Geometry… an utterly terrifying and confusing concept used to terrorize school children.

In other words, our PLP 8 class has been learning about calculating the surface area and volume of various 3D objects. Our driving question for this project was:

“How can we design an object to optimize its shape?”

I worked with my classmates Ava and Sara for this project. Together, our goal was to create a chessboard and chess pieces in a certain way in order to optimize its surface area. However, things didn’t quite go as planned, as our designs had a greater surface area as opposed to volume.

Below is what our earliest drafts of our designs look like:

As mentioned in the photo, our plan was to use various 3D shapes in order to make our chess pieces look alike to a crystal. Unfortunately, we had to scrap that plan once we were introduced to TinkerCad –an application in which we designed our objects– due to the fact it would be too difficult.

I was responsible for designing the Knight and Bishop. Here are my designs:

After we finished designed those objects, we had to calculate the surface area and volume of them, then convert them into a simplified ratio that compares surface area to volume or vice versa. This process took me a few hours, but I managed in the end. Here are my calculations: Milestone 3 – Ultimate Design Challenge

Once I had calculated the SA:V ratios, I had determined that the volume was greater than the surface area, which held true for my other group members as well. In other words, our hypothesis was incorrect.

At this point, Ava, Sara, and I compiled our research and data into a Keynote presentation. You can check it out here!

There were three curricular competencies for this project:

• Applying and innovating: How can I contribute to care for self, others, community, and world through personal or collaborative approaches?

From what I understand, this competency could be described as the act of responsibly working with others as well as by yourself. I showed this competency by ensuring my work was complete and on time, and communicating with my group members via Messages. However, I do think my time management could use some work.

• Communicating and Representing: How can I explain and justify mathematical ideas and decisions?

This essentially means to calculate the surface area and volume of our objects, and compare them using a ratio. I feel that I completed this competency efficiently for Milestone 3, albeit I also should have added a few slides in my group’s Keynote presentation that explained the math with more depth to the class.

• Reasoning and Analyzing: How can I model mathematics in contextualized experiences?

Our requirements for this competency were to design a 3D object using a design software, and answer the driving question: “How can we design an object to optimize its shape?” I feel that our group collectively did well on this competency, since we divided up the parts, and ensured that everyone was doing something. However, since our goal of designing our pieces for maximum surface area failed, I do think we could have done things differently.

As mentioned prior, although our chess set wasn’t optimized for maximum surface area as planned, we did well on the execution of this project. If you would like to read more about our chess set, feel free to check out Ava and Sara‘s blogs for their posts on this assignment! Thanks for reading!