Which sentence is grammatically correct?

The chosen sentence is grammatically correct because it properly uses the past tense of the verb "give." In this structure, "gave" accurately indicates that the action of giving the assignments occurred in the past. Additionally, the subject "the teacher" is correctly matched with the plural noun "students," showing that multiple students received their respective assignments.

The correct use of past tense is essential in conveying that the action has been completed, making this sentence a clear and effective way to communicate the intended meaning. This aligns with standard English grammatical rules for tense agreement, subject-verb agreement, and pluralization. The other options fail to meet one or more of these grammatical criteria.