Beaver and Wally send away for an alligator and they secretly keep it in the bathroom. When the alligator falls ill, the boys get some advice from Captain Jack, an owner of an alligator farm. However, keeping him a secret is going to be hard, the alligator is growing and they need a new place to keep him without June and Ward finding out.

Beaver comes home with a black eye and Ward is upset when he learns that Beaver didn't fight back. This leads Ward to teach Beaver how to defend himself. Little does Ward know that the person who punched Beaver is a girl, Violet Rutherford, the daughter of one of Ward's co-workers.

After losing his lunch money for three days in a row, Ward gives Beaver one last chance by letting him handle his haircut money. However, when he loses that too, Beaver decides to give himself a haircut just days before he's scheduled to be an angel in a play.

The Cleavers have new neighbors, the Donaldsons, and June sends Beaver over to welcome them with a vase of flowers. However, when Mrs. Donaldson thanks Beaver by kissing him on the cheek, Beaver becomes convinced that Mr. Donaldson will kill him because he let a married woman kiss him, and it's all thanks to Eddie Haskell, who planted that idea in Beaver's mind.

June has had it with Wally and Beaver's fighting and demands they make a pact to be nice to one another and do things together. However, when each boy gets an invitation for individual social outings, they each attempt to break the pact.

Wally and his friends are trying to earn enough money to buy baseball uniforms. They put a plan into action by doing their chores at a slow pace in order to maximize their hourly pay. Meanwhile, Beaver, also wanting to be on the team, begins selling water to his family and neighbors.

Beaver has a crush on his teacher, Miss Canfield. When Judy, Whitey and Larry tease him for being a 'teacher's pet,' Beaver tries to prove them wrong and places a spring snake in her desk. However, Beaver has second thoughts and becomes determined to remove the snake before she finds it.

Wally and his friends build a clubhouse and Beaver wants to join. Although the dues are $1 for 8th graders, Beaver has to come up with $3 in order to join their club. How can Beaver earn the money?

Wally and Beaver dread attending dance school, so when suddenly Wally takes a liking in it, June and Ward are dumbfounded. It seems Wally has developed a crush on a girl named Penny and Beaver soon feels neglected and left out when Wally begins spending all his time with her.

When June goes on a trip to visit her sister, Peggy, June's Aunt Martha steps in and stays with Ward and the boys. Ward and the boys do their best not to hurt Martha's feelings, but Beaver has the hardest time when she buys him a suit, knee socks, a cap, and short pants and makes him wear the outfit to school.

Wally and Beaver want to win a fancy film projector. In order to get it they have to sell 24 bottles of perfume. However, the appalling aroma of the perfume quickly leads to zero sales and has Ward trying to think up a sales gimmick.

June and Ward make Wally and Beaver promise that they won't go to the movies and see a scary movie. However, Wally and Beaver are talked into seeing it, thanks to Wally's so-called best friend, Eddie Haskell. The movie has quite an influence on Beaver, who makes a voodoo doll, names it Eddie Haskell, and sticks it with pins.

After taking an IQ test, Beaver scores the highest in his class and Mrs. Rayburn suggests that it would be best if Beaver went to a special school where his abilities can be challenged. However, little does anyone know that everything is not as it seems.

Beaver is invited to Linda Dennison's birthday party and quickly discovers that he is the only boy that she invited. Fearing for his reputation, Beaver tries his best to get out of attending, but June and Ward are insistent, not aware of the situation Beaver's in.

The local bully, Lumpy Rutherford, has been picking on Beaver and Wally and, thanks to a story Ward tells them, they decide to play a joke on Lumpy. However, their ploy catches the wrong person—Lumpy's father and Ward's co-worker Fred Rutherford, is caught in the trap.

Wally and Beaver want to get brand new bike and they ask Ward for some money. He suggests that they earn the money. This leads Wally and Beaver to get a job delivering papers. Later, while trying to help the boys out, Ward and June inadvertently almost get Wally and Beaver fired.

After Ward's bragging about Wally and Beaver being responsible, Herb and Janet Wilson assume that it would be all right to leave their 4-year old daughter in Wally and Beaver's care while they go out to a party with Ward and June. Trouble begins when the youngster locks herself in the bathroom.

Ward tries to teach Wally and Beaver the importance of saving by giving them a piggy bank. The boys quickly save up a handful of change and are all ready to spend it on some baseball equipment. However, unknown to their parents, they change their minds and decide to spend the money on a most unselfish gift.

Wally goes away on a trip with the Boy Scout troop that he belongs to, leaving a lonesome Beaver behind. Finding his friends to be busy, Beaver takes up other means to make the time go by.

Wally begins to outgrow his "sloppy" faze and becomes much neater. This is noticed by Ward and June who try to encourage Beaver to undergo the same transformation. However, Beaver changing like that just seems too extraordinary of a task.

Ward becomes a bit jealous when Wally and Beaver begin spending time playing basketball at Willie Dennison's house after Willie's dad put up a backboard and a basket. This prompts Ward to do the same thing but it just seems like things are working against him being the perfect father.

Beaver makes a trade with Larry Mondello: a glass doorknob for a Chihuahua. Larry found the dog in his garbage can, so when Beaver brings it home, Ward immediately breaks the news that he's going to place an ad in the lost and found and that Beaver probably won't be able to keep the dog. Despite this, Beaver quickly begins to grow close to the little pooch.

Ward helps Beaver and Wally build a miniature race car powered by a lawn mower motor and Ward makes the boys promise not to use it without him being with them. Later, Larry talks Beaver into taking it for a spin resulting in being pulled over by a traffic officer.

While playing baseball in the street with Wally, Chester and Tooey, Eddie hits a baseball through the Cleaver's window resulting in Ward forbidding the boys to play baseball so close to the house. However, later, Beaver talks Wally into pitching one, but this results in a broken car window.

After a week long visit with their Aunt Martha, Wally and Beaver prepare to head home to Mayfield on a train. After talking Martha into letting them buy their own tickets, they discover they're short the money after spending it on junk food and find themselves wondering how they are going to get home.