Some Teapot Math: Take 2, Part 1

Several years ago, we began a teapot project. Created in collaboration with teachers from China and YIS in Japan, the idea took off and has been running the last several years. The teapot has traveled from Japan to the US to Indonesia and then back to the US. What it involves is willing teachers, upper elementary or middle school students, and the desire to do some project-based learning. It’s a chance to do some good math inquiry.

This year, Melvina and her 6th grade class in Hawaii started up the project again, and we jumped in to receive their teapot. We will then send on to Aviva, and her 5th graders in Canada. The goal is to create a box that can hold a teapot that can be shipped to another country. A teapot is an odd enough shape that’s not easy to fit into a typical box. I like that it gives students a challenge to design something that can hold the teapot tightly. Here are some learning intentions for this teapot package project.

Our Beginning

To start off the project, we looked at packaging and sustainable design. We took a trip to the local supermarket, a store that specializes in foreign goods, to look at different packaging. Students were introduced to the project and told to do some analysis of the unique designs used to package items.

What they found is that the rectangular prism is the most common type of packaging although there are some unique ones out there. We talked about making the package environmentally friendly and that we’ll be using recycled materials as much as we can. We don’t want to use packaging materials if possible, or at least use minimal ones.

After our walking trip and package analysis, we looked at some packaging designs online. Apple has a lot of interesting packaging ideas that are supposed to be eco-friendly. This site also has some cool, creative designs we all looked at for inspiration.

A Skype Call

Next we got a chance to talk with the class in Hawaii who had designed the teapot package we would receive. They had spent about a month working on the project, and their winning designs were fantastic. The students shared their design and why they had chosen the one they did. They talked about the challenges of collaborating and designing the package. They had chosen four different designs. One of the winning ones was a box shaped like a volcano. All were colorful, all different shapes and all represented Japan. The students enjoyed talking with the students in Hawaii and got some great ideas about how to approach their own teapot package, bound for Canada. We had to choose one teapot package but really wanted them all!

Teams and Design

Next students were placed in teams of 3 or 4 and they started brainstorming ideas for the package. Everyone in the team wrote out their own design, and then their goal was to come to consensus. In words and pictures, they came up with ideas about colors, shapes, type of materials, durability and functionality. I wasn’t in the day they brainstormed, and it was fun to come back and see their ideas taking shape. Based on their investigation of packaging and their conversation with Hawaii, they independently thought about what a package needed.

They then got some ideas from the class in Canada. Their Canadian friends there brainstormed things important to Canada like the maple leaf on the flag, hockey and even the say “Eh.” We looked at their pictures of images and words for ideas.

Doing the Math and Planning

Now it was time to do some concrete math. Since we hadn’t received the teapot yet, but knew the dimensions, students created a model of the teapot’s size. With recycled materials, they put together something that was approximately the size of the teapot–although different in shape. It was a good chance to observe everyone’s measurement skills and 2-D to 3-D conversion as they put together rectangles to make a rectangular prism.

From there, students had a physical model to look at and came up with exact measurements for their teapot package. Since our goal was to use as little packaging as possible, students thought about how to make a small package, leaving only some room inside. One group came up with a box with sides that flexed inwards. This led to some interesting math about how much the sides should indent in order to leave enough room for the teapot. On their own, they began inquiring into angles, talking about the size of angles and what would be the best angle for those indents. Students drew out trapezoids, a rocket ship shaped package and finally a maple leaf.

In drawing and talking about their teapot package designs, we discussed perimeter and area and introduced volume. I then introduced scale and had students attempt to scale their designs on 1 cm graph paper. As it turned out, that exercise proved to be one of the most challenging so far. The trapezoid and rectangular prism with indented sides was easy enough. The maple leaf was suddenly a huge challenge and chance for inquiry.

Some Complex Math

Trying to scale the maple leaf proved to be a great inquiry, unexpectedly. As one of the students started working on it, with each leaf having a different perimeter, she became frustrated. She declared it impossible to scale or something that would take so long she dreaded it. One of her teammates came through and thought it might be possible based on something she had seen before. She couldn’t quite place how to do it though. Then, another student came over and suggested dividing the shape into triangles so they could figure out the area. Then, they could scale the area. Suddenly three of them were working on it, measuring out acute, right and obtuse triangles. They decided to find the area of each of the triangles and then add them altogether. They figured out how to do the area of triangles and had conversations about how to find the height of the triangles. It was amazing. I stood back and watched as they figured and figured as a team, completely engaged for about 45 minutes. I love those moments in teaching. The next day they were back at it again.

Technology

Meanwhile, students have been learning SketchUp to use as an assistant design program. They did some tutorials on Sketchup and then had the goal of creating a house, as practice. I’ve never completely learned SketchUp myself but I leave it up to the students who are so much quicker at learning tools like SketchUp. They loved it and within several hours of using it, all of them had created at least a house. Some were creating cities. Now, they’re moving into using SketchUp to make their actual teapot design. Since they can’t find a cm tool on SketchUp, they are independently converting between mm and cm or m and cm. Hopefully, we will be able to print out one of the designs on the school’s 3-D printer.

The Teapot Arrives

Just before spring break, the teapot from Hawaii arrived. We opened the package with excitement to find an intact teapot and beautiful teapot package. The package was a spam musubi box, which was carefully coated in rice with a homemade felt spam on the top. Inside the box was the white teapot, some tea from Hawaii and a postcard from the students. It was like getting a birthday present, and students were all excited. We now are ready to start constructing our own package, using recycled cardboard students found at school. We also got to have a nice tea party with the tea and teapot that arrived, while listening to some soothing Hawaiian music. We’re ready for the next stage of the project…and spring break, of course.