S17: Blog 12: Decimal Division

This past Friday I was the substitute in my classroom while my CT was out and thus had the opportunity to kick off our final math unit of the school year- dividing decimals! I planned Friday’s lesson with the assistance of my fellow resident Sara, as we would be co-teaching the lesson to her group of students for our final mathematics coaching cycle. The specific concept that we were focusing on this day was how to model dividing decimals by whole numbers. For example, 2.4 divided by 6. During our pre-conference meeting with our coach, Lakesia, we decided that our goal was to have students begin by modeling decimal division problems using the Base 10 block manipulatives, before moving on to drawing quick pictures of the Base 10 blocks. We also wanted students to be able to explore and explain the connections between the concrete and the pictorial models. Concrete models, like manipulatives, are especially important in helping to build understanding for all students, but especially those who struggle with abstract concepts. We therefore planned in the lesson to have students work to model decimal division problems they would get from word problems we created. We would formatively assess students during each problem by looking at the model they created and the answer they came up with. We then planned to differentiate by splitting into two separate groups, one for re-teach and the other for core/enrich, to practice more problems and better meet the students where they were at. The re-teach group could continue to focus on the concrete model and building understanding while the other group moved on to working with the pictorial model and making connections back to the concrete model or even forward to the standard algorithm. Because I knew that I would be teaching the lesson solo two other times during the day, I planned differently for the independent practice portion, choosing to plan for students to work on select problems from their GO Math workbook.

Things on Friday did not go exactly as planned. I had my first class of the day beginning to work on modeling the second word problem when an announcement was made that we were under a tornado warning. This meant that we had to stop what we were doing and move into “duck and cover” positions along the walls of our classroom that didn’t have any windows. This lasted a long 10-15 minutes before we were given the all clear and allowed to go back to our business. This proved to be challenging after such a disruption but I was proud of the effort most of my students made to get back on track. This first group of students was even able to begin making connections from the model to the standard algorithm for dividing with decimals, which we will be talking more about on Monday.

For my second group of students I chose to change things up a little. I knew because of the students in the room that giving them a lot of time to explore on their own with model would only lead to a lot of frustration on both theirs and my part. So, after having a student read-aloud the first word problem and going through and coding for important information together, I had the students gather around one of our large tables so that we could work through modeling the problem together. I made sure to use a lot of questions with my students, to ensure that I wasn’t the one doing all the work and they were just passively listening to me. Students identified what each Base 10 block represents when we’re working with decimals, as well as told me how to model the dividend of the problem (5.5). I then asked students about what we needed to do next. They were able to come up with that 5.5 being divided by 5 meant that we need to make 5 equal groups. Students were able to give me directions for how to do this as well, coming up with our quotient of 1.1. Students then expressed the desire to model one more problem as a class, so we followed the same procedures with the second, more tricky problem. I was blown away by how automatically students came up with the idea that we would need to regroup in order to solve this problem (2.4 divided by 4). I was then able to confidently release them to work on modeling the 3rd word problem on their own or with a partner. My students did a great job modeling the problem, we just had to have a discussion about how to write our answer! We discussed the difference between 1.7 (what many students were writing) and 1.07 (the correct answer and what the models showed).

My third and final time teaching this lesson Friday was with Sara for our coaching cycle. We got off to rough start right after lunch with the students being a little extra active. However, once we were able to get started we flew through the first problem! We spent a much longer time on the second problem. We noticed that many students were creating only 2 groups instead of 4 as the problem asked for. We were able to figure out that this was because they were starting with 2 wholes and were unsure what to do with them. After the students had been given time to model independently or with a partner, we spent time discuss the problem as a class. This led to Sara and I decided to have students come up to the front of the room to create another physical model of the problem. This seemed to lead to the breakthrough that students needed to truly understand what the problem was asking and how they could regroup to solve the problem.

It’s hard to believe that this was the start to our last math unit of the year! Time is flying by! We’re gearing up for one more week of new content before we move into reviewing everything we’ve learned this year so that students can go in and rock the FSA at the end of April. But at the end of the day, I think it matters even more that students are gaining the problem-solving experience they need to be successful for the rest of their lives.

FEAPS: 1a - Aligns instruction with state-adopted standards at the appropriate level of rigor

1c - Designs instruction for students to achieve mastery

1d - Selects appropriate formative assessment to monitor learning

1f - Develops learning experiences that require students to demonstrate a variety of applicable skills and competencies

2a - Organizes and manages the resources of time and space to support student learning

2b - Manages individual and class behaviors through a well-planned management system

2c - Conveys high expectations to all students

2g - Maintains a climate of openness, inquiry, fairness, and support

2h – Develops a climate that fosters inquiry

2i - Integrates current information and communication technologies

2j - Adapts the learning environment to accommodate the differing needs and diversity of students

2k – Utilizes current and emerging assistive technologies that enable students to participate in high-quality communication interactions and achieve their educational goals

3a - Delivers challenging and engaging lessons

3d – Modifies instruction to respond to preconceptions or misconceptions

3f - Employ higher-order questioning techniques

3g - Teaches for student understanding using varied and appropriate strategies

3h – Differentiate instruction based on assessment of differing needs and diversity of students

3i - Support, encourage, and provide immediate and specific feedback to promote student achievement

4b – Analyzes and applies data from multiple assessments and measures to inform instruction based on those needs, and drives the learning process

4c - Analyzes and applies data from multiple assessments and measures to drive the learning process

4d - Designs and aligns formative assessments that match learning objectives

5a – Designs professional goals based on students’ instructional needs

5c - Reviews data with colleagues to evaluate learning outcomes and plan effective lessons

5d - Collaborates with stakeholders to support students learning