In which type of mathematical proof are axioms and logic used to prove or disprove conjectures?

A mathematics teacher of Class II gives the following word problem on addition to the students: 'A bag contains 4 mangoes and 6 more mangoes are put into it. How many mangoes are there in the bag in total?' This type of word problem belongs to which of the following structures of addition?

A teacher wrote the number 308 on the blackboard and asked the children to read it aloud. A child said, 'It is thirty-eight.' Which of the following is the most appropriate strategy to rectify the error made by the child?