In Chapter 9, Kit is helping teach the children to read when she gets in trouble for having them act out a little play. When she's upset because people are so angry with her, she goes for an emotional walk—and ends up meeting Hannah Tupper, who becomes important in her life.
In Chapter 10, Kit finds that Nat already knew Hannah, and that they are friends. This puts the two of them back in close contact.
In Chapter 11, Kit starts teaching Prudence to read, and, later, realizes that Mercy loves John Holbrook.
In Chapter 12, Hannah sees Nat again, and they become more friendly still.
If you have to choose just three:
1) Kit meets Hannah.
2) Kit and Nat grow closer.
3) Kit starts to teach Prudence.