「これ（教材）は前にやりました。」って英語でなんて言うの？

The teacher has a busy timetable and has forgotten that you have already looked at this topic in a previous lesson. You may say: "We've already covered this," or, "We've already done this," meaning that you worked through this subject matter before. "Teacher, sorry, I think we've already covered this." "Oh, very sorry. Well let's skip to the next unit."

Using the word 'finished' describes that you have already completed the material and you would now like to move on to new material.

*We have covered that already. Can we do Discussion Materials instead. This means that you do not want to do the material that the teacher was suggesting because you have done it before but you would to do something else. To cover something means to have done it before.

"We've already been through this section." This is a way of telling your teacher that what you are going over has already been covered (been over/through). "We haven't looked at this section yet." This is a way of telling the teacher that you haven't read or looked at something yet. And is a polite way of drawing (directing/guiding/showing) their attention to it.

"to go over (something)" - this means to go through the material, to complete to the material A. I don't want to do this lesson, teacher. B. Why not? It's very useful to know. A. I've already gone over this in another class, but I haven't done the other lesson yet.

While you go through a lesson you are "using" the material to learn so you can say "We've used this material before." "We haven't used this material yet." You can say "haven't used yet" which means that until now this material hasn't been used. "We completed this exercise already." You can say "complete this exercise" to indicate that you finished or completed a specific exercise already.