I have not used Google Classroom with Canvas with the same class, but can offer some advice because I have used both.
Think of Google Classroom as really Google Drive Management for your Classroom. It is a superb tool for teachers who want to send out a template of a Google doc/slideshow/sheet to their classes to allow students to make a copy of it to begin their work from. Another big plus of Google Classroom is that when students turn in a Google doc/slideshow/sheet, the document is automatically shared with you (as an editor) and the students' edit rights are automatically revoked until you return the assignment back to them. So we have two really nice thing here in Classroom that aren't built into Canvas.
1) Make a template Google document/slide/sheet for students, so when they click on it they have their own copy.
2) Automatically share doc and automatically revoke their edit rights on the Google document/slide/sheet when they submit it and then you can return it when you are ready.
If all you want to do is #1 then you don't need to use Google Classroom. Simply make your Google file (view only, anyone with link can view) and change the end of the URL removing edit and everything after it and replacing it with copy.
For example:
Change: https://docs.google.com/spreadsheets/d/1tO8F3H7wp65DYpKP3k1N6bCfAfY5shygLX0M8KVkFgk/edit#gid=0
To: https://docs.google.com/spreadsheets/d/1tO8F3H7wp65DYpKP3k1N6bCfAfY5shygLX0M8KVkFgk/copy
Now use the new URL with copy at the end to give that link to your students in Canvas. When they click on it they will be prompted to create a new doc from yours, that is theirs to edit with no worries of them changing your master document. This works on all Google doc types (docs, spreadsheets, slides and drawings).
If you want to do #2 using Google Classroom is the best way to accomplish this (for now). However, you could still use Canvas as your home base for this. You would setup the assignment in Google Classroom then go over to Canvas make it an assignment in Canvas (with no submission options) instruct your students to turn in the assignment in Google Classroom and provide a link to the Google Classroom Assignment like: https://classroom.google.com/c/Mjg0MDc1/a/MTE4NTMzMDU2/submissions/1
If Google opens up the API they are using for Classroom Canvas and other companies could leverage it to provide the same functionality inside of their systems. So for now, you can use both or just Canvas. When having my students turn in Google Docs in Canvas I made the assignment a URL submission only and trained my students to share their docs so (anyone with link can comment) then submit the share URL in Canvas. This allowed me to use all the Google commenting features right in SpeedGrader, but it does not revoke their editing rights. I suspect Google does this so a student can not make changes after the due date. If that is ever an issue you could instruct students to share the Google doc with you as an editor before they submit it and then look at the Docs revision history to see if they have edited it after the due date.
Hope this helps and I hope to see Google follow Canvas' model of open APIs
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