Is rain fell a complete sentence?

In English classes, we're expected to advance from simple sentences to more complex sentences. So, while "Rain fell" technically has a subject/noun and a verb, most people would expect more information, such as an adverb to make the sentence sound more complete. For example: Rain fell hard all day.

Consider these simple sentences:

I walked.

He ran.

Both are more complete when we add information:

I walked to the store.

He ran home to get some money.