AOPS Intermediate Algebra

[rdj2027]

WTMA offers Alg 1 and Alg 2 using the Intro to Algebra book.  The next step would be pre-calculus (apart from geometry) for which AOPS also offers a book.  How does Intermediate Algebra fit into the sequence?  I thought Intermediate Algebra would be part Alg2, part pre-calculus.  Do people skip Intermediate Algebra and go straight to pre-calculus or are those classes really geared towards students starting prior to 9th grade?

[Penelope]

I started a thread a while back that touched on this. I considered the AoPS algebra 2 class, but for now have decided to go another direction. But I have the same question. I am really curious over whether they will put the extra year of math in, and what they will call it, or whether they will combine some chapters from intermediate alg. and the precalculus book into a one year course.

 

You might try emailing Heather Quintero, who is teaching all of the WTMA AoPS courses, to find out if she has a plan mapped out.

[Julie of KY]

A "typical" precalculus course covers college alegbra and trig. This is some of the material in the two AoPS books. The AoPS books go deeper and further than what is typically taught. I would not try to combine the AoPS Intermediate Algebra and Precalculus books into one year for most students and I'd be hesitant to do much of the AoPS precalculus book without having done a chunk of the Intermediate Algebra book.

 

My oldest did the AoPS books, my second son will go with a solid but not quite as rigorous precalculus.

 

 

[MarkT]

Currently they offer:

 

http://www.wtmacademy.com/courses/classes/algebra-1-aops-singapore-methods/

 

http://www.wtmacademy.com/courses/classes/algebra-ii-aops-singapore-methods/

 

Which I would best describe as "Honors Algebra 1 parts 1 and 2"  (which may be a good sequence for middle schoolers).

 

 

You can't just skip over the Intermediate Algebra book in the long run.

Edited February 25, 2016 by MarkT

[AEC]

WTMA offers Alg 1 and Alg 2 using the Intro to Algebra book.  

 

so...two years of high-school math, both from the Intro Alg book?  The AoPS Intro Alg book is more thorough and somewhat broader than typical Alg1 classes, but I'd hesitate to call it two years of HS math.  In particular, there's very light treatment of exp and log functions, nothing on matrices (as I recall) or conic sections, etc.

[rdj2027]

That is what I was wondering about.  I think they are talking about Alg A and B but their labeling as Alg 1 and 2 threw me off.  My son wants to go with the actual AOPS classes, I think they move a little too fast. His argument is that if he starts in May, he will be done with the Intro book in January and have plenty of time to review if necessary.  

[Lilaclady]

The labeling might be the problem. Aops has intro to Algebra book, intermediate algebra book and precalculus. It will be very hard to jump from Aops algebra 2 into precalculus without doing the intermediate algebra

[Brad S]

People don't generally skip the AoPS Intermediate Algebra book; it comes after their Intro to Algebra book and before their Precalculus book.  I think their Geometry book is usually used after Intro to Algebra, but you don't need it for Intermediate Algebra.  If you're looking to cut out sections of Intermediate Algebra and Precalculus for the minimum needed to progress to calculus, etc., Kathy in Richmond and Regentrude had some excellent posts on that about 1-3 years ago.

[wapiti]

That is what I was wondering about.  I think they are talking about Alg A and B but their labeling as Alg 1 and 2 threw me off.  My son wants to go with the actual AOPS classes, I think they move a little too fast. His argument is that if he starts in May, he will be done with the Intro book in January and have plenty of time to review if necessary.  

 

They do move fast and involve quite a bit of work.  One idea might be to start the book before the class, maybe by 2 months, and/or get a head start with Alcumus.

 

FWIW, the confusion over the online algebra 1 and 2 vs a standard school algebra 1 and 2 is presumably the reason that AoPS changed the course names to A and B.  I'm surprised WTMA went with 1 and 2, though I haven't looked at their website.

[wapiti]

For reference, this is one such post by Kathy re bare bones precalc:  http://forums.welltrainedmind.com/topic/361425-aops-or-college-algebratrig/?p=3744226

 

College algebra is in the Intermediate Alg text, and Trig is in the Precalculus text. But he doesn't have to complete those two volumes in their entirety in order to do precalculus. The material is wonderful and certainly worthwhile if you have the time, but it goes far beyond what we usually see in a precalc class.

With a good algebra 2 background, he could probably go quickly through the first 4 chapters of Int Alg, then move on to chapters 5 through 16. Then he could cover Chs 1 to 7 and 9 to 11 of Precalculus.

My 'bare bones' precalculus suggestion would be as follows: (This is for a kid who wants to cover what's usually done in precalculus in a text such as Foerster, but who wants an AoPS flavor & doesn't have two years to go through these volumes. Even so, this course outline would still be well beyond Foerster in depth and difficulty.) Do the exercises in each section and the Chapter Reviews. Starred problems and the end of chapter Challenging Problems could be sampled, but don't feel you have to do them all (it's not possible ).

Intermediate algebra textbook:
Ch 1 - 4: review
Ch 5 - 6: all
Ch 7.1 - 7.5
Ch 9.1 - 9.2
Ch 10.1 - 10.5
Ch 11.3 -11.4
Ch 13.1 -13.3, 13.5-6
Ch 14.1
Ch 15.1 - 15.3
Ch 16.1 - 16.3

Precalculus textbook:
Ch 1 - 2
Ch 3.1 - 3.4
Ch 4 - 7
Ch 9 - 11

Anything extra beyond that would be icing on the cake (and the skipped sections are the ones I consider my favorites:), but I understand time constraints).

 

Eta, I can't recall whether there's a post detailing what chapters of Intermediate Alg would be needed for a standard alg 2....  I found some thoughts of regentrude on that:  http://forums.welltrainedmind.com/topic/502281-quick-questions-on-aops-algebra/?p=5441976

 

EL: for algebra 2, I believe polynomials are usually covered, which would be ch. 6-9 in Intermediate Algebra.

Also, ch. 13 on exponentials and logarithms which are only briefly touched on in Intro, and ch. 14 on radicals.

Ch. 1-4 in Intermediate are review from Intro.

 

Just curious: does it really matter?

I simply gave credit for algebra 1 for the entire Intro to Algebra text and credit for algebra 2 for Intermediate Algebra, being fully aware that this is not identical to scope and sequence of public school courses and my students did more. I think packaging math into nice one year parcels with specific labels is nonsense.

 

ETA: The question is a tricky one because schools group math very differently, Some teach a full year of precalculus, containing a semester of trigonometry and a semester of algebra (3), while others only do trig, or cram it together with algebra 2 into one year. So, what counts for "algebra 2" varies quite a bit from what I have seen.

So, where sequences and series are placed, and how deeply they are studied, depends on whether there is precalc or not. From a systematic point of view, I prefer an extensive treatment of sequences and series in precalculus, just prior to calc. OTOH, there are simple sequences and series on the SAT, so you'll want some in algebra 2. Now, Intro does some sequences/series, and intermediate goes deeper; if you really need t decide what goes where, I'd say the sequences/series in intro should suffice for alg 2, and the more extensive treatment in Intermediate could be part of precalculus. But again, this just shows how artificial those "packages" really are...

 

Edited February 26, 2016 by wapiti

[rdj2027]

Oh I am not looking to cut sections out, on the contrary.  I was just wondering how they can make this sequence work for high school.  The way it is set up, it really is a middle school sequence.  Nothing wrong with that.  My son will be in 9th grade and is determined to get through calculus.  His plan is to double up algebra and geometry, I just talked him out of doing Alg 1 and geometry concurrently.  I am happy if he makes it through pre-calc.

[AEC]

 My son wants to go with the actual AOPS classes, I think they move a little too fast. His argument is that if he starts in May, he will be done with the Intro book in January and have plenty of time to review if necessary.  

 

YMMV, of course, but for the motivated student it's totally do-able.  DD12 is on pace to complete the IntroAlg text in 5ish months.  That's roughly a section a day, 5 days a week, every week.  It helps that the first 4ish chapters of the book are, by comparison to the PreAlg text, fairly straightforward.

 

 

[madteaparty]

WTMA offers Alg 1 and Alg 2 using the Intro to Algebra book. The next step would be pre-calculus (apart from geometry) for which AOPS also offers a book. How does Intermediate Algebra fit into the sequence? I thought Intermediate Algebra would be part Alg2, part pre-calculus. Do people skip Intermediate Algebra and go straight to pre-calculus or are those classes really geared towards students starting prior to 9th grade?

I think they only offer two because they are adding to their line-up; geometry and algebra 2 are new this year.

I am guessing they will offer Intermediate algebra the following year, when the kids taking algebra 2 this next year are ready for it (hoping and wishing). Either way, we are not skipping intermediate algebra.

[rdj2027]

LOL, we both thought pre-algebra was straight forward. I am sure it will all work out in the end.

[...................]

Intro to Algebra is expected to be one entire year of math.  It is Algebra 1 with some advanced concepts usually covered in Alg 2 and some concepts not covered at all in some Algebra courses. So it's like "Algebra 1 plus"  On your transcript you would definitely give it an HONORS title for a higher weighted GPA.

 

 

[Penelope]

Here is the thread I mentioned. There are a few others linked within that one.

http://forums.welltrainedmind.com/topic/582321-aops-algebra-2-at-wtm-academy/?hl=aops+algebra&do=findComment&comment=6771681

 

I would think that ventually WTMA would have a blurb on their site about their particular sequence and how it has an extra year (if it will). Probably at this point, though, most parents who would choose the WTMA AoPS classes are familiar with AoPS sequence and are looking for that approach but with a slower pace than the classes at AoPS.

[rdj2027]

Thanks for the thread link, for some reason I couldn't find it.  I really would have liked the WTMA for middle school but my son was dead set to go back to PS.  He has come to see the error of his ways and will hightail it home for high school.  Unfortunately we are now at least a year behind where we could have done math leisurely.  Like I said, I am happy with getting through pre-calc, everything else is icing on the cake.

[Julie of KY]

Locally, there is not anything taught in Algebra 2 classes that isn't covered in the Intro book except a little bit of matrices and ellipes/hyperbolas. Local precalc classes covers the main topics of both the Intermediate book as well as the precalc book.