You can upload photos of handwritten work to Google Classroom via the computer version of Classroom or the mobile app.
If you're using the computer interface, you'll need top open your Chromebook or laptop's camera app to snap the photo, and then upload the image to Classroom. With the mobile app, you can snap a pic directly from the Classroom app. (Hint: even if students are primarily using a Chromebook, they can use a phone or tablet as their homework uploader.)
Save your teacher's eyesight! Make sure all writing is dark, big, and easy to read.