Bad/Crackable Encryption Example?
Start with the Caesar Cipher.  It is important to know the flaws and important for students to know the history of it.  It would be quite easy to break considering the background of the learners.  You probably want to include the algorithm as well as the cipertext.

From here you can build more advanced problems since they have the basic understanding of what's going on. 


LM Hash
Small Keys
WEP


Simple problems, but we must crawl before we can walk.