Wally becomes the chairman of the blind date committee for an upcoming dance. However, Wally quickly wants to resign from the position when he can't find anyone to go with the new girl, Jill Bartlett.

Ward and June allow Wally to babysit Beaver one evening, while they attend a party. However, things go awry when Beaver gets ready to take a bath he accidentally lets the bathtub overflow causing the water to leak onto the bathroom floor and into the downstairs ceiling.

A new school year has the bus service being extended to those students living in town. However, after not even a week, Beaver gets suspended from riding the bus after getting into a fight.

After leaving the cap off the ink, Beaver is grounded to the house for a whole day after the ink ruined some of Ward's papers. However, Larry and Beaver sneak out to the movies and when Beaver wins a bike, he must find a way to keep it a secret from his parents.

Beaver's class holds a ""Most Beautiful Baby"" contest and each student is supposed to bring in a baby picture. To make the deadline, June picks out a cute picture of Beaver at the last minute and sends it to Miss Landers, not realizing that the cute picture may cause Beaver embarrassment.

Ward saves an old pedometer from being thrown out and gives it to Beaver, but not before telling him a story about when he was a kid he would walk 20 miles a day. Taking the story literally, Beaver makes a bet with Whitey that he too can walk 20 miles in a day.

Larry and Beaver spend the day at lake which is where they encounter two kids who let them borrow their boat. However, little do Larry and Beaver know that the boat is stolen.

Inspired after teacher Miss Landers reads a poem to his class about trees, Beaver worries about the tree that Ward planted for him on his birthday in the old neighborhood and decides to bring it to the Cleaver's new yard.

Beaver gets a surprise when June invites Miss Landers over for dinner and Larry convinces him that something bad might happen. This leads Beaver to becomes a nervous wreck and tries to make sure his parents don't do anything to embarrass him. Meanwhile, Larry charges a quarter to anyone who wants to spy on Miss Landers eating dinner at the Cleavers.

Beaver has his fortune read by a machine and becomes convinced nothing but good luck is headed his way. However, he doesn't feel that way when Larry sets it up so that Beaver will have to fight a 5th grader, Sonny Cartwright.

Ward loans Beaver 25 cents but gives him a dollar, expecting 75 cents as change. However, Larry manages to convince Beaver to loan him the 75 cents and when Larry doesn't pay him back, when he said he was going to, a feud erupts.

Beaver buys a common magic trick but is disappointed by everyone's ""that's nice"" reaction, but he gets a totally different reaction out of Bengie when Larry and Beaver convince him that Beaver has been turned into a rock.

June's birthday has Wally and Beaver fighting over what to buy with the five dollars that Ward gave them. Wally buys her a wallet while Beaver buys an ugly blouse that June kindly thanks him for, but she has a hard time bringing herself to wear it.

Beaver wants to raise chinchillas and begins building a cage in the garage. However, when Beaver changes his mind, Ward tries his best to get Wally and Beaver the clean the mess up in the garage. Things get worse, when Ward unknowingly runs over some of the wood and nails that Beaver left laying around with the car, causing the boys to try to patch a flat tire before Ward finds out.

While Beaver is staying at the Mondellos, Larry sneaks a peak at his sister's diary and his mother discovers him and yells at him right in front of Beaver. This prompts Larry to run away, to Beaver's house, who secretly hides him in his bathroom.

A pet fair at school has Beaver feeling left out since he doesn't have a pet, but he tells everyone he does, a parrot. Meanwhile, Ward tries to find a pet for Beaver and buys him a hamster.

An upcoming test in history, Wally's weakest subject, has Wally studying all weekend and has Larry and Eddie coming up with a plan that will give them good grades on the test.

Ward allows Beaver to check out a book on his library card but when Beaver loses the book he becomes convinced that Ward will be put in jail, thanks to Eddie Haskell's wiseguy comments.

Eddie nominates Wally for class president and Wally has no interest in the position, that is until Ward gives him some encouragement. Wally quickly gets wrapped up in the election and his friends see a change in him, a change that prompts them to vote against him.

An old acquaintance of Ward's stops by and offers to paint the trim on the house. However, June and Ward are both apprehensive about the prospect of an alcoholic coming in contact with Wally and Beaver, despite the fact that he says he's cleaned himself up.

Both Beaver and Larry are forced into attending dancing school by their parents and after one lesson, they find that they absolutly detest it, like they knew they would. This prompts them to skip class next time and they hide out behind a barn until it's time to go home.

Larry is furious when Beaver leaves him out when he joins a club called the Bloody Five. To get revenge, Larry makes up a story that he is starting his own club and that people are waiting in line to join. This prompts Beaver to resign from the Bloody Five and he tries to join Larry's bogus club.

Wally lends his school sweater to Frances and quickly finds getting it back is going to be difficult since the girl keeps making up excuses. Things reach a boiling point when Ward and June overhear Frances bragging to her friends how Wally is chasing after her.

After seeing someone being hypnotized in a movie, Beaver sets out to do the same but Eddie wants to play a trick on Beaver and pretends Beaver has hypnotized him and Beaver gets scared when Eddie doesn't snap out of the trance.

After drawing Alma's name for a school picnic, Wally finds himself meeting her parents and her mother takes an immediate like to Wally and begins setting him and Alma up on numerous dates then turns around and accuses Wally of monopolizing Alma's time.