Eighth grade math kicks off with a unit on geometry. More specifically, geometry transformations – understanding how translations, reflections, rotations and dilations affect congruent angles and sides of a polygon. Eighth grade students can plot vertices on the coordinate plane until the cows come home, but the real power of this unit comes from understanding the geometric properties that govern the shapes and transformations themselves. Mr. Williams, our eighth grade math teacher, approached me about creating a Chrome app (which would run on our students’ Chromebooks) that allowed students to more quickly explore these transformations without being hampered by manual vertex plotting.
Fortunately, I had the foundation of this app already from a lesson on algorithmically creating line art point-by-point last winter. The first round of feature requests included:
- Creating a closed polygon out of a series of vertices entered as ordered pairs
- Translating, rotating and reflecting that shape, while keeping each result on-screen
- Labeling each polygon in sequence – ABC, A’B’C’, etc.
That seemed simple enough, and was up and running within a day or so. But Mr. Williams wasn’t done yet – he was just getting started. Throughout the week, I’d wake up to a new round of feature ideas, and I’m not one to turn down a challenge. Additions over the next several days included:
- A toggleable list of coordinates for each shape displayed below the grid
- Showing each transformation step in text after execution
- Dilations about the origin, scaling the polygons to any size
- Plotting single points and lines, rather than requiring closed polygons
- The ability to undo any transformation
- A console-only feature to hide intermediary polygons, allowing for rapid homework creation
Each feature was added with near-immediate feedback from the classroom and with a focus on allowing students to focus on the geometric properties, abstracting away everything else that is usually required to see what a polygon looks like and where it is in the coordinate plane after some transformation. Excel students are hooked, and the app has already been leveraged in several other middle school classrooms as well!
Get this free app for yourself and your students by clicking here. Have additional feature ideas? Let us know in the comments!