Learning Long Division

Math was definitely not my favorite subject growing up... I had trouble remembering multiple steps to solve problems and never had a good idea if an answer was "reasonable." Nevertheless, one of my favorite memories of doing math in elementary school was creating and solving extended long division problems during indoor recess in 5th grade.  We would write up 25 or more random digits and then try to divide by 2 or 3 or 5, working our way across the entire chalkboard! It was so satisfying to simply "divide, multiply, subtract, drop down" and get a huge answer that I could feel confident was correct! I now realize that I had no understanding of why those steps worked or what that answer meant, but it felt "smart."

Now as a math teacher, I don't want my students to

blindly accept that a set of steps "just works" -- I want them to be able to explain how, why, and when any algorithm is useful and efficient. Last year our math curriculum intentionally avoided teaching long division in 4th grade to encourage students to use place value understanding and other strategies to divide.  I enjoyed teaching this way... I could explain why each method worked and observed students making logical connections between multiplication and division to solve complex problems.

This year, however, we are using Eureka math which does teach the long division algorithm (alongside other place value strategies) in fourth grade. As much as I loved using this method myself, I was anxious to make it meaningful for my kiddos. We began with mental math division (25 ÷ 5 or 18 ÷ 3), which required students to use multiplication facts to solve quickly.  I wrote the equations out using the long division symbol, but resisted reciting the "divide, multiply, subtract, drop down" mantra. Instead I asked the kiddos questions like "why do I write this here?" and "what should I do next?" and "what does this number represent?"

Then we added in using "place value disks" to represent the division (see above).  I demonstrated using the long division algorithm alongside the place value disks to help students see the connection. The kiddos totally got it!  My Teaching Fellow even commented how clearly she could recognize the steps of the algorithm within the place value model when it was taught this way!  

After two days of using the place value disks and word problems to provide context, it was time to go all in on using the long division algorithm!  Rather than keep everyone on the carpet for a traditional lesson, I allowed the kiddos to decide when they had mastered this new skill. When they felt confident with the algorithm (without drawing out the place value disks),  they could leave the carpet to start the Problem Set. Those who still felt stuck or unsure, stayed with me to keep practicing. I could practically see the gears turning in their heads and they pictured each step. When the lightbulb finally went off, they were so proud of themselves! 

Naturally, there were a few kiddos who were still struggling at the end of class. Rather than move on or wait another day to review, I offered to host a "Long Division Lunch Bunch." I ended up with 24 fourth graders eating lunch and doing long division in my room that day (I teach three classes so I offered the Lunch Bunch to all of them.) As the kiddos ate and worked together, I could see them gaining confidence!  By the end of lunch, most of them had the same satisfied, smart feeling I remembered from 5th grade. But this time, as they followed a set of steps to solve multi-digit long division problems, I knew they really understood what it means to divide one number into another and how those set of steps make their problem solving more efficient! 😄