After taking an aptitude test, Bart is held back a grade, and Lisa is skipped ahead, landing them in third grade at the same time, and in the same class. Tension develops between the pair, but they are forced to work together when they become lost on a school field trip.
The family is bored with reality shows on the six major networks. Luckily, Bart has a suggestion: buy a satellite dish. They do when Homer makes money from betting on a horse named No Risk. Eventually, they buy a satellite system with over 500 channels. Homer and Bart get addicted to it, leading Bart to not study for an important achievement test that is about to occur, even as Lisa is studying. During the test, Bart begins hallucinating, showing what he's seen on TV in the school. Once the test is done, the results are in: Lisa passes the test and goes up to the third grade, but Bart fails the test and is held back to the third grade, where they meet their new teacher and sibling rivalry ensues.
In third grade, Bart and Lisa each have their own results. While Lisa has a hard time adjusting to the conditions of third grade, Bart does well, although only because he has memorized the answers rather than actually knowing the material. Their new teacher, Mrs. McConnell, chooses to clamp their desks together, assuming that Lisa needs Bart's help to adjust. Bart gives her some homework tips for their geography homework but Lisa doesn’t want Bart’s help. One day, when the results of a test are handed, Lisa is appalled to discover not only that she got an A-, but Bart got an A as well, a better score than her. Bart says that the test was easy because it was the same as the year before. Lisa proclaims that Bart cheated but Mrs. McConnell warns Lisa not to tattle on other students, and changes Bart's grade to an A+ on the spot, which makes Lisa cry. Later on, their relationship worsens especially when Marge makes them embarrassing fanny pacs for a field trip to Capital City. As part of a buddy system everyone chooses a buddy. Bart and Lisa both pick different kids but Mrs McConnell puts them together because they are not supposed to pick their buddies out loud. On the way Bart does punch buggy on Lisa, who gets him back. When the third grade gets in on it, they all end up having sore arms after they arrive. As they cross the street they have to hold hands and some kids passing by call the two a couple. When they are at the Capital building, they hear that the flag for the state Springfield is an embarrassment (it contains a Confederate flag, despite the state being from the North), and their teacher assigns for homework an assignment to design a new flag. Lisa calls Marge as she designs her flag, which says "To Fraternal Love". On the phone, she complains about and makes fun of Bart, unmindful of the fact that Bart is overhearing the conversation on another phone. A vengeful Bart then changes the flag.
The next day, Bart, Lisa and the other third-graders hand over their flag designs to the Governor. When the Governor sees Lisa's flag, she starts crying and displays the flag, which now says "Learn to Fart" and has a butt crack added to Lisa's rising sun design. This appalls Lisa, as Bart innocently admonishes her for making the Governor miserable. Later, Lisa lashes out at Bart, and when he provokes her, she snaps and strangles him à la Homer, causing them get in a fight and roll down a hill into the river, missing the bus heading back to Springfield. As a result, the two wind up getting lost in the forest. They continue to fight with Bart continuing to call Lisa stupid while Lisa continues to strangle him.
Back in Springfield, Principal Skinner informs Homer and Marge that Bart and Lisa are missing. He says that they will not spare any expense to find Lisa but when asked about Bart, he simply says they are looking for him, but have already elected a Class Clown pro tem (Milhouse) in Bart's absence. They go to Capital City to find them, but Bart and Lisa are confronted by a family of hillbillies, who save them by driving them back to Capital City. Marge is ecstatic on seeing her children safe and sound. Principal Skinner, worried about the effects of placing Bart and Lisa in the same class, suggests that they return to the "status quo" - both Simpson kids go back to their proper grades.