AOPS - progression

[3sapphires]

I've tried to use the AOPS website to figure this out, but I think I am missing something. . .

 

What is the typical progression through the AOPS books? (and I admit I'm planning ahead)

 

We just started Introduction to Algebra, and I see that it is "more" than a typical Algebra 1 course. But it's not enough to be Algebra 1 and 2, is it?

 

Should I plan on it taking more than a year with a bright but not particularily math-confident 8th grader who has a solid Pre-Algebra foundation?

 

I was assuming I would do Geometry next year, following the progression that my older daughters did at their school (although this is changing), but is that right for AOPS? I see that there are two books - Introduction to Counting and Probability and Introduction to Number Theory. Where do these fall? They look like something we would like to go through. . .

 

Or are those books just used for contest prep?

[kiana]

c/p and number theory are electives, about a semester each. I'd highly recommend them for most students because they're really interesting math that doesn't get covered in the school curriculum due to time constraints.

 

It will take as long as it will take -- I don't think that I'd try and make it fit into a schedule. Some people have done it in a calendar year and some have taken more. Unless your dd is planning on leaving homeschool for high school, the schedule shouldn't be an issue. If you do decide to do c/p and nt, they are frequently done before geometry as they are considered less challenging, so if she's halfway through the year when she finishes algebra and you want to get back on track at one year per course, you could round out the year by doing one of them.

[Julie of KY]

I agree with Kiana.

 

Wanted to add, I think the Intro to Algebra book does cover algebra 1 and 2. I asked if it really covers all of algebra 2 and went looking through other books and the only topics that I found might be touched on in other algebra programs are hyperboles, ellipses, and matrices.

 

The Counting and Probability and Number Theory books are great books. They can be done anytime in the sequence or skipped if you are crunched for time. I did them interspersed with algebra and geometry as a break from those subjects.

[chiguirre]

My dd is enrolled in the Well Trained Mind Academy's AOPS Algebra 1 class. They will cover chapters 1-10 of the Intro to Algebra book. They do also use a fun, puzzle-based, drill and kill workbook for extra practice for tough topics. This is the first year they're offering AOPS Algebra in addition to Saxon Algebra, but I think their scope and sequence is a reasonable level for Algebra 1. It's certainly not intended to be a lite class, it's meant to be a deeper class for kids who like math and want a challenge. So far it's lived up to my expectations, but it's only week 3.

[Penelope]

You can find this info on the AoPS site, where they explain their online classes.

 

They don't consider the Intro to Algebra book to be a complete Algebra one and two, compared to more traditional school textbooks. A few of the topics typically found in an algebra 2 course will be covered in the Intermediate Algebra book.

 

Disclaimer: I am not a math teacher!

 

Often on this board, it has been shared that the first 13 chapters would be about equivalent to algebra 1. I would agree with this, after comparing very closely with the Foerster's and Dolciani texts. I don't own Larson or Jacobs, so can't compare with those except by looking at scope and sequence. The first 13 or 14 chapters of Intro to Algebra covers quadratics in a manner equivalent to those textbooks. It also covers a few topics that wouldn't normally be hit until algebra 2 (imaginary numbers is what comes to mind first). However, it doesn't touch on functions at all until later in the book; when it does, it goes further than algebra 1 textbooks, but most algebra 1 books seem to cover functions as a topic, and if you look for algebra 1 exam examples online, you will see them all over. There are a few other topics that are in Foerster's that aren't in AoPS ch 1-13. Some of them, I think, are covered in a deeper way in the C and P course. But these topics will include typical sorts of standardized test problems, so if you don't use the extra books, it might be a good idea to have another textbook to pick up on these topics.

 

AoPs is so different that I think one has to be very careful if not planning to use the whole sequence. I wouldn't think it would be a good idea to say the first 10 chapters are algebra 1, and then move to another class with another algebra 2 textbook. I think its the same with probably many programs, though. I did stop after 14 chapters to move to Geometry for a year (at student request), and because I wasn't sure whether we would go back to AoPS afterward or not, spent the summer going through Foerster's and doing the few topics that we did not yet get to in AoPS.

[Julie of KY]

AoPS offers chapters 1-13 as Algebra 1. While some of this material is arguably more often taught in algebra 2, other pieces of these chapters are expected to be known before starting algebra 2 so I would argue that it would be best to finish chapters 1-13 to call it algebra 1.

[go_go_gadget]

We just started Introduction to Algebra, and I see that it is "more" than a typical Algebra 1 course. But it's not enough to be Algebra 1 and 2, is it?

 

Should I plan on it taking more than a year with a bright but not particularily math-confident 8th grader who has a solid Pre-Algebra foundation?

 

I was assuming I would do Geometry next year, following the progression that my older daughters did at their school (although this is changing), but is that right for AOPS? I see that there are two books - Introduction to Counting and Probability and Introduction to Number Theory. Where do these fall?

 

Right, the Intro to Algebra book covers extra topics, but those topics don't take the place of Algebra 2. You can do Intro to Geometry after the first 11 chapters of Intro to Alg, and then do the second half of Intro to Alg,then Intermediate Alg, then Pre-Calc, then Calc. The Intro to Number Theory and Intro to Counting and Probability can be used anytime after the first 11 chapters of Intro to Alg (although some have successfully used Intro to Num Theo concurrently with Intro to Alg), and I believe the Intermediate Counting book is best used following the Intermediate Alg book, though I'm not as sure about that one. However, the Number Theory and Counting books are not essential, and not part of a typical high school sequence. I wouldn't cover those unless the student were particularly keen (so I hope mine are, because discrete math is my thing).

[Penelope]

Interesting that here, they show that Intro C and P is an essential part of the sequence, which would go along with what I said above about probability and number topics being part of a usual math sequence, as part of an algebra course. Of course AoPS would be more intense.

 

http://www.artofproblemsolving.com/school/recommendations

 

And this is from their page about the Intermediate Algebra class:

 

"This course goes beyond what you would find in a typical honors Algebra curriculum. Algebra courses vary widely in their definitions, but our Intermediate Algebra class covers topics typically found in honors Algebra 2 and Precalculus classes, as well as many topics that are not found in most other curricula. "

[AEC]

It's a really great Alg1 course - it both covers a few more topics, and in more depth, than most Alg1 courses but does not, IME, cover the full set of topics of a good Alg2 course.  It probably covers 90% of the topics in _some_ alg2 course, but that's not really the goal here, is it?

 

"What is the typical progression through the AOPS books? (and I admit I'm planning ahead)"

 

per- AoPS (and my own experience - we're part-way through this sequence)...

 

* pre-alg

 

* IntroToAlg (alg1)

 

* Your choice of order of Geometry, Intro to C&P, Intro to Number Theory.

The C&P and Number Theory books are, as someone mentioned really great for an interested math student.  They're very useful and quite interesting but not usually covered in this depth in highSchool.

Geometry is a full year course and I'd consider it required.  C&P and NumberTheory are shorter - maybe a 1/2 year, maybe less.

 

* Intermediate Alg (alg2)

 

* (optional: Intermediate C&P and Intermediate NumberTheory)

 

* Pre-Calc.

 

 

 

"Should I plan on it taking more than a year with a bright but not particularily math-confident 8th grader who has a solid Pre-Algebra foundation?"

 

it takes as long as it takes...but IME a year is a reasonable schedule.  Plan on some bumps, especially if the student hasn't solved AoPS/math-contest difficulty problems.  There is a learning curve on how to solve problems, regardless of the math involved.

 

"I was assuming I would do Geometry next year, following the progression that my older daughters did at their school (although this is changing), but is that right for AOPS?"

 

Personally - we're completing the IntroToAlg book (alg1), then doing C&P, then NumberTheory before going on to geometry.  DS13 finds C&P fun and interesting and they're really really useful.  (DS is currently into making up games, so probability of events is seeming useful to him.)  Strictly, both books are 'optional' and a bit outside the mainstream math sequence.

 

For me, I think the decision would come down to how quickly the student moves through the material.  It's important to me that my kids take calculus by their senior year in HS (so they can take 'real' physics concurrently and have seen calculus pre-college).  If C&P and NumTheory takes an extra year you won't hit that.

 

I'd play wait and see.  If you can fit them in and still do pre-calc as an 11th grader I'd do them....but that's just me.

 

-andy

[Penelope]

I would add this: look for Regentrude's posts about the sequence, on many threads, where there are other posters who have been through many of the books or classes and also have good insight. All of those threads have been helpful to me.

[Arcadia]

For progression through the aops books, you could just follow your child's pace. If you want to you could compare scope and sequence with your state's math textbooks but the aops books don't align nicely with state standards.

 

Interesting that here, they show that Intro C and P is an essential part of the sequence, which would go along with what I said above about probability and number topics being part of a usual math sequence, as part of an algebra course.

My kids did C&P. However the probability for SAT math section is covered in math prior to prealgebra. There is no probability in ACT math.

 

The book can be finished over the summer by a child who likes C&P and/or if the parent would like the child to have more exposure to C&P prior to a Statistics course.

 

ETA:

At the library and checked that there is very little probability & statistics in SAT Math 1 & 2 subject tests.

[3sapphires]

Wow, there is a lot to consider here. Thanks for all of the thoughtful responses.

 

At first reading of this thread, I am leaning towards having her do the intro to C&P and Intro to Number Theory next year, then Geometry in 10th, Intermediate Algebra in 11th and Pre-Calc in 12th.

 

But, another option I am considering is to use one of them over the summer, a bit each day, to stay "math-brained". She could do one the summer before 9th grade and one the summer before 10th. That wat we would get to Calculus.

 

I'll have to read this thread a few times, and see how our year goes to make a decision. She is liking the curriculum so far, though, so that is a giant plus, as I love it.

[kiana]

c/p and nt would make *great* summer classes. One great thing about doing them that way is that if you do not finish them, they are fun electives anyway -- it is similar to not finishing a fun history class on vikings or whatever.

[MomOfABunch]

http://forums.welltrainedmind.com/topic/361425-aops-or-college-algebratrig/

 

http://forums.welltrainedmind.com/topic/553416-rethinking-math-from-aops-to/

 

These posts may be helpful.

[lewelma]

I think that both the Intro Algebra and the Intro Geometry books take longer than a 9-month school year.  I would expect each one to take a full calendar year or more.

 

Also, the intermediate number theory class is HARD, so if you plan to do that, do it *after* PreCalc. 

 

My ds completed the Intro Algebra, Intro geometry, and calculus books on his own, and has taken the classes in intro and intermediate counting, intro and intermediate number theory, and Precalc. He is currently taking the WOOT.  So if you have any specific questions, I can ask him.

 

Ruth in NZ