On March 23, 2016, I visited the Expeditionary Learning Academy at Moylan School (ELAMS) to teach my second guest lesson to a third grade class. This time, I had prepared a math lesson on area which utilized architecture and design vocabulary to connect learning to real world scenarios.

My lesson focused on **three key learning objectives: **

- Students will be able to determine the area of a large rectangular space by first determining the areas of smaller rectangles within that space.
- Students will be able to adapt to changing circumstances in order to solve real world problems.
- Students will be able to translate spacial/visual manipulatives into an algebraic formula.

These objectives are grounded in the Common Core State Standards for third grade math. In particular, I utilized MD.C.7.D, which asks students to, “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.”

**Teaching activity**

In order to help students meet the learning objectives, I designed a teaching activity which required students use a 10 x 10 grid to design their own floor plan made up of various rooms. To make this activity mimic a real world scenario, the activity involved “building phases,” and in order to move from one phase to the next, students had to correctly calculate the area of each room.

**Phase 1: **Design a floor plan with one bedroom and one bathroom. Each room must be either a rectangle or square, and both rooms must connect. Calculate the area of each room.

**Phase 2: **Your house is too small! Add another room (of your choice) onto your floor plan. Once again, this room must be either a rectangle or a square and it must connect to the rest of your house. Calculate the area of this new room.

**Phase 3: **Your house is too big! The construction team says they do not have enough materials to build your design. You must decrease the size of one of your rooms and then recalculate the area.

**Phase 4:** The construction team is ready to turn your floor plan into a real house! However, before they can start building, the team needs to know the area of the *entire* home. How could you find the area of the whole house if you already know the area of each individual room?

**Lesson introduction**

To begin, I showed the class an example floor plan I designed and told them they were all going to be architects today. I explained that as a senior at Trinity College, I was graduating soon and needed a house of my own. This “hook” immediately engaged students by involving them in my story of designing a dream house, and I was able to naturally transition into the concept of area.

**Connecting real world scenarios to math concepts**

One of my main goals for this lesson was to encourage students to see the natural connections between real world problems and math concepts, such as area. In the video above, I encourage students to draw a link between the tasks they had to complete as an architect and the notion of “area,” which they had been learning about in class.

After introducing this concept, I outlined some basic guidelines each student needed to follow while designing his or her home. This “building code” required students to make sure that all of their rooms were either a square or a rectangle and that all rooms connected to one another.

**Lesson adjustments**

While designing the lesson, I initially planned for students to use pipe cleaners to represent the outline of each room. However, I quickly noticed that many students were struggling to manipulate the pipe cleaners. I chose to adjust the instructions by letting the class know they could use their pencils instead, but they should be ready to use an eraser as well, since architects often make many changes to their floor plans.

I also noticed that the pacing of my lesson was a bit off. Although nearly all students grasped the concept of area, the time it took each student to calculate the area of their rooms took longer than I anticipated. Ultimately, my class only finished “Phase 1” and “Phase 2” of the design process before moving onto the final task of calculating the total area of their home. However, in a classroom where students felt more confident calculating area, “Phase 3” would be a great additional challenge.

**Examples of student work**

This photo of one student’s floor plan serves as an example of the kind of work I saw most students produce that day. Overall, this student clearly drew a connection between the visual representations of rooms and their corresponding area formula. If I were to have this student revise his work, I would encourage him to make sure his units were consistent. As you can see in the image, this student initially wrote “70 units all together” before erasing these words and simply writing “70” at the bottom of the page.

An exemplary response would read “70 square units.” However, I did notice that many students had trouble grasping the concept behind “units” versus “square units,” so I anticipated this error might arise.

I would also encourage this student to show all of his work. While his ability to calculate the total area in his head shows a certain level of skill, I would push him to write down his calculations in order to truly demonstrate how area is additive.

**Reflections on the process**

While some students definitely found this exercise more challenging than others, I believe the learning objectives were appropriate. Around one third of the class quickly grasped the material, another third needed some teacher support, and the last third struggled significantly. As a guest teacher, this distribution lets me know that my material was challenging but not overly rigorous.

One aspect of my teaching I would like to improve in the future is my ability to fully and deeply explain concepts to students who need additional help. When I initially began the lesson, I assumed the class already understood the idea of area, so when I realized many students still had not mastered this concept, I fell short in providing proper support. If I had used more precise and clear language to explain the reasoning behind area, length, and width to individual students, I think I could have better helped them meet the learning objectives.