"I send a note to the teacher."
Translation:Yo le mando una nota a la maestra.
It's being accepted without the "le" now.
As "alezzzix" mentions, with spoken Spanish it's often left in.
"le" is for the indirect object - to the teacher/a la maestra
the direct object is the note
"La" is the singular feminine direct object pronoun (and "lo" is the singular masculine direct object pronoun), but "le" is the singular indirect object pronoun (both masculine and feminine). You need an indirect object pronoun here because it answers the question "to whom do you send a note?" You send it to her.
The direct object answers the question "what do you send?" You send the note.