Eighth-grade students at Bronxville Middle School used two pieces of paper, popcorn and plastic cubes to figure out the mathematical formula for volume of three-dimensional shapes. The exercise was part of a lesson that sparked their curiosity and spurred them to think critically, solve problems and make discoveries on their own.
Middle school math teachers Connor Mitchell and Jennifer Oliveri and high school teacher John Ruiz, who teaches an eighth-grade math course, designed the lesson as part of a long-term professional development method at the district called lesson study. Instead of giving their students the formula, the teachers asked them to create two different styles of containers out of paper, determine which container would hold more popcorn and then derive the mathematical formula for volume.
“Our theory was that if we engaged students in a project-based learning approach, they would be more likely to move from a procedural to a conceptual understanding regarding the volume of three-dimensional shapes,” Oliveri said.
The students brainstormed ideas as a class before engaging in the discovery activities. In one activity, they filled their containers with popcorn, while another activity had them estimate how many plastic cubes could fit inside each container. In the process, they developed formulas and were challenged to explain why their calculations accurately found the volume of the containers.
“The rich and meaningful conversations students had with each other at the conclusion of the lesson proved that helping kids understand a general formula for volume, which is the area of the base times the height, would lead to long-term understanding of the concept, not just simply memorizing a formula,” Oliveri said.
Oliveri noted that at the conclusion of the lesson, the students had discovered which container held more popcorn and had an enriching discussion about surface area versus volume.