Question

The teacher ------ us a new lesson (teach/taught)

Answer 1

The correct option for the blank in the given sentence will be as given below:

The teacher taught us a new lesson.

The verb in the sentence is ‘taught’. Its tense is ‘Past Simple’. Past Simple Tense form ends in ed. Simple Past tense form of the irregular verbs is used. We use did+V1 form in negatives and questions. The form ‘teaches’ is Simple Present tense. We use the present simple for:

•states, things staying the same, facts and things that are true for a long time: We live quite near.

• repeated actions: We come here every week.

We usually use expressions such as ‘always’, ‘everyday’, ‘often’, etc. with Simple Present Tense. Since there is no such expression in the sentence, hence we used Simple Past Tense form ‘taught’. 

Answer 2

The answer to be filled in the blank is "taught"
So the whole sentence will be like " The teacher taught us a new lesson"
This is because the nature of sentence showing that the something happen in the past . So the past tense terms will be applied here, in the Past simple/indefinite tense we use the second form of verb so the "Taught" is the words to be filled here in the blank.
While the "teach" word representing the present simple tense there is no expressions showing that it's a present tense .