Fair Use allows the full length of a movie to be shown during regular class time where only enrolled students and the instructor are present and in situations when viewing the movie in its entirety is required for the course. In an online only class, a professor cannot convert the full length of a movie to a streaming format without obtaining the permission of the copyright holder because according to copyright law the right to reproduce a copyrighted work in copies is the exclusive right of the copyright holder.
The TEACH Act [Section 110(2) of the US Copyright Act] does provide for the digital transmission of films for the purpose of distance education in limited circumstances. However, this act does not apply when a film's distributor limits use with their license, which always overrides any provisions of the TEACH Act. Streaming entire commercial, general release movies through classroom management systems such as Moodle is also questionable under Fair Use, and it is usually not possible to get streaming rights to commercial movies. Educational videos usually come at a cost that allow streaming rights.Thus, streaming of commercial films and educational films is on a case by case basis depending on whether a film is still in copyright or if it is from a vendor that requires a license to be signed for streaming rights.
Consult with your library liaison who can follow up for you as to the options for streaming a particular video and the availability of substitute copyright free videos that are available in library databases. The University Libraries provide copyright access to Kanopy, an academic video streaming database with over 26,000 educational documentaries and feature films, including portions of The Criterion Collection. Commercial films can sometimes be accessed through the Library's relationship with SWANK, but as this is not a very cost effective option an alternate can be to ask your students to view a film via Netflix, Amazon, or iTunes as part of their required resources for a class.