Describe what happens in the middle of the story of The Hunger Games?

The question is a little bit vague because it doesn't define what chapters would be the "middle" of the story. It's also unclear as to whether or not the question is asking about a single event or a set of events that happen in the middle third (or so) of the book.
In a very broad stroke, the middle of the story narrates events that happen during the actual Hunger Games competition. The beginning of the book would be Katniss volunteering to go to the games and being coached by Cinna and Haymitch. The middle of the book has Peeta and Katniss fighting for their lives, Rue's friendship with Katniss followed by Rue's death, Katniss shooting Cato, and Katniss running from the sadistic traps set by the game makers. Additionally, the middle parts of the book have Katniss realizing that she has to play up the romance with Peeta in order to secure gifts from sponsors.