Each of the main characters faces major and minor problems. For Mrs. Olinski, the major problem which she must face involves rediscovering her confidence as she returns to teaching after being rendered a paraplegic in an auto accident. Some minor problems with which she must contend include dealing with impudent, unruly students such as Hamilton Knapp who wish to challenge her authority, and choosing the best children to make up her academic team.
A major problem faced by Noah Gershom is having to spend the summer with his grandparents at Century Village, a place that appears to him to be "a theme park for old people". Minor problems related to Noah's experience at Century Village include having no tux to wear after he volunteers to fill in as best man at a wedding, and being forced to write a thank you note to his grandparents after his summer experience.
The toughest problem Nadia Diamondstein must face in the story is overcoming her bitterness after the divorce of her parents. Smaller problems Nadia must resolve include having lost contact with her old friends after she moves away to live with her mother, her anger at Margaret Draper for her role in facilitating the divorce, and, at school, dealing with Hamilton Knapp's mean-spirited attempts to eliminate her dog Ginger from her role as Sandy in the school play.
Ethan Potter's major challenge in the story is deciding how to deal with Julian Singh on the schoolbus. Julian is different, and the object of much teasing by the other students, and Ethan does not want to be associated with him. A minor problem Ethan must face is the fact that he lives in the shadow of his older brother Lucas, who, as "a genius (and) a star athlete", is a tough act to follow.
The major problem faced by Julian Singh is the cruelty of the students at school, who ostracize him and treat him with malice. Julian has not been raised in this country, and his mannerisms and dress are different from what the others are used to, and so he is the target of bullying and cruel pranks. Minor problems Julian faces include having his correct answer about acronyms questioned by the judges in the Academic Bowl, and being caught in the classroom as he tries to erase a classmate's unkind reference to their handicapped teacher on the board.