The high school years
Is there anything that your high schooler absolutely HAS to do (i.e. Algebra, foreign language, etc).
I don't have a high schooler yet, but the answer will still be no.
There are two misconceptions that make that question seem an obvious one to ask:
That there's some body of knowledge needed for success that can't be gotten without it being deliberately put there.
That body of knowledge is difficult to acquire and needs time and expert help to get it in.
The reason that 1) seems obvious is because that's what schools do. But schools use the methods they do because they have 1 teacher trying to teach 30 kids. She just physically can't help each student explore their interests. So teachers lead all the kids through the same material at the same time. Not because that's what's best for the kids but because it's what allows schools to provide low cost education. It's meeting a need of schools, not of kids.
The reason that 2) seems obvious is because of reason 1). Kids aren't learning what interests them. They aren't learning because they need the information. They're learning what someone has decided they need for the future. It's akin to someone making you memorize Mandarin Chinese even though you're becoming increasingly certain that you have no interest in China and don't want anything ever to do with it. That makes learning hard.
But if you look backwards over the lifetime of a happy person, they're happy because they're doing what they enjoy. If you turn that around, and allow kids to pursue what they enjoy, they'll end up happily pursuing what they enjoy.
It's really hard to design a school around several hundred kids pursuing what they enjoy. Especially so since parents are handing their kids over and trusting that the schools will help them. Parents understandably want feedback that the schools are doing their jobs. But when real learning is happening, there often isn't a lot of feedback. So, though schools claim to be serving kids' best interests, they're actually serving the needs of themselves and parents and others expecting feedback. Schools end up using very poor methods for learning because they couldn't function if they used what's best for kids.
So we end up with the false idea that school methods are the best methods for kids to learn. When in reality school methods are the best methods for schools to function.
When things are learned because they interest us and because we need the information right now, it's incredibly easy to learn. Yes, even Algebra :-)
I would like some input when it comes to homeschooling high schoolers. He is showing an interest to join the charter schools but I'd like to find out more information about homeschooling your kids in their high school years.
It depends. What does he want? What does he plan to do in college? Is he looking at charter schools because he thinks that's the only way?
I don't think in terms of preparing for college so much as living life and exploring what's interesting. College is then a way of exploring something in more depth and meeting people who have the same interests.
It also helps to not think of college as what happens when you turn 17. It takes the pressure off if kids realize they can attend any time they want. Colleges like older students because older students have a better idea of what they want to do with college. College to them isn't just the next hoop to jump through after high school.
If he's interested in something in particular, then I'd help him find ways to experience it for real, like apprenticeships or job shadowing. Think in terms of helping him explore his interests. That will give him a foundation for further exploring.
If he honestly likes subject-style learning (and isn't just choosing it because it's comfortingly familiar) there are also community college courses he could take. And lots of real books. (Like if he's interested in science I'd make sure he had a subscription to Discover magazine and cable and a TV Guide to find science programs.) Tutors. But preparing for college is just too vague and not really the focus of unschooling.
Have you read Grace Llewellyn's The Teenage Liberation Handbook? That's a good one to start with. The Teenagers Guide to School Outside the Box by Rebecca Greene is for kids in school but looks useful for kids out of school. And The Uncollege Alternative: Your Guide to Incredible Careers and Amazing Adventures Outside College by Danielle Wood.
And here's some websites about high school years and college.