Review the item:
Unaware that his alarm clock had not rung, Levi slept under warm blankets while Professor Ribley tought the semester's most difficult algebra concept to the students who had arrived to class.

The third verb, tought, is the problem. This sentence requires the simple past. Teach is an irregular verb; taught is the correctly spelled form.

Verb Simple
Present
Simple
Past
Past
Participle
teach teach(es) taught taught

Had rung (not is an adverb), your choice, is perfectly correct. Before you continue, review the rules for irregular verbs.

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