If you are a teacher and you cancel today's class, is it correct to say 'I gave off to students'?
No, that is not correct. The verb to "give off" means to emit something, typically a scent or gas.
Any of the following would be correct:
- I gave the students the day off
- I gave the day off to the students
You could be more specific and say "I gave the students the class off" (although that's an unusual construct) or less specific: "I gave the students time off".