How do we move the typical “ray, line, and line segment” lesson beyond mere memorization and towards actual thinking? As always, it helps me to take some time and ask myself, **“What is interesting about this concept?”**

As I pondered, I realized that the concept of **infinity** was staring me right in the face. Infinity is a fascinating 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 involve this concept of infinity. I started focusing on how a ray has an end-point but 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 the controversy! A question to **get my kids’ brains sweating** as we went about the humdrum of memorizing the three shapes.

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 had two endpoints.

But I want my kids to go home still pondering this baffling paradox: **is a line longer than a ray if they both stretch into infinity?**