Quite honestly I'm not sure if another calc-based textbook is the right thing for you at the moment. I think you might be better off going through a conceptual textbook first, to really understand all the concepts they're getting at, and then go through the math again, if you can't afford a tutor. For most students it's VERY hard to learn the concepts and the math at the same time, and that's the whole reason for conceptual courses to exist.

I think a tutor would be a better option. Physics 1 books are pretty similar, and a physical person might be able to explain to you why they expect you to find D given A B and C.

Dolciani is an excellent book with a comprehensive coverage of pre-algebra. It's just not insanely challenging like AOPS.

Foerster's is an excellent book with a comprehensive coverage of Algebra 1. It is particularly good with word problems.

What do you mean by red flag? I mean, yes, students should correct mistakes, but it's normal for students to make mistakes here and there, even on stuff they *do* understand. If a student is getting 100% on every assessment, it's too easy and not making them think hard enough.

Yes. Don't record her as grade advanced NOW (imo) -- then if she starts to slow down, it'll be a lot harder to repeat. But keep records next year as if she were going to be a 9th grader. Then when the time comes, you can declare her to be graduated and submit records of the last 4 years of school, just as colleges want.

I think one thing that really causes profound interests to be *ruined* for young kids is when the kid wants to back off and go at normal speed for a while/pursue other interests and the parent/teacher/coach keeps pushing. Be alert for this tendency in yourself, and also watch your children. Make sure that they know (and you probably are doing this already, but I'm just reminding) that it's okay to be interested in other things too, and that although you love doing math with them, you'd love to support their interests in other areas too. You sound like you're doing everything right so far.

Ask regentrude's advice, along with a little more detail as to what your textbook doesn't do well for you.

Both methods can work. A lot of geometry programs include algebra 1 review (and if not, you can add it in yourself) so unless you're using a program for which algebra 2 is really supposed to come before geometry (like videotext) it's usually a good idea to get geometry in next.

Weight training really doesn't burn much. It does help with muscle tone and for me doing a lot of leg work has really helped with my really bad knees. Running isn't for me but I get my cardio in through Aikido. I love it. I do think that getting exercise in for health benefits is really, really beneficial. It doesn't have to be running or swimming or Zumba class or anything traditional, but it should be *something* that involves moving around and bearing weight. (chasing after toddlers counts too, but not teenagers :D). I have PCOS and my blood sugar used to be really, really unstable. I really had to eat small frequent meals. After I started doing lots and lots of martial arts, I found that my blood sugar stabilized and so did my cycles. I've been off The Pill for 2 years straight now and my cycles are still running when they're supposed to. I also feel just fine eating 1-3 meals a day (depending on activity during that day) now instead of the every 2 hours I used to need.

Doing this from the beginning with your kids will help. Another option could be to work ahead of your kids using a textbook that's designed for adult learners who have forgotten all their math (sound familiar?). Lial's Basic College Mathematics is one such textbook that's available cheaply on amazon. If you make it through that text, you'd be ready up to pre-algebra -- and that's a long way off.

4x4 meaning 4 of each core subject in order to apply to university if she decides she wants to go. I'd be really reluctant to declare a student 'finished' early if they weren't ready for anything but a community college. If at 18 or later she changes her mind and wants to go to university, I wouldn't want her to be at a serious disadvantage.

I don't think there is one. I know people who thrive on a super-high-carb diet. I know people who thrive on a super-low-carb diet. I think one big reason that people have had such good results from such a wide variety of diets (from paleo to fruit+veggie vegan) is because: 1) We're pretty adaptable. Most of us can adapt to a wide array of diets with time. 2) Many of these diets significantly restrict heavily processed food. They all have rationales behind it, and they're all different, but they very frequently restrict things like sugars and soda. 3) Many of these diets include a lot more fruit + veg than people are used to. In general, increasing the proportion of food that comes from plants has pretty positive effects. I don't know if I'd go with 'Mostly plants' but I'd definitely say 'Eat real food. Not too much. Plenty of plants' is a pretty good general guideline. Now, one real issue is that a lot of people will move from the SAD to something else with more plants, more real food, less overall food, and less processed food. And they will feel so much better. And they will jump to the conclusion that this is THE way to eat, and become nearly evangelical about it. But it's not that their specific diet is THE way to eat, just that it moved away from the SAD.

Are his grades because he tested poorly or did poorly on homework or both? In Saxon, you HAVE to do the work to learn the material.

Make a list of what you consider as essential high school credits, and then start back-tracking to make sure you can get there. Will she be doing high school work in all the core courses in the fall? If so, you can just do a standard high school plan, starting now. If she is not in legit high school coursework, it's going to require some doubling up on courses to get 4x4 + some electives.

It's going to depend somewhat (in the advanced levels) on which area of STEM you want to go into. Biology would be somewhat different than physics. However: Math: The student should take as much math as they can with as rigorous a curriculum as they can handle. This does not mean rushing through without understanding -- if your student is not ready for algebra before 9th grade then they should not take it before 9th grade. They should be competent with all levels of math that they have taken, including word problems. A student who aced the computation part of algebra but can't do word problems is going to struggle with STEM courses which require application of mathematics. Strong math skills are utterly essential. Science: At a minimum, a student should have a solid, high-school level course in bio, chem, and phys. These do not necessarily need to be taken during high school years, but they should be taken. This leaves time for at least one advanced elective in the student's area of interest. The science is not quite as important as the mathematics, as it is easier to make up shortfalls there, however, exposure is one way to tell if the student is actually interested in a career. Computer science: Some exposure to programming is nice, but not required. Electives will depend on the student and their capabilities. For specific examples, a student who wants to do environmental science might decide to fit in an introduction to statistics and a course in ecology -- a student who wants to do geology might work to fit in a course in geology and some extra chemistry -- a student who wants to do physics might fit in some advanced math work as well as physics -- really, after you get the "core" in there's a lot more room. But strong math skills are of paramount importance.

If the student is making B's, I think re-doing any missed problems plus an extra one of each type would suffice. I would frame it as "Gosh, honey, I didn't realize you needed extra practice on this" rather than "here's your punishment". ETA: I wouldn't do this with someone who was making less than C's. In that case I think re-doing the missed work would be sufficient.

If a slight variation in problems scares her, it might not be the best fit for her. Is there anyone near you where you could borrow the book for a week or so?

Yeah, there's a big difference between acceleration and maturity. I have seen students who were very accelerated computation-wise but whose maturity lagged behind. This type of student frequently really "gets" the algebraic computations but struggles with the proofs in geometry because they require a bit higher level of reasoning. I have also seen students (in my university classes) who were not accelerated and mathematically very mature. For example, one student was concurrently taking calculus 2 and a jr/sr proof-based class (not going to go into the scheduling reasons) and was a very strong student in the proofs course. The wonderful thing about homeschooling is that we can feed them material at different levels. It's perfectly okay for an asynchronous child to be doing computation at a different level than problem-solving. What matters is that they're being fed material to help them grow in both areas. With specific respect to the lining up columns, are you allowed your own scratch paper? If so, I would give her graph paper with large boxes for her to work on.

grr

I like what Gil said. You could also get a 'summer first grade math review' workbook at the dollar store if you need something preplanned. Another option could be to go ahead and buy the McRuffy grade 1 math and just start it now, skimming any parts that you feel she does understand well. You don't have to follow the school academic calendar. I don't think I'd just go for taking the summer off and then doing first grade math in grade 2 and second grade math in grade 3 etc. unless you think she has a learning disability. While this would be preferable to just continuing with an inadequate foundation, I'd rather try to help her catch up to grade level by using the summers.

As an addendum: I would not assume that just because he has passed the ALEKS ACE assessment, he will be granted credit automatically. Many (most? none I've been at) universities do not have procedures to deal with credit granted by ALEKS and would require him to take a different test as well. Of course, this is irrelevant if you've already got one in mind.

I wonder if either of you realizes just how good at math she really is? Her scores and her ability to place significantly higher than she's actually learned indicate a strong natural ability to fill in the gaps, interpolate, and make connections.

I really don't think the ACE will matter. Intermediate algebra is rarely granted college credit anyway (it is considered to be a developmental class).

I agree with Mark, how long ago did she complete the class? College algebra usually is not just algebra 2, but review/extension/beginning of precalculus. I don't think most students would be ready to CLEP out after algebra 2. It might be beneficial to acquire a college algebra textbook or learning software and actually work through it.