Here's a thread: http://forums.welltrainedmind.com/topic/368951-why-not-delay-math/

I agree with everything Kendall said. But -- if the teacher says that the variables and range he gave before are correct, the only possible choice for domain is the weight per kitten. This is not a good problem to help students understand independent and dependent variables.

If she says that that's the only thing wrong then domain should be 10-12. Why? Because your input will be the weight of each kitten, not the number of kittens.

Frankly a lot of ps'd students don't know anything either. Profs are used to it. I do agree with you that some experience learning to crank out academic writing in HS would be good for the youngers, but your dd is going to be just fine as long as she puts in the time. She should definitely patronize the campus writing center (nearly every campus has one) and the professor's office hours.

Redwall and the whole series, Brian Jacques. Mrs. Frisby and the rats of NIMH (she's a mouse) The Mouse and the Motorcycle and related books by Beverly Cleary

What do you mean, CD? There is only AB and BC. In order to get credit for more than BC (covers Calc II or Calc C on a quarter system) you would need to talk with the specific school they end up attending. The next step after BC would be multivariable calculus, and many schools DO allow placement for that upon specific request, but it's an in-school exam and not an AP exam.

In general, I think that if switching from any other program to AOPS it might be a good idea to step back exactly one course, even if it means re-covering some material. This would obviously vary for some exceptionally mathy students, but I think it would be a good idea to get used to the way AOPS presents ideas.

No slope is a very confusing way to phrase it. I wouldn't know myself what they meant without checking the answer manual.

I would look into knocking out some general education requirements and any needed developmental courses at a community college part-time. If he took, say, 6 credits per semester, he could get his 'freshman year' done by the time he's old enough to move off your FAFSA and be ready to attend full-time as a sophomore. This also gives him time to think about what he actually would like to do.

Only if she's had 8 college semesters.

No. One thing that would START to fix the flippin' problem is if we stopped equating equality of outcomes with equality of opportunity.

Well, not only that, but then we pass students who haven't learned a reasonable amount of the course material into the next course.

I would ask your friend if she can still do the labs with her if she's working on Conceptual Physics. If that wouldn't work, then I wouldn't do it. She isn't ready for a math-heavy physics and doing the labs without the physics class wouldn't be really helpful.

+1 googolplex. I see people do this all the time in my classes (so it is a very common error), but if there is no equation, you cannot solve the expression. Or, as I tell my students, "If there is no 'equals' in the problem, why are you putting one in the answer?" This is compounded by the use of equals to mean "and my next step is" which is another extremely common error. Equals should only be used between things that are actually equal. This hinders students when they need to reason through chains of equalities using transitivity. Sorry about the continued sidetrack.

I would also recommend getting a preparation book for the CLEP and studying that to make sure that your kids are familiar with the types of questions and format. I looked up the CLEP Precalc and found that there's a free download with a brief tutorial that gives you 30 days of access, so I would put that on your notes so that you can become familiar with the calculator (they include an onscreen calculator) before the exam.

I agree 100% with everything Creekland said. TT may be a good fit if it's within your price range.

I would suggest that the problem-solving I and II texts would be ideal for someone wanting to add challenge to a different curriculum.

If they are in Singapore 3 there's no way they're ready for AOPS, and Jousting Armadillos is likely to be over their heads as well. They would be better served by doing fewer programs at a greater speed as they are a bit behind at the moment. They should be working through the summer on their regular program -- not doing an extra. Pick just one -- Singapore as others suggested if you like it -- and work on that steadily. If they need extra practice on a topic, use the 'key to'.

I would recommend going for the AOPS C+P book, and if he enjoys that he might like the number theory book as well. C+P would also be a great lead-in to statistics, and if statistics goes well with your planned science for next year that seems like a great idea. FWIW, Discrete Math (which includes an intro to C+P and NT usually) was the course which made me change my major to mathematics. I would recommend against 5 -- there's no reason to jump there instead of doing precalculus first. If he were in a school setting, it might be necessary to keep him challenged, but where you are he can go through rapidly and skip anything he already knows. Larson is a solid text but I would prefer Foerster for a young mathy kid interested in applications, if you decide not to go with statistics.

Pre-calculus usually includes a review of functions, exponential and logarithmic functions, and a large amount of trigonometry. Other frequently included topics are a brief introduction to conic sections and/or matrices. Pre-calculus courses with better prepared students will often spend less time on functions, exponential and logarithmic functions, and use the time saved to do a brief introduction to calculus (usually limits and/or sequences and series). You would find a substantial amount of overlap between a standard pre-calculus course and your trigonometry/analytical geometry class.

Out of curiosity, when you mentioned that he took the placement test this spring, had he finished Algebra 2 at that point? It seems entirely reasonable for someone who has not yet finished Alg 2 to not quite place into college algebra. Why does he think he doesn't understand math? What is his reasoning?

Usually pre-algebra is a review of all the arithmetic computations learned in elementary math, including addition/subtraction, multiplication/division, fractions/decimals, percent/ratio, an introduction to signed numbers if negative numbers have not previously been taught, an introduction to square roots if not previously taught, an introduction to exponents if not previously taught, and some work on beginning algebra. The beginning algebra usually includes properties such as associativity, commutativity, and distributive, as well as order of operations. It also includes manipulation of linear equations. Graphing (at least plotting points) is also usually included. Topics in geometry (such as the Pythagorean theorem) are frequently included as well. It is less common to see a chapter on probability but this still frequently appears. Pre-algebra courses designed for more talented students or which follow a more challenging elementary school curriculum frequently go further into the beginnings of algebra.

Sparkly stickers and colored pens/pencils. I have some amazing sparkly little airplane/bus/train stickers.

I'd be doing 125x4 - 2x4 as well -- 125x4 is something I recognize because of .125 being 1/8.

Using the distributive property is exactly what we are doing in the standard long multiplication, fwiw. If we're doing something like 123x45, that's 123x(40+5). We put 123x5 on the first row, 123x40 on the second row, and then add them up to get the answer.