AoPS sequence? Alg 3??

[rbk mama]

I only just realized that the AoPS Algebra 2 course uses the second half of the Intro to Algebra textbook. The Intermediate Algebra textbook is actually Algebra 3. So I'm wondering how important Alg 3 is and if most people using the AoPS sequence include it? If you have used AoPS, can you please share the order you used each course? Richard Rusczyk says they encourage taking their Algebra 2 before Geometry (he says the Intro to Geometry is the toughest of the Intro books and should come last). Thanks!!

[Tattarrattat]

We took Algebra 2 before Geometry. I think AoPS Algebra 2 and part of Aglebra 3 cover what a school Algebra 2 normally covers. But AoPS Algebra 3 go beyond an Algebra 2 at a school.

[Tattarrattat]

RR explained a little bit what was covered in their Algebra 2 and 3.

 

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=140&t=397640

 

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=140&t=412729

[JeanM]

We haven't gotten there yet, but I was just going to suggest posting on the high school board as well. My older ds is doing Jacob's geometry now, but we're planning to switch to AOPS next year.

[regentrude]

The AoPS Intermediate Algebra text contains many algebra 2 topics in more depth, but also topics that are usually taught in a precalculus course. I found this a very important book. You can not skip it if you want to continue in the sequence ! We omitted the last chapters that were clearly competition math (as explained in the foreword) and not a prerequisite for anything in the standard math sequence.

The AoPS precalculus book, in turn, contains topics that are not part of a typical precalculus course. It goes a lot more in depth about vectors and matrices and contains some Linear Algebra concepts that are not usually taught in precalculus.

[Kathy in Richmond]

The AoPS Intermediate Algebra text contains many algebra 2 topics in more depth, but also topics that are usually taught in a precalculus course. I found this a very important book. You can not skip it if you want to continue in the sequence ! We omitted the last chapters that were clearly competition math (as explained in the foreword) and not a prerequisite for anything in the standard math sequence.

The AoPS precalculus book, in turn, contains topics that are not part of a typical precalculus course. It goes a lot more in depth about vectors and matrices and contains some Linear Algebra concepts that are not usually taught in precalculus.

 

 

Yep. In the 'old days' of AoPS (i.e. pre-textbooks), their precalculus consisted of a combination of both the Alg 3 class and their old Intermediate Trig & Complex class. The latter class was expanded with the addition of some linear algebra material and became what is now their Precalculus course. So, in order to get a full precalculus class, you need both courses (alg 3 first, precalc second). Otherwise you will miss all of the advanced algebra materia that is typically a part of precalculus.

 

I'd suggest that you do their alg 1, alg 2, geometry, alg3, and then precalculus and calculus. The other courses in number theory and counting & probability are wonderful but not usually a part of the standard math sequence. You can insert them at various times into the sequence as a breather from the standard fare or as enrichment. 'Competition math' is really just a part of mathematics that is often overlooked. Our standard sequence in the US is strongly oriented toward the future engineer or scientist. Discrete math (aka competition math) is highly useful, too (computer science, etc)

[Tattarrattat]

I'd suggest that you do their alg 1, alg 2, geometry, alg3, and then precalculus and calculus. The other courses in number theory and counting & probability are wonderful but not usually a part of the standard math sequence. You can insert them at various times into the sequence as a breather from the standard fare or as enrichment.

 

We are on this track, except that we do NT/CP on our own and will probably add competition courses somewhere down the road.

[lewelma]

Is it too difficult to do this sequence: Intro Algebra book, then Intro Geometry, and then Intermediate Algebra? I did not realize that the intro geometry book was particularly difficult. I would like to do them in this order to help with studying for the IGCSE exam (which he would take after geometry but before intermediate algebra). But if he is likely to find the Geometry book too difficult, we can do the intermediate Algebra book next and do Geometry prep directly for the exam. Suggestions?

 

ETA: I have reread the previous posts and it might be that I am just confusing the textbooks with the course names. But I would still love some clarity.

 

Ruth in NZ

Edited March 21, 2012 by lewelma

[Tattarrattat]

Ruth, Intro. Algebra book matches their online Algebra 1 and 2 classes (they split the book in half), intro. geometry matches their intro. geometry class. Intermediate Algebra book matches their algebra 3 class.

 

It'd be fine to go through the books in the sequence you mentioned: intro. algebra, intro geometry, intermediate algebra. That's what they usually suggest on AoPS forums.

[lewelma]

Ruth, Intro. Algebra book matches their online Algebra 1 and 2 classes (they split the book in half), intro. geometry matches their intro. geometry class. Intermediate Algebra book matches their algebra 3 class.

 

It'd be fine to go through the books in the sequence you mentioned: intro. algebra, intro geometry, intermediate algebra. That's what they usually suggest on AoPS forums.

 

Thanks!

[rbk mama]

RR explained a little bit what was covered in their Algebra 2 and 3.

 

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=140&t=397640

 

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=140&t=412729

 

Thanks for these links! I don't know why I never thought of the AoPS forums :blink:. RR answered my questions exactly.

 

The AoPS Intermediate Algebra text contains many algebra 2 topics in more depth, but also topics that are usually taught in a precalculus course. I found this a very important book. You can not skip it if you want to continue in the sequence ! We omitted the last chapters that were clearly competition math (as explained in the foreword) and not a prerequisite for anything in the standard math sequence.

The AoPS precalculus book, in turn, contains topics that are not part of a typical precalculus course. It goes a lot more in depth about vectors and matrices and contains some Linear Algebra concepts that are not usually taught in precalculus.

 

Thank you for confirming that its necessary to the sequence! So does each of these take a full year?

 

Yep. In the 'old days' of AoPS (i.e. pre-textbooks), their precalculus consisted of a combination of both the Alg 3 class and their old Intermediate Trig & Complex class. The latter class was expanded with the addition of some linear algebra material and became what is now their Precalculus course. So, in order to get a full precalculus class, you need both courses (alg 3 first, precalc second). Otherwise you will miss all of the advanced algebra materia that is typically a part of precalculus.

 

I'd suggest that you do their alg 1, alg 2, geometry, alg3, and then precalculus and calculus. The other courses in number theory and counting & probability are wonderful but not usually a part of the standard math sequence. You can insert them at various times into the sequence as a breather from the standard fare or as enrichment. 'Competition math' is really just a part of mathematics that is often overlooked. Our standard sequence in the US is strongly oriented toward the future engineer or scientist. Discrete math (aka competition math) is highly useful, too (computer science, etc)

 

Thank you! Again I'm wondering how long this typically takes. If each course is one year, than the sequence is one year longer than the traditional, correct?

[Kathy in Richmond]

Again I'm wondering how long this typically takes. If each course is one year, than the sequence is one year longer than the traditional, correct?

 

Not necessarily. The AoPS algebra 1 and algebra 2 classes are both taught out of the same Introduction to Algebra textbook. Most students with sufficient preparation could cover that textbook (or both online classes) in one year. Of course, younger kids who start the sequence early might spend more than one year.

[catz]

Not necessarily. The AoPS algebra 1 and algebra 2 classes are both taught out of the same Introduction to Algebra textbook. Most students with sufficient preparation could cover that textbook (or both online classes) in one year. Of course, younger kids who start the sequence early might spend more than one year.

 

If you do the online classes, the Intro to Algebra book will take one year. I think many people doing it on their own will take longer? I know it will probably take my 5th grader about 2 years to get through it. We spend about 3-5 hours on math a week though and I'm thinking if we spent twice as much time, we'd be moving that much faster. I also have no problem sitting for a week or so on a challenge problem set, doing a problem or 2 a day, if I feel like my son is gaining while trudging through them.

[fractalgal]

Thanks to all who posted in this thread. I have learned a great deal from you.:)

 

My daughter is on track to finish AoPS Intro to Algebra book in the next few months. I did think the scope of topics went well beyond a typical Algebra I book, but did not realize much of Algebra II was also covered. I was thinking that AoPS Intermediate Algebra was Algebra II.

 

I agree that AoPS Intro to Algebra can be completed in a year or less. She works through it independently, but does ask me occasionally about a *'d problem. She has told me several times how it is her favorite math we've done, so that is a good sign.

[Kathy in Richmond]

If you do the online classes, the Intro to Algebra book will take one year. I think many people doing it on their own will take longer? I know it will probably take my 5th grader about 2 years to get through it. We spend about 3-5 hours on math a week though and I'm thinking if we spent twice as much time, we'd be moving that much faster. I also have no problem sitting for a week or so on a challenge problem set, doing a problem or 2 a day, if I feel like my son is gaining while trudging through them.

 

And I think that what you're doing is perfect for a 5th grader. FWIW, it's pretty much what I did with my daughter (sans AoPS texts - they didn't exist then). My dd studied algebra over two years (grades 5 and 6) from different texts & with lots of thought-provoking problem solving thrown into the mix.

[rbk mama]

Thanks to all who posted in this thread. I have learned a great deal from you.:)

 

My daughter is on track to finish AoPS Intro to Algebra book in the next few months. I did think the scope of topics went well beyond a typical Algebra I book, but did not realize much of Algebra II was also covered. I was thinking that AoPS Intermediate Algebra was Algebra II.

 

I agree that AoPS Intro to Algebra can be completed in a year or less. She works through it independently, but does ask me occasionally about a *'d problem. She has told me several times how it is her favorite math we've done, so that is a good sign.

 

How does your daughter work through it independently? Does she check her work with the solutions manual and only get you when she doesn't understand something? I'm curious how others use the books. I've been correcting my son's work, but more and more often I'm just referring him to the solutions manual.

 

My sixth grader started Intro to Algebra in mid-June (after completing about half of Foerster's last year) and is only now completing chapter 11! So it will most likely take all of next year to complete the second half.

[regentrude]

How does your daughter work through it independently? Does she check her work with the solutions manual and only get you when she doesn't understand something? I'm curious how others use the books. I've been correcting my son's work, but more and more often I'm just referring him to the solutions manual.

 

My kids now work independently through AoPS. In the beginning, they would work with me or Dad close by, because they needed more frequent help clarifying concepts and answering questions. Now they work by themselves for the most part and check their own work with the solution manual. They consult us when they get stuck.

 

 

My sixth grader started Intro to Algebra in mid-June (after completing about half of Foerster's last year) and is only now completing chapter 11! So it will most likely take all of next year to complete the second half.

 

My son did Intro to Algebra in 6th grade, and he got through chapter 12. So for him, it will take two years. We spend anpother semester working onchapters 13-15, but now the material gets more abstract and we are taking a break from algebra, spending as semester on C&P. It makes no sense to rush, it will take whatever time it takes.

My DD worked through Intro in 7th grade and finished over the summer, but she worked for 220 hours on that book. Definitely more than a typical one-year course.

[rbk mama]

Not necessarily. The AoPS algebra 1 and algebra 2 classes are both taught out of the same Introduction to Algebra textbook. Most students with sufficient preparation could cover that textbook (or both online classes) in one year. Of course, younger kids who start the sequence early might spend more than one year.

 

It's taken us about 8 months to do the first 11 chapters (after completing the first half of Foerster's the prior year), so I'm thinking it will take all of next year to complete the second half. I've been wondering all year if this is the right fit for him. I exchanged a few emails with RR from AoPS who was encouraging, but I'm still unsure. I don't mind taking this long, now, but I'm wondering if the other courses will be equally difficult for him (?)and I'm making things harder than they need to be. On the other hand I really appreciate the emphasis on problem solving skills (great talk by RR linked in another thread recently).

 

ETA: RR said the online class goes through the first 10 chapters in 3 months! :tongue_smilie:

Edited March 21, 2012 by rbk mama

[fractalgal]

How does your daughter work through it independently? Does she check her work with the solutions manual and only get you when she doesn't understand something? I'm curious how others use the books. I've been correcting my son's work, but more and more often I'm just referring him to the solutions manual.

 

My sixth grader started Intro to Algebra in mid-June (after completing about half of Foerster's last year) and is only now completing chapter 11! So it will most likely take all of next year to complete the second half.

 

When I mean independently, I mean that she reads the assignment by herself, does the assignment on her own, then I correct her work daily. We will discuss problems after she attempts them and misses them. I usually have here attempt fixing her mistakes several times before I discuss with her. She usually is able to solve them on her own after several attempts.

 

She does not look at the solution manuel EVER, unless I ask her to look at the way the author solves a problem. She is stubborn, thinks looking at the solution manuel is 'cheating', and usually thinks her way of solving something it better -even when it isn't.;)

[Kathy in Richmond]

It's taken us about 8 months to do the first 11 chapters (after completing the first half of Foerster's the prior year), so I'm thinking it will take all of next year to complete the second half. I've been wondering all year if this is the right fit for him. I exchanged a few emails with RR from AoPS who was encouraging, but I'm still unsure. I don't mind taking this long, now, but I'm wondering if the other courses will be equally difficult for him (?)and I'm making things harder than they need to be. On the other hand I really appreciate the emphasis on problem solving skills (great talk by RR linked in another thread recently).

 

ETA: RR said the online class goes through the first 10 chapters in 3 months! :tongue_smilie:

 

I'd also encourage you to take your time for now & keep going through the AoPS algebra as long it's working for your son and he's enjoying it. I do think that it's highly beneficial to have a solid grounding in algebra, and AoPS is about as solid as it gets.:)

 

Yeah, that RR talk is great! I was in the audience that day, and everything he said resonated with me and our experiences.

[rbk mama]

My kids now work independently through AoPS. In the beginning, they would work with me or Dad close by, because they needed more frequent help clarifying concepts and answering questions. Now they work by themselves for the most part and check their own work with the solution manual. They consult us when they get stuck.

 

 

 

My son did Intro to Algebra in 6th grade, and he got through chapter 12. So for him, it will take two years. We spend anpother semester working onchapters 13-15, but now the material gets more abstract and we are taking a break from algebra, spending as semester on C&P. It makes no sense to rush, it will take whatever time it takes.

My DD worked through Intro in 7th grade and finished over the summer, but she worked for 220 hours on that book. Definitely more than a typical one-year course.

 

When I mean independently, I mean that she reads the assignment by herself, does the assignment on her own, then I correct her work daily. We will discuss problems after she attempts them and misses them. I usually have here attempt fixing her mistakes several times before I discuss with her. She usually is able to solve them on her own after several attempts.

 

She does not look at the solution manuel EVER, unless I ask her to look at the way the author solves a problem. She is stubborn, thinks looking at the solution manuel is 'cheating', and usually thinks her way of solving something it better -even when it isn't.;)

 

Thanks both of you for sharing. That is helpful -there are obviously very different ways of using the solutions manual! I interact very little with my son over math; part of my hesitation with this program has been that it is challenging for ME, lol. So far I can follow along and get most of the problems he comes to me with (just a few/week), but there are some challenge problems that I can't see how to solve quickly enough and don't have the energy for. Somewhere down the line I can see that SM being officially handed over.

 

I'd also encourage you to take your time for now & keep going through the AoPS algebra as long it's working for your son and he's enjoying it. I do think that it's highly beneficial to have a solid grounding in algebra, and AoPS is about as solid as it gets.:)

 

Yeah, that RR talk is great! I was in the audience that day, and everything he said resonated with me and our experiences.

 

Thanks for your encouragement! My DH is completely sold on AoPS, and since we do have time, we'll most like stick with it for now.

[catz]

And I think that what you're doing is perfect for a 5th grader. FWIW, it's pretty much what I did with my daughter (sans AoPS texts - they didn't exist then). My dd studied algebra over two years (grades 5 and 6) from different texts & with lots of thought-provoking problem solving thrown into the mix.

 

Thank you for that! Sometimes it's hard to know. I think if we were using a more traditional algebra text straight up he would easily get through it in a year with the amount of time we are willing to do math right now. But don't I think it wouldn't be stretching him nearly as much. And I'm not at all in a hurry to get to college level math. Who knows what we'll do down the road, but so far so good!

[regentrude]

It's taken us about 8 months to do the first 11 chapters (after completing the first half of Foerster's the prior year), so I'm thinking it will take all of next year to complete the second half. I've been wondering all year if this is the right fit for him. I exchanged a few emails with RR from AoPS who was encouraging, but I'm still unsure. I don't mind taking this long, now, but I'm wondering if the other courses will be equally difficult for him (?)and I'm making things harder than they need to be. On the other hand I really appreciate the emphasis on problem solving skills (great talk by RR linked in another thread recently).

 

The bolded:

YES. No other program would be equally difficult for your son. He is doing harder math than he would have to do to just check the box "algebra1 completed".

But: you probably do not do math in order to check a box, most likely, your goal is that he learns math, and there is no better way of thoroughly understanding concepts than by doing hard problems.

Your son could work with a different curriculum and be done in a shorter time - but he would have learned much, much less.

 

Since you are not pressed for time, I would encourage you to take the time to continue working with AoPS as long as it works for your student. It will translate into a deeper understanding and that will be very beneficial when it comes to higher math.

[rbk mama]

The bolded:

YES. No other program would be equally difficult for your son. He is doing harder math than he would have to do to just check the box "algebra1 completed".

But: you probably do not do math in order to check a box, most likely, your goal is that he learns math, and there is no better way of thoroughly understanding concepts than by doing hard problems.

Your son could work with a different curriculum and be done in a shorter time - but he would have learned much, much less.

 

Since you are not pressed for time, I would encourage you to take the time to continue working with AoPS as long as it works for your student. It will translate into a deeper understanding and that will be very beneficial when it comes to higher math.

 

Yes, this is how DH feels, and I agree it makes sense. Thank you for the encouragement! What I was actually wondering, in the post you quoted, was if the other AoPS courses would be equally difficult for him -- taking twice the time its supposed to take for older students. Does that make sense? Any thoughts on that? Right now I'm thinking that we'll continue in the Intro Algebra book next year, but if the Geometry book seems too hard for him when we get to it, we may need to switch out. Slightly off topic but related -- I had DS read the page on "Hard Problems" from the AoPS site, and that has really affected his attitude! He is not the kid who "loves" mulling over a tough problem usually, but since reading that I've seen him working on random problems in the evening, outside of school time, and then sharing with me his discoveries. Very cool! :001_smile: And makes me feel better about AoPS.

[regentrude]

Yes, this is how DH feels, and I agree it makes sense. Thank you for the encouragement! What I was actually wondering, in the post you quoted, was if the other AoPS courses would be equally difficult for him -- taking twice the time its supposed to take for older students. Does that make sense? Any thoughts on that? Right now I'm thinking that we'll continue in the Intro Algebra book next year, but if the Geometry book seems too hard for him when we get to it, we may need to switch out.

 

The Intro to Algebra is the thickest book of the whole series. The subsequent volumes are more manageable in one year.

Should it turn out that the other parts are too hard/time consuming, you have several options:

1. You can switch to a different, more standard program.

 

2. You can use the AoPS books and strategically omit material. This is possible without losing the benefit of the series and without creating holes, but needs to be done by somebody with some math insight to make this judgement. For DD we cut one chapter from Intro to Geometry, and the last few chapters of Intermediate Algebra, and we will postpone certain sections of Precalculus until after single variable calculus. You can also assign only selections from the challenge problems, not the whole set.

 

3. You can delay the progress in the standard sequence to allow a young student to mature and spend some time on topics not usually studied such as Number Theory and Counting&Probability. This is the approach we have chosen with DS. He is through ch. 15 in Algebra, and we felt it best to spend a semester on C&P before moving to the algebra 2 topics that constitute the last third of the book.

 

Your son is still young and you are not in a hurry. I would really suggest you take the time and enjoy the AoPS journey.

[rbk mama]

The Intro to Algebra is the thickest book of the whole series. The subsequent volumes are more manageable in one year.

Should it turn out that the other parts are too hard/time consuming, you have several options:

1. You can switch to a different, more standard program.

 

2. You can use the AoPS books and strategically omit material. This is possible without losing the benefit of the series and without creating holes, but needs to be done by somebody with some math insight to make this judgement. For DD we cut one chapter from Intro to Geometry, and the last few chapters of Intermediate Algebra, and we will postpone certain sections of Precalculus until after single variable calculus. You can also assign only selections from the challenge problems, not the whole set.

 

3. You can delay the progress in the standard sequence to allow a young student to mature and spend some time on topics not usually studied such as Number Theory and Counting&Probability. This is the approach we have chosen with DS. He is through ch. 15 in Algebra, and we felt it best to spend a semester on C&P before moving to the algebra 2 topics that constitute the last third of the book.

 

Your son is still young and you are not in a hurry. I would really suggest you take the time and enjoy the AoPS journey.

 

Thanks for your thoughts on this, regentrude, that is helpful! We'll see how it goes; I'm hoping we can make it through the AoPS series, as DS is enjoying it, even though it is taking longer.