In elementary school I read The Girl Who Owned a City by O.T. Nelson. The protagonist is Lisa, who is 10. I've read books with teenagers as protagonists, and I've read an autobiography of a girl who was under 10 when the book started but an adult when the book finished. What books have protagonists who are age 10 or younger during the whole book?
The main character and the narrator age out slightly, but.... https://www.amazon.com/Edwin-Mullho...Y_1_10?s=books&ie=UTF8&qid=1493221741&sr=1-10 a novel by Steven Milhauser: Edwin Mullhouse: The Life and Death of an American Writer, 1943-1954, by Jeffrey Cartwright. This is an adult novel about a ten year old novelist who died at 11. Damn good book, which is also in part about the process of biography through the eyes of the 11 year old biographer.
Well, kids books are very likely to have a protagonist who is under 10, so I am presuming you mean adult books, and not works like James and the Giant Peach or The Magic Tree House or even the Narnia collection. So, off the top of my head... Scout in To Kill a Mockingbird Bob Starrett is the narrator of Shane. He's 10 or 11. Though your definition of protagonist may vary. Lord of the Flies -- All of the kids, I think. Jack Hawkins in Treasure Island. Is he 10? He might be older... I've never read The Kite Runner, but that kid is pretty young... That's all I've got...
I watched The Lion, The Watch, and the Wardrobe (the title might have "&" rather than "and") animated movie a lot when I was young. There were four child protagonists, and I'm confident the oldest two were older than 10. That may be the animated non-Disney movie I've watched the most times. One time in elementary school the day before a vacation, they showed some of the movie, but they never finished it. I didn't mind because I knew how it ended. The only other books of those I read were James and the Giant Peach, but I didn't think about whether James was older than 10 or not, and To Kill A Mockingbird. Scout is a good answer. I hated The Catcher in the Rye, and Holden was older than 10. I read Hatchet and I just read a preview saying the boy was 13. I read Number The Stars and I just read a preview saying Annemarie was 10. Barnes and Noble's previews of Flour Babies, Sadako and the Thousand Paper Cranes, and The Wave don't say how old the kids were. I just thought of the series with titles like "Ramona Quimby, Age 8."
Matilda by Roald Dahl. I think she's 6. Tales of a fourth grade nothing. 9. Where the Red Fern Grows. 10. I don't think he ages much by the end, but it's been a long time.
Well, he narrates the story as an adult after feeding and nursing a hound dog who reminds him of his old dogs, so he's older then.