Squidward is disdainfully watching Squilliam play his clarinet at a concert. When Squilliam finishes, Squidward leaves. He also hears someone say "He's so good he doesn't even have to play to be good!" As he walks out of the recital hall, he is mistaken for Squilliam and is then offered to teach a music class, to which he accepts.
Later, he comes to the music class wearing a wig, posing as Squilliam. He prepares his desk and a kid asks him if he's going to write his name on the board "like most professors do." Annoyed, Squidward tells the kid to write his name on the board. Shortly after that, Squidward discovers that SpongeBob and Patrick are in the music class he is teaching, which annoys him even more. SpongeBob and Patrick are then told that they are allowed to stay just as long as they behave themselves and keep quiet about Squidward's real name. Squidward starts teaching, but is interrupted by SpongeBob's laughter. When asked about it, SpongeBob tries to claim that Patrick was tickling his foot, though reveals that he was tickling his own foot. In order to avoid any more distractions, Squidward moves SpongeBob away from Patrick, but he keeps on laughing. When SpongeBob is told to stop tickling his foot, Patrick reveals that it really was him that time, much to Squidward's surprise.
Squidward starts teaching about musical scales by drawing lines on the chalkboard. Patrick then explains how they remind him of a railroad track he saw at a railroad convention last week, where he bought himself a conductor's hat. Then, he starts riding a mini train, only to get trapped in the trash can, though comes back inside a minute later.
Then, Squidward starts teaching the class about metronomes, much to the interest of SpongeBob and Patrick (though SpongeBob mistook it for a garden gnome). They start making a ticking noise and a news reporter suddenly comes in, wanting to do an interview with "Squilliam Fancyson," although he is soon more interested in SpongeBob and Patrick at how they are in a trance. Squidward then angrily kicks him out after mentioning about possible paranormal activity and SpongeBob and Patrick stop ticking when the bell rings. They forget where they are and they start calling Squidward by his real name, which upsets the rest of the class and they start to leave. Squidward blocks the door with his body and crazily claims that no one is going anywhere. However, the police come in along with the news reporter, the music teacher, and Squilliam Fancyson himself. After noticing that Squidward does not have a unibrow, he is quickly arrested for "impersonating a genius," leaving SpongeBob and Patrick alone with the metronome ticking and them, while in a trance, going "tick tick tick..." along with it.
The real name for "impersonating someone" is identity theft.
The plot of this episode is somewhat similar to the plot of "Artist Unknown" (Squidward teaches a class, to which, SpongeBob happens to apply). This time, SpongeBob is not the only student in his class and Patrick appears as well.
At the beginning, that was Squidward in the same sweater he wore from "Snowball Effect."
Although it was established in older episodes that Squidward's middle initial is J, in this episode, however, Squidward says it's Q.
When the fish said he was commuting from upstate, it could possibly be a reference to Tom Kenny's hometown, Syracuse, New York, which is one of Upstate New York's major cities.
When Patrick rides into the trash, Squidward exits the building, and places the can outside. Later, when both the police and the news crew come into Squidward's classroom, they enter the same door that once led to the outside, but instead, it lead into a hallway.