Screencastify is an ultra simple screen recorder that will supercharge the way you communicate at work.  Record, edit, and share HD videos in seconds.

Here are some video tutorials for using Screencastify.  The first YouTube link shows you how to add the extension.  The free version only allows you to create a five minute video, but you can create as many as you want.  (The unlimited costs $29.00 and the only two things I have used this for are for longer videos and trimming up videos.)  Then you can upload them to Google Classroom.  The extension button on my laptop is a pink arrow, on the video it looks a little different.