Wil Wheaton Riding a Kitten/Dragon/Unicorn into Battle against an Orc John Scalzi

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"money management, law, politics, first aid, and sex education"

I'd change money management to "responsibility" and keep first aid and sex education, and those should definitely be the domain of parents.

Law and politics are so convoluted that no one person really understands them, but a teacher with a degree in such things has a better chance at teaching them then the average parent, and the parents with law degrees probably don't have the time to teach those intricate subjects.

Math is a given, at least basic math. I think our schools take too long working our way up to Algebra, though. I was doing basic Algebra in first grade: 5 + x = 10 or 10 - x = 5, those kinds of simple things. Most schools don't even try to teach Algebra until at least 6th, if not 9th. That's a terrible waste of time, waiting that long. All the math we need to know could be finished by the time we're in 6th grade, and then those extra math classes would be replaced by...

More science classes. We don't have nearly enough science. I mean, we could have way more classroom time spent doing engineering and research experiments to SHOW science to young students rather than spending almost the entirety of our science classroom time with our noses in books. Ask anyone what they loved about science, and even people who hated science classes loved the beaker experiments in Chemistry and the Egg-Crash-Car in Physics. And all that math we learned from 1st to 6th would be put to work in real conditions with the extra science class time, meaning that we'd be seeing how the math works in the real world, like calculating the ballistic trajectory of a baseball or a cannonball, rather than merely learning concepts that feel completely separated from it.

History and literature should be combined. Most of history can be taught either through books, both fiction and non-fiction, and around books. There are tons of books that are topical to their time period that would fit this perfectly. One that comes to mind is "To Kill a Mocking Bird". There is so much US History that surrounds that novel that can be taught alongside the novel itself that it makes more sense to combine the lessons rather than treat them separately.

Now, English classes... Something has to be done very differently here, because we don't need 12 years or more of English, and too many of those years seem to do nothing for a large portion of the population that appears to be remaining at a low literacy level despite all that extra effort. I'd suggest rolling those lessons into the Science and Lit/History courses. This is similar to the math classes, where the student would learn math better by applying it in science class. Science has tons of official documentation that can be taught as part of those courses, and Lit/History would be studying various kinds of things like biographies, journals, poems, epic stories, etc. Having a separate English class is overkill with the possible exception of Business Writing, specifically for things like writing a resume or an official letter. Technical documentation in general would be covered in Science class.

While I'm at it, let's fix the school year schedule. We currently have a system that wastes part of the year in a long summer break, then wastes a part of the school year reviewing the past material that the students have forgotten BECAUSE of that long break. There should be more 2 week holidays throughout the year, none longer than that, and no review periods. That would give us almost 50% more time learning new things, and could have us graduating High School by the time we're 12-14, and have a college degree at 16-18. We spend way too much time in school, when we could be working full-time in good jobs from 18 on.

Our school system is horribly broken and needs a complete overhaul. Unfortunately, it's so entrenched that I doubt what needs to be done will ever happen.

One thing you can learn in school is the difference between infer and imply.

I have very strong feeling on this subject. To keep it short, I am leaving out personal choices and sticking to two topics: Math and Life Skills.
Math needs to be way accelerated. Skip Geometry. Algebra early. College level calculus senior year. Students can opt out after basic algebra.
Life skills should be taught even if it is as lame as the Health classes I took on junior high.

"How to speak with your fellow humans": a course on conversations, dialogs, eye-contact, how to wait your turn, etc. without once staring dumbly at a smart phone.