Since you provide no options, i recognize that this is a part of the story 'farewell to Manzanar'
The loyalty oath that referred in the lines refer to the Government's policy that require any person above the age of 17 to swear their allegiance to the united states.
I think the author include the hopscotch scene to highlight the innocence of the little girl who still has no clue about the complicated political matters that surround her
hope this helps
