Whenever a phrase does not convey a complete thought on its own because it is missing the subject, the verb, or both, it is a sentence fragment. In other words, a fragment is a group of words that looks like a sentence but lacks something essential to make sense. An example of a fragment is: Wants to go (there is no subject).
"In every class" is missing both the verb and the subject, meaning it is incapable of expressing a full idea. Therefore, it is a fragment.
