Professor Everett's three rambunctious children scare away another housekeeper. Suddenly at the door appears Nanny, unbidden and undaunted, bringing mystery and magic to a family that doesn't know how much they need her.
A new girlfriend of the Professor thinks that Butch and Prudence are not grounded in reality and should be involved in her children's therapy group. Butch tests whether there is a tooth "elf" by not telling his father when he loses a tooth.
Nanny suggests a family picnic on a lovely Spring day. The family members all have other ideas until their plans are mysteriously thwarted. Just when they are all ready to go on their outing, another problem pops up. Nanny keeps the picnic and fun going on anyway and they have a great Saturday together.
The Professor is contacted out of the blue by an old college girlfriend and isn't sure he's ready to see her again. Prudence's favorite balloon pops and she doesn't want to risk losing a new balloon by inflating it.
Hal feels too much pressure to complete various projects and school work, with a big science competition being foremost, it's making him irritable and miserable. Nanny offers a good luck piece, that acts like a magic amulet that restores his confidence so much he no longer worries at all and becomes careless.
The boys tell Nanny that Arabella was insulted and then challenged to a race, but Nanny is having none of it. "Old cars are not meant to be raced." Professor Everett comes up with an alternative - feed the data into the computer. The problem is computers can't account for the human element.
Prudence's kite gets stuck in the tree of the local haunted house. The children discover how the house is being "haunted", by whom, and why. Then they have to decide whether to expose the information or keep the secret.
Prudence wishes for a new part in the school play on the first evening star. She finds that she doesn't like what happens for her wish to come true. It turns out to be the best outcome in the end and everyone is happy with their parts.
Professor Everett has to file a report on conservation of the Blackhawk Wilderness Area. Nanny discovers the children have never been on a campout. Each excuse the professor makes is mysteriously overcome and the family heads into the wilderness where nothing goes as planned.
Professor Everett encounters a tough lady professor who espouses women's lib and challenges his authority. Meanwhile, Francine challenges Hal on the baseball field when she turns out to be a better hitter than he is.
It's a rainy day and the children think it will never end. The professor tells them about a time when it rained two weeks and he and his brother built a canoe in the garage. The children decide to build a raft to sail on Squaw Lake.
The professor has a date, but when the replacement sitter shows up she is not suitable at all. The only solution seems to be allowing Hal to fill in. At the restaurant Professor Everett begins to have second thoughts as he overhears and imagines all the things that can go wrong.
Butch raises the ire of a neighbor as part of an initiation of the Oak Street Marauders. Peabody wanted to press charges, but the police talk him out of it. A visit by the whole family doesn't make progress, so Nanny comes up with an idea to try to warm Peabody up o the human race.