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! 😄

Getting Ready for Middle School

A few weeks ago, our fourth grade team had the opportunity to visit our local feeder middle school. Even though our elementary school goes to fifth grade, we often have families who start looking at private and charter middle schools beginning in fourth grade, so this trip served to raise interest among the kiddos in attending the public middle school. (As part of an urban district, increased enrollment in the school feeder path benefits both the elementary and middle schools.)

The school did a wonderful job welcoming us!  The principal had a powerpoint with information about the school's academic and extracurricular offerings, achievement and behavior expectations, and tips for the kiddos about preparing for middle school. The fourth graders were all ears! They sat up straight, raised their hands, and took careful notes. It was so cute to watch them snap to attention when the middle school principal taught them his call and response.

After a brief introduction, we got to go on tours led by "Middle School Ambassadors" -- including a few former students of mine!  The kiddos had to tuck in their shirts and bring clipboards along to take notes. We got to stand in the back of classrooms and observe some 7th and 8th grade classes.  The kiddos had to record the name of the teacher and class and note the objective for each lesson in their notes packet. They did such a great job -- walking proudly and quietly in the hallways, listening to all of the teachers, even trying to participate in some of the classes!

Obviously a trip like this isn't going to make our fourth graders suddenly turn in their homework on time, stay on task without reminders, or keep their binders organized... but it's great to be able to remind them of what they are working toward! This trip was also a great reminder for me that even though we are departmentalized and expect a lot of our kiddos, they are still just 9- and 10-year-olds. Especially compared to the 8th graders, our kiddos are still little guys who need lots of handholding, hugs, and encouragement.  While we work to prepare them for what's next, we have to keep in mind what they need right now.

At the end of our trip, all of the kiddos got some "middle school swag" on their way out the door. They could not have been more excited! 💙

Essay Publishing Party

Apparently I didn't manage to write a single blog post since the school year started! Whoops!  I guess that says something about how this fall went... new principal, new schedule, new teaching team, new behavior plans, new student teacher... It's been a whirlwind.  Now that it's Winter Break, I'm going to try to work my way backwards through the year -- sharing some of the highlights, and maybe a few low points, from this crazy fall.

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Just a few days ago, as we wrapped everything up before the break, we had our second official Publishing Party, for our "Boxes and Bullets: Personal and Persuasive Essays" Unit. During this unit, the kiddos learned to craft personal thesis statements such as "My sister and I have a very strong relationship," and then related persuasive theses, such as "Having a little sister is the best thing that can happen to you."  I have an amazing student teacher this year (we call her a Teaching Fellow) who took over some of the teaching during the second half of the unit and really pushed the kiddos to create some awesome pieces.

The unit did end up being a few weeks longer than I'd intended, in part because our schedule during the first part of the year didn't allow for Writing Workshop every day of the week. I know this is a challenge for many schools that have to prioritize certain subject areas over others. For us, this was due to trying to fit in specific typing practice one day of the week and also "Science Lab Writing" on another day.  Of course, both of these other activities are important, but I really felt the affect of not having our true Writing Workshop every day. (I'm working on changing the schedule for when we get back after break).  In addition to the scheduling challenges, in early October one of the other fourth grade teachers quit. While this ended up being for the best, it meant that I had to begin planning writing for a long-term substitute in the other class, in addition to planning for my own class. This required creating some more specific teaching points and moving at a slightly slower place than we would have otherwise.

At long last, we reached the end of the unit.  The kiddos all had a typed essay (we let them choose if they wanted to type their first or second essay).  For the Publishing Party, we had the kiddos do a quiet gallery walk of each other's writing. They stopped at each desk, read each classmate's essay, and then left a short note. Miraculously, it was incredibly peaceful!  The kiddos took it all very seriously and wrote really thoughtful comments to each other!  

Afterward, everyone returned to his or her own essay, read the comments that had been left, and set some goals based on the feedback. I think goal setting is an essential part of publishing in a Writing Workshop! We always talk about the importance of reflection and revision in the writing process, and that doesn't end with publishing. I think goal setting at the end of a unit helps kiddos make connections between units and transfer skills between genres. We are starting our Journalism unit after the break and I can't wait to see the kiddos bring their essay writing skills into this work!

What a great way to close out 2017!