Peggy Arnold, and younger twin siblings Mike and Nora, are living with a harsh aunt and uncle after their parents are thought to have been killed in a plane crash. Aided by Jack, an orphan boy they have befriended, they run away to an island on a nearby lake, and together they make a new home constructed with the branches of a willow tree, this much-loved "living house" being one of the highlights of the story. However, living on one's own turns out to be far more difficult than they thought, and, along with a lot of fun and happiness, they also suffer a lot of hardship – especially when winter sets in.