Giving Concrete Structure to Abstract Math Concepts
To give concrete structure to abstract math concepts, students in Mathematics teacher Herschel Revzin’s Geometry CP and Dean of Mathematics Riley Clark’s Geometry Honors classes created 3-D visual representations to apply their understanding of the surface area of solids. ”Students often find that representing information visually is a powerful way to understand math, but as with all skills, it must be taught and practiced.” says Ms.Clark,
Mr. Revzin’s class focused on constructing Platonic solids to make a colorful mobile. Discovered by the Greek philosopher Plato, Platonic solids are geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles, or as we know them, the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron. After students cut, decorated, and assembled their Platonic Solids, they worked through a series of calculations to measure their surface area. Weber sophomore Emily Aronin had a real “aha moment” while constructing her platonic solids, noting that “this really helped me visualize connections between algebra and geometry that I hadn’t made before. The process of cutting and assembling really made something click for me!”
Students in Ms. Clark’s class collaborated with Daniel Zalik Academy faculty to laser-cut 3-D solids of their choosing. Students chose a polygon base (hexagon, octagon, nonagon, etc.) to make a prism or pyramid working within the confines of a 72 square inch piece of acrylic. “It’s hard to visualize dimensions, so this project is beneficial to help students visualize how planes work together to form 3-D objects,” said Ms. Clark. Sophomore Tia Abadi felt the constraints of the project also helped her understand iterative thinking, saying, “Not only did I have to confirm that my assembled solid’s surface area would be smaller than 72 inches, but I also had to make sure each plane forming the solid would fit on a single sheet of acrylic. Once I understood the equations, it was just a matter of working the math until I found my answer!”
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