Ninth graders who have been learning about the properties of parallelograms in math teacher Aaron Ginsburg’s accelerated Geometry-Trigonometry class used the interactive Desmos platform to create and manipulate geometric diagrams and understand the relationship with trigonometric functions.
During a recent lesson, they projected parallelograms onto a coordinate plane and used distance and slope to prove the figure is a parallelogram. Then, they transitioned these methods into proving parallelograms without the coordinate plane, backed with reasoning to apply in proof.
“Through the Desmos platform, which is a free suite of math software tools, discovering the properties of parallelograms is possible as students create, stretch, annotate and observe the geometry,” Ginsburg said.
Students get fully immersed in the lesson, arrive at their own conclusions and collaborate with their classmates to confirm they’ve made similar observations.
“Our ability to record our observations as we experiment provides the reasoning needed in proof and argument,” Ginsburg said. “The visuals can affirm our conjectures, and the approach in the lesson is not high stakes. It is less about being right or wrong at the moment and more about engaging in exploration and articulating our observations.”
Ginsburg said the tools and presentation on the Desmos platform provide a hub for the mathematical content he covers in class. In addition, the tasks, manipulatives and prompts found on the presentation slides are custom made for the lesson, which runs on a computational layer in a Java-based script and Desmos’s graphing capabilities.