Translation:After the history lesson we went home.
This sentence tells what happened after the history lesson. Yours tells when we went home. I think the distinction English makes between these two forms is the same that Russian makes with the analogous structures.
It means something very similar. It's not the same. Linguistically, I think one can say that the topic ("theme") and comment ("rheme") differ. It's up to the course contributors whether they accept both versions, but I don't think there's a particular reason to arbitrarily change the emphasis of the sentence in the translation. There is a strong tendency in Russian to put prepositional phrases relating to physical location at the beginning of a sentence. It is frequently the case that the most natural English rendering has a different word order. I don't think this applies in nearly the same measure to time expressions, however.
I think пошли may be a generic term of 'going home' here, and 'walked home' is emphasized by adding пешком at the end?
It’s in genitive (родительный падеж), since that’s the case the preposition после takes.
- history lesson = a lesson on a historical subject: a battle, a crisis, a political movement
- lesson history = compiled history of lessons taught, for example in Duolingo's spaced repetition system
if i say мы ходили домой it simply means we went home. if i say мы пошли it means that we went and we are stll there. is it correct?
Interesting question. I would think it's likely ok. We don't use the word "lesson" that often in American English. What does "урок истории" refer to exactly?
I didn't understand you last sentence. К чему относится/что означает фраза "урок истории"? Right?
There is a classroom. Pupils are sitting at their desks and write. A teacher is standng by the blackboard and talking about history