According to @sbjdorlo some years ago, one of her kids did get advanced placement in math at MIT after taking college math courses at local community colleges and/or a CSU, but had to get the courses individually evaluated with course materials, syllabus, etc…
Of course, if the student takes courses at a California community college and later matriculates to a UC or CSU, https://www.assist.org can show which courses are pre-approved as equivalents for subject credit and advanced placement.
However, staying in “high school” for the fourth year but taking mostly college courses at a local college may be helpful in a few ways:
One more suggestion: would recommend taking the calculus-based physics sequence for physics and engineering majors at the local college through dual enrollment, rather than AP physics. AP physics 1 and 2 are non-calculus-based, so they would not be useful for advanced placement for an engineering major. While AP physics C is calculus-based, it is less math-intensive than college calculus-based physics courses (where the course with E&M commonly has a corequisite of multivariable calculus), so it may be less suitable for a strong-in-math student, and may be less accepted for subject credit and advanced placement.
I would second a vote for Latin and Computer Science (if you won’t take my earlier AP Bio advice 
)
AP Credits actually used in college can be all over the map - you have to look up specific schools and specific majors.
OP - I’m enjoying this thread. we have some similarities and differences; I have one kid left who will be a sophomore. I think many of the posters here are wise, and I value their thoughts.
One thing I can add is that ** you just don’t know ** what your kid will want to do down the road, even if they have major passions/sports now. Of my oldest two, one had a major passion/sport flip; the other is actually doing what she said she’d do in second grade. (architecture.) Just had no idea how that would all turn out.
With our 4 kids in the midwest, we’ve been on a mission to find schools that offer merit, and have thoroughly examined the DE/AP structure in helping curb their ultimate education costs. We also completely followed the Kevin thread for our S20, and he applied to many of those school listed that offered auto merit.
as you look at AP and DE I’ll suggest making a spreadsheet. Choose a few colleges of interest, google “X college credit transfer” - and the school will often tell you what a DE class transfers in as; also for AP as well.
It might be interesting to see how many of those schools take CA community college credits; or if AP transfers better. I doubt anyone would make a college decision based on this alone, but it might help with clarity on how to go about with your daughter’s education. It’s like a puzzle, if you enjoy that type of thing. (I do!)
@bgbg4us That’s me - running the gauntlet so you don’t have to.
Correct - don’t know 100% if she will stick with her intentions down the road - but she’ll discuss her design passion in a thoughtful way so… not going to stop the kid. (Also, engineering does run in the family, so this is not entirely out of left field.) Needs the A-Gs either way for the UCs. The aim is for the schedule to allow her options should she pivot. If there’s holes in the courses picked - this is the time to work out options. Some years have scheduling conflicts.
Sorry @fretfulmom - two foreign languages is enough for marks. Would like her to study some Latin for fun, not grades, since it’s useful for language. As for high school CS courses, not sure which ones are available beyond C and Python mentioned above, or all of the ones she should take. Also something I’d be willing for her to do on her own, not for marks - may not be an option for STEM candidates, however.
The DE/AP spreadsheet is a great idea; sounds like it will take time, but very useful.
Yes some kids take 7 classes.Is it recommended? Well, I think something always has to give. So sports, an team and classes how does the balance work? My oldest did 7 classes last Fall and it wasn’t pretty.
Also, if you get too far ahead in math 4+ years, the student won’t have the opportunity to be with other kids at some point. We’ve held our kids back at various times in math because we thought being in a class was important.
I’m not a fan of taking college classes as a high school student. With few exceptions like in a program Simon’s Rock of Bard or BUA ( both great for the right kid).
Doing the extra work to provide stimulus to a gifted student like yours is exhausting ( and expensive) there is no way around it. Though some BS can meets the needs of these kids while keeping them in company with same-aged peers. We chose nerdy activities and normal schooling. Socialization is huge.
Engineering courses are often not at the right level at all. Kids have often surpassed the materials. Make sure they are not repeating basic tenets.
With programming, yes, she can learn on her own. A ton of resources online and in books. Or take CC classes. Same with math. Include YouTube too (as another resource we didn’t have growing up for explaining/walking through math or coding examples).
I just want to post this one more time: https://vhslearning.org/
This online program offers a wide variety of classes, including AP’s but also philosophy, Latin, CS, you name it. We used this for one kid and were so happy with it that we worked with a local foundation to fund 25 spots each semester at our local high school. After assessment for the foundation, it was found that both gifted kids and kids who usually aren’t that interested in academics, seemed to love these classes. They are very interactive, personalized and foster independent work and creativity (according to students I spoke with in the assessment). All classes were accepted by our school and some of the really excellent high schools in our area used VHS to supplement offerings.
Here is the page for the catalog of courses : https://vhslearning.org/catalog
I would add, one more time, that we did not focus entirely on academics, either for quality of life or for admissions/career prep- even for or maybe especially for a gifted kid. I know you are considering many factors and that this thread is targeting course selection, but that is not your entire concern. I know you fully understand the importance of EC’s outside of school to enhance experience and goals.
Sometimes heavy involvement in sports seems to prevent exploration via EC’s, in my view, but there are a lot of pros and cons on that subject. Just one final thing to consider as she goes through high school years. (One of mine quit soccer in 10th grade and ended up with doctorate in a performing art…)
Since you mentioned that Canadian universities are an option I just wanted to give you a heads up with regards to AP courses. AP though not ubiquitous, is offered by some Canadian high schools along the same vein as IB, and obviously universities here are also familiar with it due to international applicants. Some schools/programs will require US applicants to present with AP credit in certain prerequisite courses (most notably Calculus). With regards to awarding transfer credit for AP courses though it is decided individually by each school on a program by program basis. In general, universities in BC are far more generous with awarding credit than schools in Ontario and engineering programs are the least generous. Some schools will also require a minimum score on the AP exam in order to be granted credit (for STEM courses it’s often a 4 or 5).
My son’s high school offered AP courses and he graduated with credit for AP Calculus AB, AP Physics I, and AP Chemistry. He did not receive transfer credit for them from his university though as they do not award credit for AP/IB courses required for the major (which we knew ahead of time). They did however provide him with an excellent preparation for 1st year and made his transition to university very smooth. It’s becoming more common for students at the more selective schools to have completed AP or IB courses.
As your daughter sounds like she could be very advanced by the time she completes high school I would take an in depth look to see how her transcript would be evaluated for transfer credit if you are planning on a strategy of utilizing AP/DE credits to shorten time to graduation or provide room for additional courses.
Boom. Mic drop. As @gwnorth and a few other posters have helped clarify, the AP versus DE credit considerations are many. The Canadian school wrinkle does add an extra layer.
Already this thread has helped me with course selection this year (still considering options!) and thus, subsequent years, in a way that doesn’t shut my kid out of their dreams. Which, may change. Thanks, cc!
The kid finished the school year two days ago with fantastic marks - woot! We haven’t explored an online course option for the summer. Doesn’t necessarily have to be for school credit (would prefer it not to be, in fact, but open to anything). Potential topics:
-composition and essay/critical writing, or creative writing - poetry, short stories - more time to build writing skills in the summer without the homework gauntlet
-some programming skills - learn more Python, or another language? Or a general philosophy regarding programming?
-art history
-critical thinking/philosophy/rational thought
Trying to keep costs low - free is better. Any popular MOOCs that are a great start? Or any lesser-known sites with great content in the above topics? Would love to hear about them. Thanks!
She could watch all the Crash Course videos she’s interested in, and have as a goal to watch at least one whole series from start to finish. 
That looks like a fantastic option - thank you! Other suggestions are welcome as well.
I personally can’t stand MOOC’s and don’t understand why the media keeps presenting them as a stellar example of online classes. Most universities have online classes that have a class limit of 20-25, not the mass audience of MOOC’s. Some people used to handle the size of MOOC’s by having smaller sort of local meetings for discussion. I haven’t tried one in a few years so maybe things have changed.
If there is no need or desire for credit, consider going through these:
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-057-introduction-to-matlab-january-iap-2019/ (MATLAB, commonly used in engineering computing; note: GNU Octave is free and supposed to be similar to MATLAB)
https://cs10.org/ (general overview of CS, suitable for non-CS majors)
https://cs61a.org/ (first course for CS majors)
Thank you! This summer would actually be good for course credit due to lack of in-facility sports training and cancellation of the competitive season. Thus, a different time schedule. However, other things are happening. So having experience in different areas of expertise now might make potential credit courses run more smoothly next summer.
Any online options that cover communication skills? Working with others?
Feedback from the kid. Apparently Crash Course has too frenetic a pace (seen a few episodes at school). On the lookout to see if there’s another option that is a well-respected resource.
^ Crash Course is also, frankly, pretty shallow and not always correct. I enjoy it but in the infotainment category, it means more towards the latter than former, IMO.
I beg to differ, although they’re not MIT’s OCW, the ones I’ve used are packed with information appropriate for HS (the 4 history series). That being said, the pace is indeed very fast (speech, content). The AP Euro course is less frantic, the History of science course is fine, CS, Video games, Engineering, sociology, and economics seemed reasonably-paced.
That led me to thinking of infotainment series that can be used by a 14 year old: I’d recommend Patriot Act.
She could watch documentaries and biopics (Netflix has made some free for educational use on its youtube channel), or run a “documentary festival” in your garden for the neighborhood