silver 1,027 Posted December 3, 2020 Report Share Posted December 3, 2020 My son is getting bored with the heavy focus of polynomials in AoPS Intermediate Algebra (we're about to finish chapter eight). It's been ages since I took algebra 2, but would it be any different with a different text? Or is this just a huge part of the course regardless of the source? If I were to give him a short break from the book, what topics would be good as a distraction from polynomials? 1 Quote Link to post Share on other sites

Not_a_Number 13,040 Posted December 3, 2020 Report Share Posted December 3, 2020 9 minutes ago, silver said: My son is getting bored with the heavy focus of polynomials in AoPS Intermediate Algebra (we're about to finish chapter eight). It's been ages since I took algebra 2, but would it be any different with a different text? Or is this just a huge part of the course regardless of the source? If I were to give him a short break from the book, what topics would be good as a distraction from polynomials? I think polynomials ARE a major focus of algebra 2, so there's not much to be done about that. In terms of topics, you could do exponentials, maybe? Or start on trig as a break? (Trig is usually in precalculus.) 1 Quote Link to post Share on other sites

MamaSprout 2,059 Posted December 3, 2020 Report Share Posted December 3, 2020 We started Trig in Algebra 2,, but it's not always there. You could mix it up with some statistics or just take a break and do some AMC-type problems. 2 Quote Link to post Share on other sites

mathnerd 6,143 Posted December 7, 2020 Report Share Posted December 7, 2020 (edited) On 12/2/2020 at 7:18 PM, silver said: My son is getting bored with the heavy focus of polynomials in AoPS Intermediate Algebra (we're about to finish chapter eight). It's been ages since I took algebra 2, but would it be any different with a different text? Or is this just a huge part of the course regardless of the source? If I were to give him a short break from the book, what topics would be good as a distraction from polynomials? AOPS goes into great depth for the Polynomials topic in the Intermediate book. Normal high school textbooks like Structure and Methods-Dolciani/Brown etc do not get into such depth (at all!). There is no comparison! I remember that it contained 4 or 5 chapters on polynomials and went into advanced strategies in depth. It is more in line with what a student with a deep passion for math needs or what a Mathlete needs to familiarize themselves with before delving into high level competition. There are more chapters that can be loosely described as Algebra 3. So, the best advise is to get a standard book and compare the scope and contents with the AOPS Intermediate book if you are looking to drop some chapters. Has your son finished AOPS geometry? There is introduction to Trig at the end of that book. There is the Counting and Probability book that would work as a good distraction and give him a short break. Edited December 7, 2020 by mathnerd Quote Link to post Share on other sites

Not_a_Number 13,040 Posted December 7, 2020 Report Share Posted December 7, 2020 3 minutes ago, mathnerd said: AOPS goes into great depth for the Polynomials topic in the Intermediate book. Normal high school textbooks like Structure and Methods-Dolciani/Brown etc do not get into such depth (at all!). There is no comparison! Oh, interesting. What do they do in Algebra 2, then? Quote Link to post Share on other sites

mathnerd 6,143 Posted December 7, 2020 Report Share Posted December 7, 2020 (edited) 14 minutes ago, Not_a_Number said: Oh, interesting. What do they do in Algebra 2, then? I looked up my copy of Dolciani Algebra 2: Structure and Method Book 2 (this is the textbook used by most schools that teach rigorous math in my area). It contains the following scope for Polynomials: Multiplying, Factoring, Solving Poly Equations, Poly Ineqalities and few other simple topics related to those. @silverI forgot to mention that Algebra 2 is considered to be the second half of the AOPS Intro to Algebra book and spills into a few selected chapters of Intermediate Algebra book. So, the entirety of Intermediate Algebra book is not necessary to complete a standard Alg 2 course. But, since you are deciding the scope and sequence of your course for your son, you can do whatever works for you. There are many old posts on this forum about the scope of Algebra 2 if using AOPS. Edited December 7, 2020 by mathnerd 1 Quote Link to post Share on other sites

Not_a_Number 13,040 Posted December 7, 2020 Report Share Posted December 7, 2020 1 minute ago, mathnerd said: I looked up my copy of Dolciani Algebra 2: Structure and Method Book 2 (this is the textbook used by most schools that teach rigorous math in my area). It contains the following scope for Polynomials: Multiplying, Factoring, Solving Poly Equations, Poly Inequalities and few other simple topics related to those. Hmmm, interesting. Do they do stuff like finding remainders (like, f(x) = (x-c)q(x) + f(c)) or rational functions or stuff like that? Quote Link to post Share on other sites

mathnerd 6,143 Posted December 7, 2020 Report Share Posted December 7, 2020 (edited) 12 minutes ago, Not_a_Number said: Hmmm, interesting. Do they do stuff like finding remainders (like, f(x) = (x-c)q(x) + f(c)) or rational functions or stuff like that? Very briefly, probably a short paragraph's worth of information and a couple of examples worked out. They are grouped into the "Polynomial Equations" topic. There is some coverage and examples for Synthetic Division as well which I did not notice earlier. Edited December 7, 2020 by mathnerd Quote Link to post Share on other sites

Not_a_Number 13,040 Posted December 7, 2020 Report Share Posted December 7, 2020 14 minutes ago, mathnerd said: Very briefly, probably a short paragraph's worth of information and a couple of examples worked out. They are grouped into the "Polynomial Equations" topic. There is some coverage and examples for Synthetic Division as well which I did not notice earlier. Ooooh. When is one supposed to do rational functions, then? You really wind up seeing a lot of them in calculus... Quote Link to post Share on other sites

mathnerd 6,143 Posted December 7, 2020 Report Share Posted December 7, 2020 Just now, Not_a_Number said: Ooooh. When is one supposed to do rational functions, then? You really wind up seeing a lot of them in calculus... Precalculus covers Polynomials and Rational Functions in a little bit more detail 😉 1 Quote Link to post Share on other sites

Not_a_Number 13,040 Posted December 7, 2020 Report Share Posted December 7, 2020 1 minute ago, mathnerd said: Precalculus covers Polynomials and Rational Functions in a little bit more detail 😉 Aah, ok. Thanks!! I never know what counts as what class. I didn’t learn them in this order, my classes didn’t go in this order, and AoPS doesn’t go in this order, either!! 😂 Quote Link to post Share on other sites

calbear 1,911 Posted December 7, 2020 Report Share Posted December 7, 2020 You might want to look at WTMA's syllabus for Algebra II. I thought it was really useful for laying out what chapters from the Into and Inter Algebra texts for Algebra II. It does start off with a review of quadratics that would have been covered in Algebra I. https://docs.google.com/document/d/12WwhrH7Z8BPh24kZelazK2tpaE5Vand0Sf8Kj3zHYas/edit 1 Quote Link to post Share on other sites

silver 1,027 Posted December 7, 2020 Author Report Share Posted December 7, 2020 8 hours ago, mathnerd said: I forgot to mention that Algebra 2 is considered to be the second half of the AOPS Intro to Algebra book and spills into a few selected chapters of Intermediate Algebra book. So, the entirety of Intermediate Algebra book is not necessary to complete a standard Alg 2 course. But, since you are deciding the scope and sequence of your course for your son, you can do whatever works for you. There are many old posts on this forum about the scope of Algebra 2 if using AOPS. I've seen the recommendations that the first half of intro to algebra is alg 1 and the second half is alg 2. Comparing the topics to what I remember having learned and what the local high school lists for alg 1 and alg 2, it didn't seem to fit. Most notably polynomial division, more in-depth coverage of logarithms, and conic functions. Thanks for the mention that there are alg 2 topics in in the intermediate algebra book (assuring me that I'm not crazy). 9 hours ago, mathnerd said: Has your son finished AOPS geometry? There is introduction to Trig at the end of that book. There is the Counting and Probability book that would work as a good distraction and give him a short break. He's did the whole geometry book, so he has done the brief section on trig functions. He does like programming, and so I've debated adding some of the discrete math books that AOPS has. It'd probably be a fun diversion for him. 8 hours ago, calbear said: You might want to look at WTMA's syllabus for Algebra II. I thought it was really useful for laying out what chapters from the Into and Inter Algebra texts for Algebra II. It does start off with a review of quadratics that would have been covered in Algebra I. https://docs.google.com/document/d/12WwhrH7Z8BPh24kZelazK2tpaE5Vand0Sf8Kj3zHYas/edit Thanks for the suggestion! That syllabus seems to line up better with what I remember. Quote Link to post Share on other sites

mathnerd 6,143 Posted December 7, 2020 Report Share Posted December 7, 2020 5 hours ago, silver said: I've seen the recommendations that the first half of intro to algebra is alg 1 and the second half is alg 2. Comparing the topics to what I remember having learned and what the local high school lists for alg 1 and alg 2, it didn't seem to fit. Most notably polynomial division, more in-depth coverage of logarithms, and conic functions. Thanks for the mention that there are alg 2 topics in in the intermediate algebra book (assuring me that I'm not crazy). I remember the Polynomial Division, Synthetic Division and Complex numbers are some chapters that I covered from the Intermediate algebra book and used the Precalc book for Trig when we were doing Algebra 2. There could be a few more topics that I am not remembering offhand at this moment. If you are sticking with the AOPS books all the way, then, the topics on Sequences and Series, Exponentials and Logarithmic functions are covered in great depth in the Intermediate book. Those topics went by very fast in the Precalculus books because they are do not take up much of the book. If your son has time (as in years before graduating) then definitely go for the Discrete math books. The Number Theory book took very little time to complete for my son (but he had exposure to those topics to some extent) and then we took 2 years to complete C & P because we picked it up only when the main sequence of AOPS books was overwhelming. There are Intermediate Discrete Math books that AOPS recently published. So, that is something to consider as well. 1 Quote Link to post Share on other sites

Not_a_Number 13,040 Posted December 7, 2020 Report Share Posted December 7, 2020 1 minute ago, mathnerd said: I remember the Polynomial Division, Synthetic Division and Complex numbers are some chapters that I covered from the Intermediate algebra book and used the Precalc book for Trig when we were doing Algebra 2. There could be a few more topics that I am not remembering offhand at this moment. I think that makes a lot of sense. Pretty much all the trig is in the precalc book. The complex numbers in the precalc book are also good trig reinforcement, if you want to build those in. 1 minute ago, mathnerd said: If your son has time (as in years before graduating) then definitely go for the Discrete math books. The Number Theory book took very little time to complete for my son (but he had exposure to those topics to some extent) and then we took 2 years to complete C & P because we picked it up only when the main sequence of AOPS books was overwhelming. Those are good topics to intersperse, I think 🙂 . 1 Quote Link to post Share on other sites

daijobu 5,014 Posted December 8, 2020 Report Share Posted December 8, 2020 On 12/2/2020 at 7:18 PM, silver said: My son is getting bored with the heavy focus of polynomials in AoPS Intermediate Algebra (we're about to finish chapter eight). It's been ages since I took algebra 2, but would it be any different with a different text? Or is this just a huge part of the course regardless of the source? If I were to give him a short break from the book, what topics would be good as a distraction from polynomials? OMG, I so remember this. It felt like we had completed like 27 chapters on polynomials, and I turned to my dd and said, "Ah FINALLY we're done with polynomials." Then I turned the page and aiyiyi! More polynomials! 3 Quote Link to post Share on other sites

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