WeVideo is a tool for recording all kinds of video (including screencasts & green screen). Log in with your Google account. Training & Support
Screencastify is a basic tool to create screencasts. They save right to you Google Drive. Add it to Chrome by clicking here. See this doc for instructions on how to gain free unlimited access.
Quicktime is an option for Mac users. It's already installed on your computer and it has a screen recording option. Instructions
Loom is a free screen recording tool that's easy to use because it comes without all of the bells and whistles of other platforms. Create an account, record your video, share your video with students.