While Schoology is CCSD's learning management system, Google Classroom is the document management system that you've been looking for. Google Classroom can be accessed via their website, Chrome extension (which includes easy access to the website and more) or their Chrome app. Google Classroom is a Google product so it functions best using the Chrome browser.
Why would I use Google Classroom? What does it do?
Google Classroom a rare tool which our team can "advertise" by highlighting some of the challenges which emerge when teachers use Google Documents in a classroom setting. The days of getting large amounts of emails when kids share a document with you, students not naming the document they share with you correctly, students not giving you the rights you need within a document, and the organizational "chaos" which can occur in a teacher's Google Drive are over. Google Classroom addresses all these things and much more.
As far as the basics and what it does, our team has written pretty extensively about Google Classroom's features in the past. Please refer to posts on our blog here, here, and here.
As with everything Google, there are ongoing updates to this tool. Some new features, which came along with the release of their Chrome Extension, included the ability for a teacher to quickly and easily push a website to their students (even when the students aren't on the Google Classroom site.) Another fairly recent update included the opportunity to add a co-teacher to a course as well as the chance to host a classroom discussion within Google Classroom. We're not exactly sure what's coming in the future for Google Classroom, but we do know it is going to continue to get better and better (when it's already great!)
Many educational websites are making Google Classroom integration simpler by adding an easy to use "Share on Classroom" button/function. Definitely keep an eye out for this. Sites like Quizlet (example shown below), PBS, American Museum of Natural History, Discovery Education, Duolingo, TIME Edge, and Zaption already have this feature available with many more to come.
Google Classroom is only available in educational domains and is currently accessible to all CCSD teachers and students. Several hundred K-12 teachers in CCSD are already using it and the overwhelmingly positive feedback our team consistently receives about Google Classroom speaks for itself.
Where can I learn more?
With four million plus users of the Share to Classroom Google Classroom Extension and over ten million teachers and students already using Google Classroom throughout the world, resources and tutorials are fairly easy to find. Here's a list to at least get you started.
EdTech advocate, Alice Keeler, shares about Google Classroom extensively. Follow her on Twitter here and read her Google Classroom blog posts here.
Google Classroom's review page on Graphite.org (including a review by yours truly)