A complete sentence should have three elements: a subject, a predicate and meaning on its own (independent clause) whereas sentence fragments are incomplete sentences since they are missing any of the elements described for a complete sentence.
1 We hurry to the ice: sentence// this sentence has the 3 elements: subject (we), verb (hurry) and can stand by its own to have meaning.
2 and skate as fast as possible: fragment // this is an incomplete sentence since it is missing the subject (who) and meaning on its own.
3 Try to catch each other: fragment// this is a sentence fragment since it is missing the subject and does not have meaning on its own
