Take another look at the original sentence:

Mrs. Britton was grading papers at her desk, her students were slaving over their in-class compositions, sighing heavily and flipping through their dictionaries for the correct spellings of words.

You chose to fix it the correct way:

Mrs. Britton was grading papers at her desk while her students were slaving over their in-class compositions, sighing heavily and flipping through their dictionaries for the correct spellings of words.

Mrs. Britton was grading papers at her desk is a main clause. Her students were slaving over their in-class compositions is the second main clause. To subordinate the second main clause with the subordinate conjunction while is a perfect way to fix the problem.

Go to the next sentence.

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