@Jessievitarelli i am the same way. writing it down just uses up time and i can visualize it while still getting the answers correct and under time. i have not had an issue so far with doing this in any section. i think i remember him saying that the reason to diagram is to eventually be able to intuitively solve.

This is how i learned it in 6th grade:

any prepositional phrase in the sentence cannot be apart of the object, noun or verb. while they are important to the sentence, they are not important in the structure.

eg: "to provide adequate facilities", "for physical education", "for the grant" these are disqualified from being the subject, verb, and object in the first sentence bc they are in prepositional phrases

how you know when to cut the prepositional phrase off: if the verb/preposition are answered or another preposition is presented

hope this is helpful!