This will only work if you have permission to open the other Outlook mailbox.

Log in to Office 365.

At the top right you will see your account icon. Click on this icon and you will see the following options.

Select Open another mailbox

In the pop-up window, type the name of the account that owns the mailbox you want to open. For example if your class has an email address of (this is a fictional address) then type in 5AB and you will see a search list. 

Select the mailbox that you want to open and click Open. The mailbox will then open for you.