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.