Teaching Long Division Using the Partial Quotient Method

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 and requires a strong fluency of basic facts for not just for division, but also multiplication, and subtraction, too. To master the steps as a student requires a lot of practice, repetition, and perseverance. To teach it takes preparation and a lot of patience.

I imagine that the way I feel beginning my long division unit must be a lot like our music teacher feels when she is first starting to teach her students to play the recorder. Like listening to 25 squeaky recorders, you know teaching long division going to be little painful for you for a couple of days.

But, after some practice and the students build their confidence, they’ll soon be dividing large numbers with the greatest of ease. But for those first few days, just take a deep breath and try go to your happy place…

About three years ago, I began to teach my students the partial quotient method for long division. I had seen this method before, and I can admit that scoffed at it as being a gimmicky and convoluted way of doing long division. [Insert cranky, old man voice] “This wasn’t how I learned to divide in school.”

I was hesitant to show students a method that I thought was always going to be a slower and less accurate method for calculation. (I was wrong about both). I was also troubled by the fact that did not have one “right” way for solving a division problem, making it a little trickier to explain. Fortunately, I eventually overcame my stubbornness and started teaching this method. As I did, I began to see its merits.

So why teach this method?

As I’ve taught the partial quotient method for a few years now, students have reaped the benefits in several ways. First, it really helps them improve their mental math skills as it gives excellent practice for multiplying times 10’s 100’s and 1000’s. Second, it inherently teaches students how to estimate with division as they become adept at choosing the greatest “friendly multiple” to work toward building up to the dividend. Finally, a big advantage from the standard algorithm is that is is much more forgiving. That is, with the standard method there is just one right way to do a problem. One mistake = WRONG. With the partial quotient method, poor estimation just means that the student will do the steps more times. He should eventually still get to the correct solution.

Fair warning though, 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…

a Facebook post from one of my student’s parents

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 them.

Check out this link to see an excellent example of a video lesson teaching using this method.
https://learnzillion.com/assignments/GX6TR8V

I also like to begin by using this product from my store which uses differentiated worksheets and math notebook pages to introduce this skill.