Let's say I have a school that uses Salesforce to track its students data. 
Now I want to add the functionality that the 40+ teachers can enter the grade to the students records.

Of course I cannot advice buying full accounts for all teachers.

What would be good ways to get this input? I would very much appreciate links to tutorials or minimal working examples.

For demonstration (and learning) urposes, let's assume, that every teacher can visit a public website, fill in his name and the course and add the grade.