The children's relationship with Boo in Part One is important in that this subplot sets the stage for the greater trial coming up in the adult world around them. Jem, Scout and Dill first have their own notions about Boo and none of them are very complimentary. They are drawn to him by a sort of morbid fascination which has been encouraged by all the hearsay going on about Boo's domestic violence and night rambling. They are prejudiced against Boo in the same way that the white community is prejudiced against Tom Robinson.
Their attitude changes, however, when Boo patches up Jem's pants, then leaves little presents in the hole in the tree. Boo takes the first step to be the children's friend, even if it is only a "virtual" kind of way.
The children's attitude towards Boo Radley begins to change even if they still have a gut fear of him actually coming around. When he puts a blanket around Scout as she watches Miss Maudie's house burn down, Jem and Scout are later in awe that they actually got that close. They harbour some fear of him even if they are aware that he means them no harm.
At the end of Part One, the reader can't help but wonder if the children aren't doing a better job at overcoming their unjustified fears and prejudice than the grownups in Maycomb. Also, a correlation arises between Boo and Tom, two innocent people ostracised and "found guilty" in the Deep South mind frame of the 1930s.
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