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AOPS books- what problems are the essential problems?


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If you're using AoPS as a supplement, I'd do most of the lesson problems, and the exercise problems that are credited to various math competitions. Having said that, and recognizing that the following advice is unsolicited, I'd be very wary of proceeding as you currently are. The AoPS diagnostic tests are notoriously easy, so if you have a student in pre-calc who finds them challenging, I would consider that a big red flag that something's not working. As a seventh grader your son has the gift of lots of time, and would be much better off using that time to work through a program that challenges him and teaches him thoroughly than he would by racing through an easier one that is clearly not teaching him well. This is most especially true if he's ''smart in math''. There's absolutely zero advantage to being years ''ahead'' in math if your math isn't solid.

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What diagnostic test are challenging? or What level are you considering starting at? For a 7th grader, I'd still think about Intro. to Algebra unless his algebra background is very advanced.

 

I'd do both the lessons as well as the review problems. If these are on the easy side, then your student will move through it quickly, If it's challenging, take it slower.

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Since the AoPS books are designed to be discovery and Socratic, it is not a program where you do all the odd problems, or the first five, or whatever. Each subset has less than twenty problems for the entire thing. Skipping problems means your student is doing less than what is generally considered only one day's worth of exercises in other programs. Secondly, the first five to seven of the problems of each subset are highly intuitive once you understand the author's methodology.

 

The program is not one which is fast, skipped through, or pick and choose. The way it is designed is to give a wholistic, proof based approach. You pull out a chunk in that process and your student is left clueless or not able to provide an adequate, substantial proof. The point is that the program is dense with no fluff.

 

Regardless of what your students current math level, I'd start in either PreA or Intro to Algebra.

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I think AoPS volume 1 is what you are after. It is designed to be used as a supplement to standard curriculum, in contrast to the subject specific books (intro algebra etc) which are full curriculum. Your Ds should work through volume 1 in order doing all the problems. It would take about two years or more to finish and then you can move to vol 2 which will take 2 to 3 years to complete. Together these two books cover some amazingly difficult material in a wide variety of topics, and should span all of highschool. Make sure you get the solutions manual.

 

Ruth in NZ

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The program is not one which is fast, skipped through, or pick and choose. The way it is designed is to give a wholistic, proof based approach. You pull out a chunk in that process and your student is left clueless or not able to provide an adequate, substantial proof. The point is that the program is dense with no fluff.

 

Yes.

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If you're using AoPS as a supplement, I'd do most of the lesson problems, and the exercise problems that are credited to various math competitions. Having said that, and recognizing that the following advice is unsolicited, I'd be very wary of proceeding as you currently are. The AoPS diagnostic tests are notoriously easy, so if you have a student in pre-calc who finds them challenging, I would consider that a big red flag that something's not working. As a seventh grader your son has the gift of lots of time, and would be much better off using that time to work through a program that challenges him and teaches him thoroughly than he would by racing through an easier one that is clearly not teaching him well. This is most especially true if he's ''smart in math''. There's absolutely zero advantage to being years ''ahead'' in math if your math isn't solid.

I wish we could switch to AOPS completely but he is in a school that uses Saxon math and has completed Saxon algebra 1 and 2 at the same school with over a 90 average with weekly tests and mid term and final exams. The only way to switch programs would be to homeschool him but seeing as this school is very good otherwise and has a top ranking nationally I would not do that unless the school ends up not working for him. the school's math guru told me that saxon math has led to lots of 5's on the AP caculus exams too. I just want to shore up his understanding. 

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What diagnostic test are challenging? or What level are you considering starting at? For a 7th grader, I'd still think about Intro. to Algebra unless his algebra background is very advanced.

 

I'd do both the lessons as well as the review problems. If these are on the easy side, then your student will move through it quickly, If it's challenging, take it slower.

I agree with this too. i had him try the do I need this intro to algebra  test which to be honest he did not finish due to time constraints. He did say that the test seemed a bit hard but I have no hard data on that since he did not do a complete test.

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I think AoPS volume 1 is what you are after. It is designed to be used as a supplement to standard curriculum, in contrast to the subject specific books (intro algebra etc) which are full curriculum. Your Ds should work through volume 1 in order doing all the problems. It would take about two years or more to finish and then you can move to vol 2 which will take 2 to 3 years to complete. Together these two books cover some amazingly difficult material in a wide variety of topics, and should span all of highschool. Make sure you get the solutions manual.

 

Ruth in NZ

Thanks. I will have to look more closely at this. Do you think it helps to deepen a kid's understanding of math concepts but in a more succinct way?

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I still think Intro to Algebra might be a good place to start. You can always just skip the chapter and go to the end of chapter review questions and see how he does. The review questions start easy and move quickly to very challenging. Unless the challenge problems are easy, then I'd be wary of skipping much of the chapter. For a student that has already covered the material, I would tend to go through the exercises in the book leading up to the chapter review.

 

Alternatively, you can try out Alcumus for free.

 

If you continue to think AoPS would be a good fit, then I'd suggest going ahead and buying the book. The majority of students that AoPS caters to are just like your son - taking math in school and doing extra supplement at home with AoPS.

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We have watched many of the videos which are great. Do you think the Alcamus problems are of the same caliber as the books?

 

Alcumus is AWESOME! It doesn't go into the theory and doesn't have as many of the hard problems, but it is a great place to both start and continue for a long time. Even after doing the books, it is worthwhile to keep doing alcumus.

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Thanks. I will have to look more closely at this. Do you think it helps to deepen a kid's understanding of math concepts but in a more succinct way?

 

YES!  It was the first book AoPS put out and was designed to get kids who were doing a standard curriculum at school to bump up to competition-level thinking.  It assumes that you know the algorithmic material that would be in a program like Saxon, and then teaches you how to do deeper, thought-provoking problems in those content areas of math that your dc already knows.  But in addition, it is a very efficient introduction to Number theory and combinatorics (which are not in Saxon), more efficient than the AoPS content books.  If it moves too fast, then just buy the content book that you child needs, otherwise, have her struggle through some difficult but FUN challengers in Volume 1.  Volume 1 includes Algebra 1&2, geometry, combinatorics, and number theory.

 

I would give you some examples, but I have lent out the book!

 

Ruth in NZ

 

 

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I wish we could switch to AOPS completely but he is in a school that uses Saxon math and has completed Saxon algebra 1 and 2 at the same school with over a 90 average with weekly tests and mid term and final exams. The only way to switch programs would be to homeschool him but seeing as this school is very good otherwise and has a top ranking nationally I would not do that unless the school ends up not working for him. the school's math guru told me that saxon math has led to lots of 5's on the AP caculus exams too. I just want to shore up his understanding. 

 

That makes sense. The problem-solving book lewelma mentioned is a great option, or you could still just work through AoPS from the Intro to Alg. level, since he's not exactly short of time. Either way, he's lucky to have a parent who isn't settling for what's ''supposed'' to be good enough. :)

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