Thirteenth Child by Patricia C. Wrede
Eff is the thirteenth child in her family, so everyone thinks she is unlucky. Her Uncle Earn is especially mean about it. Eff's twin brother, Lan, is the seventh son of a seventh son, so everyone thinks he is lucky. People want Lan to learn magic, so he can be a powerful magician, but no one lets Eff learn. But when the family moves out west to the frontier, everyone's lives change.
Eff can learn magic, and no one knows that she is supposed to be unlucky. But Eff still has problems. She feels that everything bad that happens is her fault. When a sudden problem comes up, can Eff realize that she is not destined to fail?
*Book 1 of 'Frontier Magic'*
Next book: Across the Great Barrier