The February, 2007, issue of Wired considers 42 of the "biggest questions in science." The person providing answers is John Hodgman, "guest smarty-pants" and resident expert on The Daily Show.
Only one of the questions posed involved mathematics: Can mathematicians prove the Riemann hypothesis? Any idea what that is...or means? It is considerd to be the most famous and important unsolved problem in mathematics...so mathematics teachers and students houyld know about it!
Look it up...do some Google searches. On the surface level, you should find discussions of distribution of primes. On a higher level, you will find discussions of the distribution of zeroes of the Riemann zeta function. Along the way you will cross paths with many great mathematicians: Riemann, Euler, Hardy, Littlewood, Hadamard, Hilbert, etal.
The problem has been around for 100 years, being first posed by Bernhard Riemann in 1859. If you want to take it on...or cheer for a particular mathematician trying to solve it, the Clay Mathematics Institute is offering a 1 million dollar prize for the first published solution.