7 Tips for Teaching the Partial Quotient Method for Long Division

As a teacher of 4th grade for over 20 years, I can tell you that long division is easily the most challenging 4th grade math calculation your students will learn. It involves a complicated (sometimes confusing) algorithm that requires a strong fluency of basic facts for not just for division, but also multiplication, and subtraction, too. Mastering the steps for student requires a lot of practice, repetition, and perseverance. To teach it takes preparation and a lot of patience.

Here are some tips that will hopefully help your students become long division dynamo’s in to time.

TIP #1 : Use T-charts

In the early going, I would recommend having students complete a t-chart for the facts for the divisor. This can be used to refer to as they search for the best multiples. It is especially helpful for those students who are weak on their multiplication facts.

I have included some free practice pages with problems including t-charts to help get students started using this strategy. You can download the FREE pages here.

https://drive.google.com/open?id=1lULIR6GONvbePUqQFwsAkyHfulOI1_2i

Want more like that? Download this product from my TpT store which uses differentiated worksheets and math notebook pages to introduce this partial quotient long division.

https://www.teacherspayteachers.com/Product/Scaffolded-Partial-Quotient-Long-Division-Practice-Packet-28-Pages-4387919

TIP #2 : Teach area models

To build on a skill learned with multiplication, I always teach my students how to relate area models to long division.

Here’s how the area model would look for a problem solved in this way:

This model can also be used to show problems that were completed using less efficient steps. Here’s the same problem in a different way.

To help students “see” the relationship between the two, I often draw the “division bar” over the area model to show them how everything remains in the same orientation and shows the same values.

TIP #3 – Teach the Flexibility of Partial Quotients

Show students that problems can be solved in multiple ways using this method and still be “right.”

In my opinion, this is really the secret sauce of why this method is so useful. Students who are not great with choosing the best multiples can still get to the correct answer – it will just take them more steps!

TIP #4 – Use Scaffolded Design

Keeping work neat is essential in doing math calculation, right? For this reason, I always use grids to help students both to keep their work neat and to guide the process in the early learning. As students gain confidence, I pull these scaffolds away and let students just work the problem in a blank space. Sometimes I even allow students to choose when they are ready to try the non-scaffold answer document!

By the way, if your principal happens to be evaluating you, you can remind him/her that this is great example of DIFFERENTIATION!

TIP #5 – Prepare for Parent Confusion

Of all of the work I send home for homework, this is the one that will most commonly come back with a parent note/e-mail asking, “What is this?” or saying, “I don’t know how to help my child with this.” I have even spotted Facebook posts from my parents with cynical comments about not understanding this new “common core math” and questioning why we aren’t teaching it the “old-fashioned way”, etc… I’d recommend against sending it as homework, at least until you are confident students can do it totally independently.

One way I try to help students (and parents) with this problem is by sending Learn Zillion assignments home. Learn Zillion is a wonderful series of online videos and lessons (similar to the more well known Khan Academy) that can be used to help teach topics in common core math or ELA. I’m a big fan of many of them.

Check out this link to see an excellent example of a video lesson using this method.

Check out this FREE product I created to go with these Learn Zillion videos.

TIP #6 – Be Patient

This is a tough skill. Go slow. If students are doing it along with you, they will often fool you into thinking, “they’ve got this,” but then when they start working independently, you discover quickly, “they don’t got this.” Do examples with them until you think they have it, and then do a few more. Trust me on this.

This is also a skill that requires lots and lots of review. I usually set aside at least 3-4 weeks to teach both the partial quotient and the standard algorithm. And after that, we still come back and review it a lot. I often tell my students this helpful axiom:

TIP #7 – Make it fun!

Learning (and teaching) long division can get tedious if you don’t break it up, so it is important to find a way to keep it fresh for you and your students. For example, at the start of each Math class I almost always play a Kahoot game to review what we learned the previous day.

It is a great way to engage students right at the start, and it acts as a great assessment tool for me to see who needs extra help. (See my Kahoot game links below.

I have also created many task card setsthat allow students to get up and move as well as to self-check. Students enjoy this, and I appreciate the fact that because they can self-check, I am freed up to help the students who need it.

https://www.teacherspayteachers.com/Product/Long-Division-Task-Card-Bundle-5-sets-w-unique-answer-code-2375147

The kids love solving the problems to reveal the jokes, and you’ll love how easy it is to check for understanding.

In the end, teaching long division can be daunting and even exhausting. If you follow these tips, however, I think you’ll find that your students will really enjoy dividing in this way. As your students gain confidence and competency with the skill, you will feel a tremendous sense of pride from a job well done.

Good luck and   happy teaching!

~Shane

7 Tips for Teaching the Partial Quotient Method for Long Division

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