** “Please Mrs. Reed, can we do just one more division problem?”**

**Pre common core**

The first time I heard one of my students ask this question I was stunned. I thought that maybe I misunderstood what he asked. In fact 10 years ago I would usually hear groans, and painful cries of despair, not joyful cries of excitement with please for just one more problem. In the past it was painful to teach my 5th grade students the long division algorithm. It brought my students frustration, anxiety and a dislike (to put it lightly) of mathematics.

What changed all that? Several years before Common Core was unveiled, I was desperately looking for resources in my division teaching, I came across division strategies illustrated that I had never thought of nor knew existed. Partial quotients became my “go to strategy”. I found that my students grasped it quickly. Students differentiated this strategy on their own. Some students would have 12 steps to finding their quotient, others three. Every student in my class (yes everyone and I have had many categories of students) could feel success with this strategy. This has brought me to a happy place in my division-teaching career, with students enjoying mathematics again.

**Common Core strategies**

Next came the long division strategies that are incorporated into common core mathematics. The Progressions list the strategies that our 4th and 5th graders need to know, but I didn’t actually know how to teach them. I have come across a few lessons that I have found to be priceless for my students’ understanding and knowledge of the strategies needed for Common Core Mathematics.

**Partial Quotient**

- To introduce the partial quotient strategy my first go to lesson is from Placa-Schwartz Mash Up. https://gfletchy.files.wordpress.com/2014/09/scaffolding-division-through-strip-model-diagramming.pdf. This is a terrific scaffolding lesson. It starts with a tape model, fair sharing out the dividend. The students “fair share” their dividend using friendly numbers and they “discover” the partial quotient strategy. Students are engaged and they understand the math using conceptual understanding. What more could a teacher want?

**Distributive property**

**2**.I incorporate the distributive property strategy in my classroom through *Number Talks*. Because the distributive property strategy was used practically daily in our discussions on multiplication it was a natural step to use it with division problems. This has not been an easy strategy for my students to “own”, but though our number talks using easy division problems and the area model they are catching on.

**Area Model Division**

So there you have it- three division strategies that 4th and 5th graders need to know. Once taught I incorporate the attached game in my center rotation. I have my students “play” this game about once a week to keep up their strategies throughout the year.

This is what I love-teaching, engaging, and enlightening my students’ lives. And when they ask me for just one more division problem, I relent, with a sigh and great joy in my heart.

### Patty Reed

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Justin Julian says

My problem with using area model and distributive property is trying to figure out how to deal with remainders. Anyone have any models/examples/steps on this?

Alecia McAdams-Sing says

One of the toughest hurdles for teachers experiencing “new math” success (as several comments reveal), is winning over confused or skeptical or angry parents, colleagues, or community members. There is certainly a place for critique and ongoing evaluation of methodology, so I’d don’t mean to say all pushback is unnecessary or fruitless. I wondered if you had seen https://www.facebook.com/kristinacain.johnson/posts/1013210272035839? When I hear articulate elementary specialists like you reveal the thinking behind the brain work “new math” clarifies for kids, I am more and more impressed. I am always impressed with my ES colleagues’ deep understanding of how to grow kids’ brain power!

Patty Reed says

Thanks for the facebook reference. She is helping a lot of people with her post. We did a parent night at our school for math last year, it went well, but I would have liked more in attendance.

Anonymous says

I get to transition to teaching high school math next year and was struck by your description of using the distributive property to divide. As Aaron mentioned above, this method lends itself well to teaching factoring in algebra. Common Core and NGSS are powerful tools that give us a common language about teaching and learning.

Thank you for inspiring young people to ask for more. https://youtu.be/sZrgxHvNNUc

Patty Reed says

Love it! Thanks for posting.

Anonymous says

where did you get the top numbers from in area model

alisallouie says

Thank you for sharing! These great strategies lead to much greater understanding instead of just process memorization!

Next steps probably include family outreach to help families understand the differences in strategies and WHY we teach so differently than they might remember learning the same content.

Carina Stillman says

I am so excited to see (and understand) your explanation of these three strategies! My sons are in 2nd and 3rd grade and already come home with math homework that looks but yet doesn’t look like the homework I had at that age. When they struggle, my first inclination is to show them how to do it “my way” as opposed to the “weird way” they are being asked to do it. After asking some questions of their teachers and watching a few videos on my own as well as these here, I am sold! Algebra and beyond is going to be so much easier with these foundational understandings being built in the early grades. Keep spreading the information and examples, please!

cgustafson1950Chris says

While reading your post I had a flashback to fifth grade me sitting on the back porch at my house, working through what seemed to me to be an endless page of long division problems and crying. Your post made me feel so hopeful for my grandkids and their math education. Thank you!

Jill Escalera says

I had to teach two of these strategies when I did my student teaching and WOW did it blow my mind! I wish CCSS had been around when I was learning basic math because maybe it would have made a lot more sense. These strategies are awesome and I’m glad you posted a new one I can share with our 5th grade team. The best part is, YOU, the teacher, are excited about it, and that will always come across in teaching!

Aaron Brecek says

So true… Teacher excitement often breeds student engagement. Great point and something for all teachers to remember.

Francis Jequinto says

What a hook – “Can we do just one more division problem?”

As someone who has taught math, even imagining someone has heard that sentence, out loud, from a real life student, hooked me instantly. I was like “What’s your magical secret sauce?”

And then to find out that it’s all Common Core? This “evil” thing that parents and Facebook tell me I’m supposed to despise? And then to see that the steps make complete sense, and that it’s a more logical and visual form of the “mental math” I was taught as a kid? That made me truly happy.

I’m glad to see this post. I’m glad to see actual examples of what Common Core can do to give kids an base to truly build new understanding from.

kelseykorinsovikmth488 says

I really enjoyed reading this. It is not everyday you hear a student wanting to do more math problems. The use of algebra in division is a great idea so that there are multiple ways to show how you can divide and students can choose which strategy works for them.

Aaron Brecek says

As an Algebra teacher, I love how you incorporate many algebraic properties into your division section. This will really benefit the students down the road as the get into factoring.