Natalie Flanagan Timeline and Summary

When the family first moves to Alcatraz, Natalie has been accepted into the Esther P. Marinoff School, which everyone thinks is the answer for her.
After one night away, though, Natalie is sent home from school and her family is told that she's not ready yet.
When she comes home, Moose is put in charge of watching her after school. She has a new doctor, Dr. Kelly, who suggests they take her buttons away, but Moose gives them to her to play with when his parents are gone.
While her brother is looking for a convict baseball, Natalie is left alone and makes friends with Onion—a.k.a. 105—a convict who's allowed to wander around since his sentence is almost up. She feels comfortable enough to let him hold her hand. Although this scares Moose a lot, it's the only thing that has ever made her seem actually happy.
After Moose finds them together, Natalie is kept indoors, which frustrates her; she asks repeatedly to go outside.
On her birthday, she throws such a fit that Moose lets her go outside. Moose and Piper follow her to her meeting spot, where she meets with 105 once more.
She seems to be doing much better with her new therapy, so the Flanagans schedule another interview at the Marinoff School. Unfortunately, though, Natalie's turned down.
Fortunately, thanks to Moose's wily ways, Natalie is accepted to the school in the end. We assume that this ends up doing very good things for her.