Jack Powell suffers from an affliction that makes him grow four times faster than normal, so the 10 year old boy looks like a 40 year old man. After years of being tutored at home, Jack convinces his overprotective parents to send him to public school. The children don't know what to make of Jack, but with the help of his fifth-grade teacher, he makes an effort to win them over.

Cleavers are an all-American family living in Ohio - wise father Ward, loving mother June, teen-age son Wally and 8-year-old "Beaver" Theodore. Beaver hopes to get a bike as a gift from his father and to please him tries out for his school football team and he makes it, only to be embarrassed. The bike he gets is quickly stolen. Meanwhile Wally is trying to help his friend Eddie Haskell to get the heart of pretty classmate Karen, but Karen seems to like Wally more, and that leads to tensions between the friends.

Animals communicate with a boy while he's staying at his grandparents' farm and warn him about an impending foreclosure.