In To Kill a Mockingbird, the five (5) most important events before chapter 13 are, in order of importance:
1) Atticus agrees to defend Tom Robinson. This causes anxiety for the family: Scout gets in trouble at school. Aunt Alexandra will have to come to live with them. This event sets up the entire second half of the book.
2) Jem nearly gets shot by Nathan Radley as he retrieves his pants. Jem nearly dies, but it shows how desperate he is not to disappoint his father.
3) Scout begins school. Her first grade year is spent spinning her wheels. She learns nothing and only gets in trouble for trying to help. The education system is backwards, much like the social outlook of the town.
4) Arthur Radley takes an interest in the kids, and vice versa. They try to get him to come out, and he does: he leaves soap carvings for them. Little do the know that he will serve as a protector for them. He is the grey ghost who will save Jem and Scout at the end. Foreshadowing.
5) Jem and Scout go with Cal to her church. The kids see how tight the black community is as they raise money for Tom Robinson's wife. This field trip is invaluable: the kids learn more from Cal than they do in any other setting up until now.