rephrase

When you're asked to reference an article, study, journal or book you're usually required to rephrase. Yet I didn't come to the point where my grammar knowledge is failing me (I blame my school, we were barely taught any grammar, grr). Which one of the following is correct?

• There are a number of different types of design methodologies
• There is a number of different types of design methodologies

Does the 'are' belong to the "methodologies" or does the 'is' relate to "a number"? Can you Englishsters help me out please?

Kids don't fornicate! The label "fuck" is related to my university, I'm still working on my damn dissertation and I'm still not done (deadline: Monday the 7th).