At last, students’ prototypes were coming to life. The penultimate lesson was a (productive) mess of paper, tape, and running to other classrooms to borrow meter sticks.
I wanted to give students an opportunity to share their hard work with other teachers and students, so earlier in the week, I began organizing a trade show. In terms of physical set-up, preparation was minimal; the biggest hurdle was finding volunteers for students to interact with. I sent out an email inviting other staff members to join, and ended up with about 6 staff participants; another math teacher also very kindly volunteered his Grade 11 class to join in.
On the morning of the show, I taped large numbers on several of the tables in the cafeteria, corresponding to name tags I handed out to the student groups. After about 30 minutes of last-minute preparations (we were running a little late), the class headed down. The staff and student volunteers joined us shortly thereafter.
Here are the instructions that I provided prior to the trade show:
Students’ goal for this project was to design and build a prototype of a more effective and/or efficient pop box. Some groups have chosen to focus on efficiency—less cardboard, less empty space, or both—while others have chosen to focus on aesthetics, opting for a unique and interesting design.
Your role is that of a soda company executive who is looking to increase soda sales. When you meet with a group, they will present their brief sales pitch to you. You are encouraged to ask any or all of the following questions, if they haven’t been answered during the sales pitch, to learn more about their design and to push their thinking further:
- Is your design more environmentally friendly than the regular pop box design?
- Are these boxes easy to ship? to stack on store shelves?
- How will this design encourage more people to buy pop?
- Who do you think this design will appeal to most: kids, teenagers, adults, or another category of people?
- What other ideas did you entertain before deciding on this particular design? Why did you choose this design as opposed to the others?
- You have improved the design of the box, but have you thought about improving the design of the can? How might you do so?
After interacting with a group, please give a grade out of 3 (3 is the highest, 1 is the lowest) for each of the following criteria:
The pop box design is unique, interesting, and/or eye-catching in comparison to the standard rectangular box.
The prototype is functional and has been built with care and precision.
Strength of Argument
The designers present a convincing argument with regard to the efficiency and/or effectiveness of their design.
Note that these grades will not contribute to students’ marks for the project.
[Note that the informal evaluation was not meant to be the highlight of the trade show and, in fact, I didn’t let my students know that participants were going to be evaluating them until the morning of the show; this didn’t seem to stress them out (I did explain that it would not influence their grades), and maybe turned their enthusiasm up a notch. Tomorrow, I will award small prizes (obviously, a can of pop) to groups with top marks in each category.]
And, once everyone found their table, they were off!
I joined the participants in speaking with the student groups and heard some fantastic pitches. The students were enthusiastic and proud of their designs, and they sold them well. I summarize just a few of them:
- One group surprised me by making a rectangular box that was nevertheless quite innovative. The box held 20 cans in total, but instead of the same kind of pop, there were 5 different flavors, and 5 flaps that opened to reveal them. Genius! Perfect for a get-together when you want to offer a variety of options, but don’t want to buy 3 boxes of pop. The design was practical, unique, and very appealing (the group ended up earning top marks in the “Strength of Argument” category). Among all of the designs, this one made me wonder most, “Why isn’t this on store shelves already?!”
- Another group played up the environmental angle of their Pepsi Flower design. “There is very little empty space. Also, the box is so cute, you can reuse it when you’ve drank the pop! Can you imagine storing baby clothes in there?! Adorable.” (Side note: This group also engaged in some great mathematical thinking to find the surface area of their box, which was full of rounded edges.)
- The group of students who created a triangular box pitched theirs as efficient and fun: “When you’re done drinking the pop, put the cans back in the box, and you get bowling pins!” (Side note: This group refused to let go of the mathematics and insisted on finding the exact surface area of their design – despite my suggestion to estimate part of it – , which turned out to be a very interesting problem. See Part 2.)
- One group designed their cylindrical box to contain 38 cans, 19 per layer, for a very specific reason: 19 circles packed in the smallest possible circle that contains them results in the most dense packing up to 20. (See this Wikipedia article.) This was based on their own research, and was completely unprompted by me. (The abundance and variety of this group’s ideas was quite astounding – they spent two days just in the brainstorming phase, and a significant portion of this time arguing about the relative efficiency of installing a Pepsi pipeline in cities where they generated the most profit. Talk about out-of-the-box thinking – literally!)
This group’s pitch was, in fact, a rap, and its over-the-top cheesiness makes me laugh every time I watch it:
To sum it all up, I was incredibly proud of my students, and I hope they are proud of their hard work as well. Throughout the experience, I have been blown away by students’ creativity, collaboration, persistence in solving unfamiliar and challenging problems, not to mention by the variety of curricular and extra-curricular mathematics that emerged. Nat, whose Soft Drink Project this project was based on, sums it up nicely:
The sheer volume of work that went into the different designs was several times more than I could have ever gotten out of the same students with a dictated assignment. It showed me that an interesting starting point, a little bit of student control, and a willingness to learn alongside can create unbelievably powerful learning.
A willingness to learn alongside was certainly critical, as I was often pushed to exercise my problem-solving skills alongside students; as such, my role shifted even further from knowledge authority to co-participant in the problem-solving process. I found this to be tremendously exciting and fun, and I hope the experience helped to validate students’ feelings of being competent, creative mathematicians.
Finally, now that I’ve dipped my feet into project-based learning and survived, I am itching to explore its affordances further in other courses, with more curricular concepts.
Some resources related to the project, in case you are interested:
Pop Box Project – Project overview (English)
Pop Box Project – Project overview (French)
Pop Box Project – Group contract (English)
Pop Box Project – Group contract (French)
Pop Box Project – Rubric (English)
Pop Box Project – Rubric (French)
Pop Box Project – Trade Show