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Is this always the case in the United States?
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They are extracurricular in that they are in addition to the curriculum that the school teaches and in that they are not required for graduation, though some Phys Ed is required.
This varies a great deal by city and state, but typically high schools require a certain number of credits to graduate–4 credits of English, 2-4 of science, 3-4 of math, maybe some fine arts, foreign languages and speech–the specifics vary. Often, these include one or more years of physical education.
If a student attends class all day for 4 years, they will have more slots to fill than they need to graduate–electives. It’s not uncommon for participation on a sports team to count as an elective: the sports team meets during the last class of the day, say, and continue practicing after school gets out (especially in season), so that the kids can get 2-3 hours of practice and still get home in time for dinner and homework. This can substitute for as many years of PE credit as they need, but if they stay on the sports team afterwards, those later classes don’t actually count towards graduating. Other students may use those elective slots to be on the newspaper staff, leave early to go to a part time job, or be in the band or choir.
As far as the actual competition goes, most of those take place after school with a few exceptions: IME Golf and Tennis almost always take place during the day because the schools can’t rent the facilities during times popular with people with jobs. There are also many tournaments for basketball, baseball, volleyball and softball where a group of teams will play all day. Most people that play in those sports miss 2-6 school days a year for tournements. The worst offender in my district, though, is baseball, where, since there are no lighted fields here, games have to start right at 4. Since we don’t get out of school until 4, that means that for away games the boys leave at 2, missing at least one academic class. Baseball players can miss that last class 15 times in the spring. It’s awful.
So sports can take place during the day, but they are still basically extracurricular.
As a side note. “no pass no play” is a law, at least here in TX, not just a guideline.