When Wally starts dating Julie Foster, the daughter of a teacher, Lumpy and Eddie tease that Wally is only seeing her to curry favor with her father, especially when Wally is later assigned to Mr. Foster's English class.
When Beaver decides to be a writer, Ward gives him a diary, encouraging him to write down his thoughts and daily activities and assuring Beaver that no one would read it without permission. But when Beaver is late coming home one night his worried parents break the lock on his diary, hoping to find a clue to where he might be and, instead, getting quite a surprise.
After being warned against roughhousing by the track coach, Eddie and Lumpy start a towel fight in the school locker room and the coach walks in just as Wally throws a towel. But when the other boys deny any wrongdoing, Wally takes the punishment alone and must tell his parents that he is suspended from the upcoming track meet that the whole family planned to attend.
Jackie, a friend from Beaver's old neighborhood, comes for a week-end visit and the excited boys look forward to the fun of playing the same games they used to play years before. But Beaver and Jackie soon find that their interests changed as they each grew older and the week-end doesn't turn out quite like they planned.
Beaver loses his fear of a possible operation to remove his swollen tonsils when Ward reminisces about his own boyhood tonsillectomy. In fact, Beaver is so impressed by Ward's story of ice cream, pretty nurses and gifts that he can't wait to have the operation himself...even if he doesn't need it!
When the local pet store has a tropical fish counting contest with a collie pup as the grand prize, Beaver and his friend Gilbert agree to enter together and share the puppy if they win. But slick Eddie Haskell starts working at the pet store and claims to know the winning number...will Beaver want to win badly enough to cheat?
After finding Ward's old drawing tablet, Beaver volunteers to make a poster for a class project on Colonial America, hoping that his talented dad will do it for him. But Ward only offers his son advice and encouragement and, even though his friends make fun of his art, in the end, Beaver is glad that he painted the poster by himself.
When the Cleaver's former housekeeper, Mrs. Manners, is unavailable she sends her teenage daughter Margie to help June part-time after school. Ward is amused when smitten Wally skips track practice to spend time 'helping' pretty Margie but June worries when Wally neglects his homework.
Lumpy and Eddie try to sabotage Wally's efforts to help new kid Dudley fit in with the school crowd but, when they invite Dudley to a popular girl's party just to embarrass him, Dudley turns the tables on the sneaky pair.
Arithmatically-challenged Beaver is mystified by a better than average grade on his report card, unaware that dastardly duo, Eddie Haskell and Lumpy Rutherford, altered the card en route to Ward's desk drawer.
Gilbert convinces Beaver that they should both make an ugly face when their class picture is taken. Beaver does it, but Gilbert doesn't. It doesn't get discovered until the picture has already gone to press to be in the school yearbook.
June is distressed when a series of trades with school friends nets Beaver a pet rat and when Ward tells Beaver to get rid of the rodent, Beaver sells the rat to Violet Rutherford. But, in spite of Violet's protests, Fred Rutherford demands that Beaver refund Violet's money and take the rat back, unaware that another member of the Rutherford family has also developed an affection for the furry little guy.
Wally's worries that little brother Beaver will disrupt the first teen party held at the Cleaver's house are realized when, on the way to the Whitney's house for a sleepover, Beaver takes a dare from Whitey to find out if there really is soup in a steaming billboard bowl.
Beaver and his friend Gilbert volunteer to collect Community Chest donations from the neighborhood so that June can attend a school open house with Wally. All goes well until the boys stop for ice cream and Beaver puts the money he collected into his back pocket...the one with the hole in it!
At first, mowing lawns seems like an easy way for Beaver and his friend Gilbert to earn extra money for summer, but no one seems to want their services and bad advice from Wally's friend Eddie results in an angry neighbor. When discouraged Gilbert opts to deliver newspapers instead, even after a nice lady offers to pay the boys $5.00, a determined Beaver decides to try once more; but what will he do when her check bounces?
When Beaver buys a wrecked 'coaster car' from Eddie Haskell, Wally pitches in to help his little brother fix it up and school chum Penny Woods promises him the wheels from her old doll buggy. But Beaver forgets his tools when he goes to Penny's house to remove the wheels and panics when he runs into his best friends, Gilbert and Richard, while trying to sneak the buggy home.
Wally takes his responsibility seriously when he is left in charge of the Cleaver household while Ward is in St. Louis on a business trip but isn't sure he can fill his father's shoes when Miss Landers sends Beaver home from school with a note for saying a bad word.
When Wally and his girlfriend, Evelyn, frequently double date with Evelyn's older sister, Judy, and her husband, Tom, Ward and June worry that spending so much time with the happy couple will make Wally forgo college for marriage ... especially after Ward's chance encounter with the girls' father reveals that Wally and Evelyn may be secretly going steady.
At breakfast, Ward and June convince Beaver to bank his birthday money instead of buying the model race car he really wants; but when Uncle Billy's ten dollar cash gift arrives in the mail later in the day, sneaky friend Gilbert urges Beaver to keep the money a secret and use it to buy the car.
When Ward and June are away, Beaver and Gilbert play in the car and it ends up rolling down the driveway into the middle of the street. A cop comes by just as Wally is moving it back into the driveway and gives him a ticket for driving without a license and has to go to traffic court.
Beaver and schoolmate Gilbert don't know if they should tell their English teacher that they scored highly on a pop quiz because the questions were the same as the ones they had memorized the night before from one of Wally's old tests.