GitHub adds a number of mailer headers, so you should be able to define filters based on these, to filter things from separate projects or lists into different folders/labels.
If your classroom notifications come from a specific organization you can filter them using
In gmail, you can type
list:<your-organization-name>.github.com in the search box, and then click the little gray triangle immediately to the left of the blue search button:
That gives you a pre-filled filter configuration, and there's a link at the bottom right that says "create filter with this search". Click that and tell it which label to send these to.
Another thing you can do is turn off the "automatically watch new repository" setting in the https://github.com/settings/notifications page on Github.
Then you'll still get notifications for repositories you watch, but you won't automatically get notifications for every single new repository created in any organization that you are a member of.