*sings* We're men We're men in kilts TIGHT kilts!

You don't understand, clearly. They are the only important people in the world. As a matter of fact, when you saw them coming behind you, you should immediately have pulled to the shoulder to allow them to proceed through. :p

I remember once, trying to exit a parking lot -- the traffic was completely stopped. Completely, completely stopped. After 20 minutes of cars creeping past me, nose-to-tail, making sure that I couldn't possibly merge out ... finally, someone was a little slow and I managed to get into line. The person was so mad that I'd dared to come in off the side road that they laid on their horn for 5 minutes straight while the traffic did not move an inch. After the 5th minute (we were watching the clock in my car and boggling), for the first time ever in my life, I rolled down my window and flipped someone the bird. They quit honking.

bcm is going to include more review of fractions/exponents/percents/etc than pre-algebra but frankly I would buy both (if you get old editions they are very very cheap) and skim through them before placement. I'd also keep both for reference until he graduates. Between them they include pretty much every part of pre-algebra mathematics you might want to know about in two handy reference volumes. ETA: Furthermore, whichever one you go with, I would have him test through the book. It won't hurt him at all to have a preview of the beginning part of algebra before entering algebra in the fall and may make the transition easier. By "test through the book" I mean read the chapter, take the chapter test. If he gets an A/B, review/correct/reteach any missed problems -- otherwise, work the homework and retest. If you work the homework and retest, don't tell him what was wrong on the test -- just tell him that he missed a few so he'll be doing the homework and retesting. That way he can't just memorize the solution method for the problems.

Are you sure he's not joking?

Some of those problems are really cute.

Frankly I'd friend him and then hide his stuff. I've done this with a few relatives who continually post crackpot news articles that are really easily debunked with 30 seconds of googling.

You should really ask regentrude this. Math is my specialty, not physics. Personally I would rather have calculus before calc-based physics. The extra scope and sequence does not matter so much -- they need to be able to do lots of derivatives in mechanics and lots of integrals in e+m. This applies especially with the need to finish the course before the AP exam. It should work, though, if pre-calculus is finished in time to begin calculus in the summer. The student could do the calc 1 sections in the summer, in the fall do mechanics + the calc 2 sections, and in the spring calculus would be finished, so the student could focus on e+m and exam prep. There is a pre-calculus outline in the link quoted above which indicates which sections are really necessary to complete calculus and which are bonus. Some schools do run them concurrently (my graduate school did) but the students I spoke to who were taking them concurrently were pretty uniformly negative about how they wished they had waited a semester.

Any topics from honors algebra 2 omitted from the beginning algebra textbook, the algebra half of an honors pre-calculus class, plus some supplemental topics that are not commonly taught in standard high school math classes. For example, I have never seen a standard high school course that discussed the Cauchy-Schwarz inequality or delved into functional equations.

It would depend somewhat on your child's interests. Books like C + P and NT are outside the normal scope and sequence, and so would be electives that I might omit for a student who has goals which require getting to calculus faster (like one who wants to do physics). One who wants to do CS, on the other hand, might want to do the discrete math books I just mentioned and omit some chapters from precalc instead. Some books are also only a semester (again, both CP and NT should be one-semester courses).

One of the best parts about being homeschooled for high school imo was not having PE. The local high school had PE required all 4 years and it was all competitive games such as volleyball etc. For someone who was fat and clumsy like me it would have been utter torture.

Hmm I was thinking about this guy -- http://www.textbookleague.org/ttlindex.htm

Textbook League perhaps? Holt got low scores, but so did pretty much every other middle school phys. science textbook out there.

Quite often, yes. It would probably be used more in the case of marginal applicants -- a marginal applicant from a $60k/year private school is probably going to be able to pay full tuition.

I haven't looked at the whole book so I really couldn't comment definitively on that, sorry. My gut feeling is that it would be too much for a "lite" geometry -- in other words, they'd have seen too much of the AOPS material already to make the discovery approach worthwhile, although the problems would be less challenging than AOPS. I would e-mail the author and ask her opinion as well.

My ex had gone to a British boarding school and that's about what he felt about it. He read Harry Potter and said "HAHAHA ... no"

You might consider using problems from Ray's Arithmetic -- available free online.

There's also some vintage texts which offer a very good level of challenge, although most of them are so OOP it's difficult to piece together a curriculum. I also think it would be quite reasonable to make a challenging high school course sequence by using a standard, rigorous enough text and supplementing with the original AOPS problem-solving texts (as that's what they were intended for). I do think that mathy kids should *try* AOPS because I consider it supremely awesome, but it certainly isn't a fit for everyone and there are plenty of other options which will also prepare even a child who wants to be a theoretical mathematician.

412/3 is NOT the same as 137.3 -- one is exact and one is a decimal approximation. I would mark that wrong with a minor deduction, but if they wrote 137 and 1/3 I would mark it correct. If he wrote 137.3 repeating (with a line over the 3) I would also mark it correct because that is exact, but I would prefer that it be left as a fraction (improper or mixed, no issue either way) There is a difference between giving an alternate exact form of the same answer and giving an approximate form. This is an important difference and worth stressing to your children. One easy way for YOU to tell if they have given a different exact form of the same answer or an incorrect answer (some exact forms look very different even though they are correct) is to plug the TM answer into a calculator and then subtract your child's answer (do not round at any point). If the difference is 0, they are different exact forms. If the difference is not 0, they are not. For example, if you do 412/3 - 137.3, you will get .0333... This should not actually take too much time. Now, as for a grading policy when work is not shown and the answer is very different, here is MY policy that I use in classes. If the work is not shown, the answer is correct, and it's something I can do in MY head, I mark it correct. If the work is not shown, the answer is correct, and it is too complex for me to do in MY head (I teach math so this is a high barrier), I mark it incorrect because I assume an unauthorized aid was used. If the work is not shown and the answer is incorrect, no partial credit is awarded -- the score is 0.

Stop timing it. As others said, competency is more important. Put it at the end of a school period so that as soon as he's done and it is correct he can go play. He will see the value of completing it rapidly and correctly so that he can go and play more quickly, but he will not have the stress of a timer ticking away at him.

I liked this book -- http://smile.amazon.com/History-Slavery-Illustrated-Monstrous-Evil/dp/1555217680/ref=smi_www_rcolv2_go_smi?_encoding=UTF8&*Version*=1&*entries*=0 -- it can get graphic at places because it has period illustrations.

Sounds good. Teaching a student how to study for a final exam is very, very important. It is one of the largest gaps I see in my students at the university -- they do ok on doing the homework for TODAY, but not well on "ok, that was difficult, so I need to review it again tomorrow and put it on my daily review schedule until I really get it" or "ok, that was easy, I'll check back in a week to make sure I still understand it"

Combinatorics is most simply the mathematics of counting. For example, the problems like 'Alice, Bob, Chuck, and Dana go out for ice cream. How many different ways could they line up for cones? If there are waffle cones and regular cones and the ice cream comes in 5 flavors with 3 toppings, how many different kinds of cones could be made?' are beginning problems in combinatorics.

AB originally was two quarters of a three-quarter sequence (a, b, and c) while BC included all 3 quarters. AB will usually give credit for calc 1 while BC will usually give credit for calc 2, if AP credit is accepted. Some schools do not accept AP credit and some require their own exam as verification, because of the use of calculators on the calc exams. The BC exam also includes an AB subscore, so a student who takes the BC exam may get credit for calc 1 but not calc 2 based on the AB subscore.

With this clarification to your previous statement, I agree 100%. Clearly there was some misunderstanding on my part as I did not understand that you were talking about a child who did not understand yet that 9 + 6 meant 9 things and 6 more things or 6 things and 9 more things. I would absolutely not start trying to teach mental addition strategies to a child who did not yet understand what addition meant.