Hope it helps. Update in a year if you still like it - as I mentioned my book-buying budget is low and I haven't gotten it yet myself. :)

The requirements for honors are so nebulous and ill-defined that it's quite honestly a waste of time (imo) for homeschoolers to label anything as honors. But Chalkdust is a very solid and decent high school course that will prepare him for any major he wants.

For me studying two martial arts was sort of like studying two foreign languages. It was difficult at the beginning to learn to switch between them, but over time it improved. I would, however, make sure that both instructors are okay with it.

Also, Key to measurement.

If AOPS is too hard, there is absolutely NOTHING wrong with switching to Chalkdust. Chalkdust is a very solid program. Yes, it is a step down. So what? It's a step in the right direction for your student to understand and achieve. It is much better for a student to do well in an honors course than to not understand a super-honors course. What the college professors think won't really matter, it will be what the admissions people think - and all they will see is 'geometry'.

It is much more common that A=4, B=3, C=2, D=1. Each + adds .3 and each - takes away .3 (so C- would be 2 - .3 = 1.7).

Rubbish. I took algebra I/II during the year I turned ten and geometry/precalc the next year and I did just fine, tyvm. If he is zooming, finds it fun, challenging and interests him, let him fly! If he starts to struggle, there will be time then to drop back and find something else. However, since you already own the pre-algebra and he is currently finding it fun and challenging I would go ahead and have him finish it before starting algebra. If he were bored, frustrated, and complaining about how easy it was my advice would be different.

I would give him the placement test available for free online. http://saxonhomeschool.hmhco.com/HA/correlations/pdf/s/SHS_PLT_middlegrades.pdf If he does not pass it but is close, I would consider switching him into Saxon 76 instead and working through that over the summer. I think that would be the best preparation. If he misses by a mile (which I doubt) then I don't think that school would be the best placement.

My personal opinion is that when you're making a huge jump in style like that it'd be a good idea to finish the Saxon pre-algebra, then run through pre-algebra first (that is, redo the same level) so that she can get used to the AOPS teaching style, if the budget can go for both books.

For the student who wants to be a physicist, I would be much more inclined to use something like Foerster's for algebra 2 and precalculus instead of going to MUS. It is more important for him to get good problem-solving skills with the math he has than to use a weaker program just to get through calculus. If he only gets partway through calculus, that's fine -- he'll have good skills to be prepared for college calculus. The things that kill calculus/physics students are a) weak algebra/arithmetic skills and b) inability to apply math to word problems.

Basis charter schools use Saxon 87 or Algebra 1 in 5th. http://basisschools.org/basis-curriculum I am not sure this would be a good fit for all students.

Saxon and AOPS are just about at opposite ends of the spectrum and there are a lot of programs in between. I really don't think AOPS is suitable for the majority of students, but there are a lot of other good, conceptual math programs out there. Some students do very well with Saxon and are able to conceptually understand the material as well as apply it to novel situations. There are a lot of success stories. Some students are able to compute well, but only able to solve problems if they are similar to Saxon's problems. Saxon's incremental teaching works so well at drilling procedures into students heads that they may become very adept at computation without actually understanding what or why they're doing.

This depends on the state. At my undergrad, there were two four-credit courses taken sequentially and then a methods of teaching course at the upper-division. At my grad school, they took a 'math for teachers' course and then a two-semester sequence in 'how to teach math' that included a significant amount of math as well. Where I work now, they take a two-semester sequence in elementary school mathematics and then a one-semester course in how to teach it.

I assume calc 3 is multivariable. Can she do distance learning to do a linear algebra/differential equations course? EPGY offers linear algebra, differential equations, and partial differential equations.This sort of math is definitely relevant to engineering. Diffeq is required for most engineering degrees. They also offer several other advanced math topics more aimed at pure mathematics such as real analysis, modern algebra, and complex analysis. These would be very proofy classes, so if she enjoys proofs they might float her boat as well.

I don't think the program matters - I just don't think that you're going to find a program that you can hand to your kids and have them teach themselves and work industriously on. Most children of this age just aren't ready for that level of independence.

If the CC math prof thinks it's a good fit, I'd go with it.

I really wouldn't recommend it if she did not pass the placement test. You don't want to set her up for struggling and thinking of herself as a bad math student. Frequently, even when a topic is repeated the instruction is shorter, the scaffolding is less, and the problems are more difficult.

Pandia doesn't cover it in their level 1. I don't think BFSU does either. I am not aware of one that explicitly does. However, I think either of these programs could easily be supplemented with some good books on evolution. This book might be a bit over your child's head but the pictures are amazing. I loved this book from earliest childhood and we actually went through two copies because my siblings and I read it to pieces: http://www.amazon.com/THREAD-LIFE-Smithsonian-Looks-Evolution/dp/0895990105/ref=sr_1_1?s=books&ie=UTF8&qid=1386125967&sr=1-1&keywords=thread+of+life+smithsonian I don't have any personal experience with them but you could look into the Born with a Bang series - here's the first: http://www.amazon.com/Born-With-Bang-Universe-Children/dp/1584690321/ref=pd_sim_b_8 SOTW definitely doesn't include pre-history. Here's a good book for the age range you're looking for on human evolution - http://www.amazon.com/Our-Family-Tree-Evolution-Story/dp/0152017720 I think doing pre-history and evolution in K would tie in really nicely into life/earth in 1/2 and into ancients in 1 as well.

A lot of good points in there.

The accuplacer is going to be a lot more interested in his arithmetic and algebra skills than geometry skills. He'll need some informal geometry but it won't test things like proofs.

In my calculus classes, it is definitely an advantage to have seen the material before IF the algebra skills are solid. I have had students with solid algebra skills who had never seen calculus before do very well, but in general, they need to do more work and often are the solid B students. I have also had students who took "calculus" in high school fail my calculus class at the university because their algebra skills were weak. I say "calculus" because apparently the only things that they learned were how to differentiate polynomials and L'Hospital's rule.

Yes it does. They were different examples of things I like to use when teaching fractions. Pizzas are great for when you're dividing fractions by whole numbers, because people can visualize the pieces being cut into smaller pieces. The pizza I was giving was supposed to be an example for 1/6 divided by 2, which, of course, is the same thing as 1/6 times 1/2. Ribbons are great for when you're dividing fractions by fractions. For many people it is much easier to think about a physical strip of fabric when you are cutting pieces 1/6 of a foot long and how many pieces you can get from a 1/2 foot ribbon than it is to just think about sixths into halves.

I'd see absolutely nothing wrong with doing a whole bunch of exponents worksheets and then going back to redo chapter 2. One thing that may work is to just pick up a random algebra or pre-algebra textbook from your library (they should have one), do the chapter on exponents, and then go back and redo that chapter.

Yes. If you can score a cheap copy, it certainly wouldn't hurt as a supplement. It would at least answer the question you might have, when reading through the calculus text, of "What the ^%("^(£^£^$ is this technique good for anyway?!"

There's a pair of textbooks, by Andrew Rex and Martin Jackson, that I've always wanted to get my hands on. They covered integrated physics and calculus, volumes 1 + 2 - starting assuming the student had had either calc AB or calc 1, and taught, in two semesters, integral calculus, multivariable calculus, mechanics, and E and M. The calculus was taught and then immediately applied in the physics class to continue the learning. It didn't seem to catch on -- for one thing, it requires extremely close coordination, it doesn't allow for students whose schedules don't permit them to take calc and physics in the same semester (like biochem majors) -- but I always thought it was a great idea for engineering and physics majors.