AOPS sequence

[MomN]

I am looking at AOPS books and trying to sequence them.  I see the obvious Pre-algebra, Introduction to Algebra, Introduction to Geometry, Intermediate Algebra ...

Where do Introduction to Counting and Probability and Introduction to Number Theory fit in?  Are these outside of the traditional math sequence?  Are these optional? Does each book take about a year?

Thanks.

[kiwik]

There is a sequence on The AOPS website.

[EmilyGF]

12 hours ago, MomN said:

I am looking at AOPS books and trying to sequence them.  I see the obvious Pre-algebra, Introduction to Algebra, Introduction to Geometry, Intermediate Algebra ...

Where do Introduction to Counting and Probability and Introduction to Number Theory fit in?  Are these outside of the traditional math sequence?  Are these optional? Does each book take about a year?

Thanks.

Check out the suggested sequence on the AoPS website. You can also look at how long the online classes are to get a sense for how long the book takes. In our experience, doing books on our own took about 1.5-2x as long as doing them with the online class. OTOH, online Calculus BC AP is a 24-week class.

With Counting and Probability, we just did them when my kid felt like he had a hole in his schedule. Then we looked at which class was starting soon and signed him up for that. These classes were a lot easier than the core classes, and quite fun (for people who find math fun). They are totally optional.

Emily

[Gil]

Just a note:

If you're interested in a typical US Math education then NT and CP are optional, but helpful topics and I recommend that any student who is not struggling with basic math take time with at least some topics from each subject--just as a horizons-broadening experience.

Also, the AoPS NT and CP books are short so they can be worked simultaneously to Algebra and/or Geometry.

However, I will risk being a Negative Ned, to state that we really disliked the Intro NT book. The book was very boring for our family who really like mathematics and it gave our family a terrible impression of AoPS books as a whole. Definitely one of those "This was completely overhyped" type things. The NT book picks up towards the end, but it just wasn't enough.

We used a couple of the Intermediate AOPS books and they were okay. Not earth shattering, but ok

 

 

[Miss Tick]

24 minutes ago, Gil said:

CP books are short so they can be worked simultaneously to Algebra

Thanks. I've been looking for an answer to this specific question.

[purpleowl]

The sequence I'm using with my kids:

Prealgebra

Intro to Algebra

Intro to Number Theory

Intro to Geometry (this is where my oldest is now, so the list after this is planned but could change)

Intro to Counting and Probability

Intermediate Algebra

Precalculus

Calculus

 

And I'll stick Intermediate C&P in there somewhere, but haven't decided where yet. I'm leaning toward putting it after Intermediate Algebra.

 

We didn't hate the Intro NT book, but I agree that it's slow going and only really gets new material in there toward the end. Had I realized that beforehand, I probably would have allowed DD#1 to skip several parts, maybe just doing review & challenge problems for the earlier chapters. 

[MomN]

Thank you!

[Clemsondana]

We started in pre-A and are now in precalc and our sequence has been similar to @purpleowl.  We worked slowly through pre-A and A (my kid was young, so that might have made a difference).  NT and C&P were fun breaks for us.  Kid didn't find NT to be difficult, but at that point a bit of easier math was good, and I think it was kid's favorite book because it was different.  NT and C&P each took a semester.  We are debating using the second C&P book after calc, possibly on the other semester after doing DE stats, but we're not sure - kid may do DE calc instead of AoPS and may move through 3 semesters and linear algebra instead.  We'll have some decisions to make at that point, but I'm not sure what will make sense.  Kid doesn't mind challenging math for their math program but doesn't enjoy math as a hobby so is probably not going to be particularly interested in doing 2 math programs at once when there are other things that they would rather be learning.  We are also on track to finish precalc in less than a year.  Kid normally uses extra time to review the same subject with Life of Fred, which they enjoy (and they like having easier school to do at the end of the year, as baseball and science olympiad are both taking a lot of time), but kid might be interested in playing around with C&P and finsing it over the summer.  But, spouse is going to put together a computing class for kid for next year and they may decide to work on projects over the summer.  

[Clemsondana]

We started in pre-A and are now in precalc and our sequence has been similar to @purpleowl.  We worked slowly through pre-A and A (my kid was young, so that might have made a difference).  NT and C&P were fun breaks for us.  Kid didn't find NT to be difficult, but at that point a bit of easier math was good, and I think it was kid's favorite book because it was different.  NT and C&P each took a semester.  We are debating using the second C&P book after calc, possibly on the other semester after doing DE stats, but we're not sure - kid may do DE calc instead of AoPS and may move through 3 semesters and linear algebra instead.  We'll have some decisions to make at that point, but I'm not sure what will make sense.  Kid doesn't mind challenging math for their math program but doesn't enjoy math as a hobby so is probably not going to be particularly interested in doing 2 math programs at once when there are other things that they would rather be learning.  We are also on track to finish precalc in less than a year.  Kid normally uses extra time to review the same subject with Life of Fred, which they enjoy (and they like having easier school to do at the end of the year, as baseball and science olympiad are both taking a lot of time), but kid might be interested in playing around with C&P during that time and finishign over the summer.  But, spouse is going to put together a computer class for kid for next year and they may decide to work on projects over the summer.  

[Not_a_Number]

13 hours ago, purpleowl said:

We didn't hate the Intro NT book, but I agree that it's slow going and only really gets new material in there toward the end.

Interesting. There are a few people saying this now, and I'm curious why. Do all the kids know how to use prime factorization to count divisors and things like that fluently? And does everyone find working in different bases totally trivial? 

I've been working through this book with a student I'm tutoring, and while she's not finding it extremely challenging, she's also not finding it a total snooze. She already understood prime factorization well, so we went through the early chapters relatively quickly, but we slowed down in the chapter on LCMs and GCDs and the divisor-counting chapters. Plus, we've been trying to work through the Challenge Problems, and that takes a while. 

[daijobu]

My memory is hazy, but I thought the divisibility rules were adequately taught in PreA, and they get tedious and belabored in intro NT.  

I will defend the second half of the book on mods, which is a terrific introduction, but then it fails again when it stops... right... before... Chinese Remainder Theorem.  Why leave out CRT, when it flows so naturally from the previous material and the book is short enough as it is?  

AoPS needs to either update this book or publish an intermediate NT.  @Not_a_Number, I nominate you for the job!  

[Not_a_Number]

23 minutes ago, daijobu said:

My memory is hazy, but I thought the divisibility rules were adequately taught in PreA, and they get tedious and belabored in intro NT.  

I guess I believe that, but that's not most of the book?? The book is more like prime factorization and things with it, then using different bases, then mods and divisibility and other mod things. 

 

23 minutes ago, daijobu said:

I will defend the second half of the book on mods, which is a terrific introduction, but then it fails again when it stops... right... before... Chinese Remainder Theorem.  Why leave out CRT, when it flows so naturally from the previous material and the book is short enough as it is?  

AoPS needs to either update this book or publish an intermediate NT.  @Not_a_Number, I nominate you for the job!  

Hah, I am not in the running... they wouldn't pay me enough 😉 . 

[purpleowl]

3 hours ago, Not_a_Number said:

Interesting. There are a few people saying this now, and I'm curious why. Do all the kids know how to use prime factorization to count divisors and things like that fluently? And does everyone find working in different bases totally trivial? 

I've been working through this book with a student I'm tutoring, and while she's not finding it extremely challenging, she's also not finding it a total snooze. She already understood prime factorization well, so we went through the early chapters relatively quickly, but we slowed down in the chapter on LCMs and GCDs and the divisor-counting chapters. Plus, we've been trying to work through the Challenge Problems, and that takes a while. 

I've only gone through it with one kid so far. LCMs and GCDs were things she already knew well. Counting divisors was new but very easy for her. Working in different bases was something we had done before (a little bit in Beast Academy, but it's a topic we have played with outside of schoolwork as well). The modular arithmetic was mostly new, though I think she had discussed the ideas with DH a bit before.

[Not_a_Number]

6 minutes ago, purpleowl said:

I've only gone through it with one kid so far. LCMs and GCDs were things she already knew well. Counting divisors was new but very easy for her. Working in different bases was something we had done before (a little bit in Beast Academy, but it's a topic we have played with outside of schoolwork as well). The modular arithmetic was mostly new, though I think she had discussed the ideas with DH a bit before.

Did you guys do all the Challenge Problems?

[purpleowl]

14 minutes ago, Not_a_Number said:

Did you guys do all the Challenge Problems?

Almost all. Occasionally I let her skip the last 1-2 if we were short on time that day.

[Not_a_Number]

33 minutes ago, purpleowl said:

Almost all. Occasionally I let her skip the last 1-2 if we were short on time that day.

Cool! Maybe we're just not going that quickly with my tutee because we only meet once a week and I don't assign a ton of homework... 

How long did it take you to get through it all? 

[Shoes+Ships+SealingWax]

We haven’t begun yet, but I’m anticipating: 

Pre-Algebra

Intro to Algebra

Intro C&P / Intro NT 

Geometry

Inter Algebra

Inter C&P / Inter NT 

PreCalculus

Calculus 

If he isn’t interested in Intermediate C&P / NT he can take a competition course, Group Theory, Statistics, etc. 

[purpleowl]

6 hours ago, Not_a_Number said:

Cool! Maybe we're just not going that quickly with my tutee because we only meet once a week and I don't assign a ton of homework... 

How long did it take you to get through it all? 

I wasn't where I could check this easily earlier, but now I am. 🙂 She spent 97 school days on it, so just over a "semester." We could have shaved several weeks off at the front end. (With DD#2 I will not go any faster, for reasons that are unrelated to the actual math. When DS gets there, if he is similarly fluent with those concepts already, I probably will opt to go faster...but that's far enough away that I can't feel certain about the prediction.)

[Not_a_Number]

Just now, purpleowl said:

I wasn't where I could check this easily earlier, but now I am. 🙂 She spent 97 school days on it, so just over a "semester." We could have shaved several weeks off at the front end. (With DD#2 I will not go any faster, for reasons that are unrelated to the actual math. When DS gets there, if he is similarly fluent with those concepts already, I probably will opt to go faster...but that's far enough away that I can't feel certain about the prediction.)

Got it! I've definitely been spending longer with my tutee, but of course, that's once a week, so that's different. 

[EmilyGF]

On 10/1/2021 at 7:09 PM, MomN said:

I am looking at AOPS books and trying to sequence them.  I see the obvious Pre-algebra, Introduction to Algebra, Introduction to Geometry, Intermediate Algebra ...

Where do Introduction to Counting and Probability and Introduction to Number Theory fit in?  Are these outside of the traditional math sequence?  Are these optional? Does each book take about a year?

Thanks.

I have used books up to Calculus with my son, and want to warn you to follow your child. It is good to know what the sequence is, but AoPS isn't for everyone, not because they aren't smart enough, but because kids have different passions.

DD14 is super bright and super mathy, but she also is extremely skilled in language. She preferred different, less puzzley, approach to math so she could write a novel. DS16 had times when he wanted to dig into math deeply and also times when he was birding every morning and memorizing the most common 200 birds' calls in our region.

Knowing the sequence is important, but knowing your child is equally important. Also, I know some people have plans they've listed here but haven't used with their children yet (not everyone). We skipped Intermediate NT and Counting, though DS might decide to take those in the future. He just isn't that into them right now and is doing programming when not birding, running, or playing piano. And that's OK.

Emily