If you open the work and click "Open in new window" via the 3 dots in the top left
At the top you can then choose to "Open with Google Docs"
You can then edit within Google. Once you have finished go back to the assignment in Google Classroom and click "Add or create"
Then select "Google Drive"
You will then find the work under "Recent" or you can browse your whole Google Drive via the "My Google Drive" tab. Then click add.