Cliff and Clair are thrilled that summer vacation is over and that the Huxtable children will be going back to school. Rudy is bothered by a bully in her new first-grade class and doesn't want to go back.
Cliff buys a new juicer and is ridiculed by Clair for always buying new appliances and never using them. Rudy and Peter are bored with playing in the house and decide to make peanut butter and jelly sandwiches in the kitchen. Even though Cliff told her not to ever touch the juicer, Rudy puts grapes in it to make jelly and creates a huge mess.
The Huxtables plan a surprise anniversary for party for Cliff's parents. Cliff and Clair buy them a cruise around Europe, but Russell and Anna don't want to go. After dinner, the family puts on a musical performance for Russell and Anna, who are then presented with a portrait that Cliff and the family had professionally done.
Sondra is upset because her on-again, off-again boyfriend Elvin does not treat her with respect. Cliff and Clair convince her to go out with a boy named Daryl, whom Cliff takes an instant liking to because of his manners and the fact that he wants to go to medical school. Sondra has a good time with Daryl but decides to give Elvin another chance.
Denise invites her friend Suzanne over to observe the Huxtable family for a school project. Theo is smitten and spends the entire day trying to impress Suzanne, until his heart is broken when Suzanne's boyfriend shows up.
As Clair prepares the house for Vanessa's Halloween party, Cliff reluctantly dresses up to take Rudy trick-or-treating. Vanessa is excited that her school crush Robert shows up at the party but embarrasses herself by dropping a tray of drinks when he wants to dance with her. Robert calms her down and asks Vanessa to go steady with him.
Rudy joins a pee-wee football and impresses everyone in the Huxtable family with her skills. Clair is worried that Rudy will get hurt but is very excited when she sees Rudy score four touchdowns in her first game. In the championship game, the opposing team focuses all their efforts on stopping Rudy and beat Rudy's team by a large margin.
Denise gets her driver's license and wants to spend her savings on an expensive car, something that Cliff forbids her to do. Cliff's handyman Mr. Lucas offers to sell Denise his aunt's old car, which Cliff allows when he sees that Denise is a good driver.
Clair's sister Sarah announces to the Huxtables that she is getting married. Their mom Carrie and Clair teach Sarah a few things about marriage, while Clair's father Al and Cliff continue a chess rivalry. Al refuses to sing at Sarah's wedding unless Clair joins him.
Clair plans a romantic dinner for she and Cliff to celebrate the day he proposed. While Clair is getting ready, she breaks her toe on a chest and does not want to use a cane or be helped in any way. She makes a decorative slipper out of a paper bag to cover her walking boot, and the kids vote her as the "smoothest looking" between the two of them.
Denise's friend Michelle has a medical problem but is afraid to tell her parents, so Denise asks Cliff to talk to her. Cliff and Clair tell the kids not to be afraid to come to them with any problems.
Theo's least favorite teacher, Mrs. Westlake, requests a meeting with Cliff. Cliff invites Mrs. Westlake and her husband over for dinner, and Theo is shocked that Mrs. Westlake is very pleasant in public. Theo thinks she has come over to tell him that he failed the math test, but she wanted to see Cliff because she thinks she is pregnant. Mrs. Westlake informs Theo that he got an 89 on the test, and Cliff tells him to keep studying hard.
Clair learns that a painting by her great-uncle will be up for auction and wants to bid on it. Elvin, desperate to win over Clair after his sexist comments from their prior meeting, offers to cook the family dinner after the auction. Clair places the winning bid of $11,000 and gets the painting.
After studying together for a test, Vanessa and Robert are shocked when they both get a 'D' on the exam. Vanessa hides the test from her parents so she can go to a school dance with Robert. She steals Denise's sweater after Denise forbade her from wearing it, greatly upsetting Denise. Vanessa finally comes clean about the exam and is grounded.
Theo and his friend Cockroach have trouble prepping for an exam on Shakespeare's "Macbeth," so Denise tells them to use 'Cleland Notes' as a study aid. Theo passes the test but draws the ire of Clair, who tells him to read the play because she is going to give him her own exam. Unfortunately, Clair has difficulty remembering anything about the play herself.
Clair keeps Cliff up at night because she's upset about a water meter article in the newspaper. Cliff begins cutting upsetting articles out of the paper so he can get more sleep. Peter hides at the Huxtable house because he is afraid to go to the dentist. Rudy accompanies him for moral support, and the appointment goes fine due to the nice dentist.
Cliff convinces his father to play the trombone with his old band but is disappointed to see that Russell seems to have lost a step. Cliff's mother Anna gets him to play with more enthusiasm, and Russell brings the house down at a live performance. Meanwhile, the Huxtable clan becomes very irritated with Rudy due to her constant 'knock-knock' jokes.
Denise and Theo get into a car accident with a limo whose passenger is Stevie Wonder. Stevie, feeling bad about the accident, invites the family to his music studio to listen to him record. The family ends up providing backup vocals on a song, and Stevie sings a duet with Clair.
Cliff, finishing up a week of all-night shifts at the hospital, plans to sleep all day Saturday but is thwarted by a house full of his kids and their friends - Theo and Cockroach are comparing mustaches for a date; Vanessa and Robert are in the kitchen studying; Denise and her boyfriend Eddie are watching music videos; and Sondra and Elvin are arguing again because Elvin never shows emotion.
Cliff's friend Dr. Morgan comes to the house to discuss the hospital's annual charity benefit. Clair and Denise come home from their pottery class, and Clair's pot is a disaster that is subject to ridicule by Cliff and Denise. Dr. Morgan, seeing the love in the family, gets upset and confides to Cliff that his teenage daughter is a drug addict. Cliff helps Theo and Cockroach write a meaningful rap for their speech class.
Theo and Cockroach prepare for a math test and are upset when Mrs. Westlake is sent to the hospital due to complications with her pregnancy. Cliff delivers the baby successfully, and Theo's math class visits Mrs. Westlake in the hospital. Denise helps Vanessa to cover up a zit, and Cliff has a hard time teaching Rudy to ride a bicycle until Clair intervenes.
Theo's sisters are tired of him borrowing money and never paying them back. Cliff and Clair tell Theo to be better about this, and Theo tells them life will be easy for him because he's gonna be a model when he grows up.
Cliff's pinochle partner is sick on the day they are supposed to play against Cliff's dad and his friend. Dr. Foster, Cliff's college English professor, fills in and helps Cliff beat his cheating father for the first time. Theo buys a fake diamond ring for his girlfriend Tanya and is admonished by his family; in the end, Tanya really likes the ring.
Rudy performs chores around the house so she can save enough money to buy a new doll she wants. Cliff is asked by his old track rival Tailwind Turner to run on his charity relay team as the anchor. Cliff trains hard for the race and is very excited, until he sees that he is set to run against Olympic champion Valerie Brisco-Hooks, who smokes him in the race (much to Tailwind's delight).
Denise is getting close to making a decision about which college to attend. Vanessa wants her to go to an out-of-state college so she can finally have her own room, while Rudy is upset that another sister is leaving the house. Cliff's father continues to persuade her to go to Hillman, and Denise says she will announce her decision at dinner. Denise informs the family that she is going to attend Hillman, making the Huxtables extremely proud.