I would agree with this.

Oh, I think it's badly worded if they're trying to form a question which results in an answer of 72. If the answer key is just wrong, then I don't see any issues.

First, I would still not say "0 is not a multiple of 9 and 12" but rather "0 is not a positive multiple of 9 and 12" in my explanation of the problem. I'm surprised that Singapore Math doesn't just say "the smallest positive number" as this definition would be mathematically correct regardless of whether you assume negative numbers have been introduced or not. However, I don't have a copy available to check for myself. Second, I still do not think that excluding 0 is defensible. It states that "both trains have just left". It does not state that the station has just opened. If, in your hypothetical explanation of the problem, we are at 36 minutes, then 72 minutes later will be 36 minutes from now.

Honestly I think I'd just start with pre-algebra. I've heard so many people express their delight at being able to understand conceptually what they never really fully got before.

Nope. Your interpretation is correct. Good catch -- I'd skimmed that post and didn't notice that.

Sorry about your grandmother :/ Times like this are when I catch up on facebook and email. Also, I don't know if you're into science fiction, but this guy's one that I like and has a bunch of (consecutive) chapters from his books posted free in html (so no downloading). http://smstirling.com/books/

I can't really agree that it's unnecessary. So many programs have named their last year before algebra as pre-algebra that if you skip it, you haven't really completed the arithmetic scope and sequence. Where it's unnecessary is if you do a program such as CLE (where the last course is still named Mathematics 8) and then think that since you haven't done something labeled "pre-algebra" you still need to do a textbook called that. Just follow the scope and sequence of the program you're using. If they have pre-algebra before algebra, do it. If they have math 7 before algebra, do it. If you're changing programs, do a placement test. If you're not sure whether everything is covered, ask here.

What Maize said. Pre-algebra originally was a high school course intended for students who were not ready for algebra. Later middle schools also started calling the last course before algebra pre-algebra. In whatever curriculum you are using, pre-algebra will be the last year before Algebra. For example, in Saxon, 8/7 and algebra 1/2 are both pre-algebra (because they both review all arithmetic in preparation for entry to algebra).

I swear I read FedEx for biting. I was wondering what on earth the thread was about.

You just need to find a picture of a barefoot gentleman wearing a kilt, putting a crock-pot into his hybrid car while leaving his shopping cart in the parking lot.

Of course it is, and you don't have to have cute little perfect cubes if you're going to mash them up anyway. I just chop mine into chunks.

Asking the teacher sounds like a great idea, because if the answer is supposed to be 72, the question is really badly worded -- more of a "guess what I'm thinking" than a math question.

I'd much rather teach my kid that the answer book may not always be right than try to spin a story about why it is. Sometimes the answer book is wrong.

yep! other than that his reasoning works fine. I like his reasoning a lot actually.

For the record, MIT's 18.01 covers what is normally covered in two semesters elsewhere, that is, single-variable differential and integral calculus. Their 18.02 course covers what is covered in calculus 3/multivariable calculus. That is why Calc BC won't give you credit -- calc BC is two regular semesters, not two MIT semesters.

Post a cellphone pic or similar of the problem and describe what he did.

Are there two precalculus classes (i and ii), or potentially precalculus algebra and then trigonometry? There should be two courses between intermediate algebra and calculus 1. Anyway, they should take whichever course has intermediate algebra as the prerequisite, assuming they pass the placement test (which sounds likely)

Well, I didn't mean to do that, but this applies to everything -- not just elementary mathematics. There are so many things to learn that you could learn for the rest of the ages of the earth until the last trumpet and still have more to learn. So don't worry about making yourself perfect before you begin teaching, because you can't do it. But the important thing is to retain a sense of thoughtfulness and curiosity about what you teach -- to be open to new ideas -- and when your kid does something weird and gets the right answer anyway, if you can't figure out if it's mathematically legitimate, come here to ask! :)

As written, I believe the answer key is wrong and the answer should be 36. The only hypothetical possibility I can see for '72' being in the answer key is that they are talking about two single trains -- and thinking of it as train 1 going from station A to station B in 12 minutes, then back to station A in 12 more minutes, so it'd really be leaving every 24 minutes, and similarly for train B. But if this is what they meant, then the question is extremely badly worded.

I don't think you *need* to read it but I found it a very thought-provoking read. The fascinating part of it I found is that the Chinese teachers (on average) kept learning elementary math. They did not consider that their knowledge was complete and the only part of their job left was to impart knowledge to hungry little minds.

Jacobs is popular, some people also use the book the guy from Math without Borders selected. I've never seen it but I feel if he had the good taste to pick Foerster's he probably didn't pick a crappy Geometry book.

Definitely not wrong. Great idea if you have time. Algebra and Trigonometry is a challenging text to finish within a year, though.

Placement test. Always.

I see the same issue.

Quite probably the trigonometry material is incorporated into the precalculus text (the coverage of trigonometry in the algebra 2 text is somewhat abbreviated) and that's probably why it's out of print.