Math: Long Division

Updated: Nov 29, 2019

Long division. We all remember the steps (or maybe we have forgotten), but we know it's something important fourth graders begin doing as they learn about division. In fact Common Core standards requires 4th graders to divide 4-digit dividends by 1-digit divisors using strategies based on place value including arrays, equations and area models (4.OA.6) and 5th graders divide 4-digit dividends by 2-digit divisors using strategies based on place value (5.NBT.6).

However, the go-to in teaching long division is to teach it as a series of steps: Divide, Multiply, Subtract and Bring Down. We teach students to follow these steps using silly stories and check lists.

Does McDonalds Sell Cheeseburgers?

I know all of this, because I've done it! I have taught it this way and found the kids who could follow the steps were able to do it short term, but soon forgot the steps the moment I quit drilling them into the students! While those friends who struggled with working memory were unable to memorize all the steps and got lost easily ending only in frustration.

Dr. Ban Har once said that long division was super confusing for students, because we are telling them to divide, but then ask them to also multiply and subtract. No wonder they are confused! They just learned the meaning of division, and now we are asking them to combine operations in a series of steps!

When studying the standards, we see that we are REQUIRED to emphasize place value meaning and use area models. Where do we start? I like the following progression:

Expanded Form

Area Models

Partial Quotients

Long Division Algorithm

In using expanded form, we force students to reason through the process of division. This particular problem requires regrouping, which further challenges students to understand what division means by asking about the greatest factor that can be used. This also helps relate division as an unknown factor problem. So much meaning from one tedious step!

While we don't want students to sit with this method for long due to its inefficiency, we can further encourage students to try out area models and partial quotients. Many students love the area model with multiplication and showing them the relationship to division solidifies the inverse operation.

The goal in doing these methods is to consistently ask students how they are similar and encourage them to push past their comfort zone. I often ask students to solve in the way they feel most comfortable and then try another method. Eventually, we want students to get to the most efficient method-long division- but this is not until 5th grade. That gives students an entire year to practice using the place value meaning! Some possible questions we can ask to get them going:

- How is this method similar to this other method?

- Where do you see this number in this method?

- Which method is the most efficient? Why?

- How is this method different from the other?

As you have heard me say before, fact fluency will be vital during this unit to help students focus on the standard. Provide students with multiplication charts while working in long division, but set aside time for students to work on fact fluency of their multiplication and division facts. If looking for more resources on implementing games into your fluency teaching, check out my free webinar here! You can also access over 80 pages of differentiated games and assessment in my shop!

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