How can you help maximize the volume and minimize the surface area of a cereal box to help a company lessen its costs and make more money?
Learners in a Grade 8 Mathematics class were assigned a project to wrap up and solidify concepts learned about surface area and volume. They were told that a cereal company wanted to minimize its packaging costs (surface area) and maximize the amount of cereal that could go in the box (volume) so they could keep costs down.
To start, learners were randomly partnered by choosing playing cards. Once a learner chose a card from the teacher, they had to find their partner. They were then given the specific assignment criteria and told the materials they could use. The cereal box could only be created out of one piece of poster board provided for them in class. They could decorate the box any way they chose, remembering it should have similar components that one may find on a cereal box, such as name, brand, nutrition, graphics, and so on.
Learners began to make plans, working on their calculations. They had to use and think about a variety of ideas and information to help them create this plan, and to make decisions, including about their previous learning about surface and area. Once initial plans were done, partner teams worked with another partner team to ask questions and provide suggestions and feedback for their plans. Considering the other team’s feedback, they then adjusted their plans accordingly to meet their goal of maximizing volume and minimizing surface area. Learners had to make their judgments based on the criteria and then make decisions to solve the mathematical components of the task. After some productive struggle, all groups had a plan and feedback from peers, and it was time to build. Learners were given their poster board, and they began to measure and draw a net of their box. They then cut it out and either glued or taped it together. Some learners were more thoughtful in how they made their nets and included flaps to fold down so the boxes would stay together more effectively. Some groups had to readjust their plans again in this phase.
The learners’ interests and personalities shone through in their choices and approaches to the task. They added UPCs, nutrition labels, games for kids, and even pretend cereal on and in the box.
In the end, learners were expected to hand in their cereal boxes along with a graphic organizer that showed their calculations (e.g., box dimensions, surface area, volume, volume ÷ surface area), as well as reflection questions about the process and the learning. Many groups found that making a non-traditional cereal box as a cube instead of a right rectangular prism allowed their ratio of volume to surface area to be larger.
* These descriptors represent the dimensions of global competencies in math.
