Sound recordings such as CDs, electronic audio, or live broadcasts (radio, cable, satellite or internet) can be played at an educational institution without a public performance license as long as:
Live music (as opposed to recorded) may be performed without permission under these conditions as well.
Non-educational uses of music such as for concerts, dances, entertainment, sporting events, ambience, music on hold for telephones, etc. require licensed permission through the Society of Composers Authors and Music Publishers of Canada (SOCAN) and Re:Sound. SOCAN represents the performance rights of composers and music publishers while Re:Sound represents the performance rights of artists and record companies. Re:Sound and SOCAN are distinct organisations that represent different groups and as such, both are required to be compensated.
Permission must be obtained to reproduce a song that you do not own/did not create. The Canadian Musical Reproductions Rights Agency (CMRRA) can grant a mechanical license that authorizes the reproduction of music on CDs. For reproductions of the musical work in audiovisual productions (films and video), they can grant a synchronization license.
Under Fair Dealing, you may copy up to 10% of a sound recording (for example, to stream in your online class).
Streaming an entire work in your online class requires a license.
You may want to consider using royalty-free or non-commerical music (see above resources).