The phrase "to take attendance" is used in American English. In Britain, teachers usually "call the register", so you might as well add it if it hasn't been an accepted answer yet.
This is also known as roll call, where "the teacher checks the roll".
I thought this can work for "puts a check mark next to every present pupil's name", but I asked one of our British colleagues and she says it doesn't work for that... Maybe "marking down". But even then, that's a slightly different thing, we could say that it means "Nauczyciel zaznacza obecność".