Breakdown of Мы начали урок за пять минут.
пять
five
урок
lesson
минута
minute
за
in (within a period of time)
Questions & Answers about Мы начали урок за пять минут.
Why do we use за here instead of just saying пять минут?
This ties exactly into your current lesson! The verb начали is perfective, meaning it focuses on the completion of the action. To say how long it took to achieve that result (getting the lesson started "in five minutes"), you must use за + the Accusative case. If you just used the bare phrase пять минут, you would be talking about how long an ongoing action lasted, which requires an imperfective verb.
What case is пять минут in after the preposition за?
The preposition за for time expressions requires the Accusative case for the whole number phrase. The Accusative form of пять looks exactly like its dictionary form. After that, the normal number rules apply: the number 5 requires the noun following it to be in the Genitive plural, which is why we use минут (from the feminine noun минута).
How would the sentence change if we used the imperfective verb начинали?
If you used the imperfective past tense начинали, you would drop the за and just use the bare Accusative for duration: Мы начинали урок пять минут. This completely changes the meaning from "it took five minutes to start" to "we spent five minutes in the process of starting the lesson."
Why doesn't the word урок change its ending if it is the direct object being started?
Урок is indeed the direct object, meaning it is in the Accusative case. However, because it is a masculine inanimate noun (a non-living thing), its Accusative form looks identically to its Nominative (dictionary) form. It only changes if it is a living thing (animate) or a feminine noun.