Ally, a sixth-grade student, argues with her teacher, Mrs. Hall, about her writing assignment. She's supposed to be writing about herself so that when Mrs. Hall goes on maternity leave, the new teacher can learn about the students. After some arguing, Ally covers her paper with the word "why?" She admits to the reader that she doesn't want to write because she can't read or write, no matter how hard she tries.
Mrs. Hall's baby shower is a few days later. Ally gives her teacher a card with yellow roses on it, but Mrs. Hall doesn't look happy. Shay, the class bully, reads the card and tells Ally she's dumb. Ally is confused until the principal, Mrs. Silver, asks her why she'd give a sympathy card at a baby shower. In the office, Mrs. Silver asks Ally to read a poster on the wall. There are two hands reaching towards each other and Ally pretends she can read it. That afternoon, as Ally tries to do homework at the restaurant where Mom works, Shay and her friend Jessica stop and tease Ally about being dumb. Ally draws in her Sketchbook of Impossible Things, where she records things that will never happen in real life.
That weekend, Ally's big brother, Travis, takes Ally coin shopping. The salesman doesn't take Travis seriously, which Travis uses to his advantage to buy a valuable coin for himself and a special dime for Ally. The coins were minted in the year that their Grandpa, who died about a year ago, was born. Ally is shocked to learn that coins are only valuable when they're different.
Ally's new teacher, Mr. Daniels, asks his students to participate in a show-and-tell exercise. Keisha, a new student, brings in a homemade cupcake while Albert, a hulking and science-loving boy, brings in water. Ally shows the class a steel penny, which Dad gave to her before he was deployed.
A few days later, Mr. Daniels hands out notebooks. The students can write whatever they want, and he won't grade them, so Ally tests this by drawing a black cube. Mr. Daniels asks her about it and when she says it's a dark room where she can be invisible, he tells her he's glad she's not invisible. At lunch, Ally accepts Shay and Jessica's offer to sit with them. She's jealous of their friendship bracelets and wants to be a part of something. Ally goes along with them when they tease Albert, though she apologizes to him the next day.
Backstage before the holiday concert, as Mrs. Muldoon passes out bouquets to the girls, Keisha touches her flowers and a bud breaks off. Mrs. Muldoon takes the bouquet away from Keisha while Shay makes snide comments. Ally breaks her bouquet in half so Keisha can have flowers, though Mrs. Muldoon takes her flowers away too. The girls become friends and begin eating lunch together.
Ally begins to try to do her writing assignments, as she realizes she'd like Mr. Daniels to like her. Travis refuses to help Ally with them, saying he can fix cars like a natural but writing isn't something he can do. Ally turns in one assignment, worried Mr. Daniels will think it took minutes. When he asks her how long it took, she tells the truth: hours. Despite this, Ally contrives ways to get out of writing, including faking a broken arm. Noticing that Albert is always covered in bruises, Ally invites him to eat lunch with her and Keisha. She learns that Albert gets free lunch. Shay and Jessica tease Albert, Ally, and Keisha about being misfit toys, and Ally begins to think that, just as many of the misfit toys are normal save for odd names, there has to be more to her than just being a "slow reader."
Later, Ally and Keisha learn that Albert always wears a shirt that reads "Flint" because Flint is his favorite Star Trek character. Flint lives on his own planet to escape unkind people, and Albert finds this appealing. That afternoon, Keisha and Albert come to Petersen's for ice cream. Keisha tries to convince Albert to fight the bullies who beat him up every day, but he refuses.
During a vocabulary lesson, Mr. Daniels asks a volunteer to describe the difference between "alone" and "lonely." Ally raises her hand and though her answer is brilliant, she still feels like she did something wrong. Later, Mr. Daniels asks the class to write about fictional heroes. Ally makes up a hero Roy G. Biv, who symbolizes the color spectrum. Though she writes her paper, Mr. Daniels asks her to tell him about Roy G. Biv rather than just writing about him. He praises her for being an out-of-the-box thinker. After Ally presents her hero to the class, she overhears Shay and Jessica talking about friendship bracelets and learns that Shay is actually selling them.
Mr. Daniels announces that he created a poetry competition and names Ally the winner. Though she's initially happy, she soon realizes it's a pity award and runs out of the room, humiliated. Keisha gives Ally a pep talk and says it's silly to want to fit in.
After school one day, Mr. Daniels asks Ally if reading gives her headaches and if letters move on the page. She's shocked when she picks up on the fact that these things aren't normal. He offers to teach her chess after school to excuse her from homework. Ally accepts. A few days later, while on a field trip at the Noah Webster museum, Mr. Daniels joins Ally outside and tells her that she might have dyslexia, a reading disability. He tells her that she can learn to read, she just needs to learn in different ways. Ally feels hopeful for the first time. Over the next few weeks, Ally begins to play chess and undergoes testing. She does have dyslexia and agrees to stay after school more to work with Mr. Daniels on reading as well as chess, which she finds fun and easy.
One afternoon, Ally, Mom, and Travis Skype with Dad. Ally tells Dad about all her good news, but Travis doesn't have much good news: his new manager at the auto shop wants him to look things up in the book before performing repairs, which Travis finds difficult. Ally continues to stay after school with Mr. Daniels, who guides her through an exercise to show her that anything is possible. Ally keeps the paper that reads "possible" in her pocket. Later, while hanging out at Albert's house, Ally confides in her friends that she has a hard time in school because she has dyslexia.
On Monday, there's a sub at school. The sub says out loud that Ally can draw instead of write, which encourages Shay to say mean things. Ally feels so betrayed that she writes a note for Mr. Daniels saying she won't stay after school anymore. The next day, Mr. Daniels apologizes and assures Ally he never meant to hurt her. A few days later Mr. Daniels assigns a logic puzzle, and Ally is the only one to solve it without help.
A week later, Jessica nominates Shay for class president. Shay nominates Ally. Ally agrees to run and spends all night writing a speech. The next morning, with Albert and Keisha's encouragement, Ally tells her class she wants to magnify everyone's voices. Shay promises impossible things, like bigger lockers and longer recesses. Mr. Daniels counts the ballots in front of the class and surprisingly, Ally wins. The next day, Ally receives what she believes is a love letter from Max, a popular classmate. She can't read it but later that afternoon, she discovers that Shay actually wrote the letter as an attempt to embarrass Ally. Max finds out as well and is very upset with Shay.
Mr. Daniels gives Ally a chapter book to read. She later completes a detailed diorama of the house from the book, prompting Mr. Daniels to tell Ally he's proud of her—the first time she's heard this from a teacher. That evening, as Ally draws in her Sketchbook of Impossible Things, she muses that her sketchbook isn't the only thing that makes her happy anymore. Travis asks Ally what she's learning with Mr. Daniels, but he refuses Ally's offer to teach him some of her new tricks.
During a social studies unit, Mr. Daniels asks the class to tell him about famous people including Albert Einstein, George Washington, and Henry Ford. Mr. Daniels explains that it's believed that those people had dyslexia, but they still changed the world. Ally is shaken to learn that others likely thought they were stupid too. Over the next few days, Ally's classmates tell her that they think it's cool she has dyslexia. Shay's followers even stop participating in the bullying and leave their friendship bracelets on Shay's desk. Ally tries to reach out to Shay, but Shay responds meanly.
As Ally, Keisha, and Albert walk home from school, the bullies attack them. Albert finally fights back and Ally realizes that he cares too much about his friends to let others hurt them. The next day, Ally goes to Mrs. Silver's office with a note. Ally asks Mrs. Silver to read the poster with the hands, which reads that it's brave to ask for help. Mrs. Silver apologizes for not helping Ally sooner and tells Ally that she's won student of the month. After school that day, when Travis arrives to pick up Ally, Ally realizes that Travis must be dyslexic too. She runs and asks Mr. Daniels if he'd help Travis learn to read, and Mr. Daniels agrees. Ally feels as though anything is possible.