A W here and there is not a real problem. Many W's is a problem.

In the water might be iffy. I would peel them and smell them. If they smelled fine I would eat them anyway.

I doubt the school will do any better. This is far more common than you realize. Are you paying for the school or is he? If he's a lazy student, I'd tell him that you are not paying for his school next semester due to lack of work ethic and he needs to get a job. For many people (including me) some time at a minimum wage job will really bring in "Man, I should have gone to classes". I wouldn't tell him you'll never pay for him again. I just wouldn't pay for next semester if this semester's grades aren't good. I'd let him re-visit the decision next fall. Of course, if he's paying his own way, it's his business.

I'd email the guy and ask him.

There are quite a few people who went directly into algebra before pre-algebra was written. If she is the type of kid who does not do well with things she already knows I would give it a shot. If it does not work for her you should know within a couple of chapters and you can drop back to pre-algebra. But I would not enroll in the class -- the classes run at a breakneck pace. Many people have taken 2+ years to get all the way through intro algebra with young bright kids.

Fraleigh and Wade are standard undergraduate modern algebra and analysis texts. Wade is generally used at less selective schools -- the more selective schools frequently go straight to Rudin's Principles. Fraleigh is just a great book and I teach out of it. I like it better than any other undergraduate abstract algebra text I've ever seen (and I spent a fair amount of time investigating texts for my students). It is not mechanistic and does an excellent job of motivating a difficult subject. If he takes the AOPS Group Theory class there will be some overlap but Fraleigh goes further -- I'm not sure how much of the textbook they'll cover.

I think some people naturally reason well mathematically. Those people could learn math from pretty much any curriculum that covers the basics and understand what they're doing well enough to extrapolate it to more difficult problems. There are definitely people who used MUS all the way through and aced the SATs as well. Other people, at the opposite end of the continuum, find mathematical reasoning so challenging that there probably won't be any curriculum that could teach them more than the most simple problems. In the middle, there are people who do not naturally reason well enough to solve difficult problems, and yet can be taught. This is where programs that don't present sufficiently challenging problems, or present them with too many hints on how to solve them, and don't ever remove the crutches, can really fall down. I do think TT is much better than a more challenging program which is not understood. But if she is planning on doing CS, I would be more inclined to consider a program such as Foersters (with math without borders, if you need the support) for a second go-round at algebra 1, unless you feel that it is inappropriately challenging for her.

Studying ahead before the lecture is beneficial for nearly all students anyway.

Let's put it this way: Even if she were looking at fancy colleges, a transcript with C's or potentially worse in advanced math classes due to lack of foundation (and even if you hypothetically fudged the grades, the SAT/ACT would reflect the lack of foundation) would be much worse than a transcript and test scores showing less advanced courses but a thorough understanding of what she has taken. I'd look at re-doing algebra with something else. I wouldn't even mention the MUS algebra on the transcript -- just '9th grade, algebra 1'. If she suddenly makes leaps forward you can look at accelerating later.

Man, that just sounds fowl. :)

Yes. I have a policy in my classes that answers that defy common sense will not receive partial credit, no matter how much of the problem is correct. For example: If I tell you a bank account of $1500 is invested at 3% interest, and ask how much is in it after 5 years, any answers LESS than $1500 receive an automatic 0. Quite honestly I've thought about awarding negative points for those (just to emphasize that sometimes it is more important to say "I have no idea" than to say something that you know is wrong), but I have not yet gone that far.

I think AOPS is ideal for a child who thinks math is easy but boring and not worth her time. I think pre-algebra would be too much for her at the moment, though, with the jump in difficulty level AND skipping a level from TT6. At the same time, while I don't think BA would be completely beneath her, I don't know how much use you'd get out of it for the price. It would definitely appeal to her love of comic books and story, though, so if you can afford it I would probably get it anyway. You might consider Russian Math 6 as a lead-in to AOPS pre-algebra. You can buy it in ebook form for $18, so even if it does not work it would not be an expensive mistake: http://www.perpendicularpress.com/math6.html Jousting Armadillos might also work (again, as a transition) but it is significantly more expensive.

I'd look into the Rightstart games. http://store.rightstartmath.com/mathcardgames4thedition.aspx

I would bet it's because October is when most curricula are really starting to bring in new stuff, and re-adjusting to learning instead of review is a big adjustment.

Power Basics has Basic Math, Algebra, Geometry, and Consumer Math. You can buy each course from Rainbow Resource for $45 currently. They're designed to deliver content to PS special needs students, so I think they'd be ideal for you. Power Basics does not go beyond algebra 1, so if you need something you can label "algebra 2", AGS makes courses at a similar level that you can get from Christianbook. They're pricier though, but $100 is still not that bad. Here's a link: http://www.christianbook.com/ags-math-algebra-2-homeschool-bundle/9780785471448/pd/471448?event=HPT

This is a really serious problem. If someone computes the mean of ... let's say ... 10 double-digit numbers, and the correct answer is 45, and they get 43, ok, I can see that. If they get 443, I can't see how you could possibly not realize that's wrong.

It sounds like a great supplement for inspiration and interest. I wish my mother had had it when I was preparing for algebra.

MHE is a really great way to deepen mathematical thinking before algebra and I like it a lot, but I don't think it's going to really review arithmetic very much. If his arithmetic is already solid it'd be fine, and it'd definitely be a great supplement.

I did learn them but I'm not sure they were part of any curriculum. The 3, 9, 11 tricks also work to find the remainders on division. For example -- 1234567 -- 1+2+3+4+5+6+7 = 28, 28/3 has a remainder of 1, so 1234567/3 has a remainder of 1. I don't think I've seen the 11 trick explicitly mentioned, so it's when the alternating sum of the digits is divisible by 11. For example: 1-2+3-4+5-6+7 = 4, so 1234567 is not divisible by 11.

Were these both full-year courses? Or was trig one semester? It was quite common to do one semester of trig and one of pre-calculus, and I know that when my mother was in school it was common to do a semester of trig and a semester of analytic geometry. But I haven't seen where it was common to have people do both. On a side note: It used to be quite common to do calculus after algebra 2/trigonometry -- this route could be taken if using a book such as Foerster's classic text, but many students lack the mathematical maturity to really "get" calculus at this stage. Adding another year of pre-calculus, which reviewed algebra, functions, and trigonometry, while adding in topics from analytic geometry and the beginning part of calculus, was a way for them to gain mathematical maturity without repeating the exact same material. I have a pretty decent collection of calculus textbooks, and the older they get, the less they pre-suppose in formal mathematical instruction, and paradoxically, the more they pre-suppose in mathematical maturity and intuition.

The thing about BCM as opposed to a spiral arithmetic textbook is that it is topically oriented. For someone who's had a pretty decent grounding in elementary arithmetic but has skipped around a bit, it's a decent text to go through and look for holes. I don't think there is a specific best option but I think BCM is a good option, and since you have it I would use it.

BCM is fine for finishing elementary math. Just be prepared to locate worksheets if something doesn't click fast enough.

I'd eat it.

Are you planning on having him work through a level in spring/summer or work through a level in half a year? I would actively avoid having him halfway through a Saxon book when he starts a class. If he's jumping from halfway through 6/5 to 7/6 it'll probably be too difficult, and if he's halfway through the book and they start at the beginning it'll be much too boring.

Foerster's pre-calculus and calculus textbooks are solid and if you like Foerster, I'd continue. If not, you can transition to any other solid pre-calculus textbook with the grounding from Foerster's algebra and trigonometry textbook. It is not necessary to make this decision now -- I'd pencil in Foerster and re-evaluate during algebra 2.