I would just go ahead and start precalc (not chalkdust's trig -- chalkdust's trig is half of a full precalculus course, with college algebra being the other half -- do both parts) now. I don't think the summer break would be an issue.

Just tell them they're the same grade as they would be in public school so they have something to answer when older people who are trying to be friendly. Don't make a big deal about it. Just 'oh, you're 8. That means you're 3rd grade now.'

College algebra would be okay, and she should definitely take all of her algebra-based classes consecutively. I would strongly recommend statistics as a senior-year course. I think it's an essential gen ed course for mathematical and scientific literacy in today's society. It's hard to know how people are using statistics to lie to you unless you know the basics of statistics in the first place.

I would strongly recommend doing pre-algebra with MUS. Because of the non-standard scope and sequence, if you stop after zeta there will still be gaps. For high school, MUS is more gentle than others, but if he has struggled with every other curriculum he has tried, I would continue with MUS.

I would look at earth science, biology, or possibly physical science (probably go with more of an 8th grade book though, for phys sci).

I don't know about a must read, but I recently received Eli Maor's e: the story of a number for a Christmas present and enjoyed it very much. I have his Trigonometric Delights on my wishlist as well.

It is worth a shot. The worst thing that will happen is that the professor says no, in which case he is no worse off than he is now.

Really, the worst that could happen would be that she'd end up at a community college and place into developmental classes. Even in that case, she could take a few semesters of courses, get good grades, and transfer to a pretty decent university. Assuming that she's able to read, understand what she reads, and write a reasonably literate sentence, it's unlikely that she'd place very far down in English. MAYBE into the class below Comp 1. If she can do, understand, and apply arithmetic, she should place into an Algebra class. If she can do, understand, and apply basic algebra, she should place into a college-credit math class. If she can follow directions (like using a cookbook to make a new recipe, or using a sewing pattern to make something) she should be fine in college science labs. (just answering your question on: What's the worst that could happen.)

Many universities will not grant credit if the test was not taken during the high school years. I would be more inclined to relabel the years before, classifying 9th grade as 8th, etc. and reclassify the intended gap year as a senior year if a significant amount of academic learning is to take place during that year. Another option -- many universities do not publicize this, but will actually do test-outs for courses, especially non-lab STEM courses. My university's math department, for example, does not believe that a student who could get an A on a cumulative final should be taking the course, and will grant either credit or advanced standing and placement into a more interesting course (depending on some specifics).

Freddy the Pig series, another vote. Hilarious books (when my mother was a girl, she used to read in her treehouse, and one day, when reading a freddy book, she laughed so hard she fell out of the tree and broke her arm.)

After having finished pre-algebra with Saxon, she should be able to do just about any Algebra 1 program. If you're going to stick with Saxon, I'd stick with the more traditional way with alg/geom combined. The strength of the program, Imo, is in the incremental method, and breaking it up sort of ruins the incremental method. If you want alg/geo/alg 2, I would switch to something else. There are loads of options, but if you want dvd support (based on your art reed comment) two of the good options are chalkdust and math without borders.

I do not. It's on my bookmarked list of 'interesting things to check out when the time is right, which is not now' :)

I would call the people immediately and ask them what to do.

Graphic Design or Drafting? http://www.sixbranches.com/ has courses in both.

It depends on the edition. In the older editions, this was true. In the newer editions, 87 has been beefed up a lot so the reverse is true -- you'd do 87 and then skip algebra 1/2. See if the words 'with pre-algebra' have been added to your 87.

How old is your DD? Exploring agriscience is really sort of a junior high textbook so she might find it extraordinarily easy. It would depend on how much she knows of areas of ag outside of dairy.

You could also get one of the SAT practice books with test scores on them and have her take it under test conditions, then score it yourself using the conversion chart in the book, if your only concern is to see how she would score. I would definitely look into doing math competitions. I'd also look into AOPS -- either switching to the curriculum or supplementing with the problem-solving books.

Power Basics has a consumer math course which covers loans and interest. Rainbow resource sells it for about $40. Power basics is designed for special needs students, so is supposed to be very clear with procedural explanations. I haven't used it myself, but it looks like exactly what you're looking for.

Under no circumstances would I take off math until the fall. Moving ahead would be one option. Doing a fun supplement would be another. But even over summer break, kids forget a lot -- waiting half a year would cause a lot more forgetting. If she likes Saxon I'd just go ahead with 87. If she doesn't like Saxon, she should be ready for a different publisher's pre-algebra.

I agree with both of these points. There is no reason whatsoever that an examination needs to cover the very hardest problems in the curriculum. If he can pass a standard, honors Algebra 1 examination with an A, I would record a grade of 'A' for the class with no qualms whatsoever.

Honestly, if he can follow instructions (like use a cookbook to make something he's never made before) with care, he should be fine jumping into a high school science lab.

I think doing what you're doing -- Singapore with IP/CWP and LOF for fun -- sounds just fine. I wouldn't worry about her speed now. Cross that bridge when you come to it.

When I was looking for a good multivariable calculus text, I looked at what the top universities used for their honors classes. One that I haven't seen mentioned yet is Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. Cornell uses this for their Theoretical Linear Algebra and Calculus course. BTW, I totally agree about Stewart.

+eleventy billion. I am so happy that I went to the local state school. If I hadn't done study abroad I would have had 0 debt (although the study abroad is a big reason that I was able to keep up in graduate school), but even as-is I had under $10k.

This is actually what I would expect. Calculating the grade both ways is trivial with Excel. I would suggest, also, that your DS has probably brought himself to the professor's attention in a very positive way by being one of the few students who did well on a difficult exam.