Q. Can I show Netflix movies in my classroom?
It's not usually a good idea to use Netflix streaming or DVDs in class. Currently Netflix does not allow for the public classroom display of their streaming videos. Please see Netflix Terms of Service for more information.
Most likely this question has more to do with contracts than it is a matter of copyright. If you do decide to use Netflix in the classroom, it would behoove you to contact Netflix and get the permission to do so in writing.