Overhearing a frustrated Ward muttering about ending up in "the poor house", Beaver wonders what it means to be poor and begins a quest for poor people, making new friends and teaching the whole Cleaver family an important lesson.
Distracted by a construction company digging holes, Beaver and buddy Larry Mondello are late for school and decide to skip classes altogether to avoid getting yelled at by the principal. But when the hungry boys head for the nearest supermarket for lunch they find themselves on a live, promotional television program, unaware that Wally and June are watching them from the television in Wally's bedroom.
When the television breaks down over a week-end, Ward encourages Wally and Beaver to read Mark Twain's classic book, "Tom Sawyer". But things don't turn out quite as they planned after the boys try to use fictional Tom's technique to paint the Cleaver garage doors.
While Beaver and his small toothache wait for the results of a dental X-ray, he's convinced that he will soon have a painful experience after mean-spirited Lumpy Rutherford tells him that, to make more money, the dentist will drill a deep hole no matter how tiny the cavity may be.
Beaver believes he's been unfairly reprimanded for accidentally breaking Wally's track trophy, takes his Dad's offhand comment to find new parents literally, and with pal Larry Mondello's encouragement, heads for an adoption agency to see if he can do better.
Excited about possibly moving to a bigger house in a new neighborhood, Beaver tells his whole third grade class. But when the house sale falls through, embarrassed Beaver doesn't know how to break the news to his friends, especially after they throw him a surprise farewell party...with presents!
Beaver rescues Wally's broken typewriter from the trash, gets reliable Gus the Fireman to fix it with his "special oil" and starts a newspaper with his pal Larry. But Wally soon regrets tossing the now smoothly working machine and demands the newsboys return "his" typewriter.
Wally is the envy of his friends when pretty Mary Ellen Rogers invites him to her school cotillion. But they don't know what Wally soon finds out...Mary Ellen has entered them in a "cha-cha" contest and Wally doesn't know the steps.
Beaver forgets he's been invited to old friend David Manning's birthday party, is embarrassed to give David what he considers to be a "baby" toy that June bought for him at the last minute, and must think fast to come up with a more appropriate gift.
Beaver isn't worried that he doesn't have any money to spend at the carnival after his best friend Larry Mondello promises to pay the way. But conniving Larry has spent all of his allowance too and, sneaking money from his mother's sewing basket, throws it out the window and arranges to have Beaver "find" it.
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.