One day, while running past the Radley house on her way home from school, Scout notices some gum in the knothole of a tree overhanging the Radley's fence. And on the last day of school, Scout and Jem find two old pennies in the same knothole. Jem stares at the Radley place, deep in thought.
The three-year age difference makes Jem more perceptive than Scout. Scout doesn't know who's leaving the presents, while Jem's long look at the Radley House indicates he senses Boo is trying to connect with them.
Dill arrives for the summer. After an accident rolling a tire that leaves Scout lying on the pavement right next to the Radley's house, Jem comes up with a new game: they're going to act out Boo Radley's story. Atticus catches them playing. Jem lies and says they weren't impersonating the Radley's.
In the children's' blissful world, Boo Radley continues to be their obsession. Jem's lie to Atticus shows that though he thinks of himself as an adult, he is still selfish and irresponsible like a child.