When using Google Classroom, students must type their full email address when logging in to Google, which is:
If logging in to Google Classroom on a phone or tablet, students might have to log out of all other personal Google accounts on the device. Once logged in successfully, they should be able to log back into those personal accounts.
Students can access Google Classroom through the SSO
(You will need to make sure your pop-up blocker is turned off when using the SSO.)