We use Bittinger, and I quite like it. It's also through Pearson so you can get MyMathLab if you want. For a 3-credit course we do chapters R and 1-4. For a high school course I would try very hard to add chapter 5, applications of integration (which includes two sections on probability). I'd still skip chapter 6 which is a basic intro to multivariable calculus.

I think that the reason studying the book didn't help is that his math knowledge was only really on an algebra 1 level. I think finishing algebra 2 (which he is doing this summer, correct?) and working on precalc will make the book a lot more helpful. Test prep will only really help after the subject knowledge is there. He's taking intermediate algebra over the summer. That's the prereq for college algebra. I would ask the intermediate algebra instructor, towards the end of the class, if he's ready for college algebra. They will be in a great place to judge.

I think doing the chapter tests for whatever you used for algebra 1 and filling in areas of difficulty would be a great idea.

Why do you assume that you know what everyone else thinks a "comfortable" existence is? For me, a comfortable existence is one where I can provide for people who depend on me so that we are not hungry, we have health insurance and we know where next month's rent is coming from. I have never had cable TV in my life. I have never had a smart phone. I do have a cell phone now because it was cheaper than the land line but it's a very basic model. I drive a beat-up old junker that I paid $500 for and when it dies I'll buy another one like it. And yet I still submit that encouraging a 16 year old to drop all academics and not complete high school in favor of doing nothing but music is a crazy plan. The girl in question wanted to be a wife and mother. What happens when her husband dies or is disabled? What happens when she never meets an appropriate guy? What happens when she does meet a guy and he turns out to be an outwardly charming secret abuser? Everyone ought to be prepared to support themselves in some way. I know several people who are extremely, extremely talented in music. Not one of them is a world-renowned concert musician. Every one of them has either found another career or is scraping together a living by giving lessons. "Life is not about finding a job" is a fine idea if you're independently wealthy. Those of us who are not so blessed need to find ways to mix what we really love with something that can earn us a living. And I can't picture why it's a good idea to set a teenager up so that there's a 99.9% chance that she'll always be dependant on someone else's goodwill to get food on the table.

Honestly, what I'd be inclined to do (if you really want to do calculus) is to pick a standard applied calculus text. Lial has one, Bittinger has one, Tan has one. They're frequently called "calculus for business and social sciences" and have a heavy emphasis on applications and word problems. I would have no issues giving a credit for this (it is a standard university class for business and sometimes biology majors) and would call it either Applied Calculus or Calculus for Business and Social Sciences.

FWIW, mathematically, I would see absolutely no issue with letting her be conceptually ahead of her computational ability. You should be able to separate them out just like penmanship and reading, and it's perfectly okay for her to be computationally at a 'typical grade 1' level and conceptually at a 'typical grade 5'. I think giving a 6 yr old the amount of drill you'd give a 10 year old is a mistake but giving a gifted child the concepts can be wonderful.

Do they offer Russian II in the fall? Usually, community colleges offer Language I and III in the fall, II and IV in the spring. I would rather enroll in Russian I in the fall. I would start with something much easier in the summer to get her used to being on someone else's schedule. I realize she does want to take Econ at home, but it may be worth reconsidering that. If she does well in Econ, it will probably transfer to her 4-year college, which would free up her schedule a bit. Music major schedules are notoriously tight and some breathing room would be nice. Another good option might be Psych 101 -- this is frequently required of education majors (depends on your state of course) and generally transfers well. Other options: Lit might be out, but many colleges require speech. I warn that some speech topics may be a little mature for her, though. During the school year, taking a transfer-level math course may save her from having to take math at college. Something like 'math for liberal arts' would be a decent option.

I hate it as well, but one of the big reasons that this is required is because of recycling papers from other people.

I don't think I'd have her do the technical classes while in high school. It's only one year of school after, you said, right? One thing that I would look into is whether any of the classes will transfer if she decides to do dental hygeine. I know absolutely nothing about this but it would be worth looking into. I know quite a few people I worked with had gotten a CNA license, worked at a nursing home while putting themselves through LPN, then used the LPN to get a better salary while earning an RN. Maybe something similar with dental assistant/hygeinist would work?

I wouldn't buy anything all the way through precalc now, unless of course you see books for 50 cents at goodwill or something. I would get pre-algebra, and see how you like it. The good thing is that AOPS is sufficiently ahead in scope and sequence that you can change at any point really without leaving gaps. Remember that you HAD the mathematical talent as a child, and that you have the mental maturity which so many high school students lack.

What do your girls think? Are they chomping at the bit to move ahead or are they feeling really reluctant?

You have NO IDEA whether you are bad at upper level math or not simply because this terrible, terrible teacher has messed you over so bad! I'm surprised that anyone learned anything with that kind of "teaching", and I would strongly suspect that if they did, it was mostly because they had a parent or tutor who understood it. AOPS may work for you -- you may discover that you are far better at math than you have thought. I would suggest starting out with Alcumus because you can check it out for free.

After successfully completing Saxon 87 and Keys, pretty much any solid Algebra program should be next.

I would work very hard to keep his options open. Video game designing is a brutally competitive field. However: He'll end up needing lots of computer science classes in college. Therefore his background in math should be strong, including a solid math course every year. He should definitely include physics in his curriculum (it helps to make the games realistic) and a broad base of general knowledge is very useful. Surprisingly (from what my friend who DID make it as a designer told me) a background in art was also very helpful. One of the reasons that he got picked for an interview was his undergraduate art minor. But here your mileage may definitely vary.

I would be very interested in that statistic as well. I know that recent college graduates are highly likely to be underemployed (i.e. working a job that did not require a bachelor's) but I cannot find a number that is THAT low.

I think it would depend on the quality of prior instruction and on understanding of what's been taught. If they've had a solid and challenging course through precalculus, I would be more inclined to use the discrete math texts and the problem-solving texts. If they've hurried through a weak curriculum I'd go back further.

I think it sounds absolutely perfect. Why pay for a curriculum to give you boring things to write about when she's obviously very interested in writing about this? :p

They are both, imo.

I was homeschooled and had never even heard of creationism until I discovered the interwebz. Evolution was assumed as a basic fact.

Tiramisu, on a more strictly pragmatic level, it will also help her retain her skills so that she will hopefully be able to avoid remedial math in college. At most colleges, even music majors need some sort of math class, and if she placed into algebra 2 (which would be possible after a year off from math) she'd have to retake it for no credit and THEN take the math class.

bnb, it looks likely that a student who started in alg 1 there would not get to calculus, and a student who had alg 1 in 8th grade would be able to do calculus as a senior. Personal finance is likely an alternative for strugglers. As far as math: Competency in algebra should be prioritized over 'exposure' to higher levels of math with a weak foundation. But this does NOT mean that repeating those courses is ideal! However, a student who struggles for a C or lower in Alg 1 should consider repeating, summer review, or tutoring rather than leaping blithely into geometry. It would be better for a student to have a schedule that repeats alg 1 and then A's or B's in all subsequent courses rather than a schedule that goes straight through and has all C's and D's. But it would be better yet to have a schedule that does NOT repeat algebra and still has all A's and B's.

Homework here makes up about 10% of the grade even in calculus classes. We (department) have found that if it's worth 0, most of the students will not do it and the failure rates will be quite high. Then the department starts getting nasty notes from the university wondering why we have so many failing students. So assuming that we would like to continue to remain employed, we can either slacken our standards on exams (not an option) or require homework as a minor component of the grade. It is unfortunate, but that is how it is at many non-elite universities.

The man who mistook his wife for a hat is excellent and I highly recommend it.

Starr, it's more that he wouldn't be able to get it paid for as "high school" -- he could enroll on Mom's dime. Kim, I would finish the Intermediate Algebra and then retake the test. If he does not place into College Algebra, I would look into Algebra 2 programs, but I wouldn't buy anything now. For science, I really don't think survival skills would count as a science. But maybe environmental science, astronomy, geology, botany, zoology, forensic science, meterology, oceanography, agricultural science, wildlife biology would hold some appeal?

I like the idea of redoing a test for a maximum of a C. It stops students from gaming the system by retaking the test to get a perfect score, but it stops people from giving up and just letting the whole year go. It's a hell of a lot better than 'no score below 50' or 'magical extra credit', too.