Tangible Mathematics

BY Calder Martin

Martha’s Vineyard Public Charter School

Project Description
This is a simple wood construction project that teaches a core concept in algebra: the cube of the binomial (A+B). Each student is given the tools and materials to measure, cut and build a geometric representation of the polynomial A^3 + 3A^2B + 3AB^2 + B^3. The cubes are different depending on choices made by each student, but all the cubes directly showcase the relationship between algebra and geometry. Each term in the expression represents a volume in space. Students are able to disassemble and reassemble the parts of their hand-made cubes to contemplate the conceptual framework in play.

How will the project be evaluated (e.g. how will you gauge its success)
The success of this project will be evaluated based on the enjoyment and learning demonstrated by the students. This will take the form of better use of mathematics and better understandings and enthusiasm for binomials, especially cubed binomials.

Benefit to the students and the school
The students will benefit from a change of pace from their usual pencil-to-paper routine. They will be measuring and cutting lengths, making edges flush and considering construction techniques. This project will connect students thinking about mathematics to thinking about objects in physical space. The goal of this unit is to make algebraic concepts tangible to students in ways that involve using their hands and using carpentry skills. The models are built to show the relationships between geometric and analytic representations of polynomials. The goal is also to have fun.

Timeline of Project (when will you do the project, if applicable)
This project will be implemented during a single week of the spring semester of 2020.