On March 23, 2016 I taught my second lesson as a guest teacher in a third grade classroom at ELAMS. This time, I was asked to prepare a mathematics lesson that would review a concept that the students had previously learned. Teachers at ELAMS advised me to focus on area. Because I was happy with the interactive nature of my last lesson, I knew that I wanted this lesson to have a similar, hands-on focus. With this in mind, I began to design a creative third grade lesson about area. I based my lesson on the relevant Common Core State Standard:
- CCSS.MATH.CONTENT.3.MD.C.7.D: Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Based on this standard I formulated three lesson objectives:
- Students will be able to translate spacial/visual manipulatives into an algebraic formula.
- Students will be able to adapt to changing circumstances in order to solve real world problems.
- Students will be able to determine the area of a large rectangular space by first determining the areas of smaller rectangles within that space.
To complete these objectives, students would become “architects” and design floor plans for a “dream house” using a paper grid and pipe cleaners. To complete objective one, students would first lay out a floor plan on their grid by manipulating their pipe cleaners into a two room house, and then calculating the area of each room. With objective two in mind, I then would ask students to add another room and calculate its area. Finally, students would be asked to decrease the size of one room and find its new area. To fulfill objective three, students would then be asked how to find the area of the whole floor plan, which is done by adding the area of each individual room.
One of the strongest parts of my first lesson in February was beginning with a “hook” and because this strategy was so successful in grasping the students’ attention and getting them excited about the lesson ahead, I incorporated it again in this lesson.
I used this to segway into the broader lesson about area. I showed an example floor plan that I created on a poster board that had the outline of a bedroom and bathroom, and told the students that my building team needed to know the room dimensions. After a bit of prompting, students realized that to find the size of a room, they needed to calculate the area, and together, the class and I calculated the area of each room on my example. While doing this, I presented a powerpoint slide explaining the area formula and showing an example area calculation. To conclude the introduction, I explained that it was the students’ turn to design their own floor plans, and I handed out to them their own grids and pipe cleaners.
Design a Dream House Step One
Before the “architects” could begin, I explained that my construction team gave me a strict building code that I presented on the screen. They needed to design a simple floor plan consisting of an adjoining bedroom and bathroom, with both rooms being either square or rectangle. I explained to the architects that they could bend and manipulate the pipe cleaners to give me a two room design, and once they did that they could calculate the area of each room.
As students worked, I walked around the room answering questions and making sure everyone was on task. While circulating, I quickly realized that the pipe cleaners were difficult to work with because they moved around a lot. I noticed students struggling to keep them in place and it seemed difficult to create structured squares and rectangles. The design tool actually became more of a distraction than anything else.
Additionally, after noticing the lack of computation on many worksheets, I realized that students did not have as much experience with area as I anticipated. I soon learned from the teacher that they only learned the area formula the day before my lesson. Therefore, as I walked around I needed to assist with the area formula and multiplication facts. Many students, instead of calculating area using length times width, were just counting how many boxes were in each rectangle. In situations such as this, I explained that although this strategy would produce the correct answer, it was very time consuming, and it would be a smarter technique to apply the area formula. Once students completed this step, I asked them to raise their hands so I could check their work. This was my evaluation method to ensure that the learning objectives were being met. Successful students produced results such as:
Student difficulty with the area formula caused the first portion of the lesson to take longer than expected and I quickly moved into step two, which entailed informing the architects that I needed more space in my home.
An example of completed work at this step:
While the counting in this example is slightly off, the student did grasp the concept of the floor plan layout, and correctly calculated the area of each room based on the number of boxes that they counted.
Intended Step Three
In my original lesson plan, there was a third challenge for students. I was going to present this email on the powerpoint presentation:
Unfortunately, because the first two steps took longer than expected, I was not able to present this challenge. Looking back now, I think it would have been far too difficult for many of the students, but, nevertheless, I think it was a creative aspect in the original plan.
The students’ final step was to calculate the overall area of the floor plan. I asked students how they would complete this, and students responded that they would add up the area of each individual room. I had the students complete their calculations and then checked their work as a final evaluation method. A final example is:
I finished the lesson by sharing an example of a real floor plan with the students and asked them to work with a partner to compare their floor plans to a real one.
Strengths, Weaknesses, and The Rule of Thirds
A strength of my lesson was how relevant my activities were to the CCSS and my lesson objectives. This was something that I wanted to improve on after my first lesson, and I am happy that I was able to do it successfully. My objectives matched nicely with the standard, which was to make sure that students understood that area was additive.
Secondly, compared to lesson one, I think I had somewhat better classroom management in that I was less likely to let students shout out answers. For example, I was quicker to ask students to raise their hands when asking a question. Similarly, when giving instructions, I was more strict on making sure students eyes were on me.
I felt that this lesson had many weaknesses, which made it a strong learning experience. A weakness I noticed in my video occurred when responding to students incorrect answers to questions. An example of this occurred at the beginning of the lesson when I asked students how to find the size of a room. The answer I expected was to calculate the area, but instead one student said, “you need a really long measuring tape.” I responded that the student was correct, but instead I should have said “that is one way, but not the answer I am looking for, can anyone think of a mathematical calculation for finding the size of a room?” Next time, I would like to employ stronger strategies for guiding the students to the correct answer.
Ultimately, while I wish this lesson went smoother, I learned a lot from it, which made it a success. While the concept was more challenging than the first lesson I taught and the students only learned the area formula the day before, I felt as though one third of the class mastered the topic, one third was improved their skills with area, but had not yet mastered it, and the final third still did not understand the topic. As I continue to grow as a teacher, I want to work on how to adapt to different levels of learners in the classroom, so that 100% of the class is always engaged in the lesson. Hopefully, this supplemental lesson provided good practice, and the teacher can refer to it as she continues to teach the class about area. In the long run, I hope this lesson was a learning experience for students just as it was for me.