding up the numbers across the top, you get your quotient!
278!

Now for the more abstract model... using numbers. Same idea as with manipulatives! You are only dividing the hundreds first, so 3 x ___ = a number close to 8?
Area Models With Ideas by Jivey
Just to show you what might happen (and probably will), here is a student who doesn't start off grouping correctly:
Area Models With Ideas by Jivey
The same could go if they said 300 could be in each group... when they go to subtract 900, they are going to see that 300 can't be correct! But luckily, this student figured out it was 200. :)
Area Models With Ideas by Jivey
Moving to the tens, same idea- I like to have the students "box" what they are going to be dividing. This way, they remember it is 23 tens, not just 3 tens.
Area Models With Ideas by Jivey
They will have that remainder of 24 to move over to the ones, which hopefully they can very easily answer 8x3=24! :)
Area Models With Ideas by Jivey
Finally, just like before, add up all those numbers across the top of the model to get your quotient!
Area Models With Ideas by Jivey

I like to give students this larger workmat (laminated) with a dry erase marker to help them do their work. Not only is it more fun, but of course, it is also easier to erase, and erase, and erase... :)
Area Models With Ideas by Jivey
You can find this activity (and many other division stations) in my Differentiated Division Stations for Math Workshop pack! I also have other math station sets in my store.

Check out these blog posts, too, on why to use Math Workshop and how to Manage Stations!

Follow my Math Workshop Pinterest Board for even more great ideas!

9 comments

  1. I really enjoy teaching with the partial quotient method (and our school taught division that way even before common core!). I think it helps the kids to really *see* the parts that they are working with. It also is a more direct connection to when they will use the standard algorithm.

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    1. That is a good one too! Area models are specifically listed in the 4th grade CCSS so that is what prompted this post. I also like that it allows students to move from concrete to abstract easily. :)

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  2. Wow! thank you for taking the time to share this!!! Great information.

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  3. Perfect timing! I will use this tomorrow in my lesson. Thanks for posting it. I've never seen the area model for division.

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    1. WOW! I just taught the first part of this lesson today. I can't believe how enlightening it was for my students. They caught on quickly. I was able to easily teach into their mistakes, and some of the more advanced students are already starting to connect it to the algorithm while my less advanced students are feeling successful and solving problems accurately. We used the free Number Pieces iPad app for modeling and it was just right. None seemed to need physical blocks. Thanks again. It is great to have children excited about division.

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    2. That makes me so happy! Thank you for sharing!!!

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  4. I love using the area model (or rectangle model as i often call it) for division! I enjoyed seeing your take on the method and following the steps to go through with kiddos. I especially liked the use of base-10 blocks to model the method and build understanding before teaching the steps. I will definitely be using this post as a guide in the next week as I teach division! Thanks!

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  5. I've seen your video for teaching mentor sentences, by any chance do you have one that teaches this method of division?

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    1. I don't- but I bet there is one on LearnZillion! :)

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