Students will learn what the hinge theorem is, why it's true, and how to use it. Then students will learn what the converse of the hinge theorem is, and why it's true.

Conclude by giving your students these challenges:

- Poly Plug Pattern by NRICH
- Number Lines in Disguise by NRICH
- 2018 Math Kangaroo Levels 11-12 Problem #22 by STEM4all
- More Mathematical Mysteries by NRICH

2021 Math Kangaroo Levels 11-12 Problem #23: \(f(x)\) is a function of real numbers such that \(f(x + y) = f(x) \cdot f(y)\) and \(f(1) = 2.\) What is the value of

$$\dfrac{f(2)}{f(1)} + \dfrac{f(3)}{f(2)} + \ldots + \dfrac{f(2021)}{f(2020)}$$Here's the solution.