Paradoxes are fun! In fact, they've helped get people interested in a lot of complicated math. Although this is probably too advanced for your level (since it deals with calculus), you might be interested to hear about Zeno of Elea. He designed paradoxes back in ancient Greece that led people to think about certain fundamental things in physics and calculus!

Anyway, my favorite paradox has to be the Berry Paradox, named after the librarian who came up with it:
What is "the smallest whole number that cannot be named in less than fourteen words?" This description is a valid way to name a number, correct? Yet it is 13 words long. So if the number can't be described with 13 words, we are saying it can be described in 13 words.

It's a funny paradox, but it actually turns out to be useful. Hope you enjoy it.