As the result of custom, more than by strict rule, many verbs require that the object is placed between the verb and preposition and not after the preposition.There are time expressions like to be on time which require that time be said after on. This expression means having arrived at the required moment. Students looking to find an exact opposite to that may be disappointed knowing there is no "to be under time" but there is "to be late" which by the way is the opposite of "to be early".
Is it important for the student to know what parts of speech he is using to describe the lateness or earliness? Well if he wants to understand that these are best said using adverbs of time, or to be able to explain how people can talk about how they can arrive before or after a set time, then it is advisable that he know some grammatical structure.
One thing that I have noticed is that when teaching an analytical person who is often but not always likely to want to reason the origin of the language out, that person will want to know why one can say "to sleep in" to express the idea of a person staying in bed late in the morning as opposed to saying "to sleep on". If a person is looking for a translation which he will inevitably do because he has always reasoned in that language, if he is French he will be thinking of something like having " a big morning" and there is nothing about a big morning by sleeping in.But the French have interpreted "sleeping in" as in having an extended morning so that is another rationality that unfortunately has not hit the English language.
To get the person understand the choice of preposition in the expression, I gave an explanation that "sleeping in" could mean being under the covers and on the mattress and so stick to the classical sense of the preposition in but the person can also continue his sleep without being "in" anywhere. So if the person were to use the preposition "on" that would signify something entirely different and that is the person continued sleeping.
It would be good for the teacher to explain the use of on with other verbs to suggest a continued extension of that verb. So to go on would mean to continue going and therefore the student would understand that to sleep on would mean to continue sleeping and not sleeping in late.