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.
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'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.
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.
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.
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!