Are you unsure of how to teach division using the area or box method using partial quotients? Are you looking for a better way to teach the area method dor division but you aren’t sure how?
Teaching Division for Conceptual Understanding
If you are like me, you grew up learning how to do long division with the standard step-by-step method or algorithm. I remember being clueless about what I was doing and I had no number sense at all because math was taught so differently back then.
Now that we have Common Core standards (thank goodness) students are expected to have a conceptual understanding of math before they develop procedural fluency. Plus, they are taught in a way that fosters number sense.
Math Trainings Don’t Always Teach the New Math Methods
As a teacher, I went to math training to learn this new “Common Core” way of math. I was presented with the box or area method in a few minutes and I was expected to just get it and teach it.
I left that training thinking, “I’m just going to do it the old way. How can I teach something that I don’t really get myself!”
I taught division like this for a few years and I wasn’t methodical about how I taught the area division method. Teaching is an art and it’s critical to scaffold lessons so that you see the aha moments on your students’ faces.
After doing some reading on how to teach long division with the area model method, I finally decided to give it a go. I will say that when you teach the problems, you yourself, will have the method more ingrained in you and will get it!
What Are the Steps to Teach Long Division with Partial Quotients Using the Area/Box Method
Start with Manipulatives
Start out with a simple 3-digit division with a 1-digit divisor and use base tens blocks to demonstrate what division truly is. Show your students a few examples, and then have them do problems on their own while guiding them.
Making sure they are exchanging and dividing their blocks correctly.
I recommend that students sit on the floor so they can easily spread out their blocks and have space.
Manipulatives are so important because students touch and feel them while they are physically dividing them into equal groups.
Even your most struggling students will understand the meaning behind exchanging blocks. If you aren’t sure how to use base tens blocks to show how long division works, I got you! I demonstrate how to divide with tens blocks in the video below.
Demonstrate the Box/Area Method Using Moveable Base Tens Blocks Online
The next day, your students are ready to see the box method. I use a resource I created on Easel, which is a free interactive computer program on Teachers Pay Teachers. It allows students to move base tens blocks around on a PDF that I created.
I demonstrated how the blocks were divided in equal groups by clicking and dragging them on my large View Board. Then I recorded how many blocks were in each group and how many we were subtracting or taking away. If you are unsure how to do this, check out this video where I explain the steps.
Next Step: Guided Practice
After demonstrating a few examples, my students practiced on their own. What I love about using digital manipulatives is that each block has a different color.
This is especially important for your kiddos who need that color coding to assist them in their mathematical thinking. Plus, doing any math activity on the computer is fun for kids.
You can find this resource by clicking HERE.
Practice Drawing Pictures of the Number Being Divided
The next day, I taught my students how to divide base tens blocks through drawings while at the same time recording the numbers in the box. After I demonstrated a few examples, which I call “watch and learn time”, we did 2-3 together using the worksheet below.
While I was drawing and recording on the board, the students were doing the same thing on their paper. We did this for about two days, until they were able to do it independently. I explain step-by-step how I did this in the video below.
Use Simple Numbers
I believe that when you are first teaching a new method in math, you should always use simple numbers so that students aren’t struggling to remember their division facts.
The reality is that many students will still not know their multiplication and division facts when you start teaching long division, so why present division problems with divisors of 9 or 8? Start with simple divisors like 3, 4, or 5, which can be easily drawn on paper.
Should You Teach the Standard Algorithm?
Yes, but only to your students who are on or above grade level. For your struggling students, the box/area method is the way to go!
The problem below shows how the box method can be flexible to demonstrate student thinking. Some of my students who struggle in math, may write the partial quotients as 100 + 100 + 40 + 1, but they will still get the same answer as a student who writes their partial quotients as 200 + 40 + 1.
Another reason is that using the box method prepares students for more difficult 2 digit divisor problems. In the problem below, students can easily multiply the divisor by 1,000 or 100 to get the first number to subtract, which will make the problem easier to solve.
My last reason for not teaching the algorithm is that my instructional time is better spent teaching problem-solving skills with real-world problems.
As adults we problem solve mathematically all the time, but do we ever do long division? Nope, we whip out our cell phone and use our calculator.
Knowing how to solve calculations is definitely critical but practicing and teaching higher-level critical thinking skills to solve problems takes time and practice. You can get my division box/area method resource by clicking HERE.
So I want to know– do you think that the long division algorithm is obsolete? Find me on Instagram (@schoolhouseengage) and let me know your thoughts and/or questions!
You got this!
Giselle