Teaching Workshop #3
On Friday, April 28, 2023, I went to guest teach my third and final workshop, which was on Equivalent Fractions, to 4th graders in Miss Formaggioni’s class at Expeditionary Learning Academy at Moylan School (ELAMS). After my second workshop, I asked Miss Formaggioni what her students were struggling with or what was something she wanted me to teach her students for my last workshop. She said that she and her class were working on Long Division and that her students were struggling with it so a workshop on Long Division would be helpful.
The learning objective of my lesson was:
- Students will be able to solve problems in which they divide three-digit numbers by a single-digit divisor using DMSBR 4.NBT
This learning objective was made with the Common Core State Standards for Mathematics in mind.
The Guiding Question for my lesson was as follows:
- How and why does the DMSBR method help us do long division?
My lesson plan which I carried out was the following:
Launch
Students received an Opening Activity slip with two division problems. For the first question, they solved a question in which they had to divide a 2-digit number by a single digit. For the second question, they solved a question in which they had to divide a 3-digit number by a single digit. After they completed the slip, I collected them. I used the Opening Activity to determine if any learning happened throughout the workshop. As I was collecting them, students received a Long Division – DMSBR guide. Once I finished collecting the slips, we solved the questions that we did in the Do Now as a class. When solving the second question of the Opening Guide with the class, I used a method by math educator Howie Hua to explain to students that long division can be seen as sharing! Showing students to see long division as simply “equally sharing” money with friends and also using the DMSBR guide really helped them understand how and why long division works.
Activity
After that, students went around the room to solve 4 division problems. They were split up into groups which were based on the rows they sat in. Their mission as a group was to solve 4 division problems that were posted around the room. Students were able to choose which question they did first. Questions varied in difficulty with 1 having a two-digit number to divide, 2 having a three-digit number, and the challenging one having 4 digits. Students received the Activity Packet which had a page for each problem.
Students went around the room to solve questions. They for the first half of the page, students solved Long Division problems using their DMSBR guide! For the second half, students showed how long division worked by using the Howie Hua method. Students filled in the blanks with the numbers that corresponded to the spaces and drew pictures. Students reported to me once they completed the questions.
Challenge Inequity
This lesson challenged inequity because I provided students with a long division guide (DMSBR) which helped them with solving these kinds of problems. DMSBR can be applied to not only three-digit numbers but 2, 4, and more! Miss Formaggioni expressed that her students were having difficulty with long division. Long division can be difficult to learn because it can be a difficult concept to grasp. This guide will hopefully help students in the future! I also gave students a new way to think about Long Division by using Howie Hua’s sharing method!
Assessment
I assessed students by seeing their progress across the Opening Activity and the Main Activity. I was not only looking for students who successfully solved the Long Division problems using the DMSBR guide but was also looking to see if students could show me how and why it worked by drawing me an image which was the purpose of the left side of the Activity sheet. This will show if students understand how to divide three-digit numbers into a single digit and will help me determine if they understand how Long Division works.
The students above understood how to do Long Division using DMSBR and also showed me how and why it works.
The students above successfully answered the equation using the DMSBR guide but from their responses on the left, it seems like they do not fully understand how or why Long Division works.
Reflection
This lesson went pretty well overall. There were definitely some challenging aspects that came up throughout the lesson but despite all of that, I think the students had a lot of fun and most importantly, I believe that learning happened throughout the lesson!
Again, with help from Professor Jack Dougherty, I came up with an effective way to see if students know how Long Division/DMSBR works. Professor Dougherty gave me the idea to have students draw their understanding of Long Division which definitely helped me with assessing students and showed me that they understood. Howie Hua’s method of showing how Long Division works also definitely helped students understand how it works! I believe that the launch of my activity where students and I solved a question from the Opening Activity was successful because the students were very engaging and while a few students still struggled to show me how Long Division works, some students were able to clearly show me their thinking by using images and others were at least able to attempt showing me.
Some of the challenges that came up in my lesson were that I was planning on using the SmartBoard and props where I could easily show students how Long Division could be seen as sharing money with friends. When I taped my props to the SmartBoard, it stopped working because the tape made it seem like someone was touching it and therefore, I was not able to write. Because of the layout of the classroom, I was not able to use the dry-erase board since there was already writing on it which was intended to not be erased. Because of this, I was not able to use my props. Thankfully, I learned how to use the SmartBoard last minute and managed to make it work. I was able to move my writing on the SmartBoard which made explaining easier than if I would have had to erase stuff and rewrite it. Another challenge that came up was that many students in the class had to leave early for a field trip to the movies. I was not made aware of this until I actually came into the classroom. Because of this, many students were not able to finish the activity completely. Another challenge that also came up was that I went a bit over time again. Although my timing for the opening activity was as expected, the activity itself was longer than I anticipated. I originally had an Exit Slip for students to complete but ended up not handing it out. Although I was not able to distribute the Exit Slip, I was still able to assess students and it ended up not being needed at all.
Compared to my last few lessons, I definitely felt like I have improved. Despite the challenges, I was able to be flexible and still teach and engage with the students in class. I definitely feel like I was more engaging with students than in prior classes because I have been more comfortable speaking to them and explaining things. My opening activity went great. Students were very engaged when we solved the Long Division problem as a class and most either did or at least attempted to show me how Long Division works by drawing an image that was similar to the one we did as a class. A lot of them found the guide to be helpful which is great because the intention of the guide was to help them memorize the steps needed to solve a Long Division equation. The goal was not only for them to know how to solve a Long Division equation but to show me how or why it works and that’s exactly what they did when drawing their pictures!
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