How do we move the typical “ray, line, and line segment” lesson beyond merely memorizing definitions? How do we get students actually thinking about this topic?
As always, it helps me to ask myself, “What is interesting about this concept?” (Not just “challenging”).
I realized that the concept of infinity was staring me right in the face. Infinity is a go-to interesting topic! I remember being a kid and struggling to imagine a line that truly went on forever. As I thought some more, I realized that both a ray and a line have infinite lengths. But a ray stretches into infinity in one direction while a line goes to infinity in two directions.
I knew I had my interesting idea! I had found some controversy!
As we learn about these three similar shapes, I want you to wonder with me: which of them is the longest?
Obviously, the line segment is out right away. It has a defined length. But what about the ray versus the line? Both stretch into infinity. But one also has an endpoint.
I want my students to go home pondering this baffling paradox. Are a line and ray both infinitely long, even though one keeps going and one clearly stops?
Are there different sizes of infinity!?!?!?!? 🤯
We’ve gone from “memorize-the-definitions” to “argue about infinity” by finding a bit of controversy.