Translation:Next time, pay attention during the lesson.
A lot of times I try to translate the sentence literally to get a feel for how sentence structure works in Russian compared to English. I have no idea how this sentence works.
We can break it into three parts. The first one is 'next time', it's an adverbial modifier:
- в = in
- следующий = next (accusative case, singular, masculine; modifies раз)
- раз = time, when 'time' means 'instance, try' (accusative case, singular, masculine)
The second is 'pay attention', it's the most important thing in the sentence:
- будь = be (imperative form of the verb 'to be')
- внима́тельна = attentive (nominative case, singular, feminine; short form; it's feminine because the sentence is addressed to a female)
The last one, «во вре́мя уро́ка», is also an adverbial modifier:
- во = in (it's a form of в used before some consonant clusters),
- вре́мя = time, when time means 'period, duration' (accusative case, singular, neuter),
- уро́ка = of [the] lesson (genitive case, singular, masculine; nominative-case form is уро́к).
Hope that helps.
Can the "в" in в следующий раз be left out with no change to the meaning? I feel like I've heard it said like that.
Saying it without "в" is not correct grammatically, but it can be encountered as a colloquialism. Also some native speakers pronounce this preposition in such a way that it is almost inaudible, especially for learners.
Strikes me as something a teacher might equally likely say, but they probably want an imperative.