"I go to school during the week and work on the weekends."
Is "the" necessary?
*Not a teacher
In some cases, The can often be taken out. Eg I will do it [the] next time; [the] next time you do that kind of stuff, you will get sacked; etc
In American English, at least, you could omit the preposition, too: "I work weekends."
I was very surprised to learn that Brits say, "work at weekends." It doesn't really make any less sense; I've just never heard it before. Prepositions are so weird!