I'm assuming "core" subjects means the curriculum courses you have to attend until the last few years of education. I think the school core subjects are sufficient as they are now, which is Mathematics and English/Literature. All subjects should be on the schedule for the first few years of secondary school (idk wtf it is in America, Middle school?) to introduce the students.
The only exception I would make is Gym class. I know many teens are overweight but the only thing that class did for me was discourage me in partaking in any sport. Schools should make kids aware of the opportunities of sports outside of school, but should not be forced to do it in school. Unfortunately this won't change anytime soon. The rule changed in my whereabouts during my last years of school. I really needed the time to study, but no, have to go to gym class. Most people didn't turn up or got lectured after getting caught trying to skip it.
Another thing, students should really be taught the ways of money, and not through presentations that put you to sleep by visitors, but just the usual class teachings. I left school without having a clue how to pay bills and pension saving, or how to obtain my funding at universities, and my parents weren't wise enough to inform me themselves just because they had a simple and very non academic lifestyle.