Although this is my sixth year teaching, I’ve been struggling with classroom management issues this fall in my last-period Geometry class. So we haven’t been able to do some of the cool projects I talked about last year (click the Geometry tag to see more). And a few topics we haven’t been able to delve into at quite the same level as I could with a more-motivated group of students.
A few details on some topics we’ve worked on during the past month or so:
The lesson on three-dimensional polyhedra went fairly well for the first two parts. Students constructed polyhedra from nets and by building their skeletons out of gumdrops (vertices) and toothpicks (edges). They discovered the relationship between vertices, edges, and faces found by Euler (V+F=E+2). But when I tried to bring the whole class to proving that only five regular polyhedra exist, I lost 80% of the class. I don’t know if it was too many steps, too long for their attention spans, an aversion to the logic of proofs, or the overall class dynamic. I don’t believe the math was too complicated for them (it just has to do with angles in regular polygons, spatial relationships, and our previous topic – tilings of the plane). I provided a sheet for taking guided notes. But much of the class turned that sheet in without having taken any notes.
Some of the more successful lessons have been a few that tied into what my students were learning in their engineering class. In late October – early November, my sophomore Geometry students were building and analyzing truss bridges in their Principles of Engineering course. Several teachers got together to plan lessons in various subjects that tie into the topic of bridges. In October, near the beginning of that unit, I did a lesson on the strength of various shapes. Students tried to use paper to hold the most books at least one inch off the table. They constructed a bridge that could hold the most rolls of pennies, using just one index card. And another bridge of multiple index cards, designed for length.
A couple weeks later, after they had developed designs in the engineering class, I had them analyze some of the geometry of triangles. This connected their bridges to what we were currently talking about in Geometry, with triangle congruence, proof, naming, and the Pythagorean Theorem.
We’ve also learned about isosceles triangles, angle relationships, and circles in the past month.