On April 4th, 2019, I visited the Environmental Sciences Magnet School at Mary Hooker (ESM) to guest-teach a sixth grade math lesson on area in real world situations. Prior to my visit, the students had been practicing solving the area of triangles, with an emphasis on right triangles, as well as parallelograms. I was in contact with the class’s regular math teacher, Mr. Smith, in the days leading up to my workshop, to clarify what the students’ needs would be. He informed me that reviewing shapes and area formulas would not be necessary, as the students had done much practice with it over about a week and should be very comfortable with solving for area of triangles and parallelogram. This was excellent as it gave me more time during my workshop time to do take the students further with a skill they had already been practicing.
The learning objective of my lesson were as follows:
- Find the area of right triangles, other triangles, special quadrilaterals, and polygons, by composing into rectangles or decomposing into triangles and other shapes: apply these techniques in the context of solving real-world and mathematical problems.
These objectives are outlined in the Eureka Math Instructional Guide, which is the math curriculum used by ESM.
My lesson plan which I carried out was the following:
Grab the class’s attention by asking them about some of the basic features of zoos. Have they been to the zoo before? What kind of places are the animals kept? What is different about the places each animal lives in at the zoo? I wanted to get the students excited and engaged with the idea of the zoo for the first moments of the lesson before introducing the math of it.
- Introduce the activity
I transitioned into explaining the activity I had planned. It was essentially a group activity in which students designed a map of their own “zoo” on a sheet of poster paper, making animal enclosures out of shapes. I used this Zoo Area powerpoint as an aid to show the steps of the activity, and below is the slide I projected as a visual aid while I explained the rules of the activity.
- Show an example
I showed the class a list of instructions for what they were expected to do in making each animal enclosure. I then showed photos (pictured below) of the steps I took to make my own zoo map, which I had posted on the board for the duration of the lesson.
With this I introduced the next step. Relating back to my launch when we established that different animals need different sizes of enclosures, I passed out a sheet listing all the options of animals the students could choose from to put in their zoo, along with the minimum area one of each animal needed in its enclosure. I explained that once the students had found the area for an enclosure in their zoo, they could call me over to check their work and give them them a paper cut-out of the type and amount of the animal of their choice.
Next, I projected the instructions for the lesson onto the board, which I also left up, as a reminder for what was expected in the process of making each zoo enclosure.
With that, each group was given their larger sheet of paper, took out their rulers and calculators, and started designing their zoos.
The kids all did really well with this activity, and at one point I even heard a few students talking amongst themselves call my activity fun! Mr. Smith was right in that the kids generally did not need much guidance as they clearly all knew how to find the areas of the shapes we were working with. I found that whenever mistakes were being made, most of what I had to do was make them aware of them rather than give much explanation. Most of the mistakes I saw were
- Forgetting to label the units or to write units squared
- Using the hypotenuse in a right triangle to solve for area instead of the legs
- Mixing up the formulas for area of a triangle and area of a parallelogram (b x h vs ½ b x h)
In all these errors I found that all around I only needed to point out that there was something missing, or remind them to check their work for them to quickly realize what they had missed, and promptly fix it and call me back over to give them their animals
Below are some clips of the students working on the activity. Unfortunately due to all of the groups talking during the class, it is difficult to hear most of the audio in the clips.
The animals proved to be a big motivator for the class, because they had to find the area and do it correctly in order to get them. By the time the activity was in full swing, I was having a hard time keeping up with all the requests to check work and get the animals for groups. Below are a few of the groups maps- most did not fill the whole page but finished several of the enclosures within class time.
My lesson was equitable in that the subject matter was something that all of my students had knowledge and interest in- animals. Some of my students actually did not say they had been to the zoo, so perhaps I could have addressed that. However, all of the students did say they were familiar with the idea of the zoo, and in making their animal’s enclosures, seemed to understand that different animals needed different amount of space as their habitat. For this reason the lesson was equitable.
Formative assessment was built into my lesson in the form of handing out the animals for the students to put on the page. I had a calculator in hand and looked at each groups enclosures and area calculations as they went, checking their work and directing their attention to mistakes to fix in order to earn their zoo’s animals.
Compared to my last workshop, I think that this one went far better with much fewer issues. I’m happy with how engaged the students were, to the extent that it seemed like they didn’t even mind doing the math if it earned them different animals for their zoos.
The area I think needed improvement the most was in my launch and introduction of the activity. I was worried that I still spoke too fast, and did less engaging of the students by asking questions. I think this was a result of there being many factors to be explained of the activity, and I was too focused on making sure I did not forget to say anything than on making my launch interesting and ensuring the students understood. There was a moment when I had finished explaining that I was feeling very nervous that none of the student had understood me and that I had designed a lesson too complicated for them to complete. the students did have a couple of questions following my explanation of the instructions, and watching it back, I realized that I probably should made the small improvement of repeating the students’ questions before answering them. The rest of the students likely would have benefitted from hearing the questions, because I ended up getting the same questions later as students worked on the activity.
I think I missed an opportunity to address equity at the moment in my launch when I asked if everyone had been to the zoo before and not everyone said yes. While I can not change that not every student had been to a zoo before, I definitely could have spent a moment leading a discussion with the students about the features of a zoo. I worry that while all of the students had few troubles with the actual math of the activity, some may have missed out on the imaginative aspect of designing a zoo that engaged some of the kids. For example, I had one group call me over and ask to exchange their deer for another animal, because they said the deer kept running away and hiding, and it was too boring for the guests at their zoo. I was happy they got so into the activity and really imagined what the experience of visitors to their zoo would be like, and I wish I had done more to try to promote this fun side of the activity for all of the students, making it more “real world”.