When the babysitter cancels at the last minute, Ward and June leave Wally in charge while they are out of town overnight. They have a bathroom mishap in the new house when Beaver takes a bath.
Beaver needs a baby picture for a class project. June comes up with one where he doesn't have any clothes on and mails it to Miss Landers without showing it to him first.
Impressed by Ward's tales of walking 10 miles each way to school as a boy, Beaver takes his dad's old pedometer to school and bets his friend Whitey that he can walk twenty miles in a day, just like his dad.
Beaver and his friend Larry Mondello end up at the Mayfield police station after they are tricked by two older boys into using a stolen rowboat while picnicking at Friends lake.
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 Cleavers' new yard.
Beaver's last penny from his allowance buys him a ticket from a sidewalk weight/fortune telling machine that predicts good luck for him, making him think that, as a result, he can beat up the school bully.
Beaver is forced to break his promise to bring home the change from the dollar his dad gave him to buy a 25-cent notebook, after his unreliable pal, Larry Mondello, takes the money to buy a notebook for each of them, and pays off an old debt with the rest.
Not wanting to hurt Beaver's feelings when he gives her a tacky blouse for her birthday, loving mother June promises Beaver that she will wear the blouse to a mother's club tea. But June wears another outfit instead, unaware that Beaver's grammar school class will also be at the tea to sing a special song.
To impress his teacher and friends, Beaver fabricates owning a pet parrot to bring to the school pet fair but finds out that he can't afford to buy one when he goes to the pet store to make good on his claim.
When their plans to cheat on the history exam are foiled, sneaks Eddie Haskell and Lumpy Rutherford try to make it look like high-scoring Wally was the real cheater.
Eddie Haskell convinces Beaver that the "library police" will soon come to arrest Ward after Beaver ignores the late notices for a lost library book he checked out with his father's library card.
After Eddie Haskell nominates a reluctant Wally to run for sophomore class president against Lumpy Rutherford, fathers Ward and Fred try to fulfill their own ambitions through their teenage sons.
A middle-aged man named Andy stops by the Cleavers seeking work as a handyman. Ward agrees to hire his friend, despite June's concerns that Andy is an alcoholic and may influence Wally and Beaver.
Beaver and Larry are forced to attend a series of high-class dances. After the first one, they decide to ditch them. Then they meet a young cowgirl and ride a horse.
Beaver regrets joining the secret "Bloody Five" club without his friend Larry, when he finds out that Larry has joined an even more secret club, the "Fiends."
Ward and June start to worry when it looks like the matchmaker mother of Wally's school picnic date, Alma Hanson, is arranging for young Wally and her pretty daughter to spend too much time together.
Beaver and his friend Larry Mondello find a lost wallet stuffed with money, turn it in to the police station and hope that no one claims it so they can split the loot.
Beaver finds it a challenge to write a fifty word composition for a school assignment about his mother's life as a girl, especially when his classmates' mothers' lives seem much more exciting than June's.
The Cleavers' and the Rutherfords' picnic day turns into embarrassment for Beaver when a snapshot of Violet kissing him on the cheek appears on the cover of Ward's company magazine.
Wally is sure that carefully hanging his jacket in his closet will keep it clean for an upcoming dance, forgetting that he shares the closet with a younger brother whose middle name is trouble!
When Ward gives Wally permission to get a job, Wally discovers that there is more to making money than just selling ice cream bars and that allies come from unlikely places.
When Beaver's teacher Miss Landers assigns the class a book to read Ward suggests Ivanhoe, one of his favorite boyhood books. Impressed by the tale of knighthood, Beaver forms his own knight club and sets out to defend his neighborhood.
Wally considers it an honor to be inducted into a popular school club but has second thoughts when he finds out what his part will be in the club's annual play.
Over breakfast on the last day of school before summer vacation, Beaver and Wally sneak a peek at the gift June bought for Beaver to give to his teacher. The embarrassed boys find a lacy slip, and not knowing that the department store made a mistake and that his gift was supposed to be handkerchiefs, Beaver must decide whether to give Miss Landers the slip or nothing at all.
When Wally and Eddie coach Beaver's summer football team and give them a secret play to use against the opposing team, Beaver finds out that the best way to keep a secret is to not tell it...to anyone!
