Google Classroom is an tool that Google created for Google Apps for EDU schools which allows for easier transfer and assignment of files in Google Drive. More information can be found here: https://www.google.com/intl/en-US/edu/classroom/
Hope this helps!
I have a "beta invite" to Google Classroom. I understand that to use Google Classroom, you must have an Google email account associated with your district. At this point, my students have not been able to do much with it. I think the problem is that my district has staff and student email addresses on different domains. I spoke with our district tech director and asked to have the email addresses on the same domain (perhaps with students on a sub-domain.) I am still waiting. I've been told my students can submit assignments through their Google Drive and these will show up in my Google Drive associated with that class. I think this could be a convenient way to make a class "paperless."