Because Jem, Scout, and Dill’s little to no insight about Boo they started playing games about him. In chapter 4 we learn about said game; it was when Dill, Scout and Jem would act out the stories they heard about Boo Radley. They would always start with Boo getting sentenced to the industrial school but his father not allowing him to go. It always ended with Boo stabbing his father in the leg with a pair of scissors. Later on in chapter 4 Scout believes it would be best to stop playing the game when Atticus walks in on them.
Boo does try to make effort to try to make friends with Jem, Scout, and Dill. As stated in chapter 4 Scout finds gum under a tree, said tree will play an important part in the story. We later find out it was Boo leaving them presents under the tree. Along with the gum Boo leave; a Indian headed pennies and in chapter 7 he leave them a ball of twine, 2 figures carved in soap that look like Jem and Scout, more chewing gum, a spelling bee medal, and a pocket watch. While Miss Maudie Atkinson's house was burning down in chapter 8 someone drapes their blanket onto Scouts shoulders. Jem realizes that Boo Radley put it on her, and he reveals the whole story of the knothole, the presents, and the mended pants to Atticus. Atticus tells them to keep it to themselves, stated in chapter 8, when Scout realizes that Boo