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Art of Problem Solving sequence?


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If you were going to do AoPS, how could you do it so you were done in 4-5 years?

8th grade:: Algebra 1

Summer before 9th grade: Intro to Number Theory

Summer before 9th grade: Intro to Counting and Probability

9th grade: Intro to Geometry

Summer before 10th grade: Algebra 2

10th grade: Algebra 3

Summer before 11th grade: Precalculus

11th grade: Calculus

12th grade: Intermediate Counting & Probability and Number Theory Seminar

 

Does this seem feasible? Any insights? Ideas?

Has anyone followed this sequence? Was it way too hard?

Let me know what you think!

Edited by jhschool
I changed the sequence a little bit.They do offer Algebra 2 and Precalculus over the summer
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Does this seem feasible? Any insights? Ideas?

And if they don't offer the core courses over the summers, what to do? We have been pleased with A Beka high school math & science, but I can't imagine it would give the brainpower that AoPS gives you in math.

Let me know what you think!

 

This obviously, is just my opinion based on my kids' experiences with AoPS: Unless your child was going to devote a great deal of time to math in the summers, I don't think your schedule is feasible. My oldest took the online pre-calc class last year during the regular school year. It was very challenging and time consuming. He would not have wanted to devote that much time to math during his summer.

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Your schedule is possible for a student who lives and breathes math.

 

The online classes move at breakneck speed and are only suitable for few students. I have two very strong math students, but we prefer to use the books only and progress at their pace.

 

Your summer schedule sounds extremely challenging. Each of C&P and NUmber Theory usually takes a semester of study.

Btw, those course are fun topics, but not a prerequisit for any of the subsequent courses and books.

 

Our sequence for DD looked like this:

8th grade + summer before 9th Intro to Algebra - complete book (very long!)

9th grade: Intro to Geometry

10th grade: Intermediate Algebra through ch. 16; Precalculus

summer before 11th grade: Calc 1 portion of AoPS Calculus

11th grade: finish AoPS Calculus, supplement with Stewart calc (needed for AP Calc exam)

plan for 12th grade: multivariable calculs/diff eq- no AoPS curriculum available

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I think the sequence I'd use is:

 

Intro to Algebra (1 and 2)

Intro to C&P and Number Theory

Intro to Geometry

Intermediate Algebra (3)

Intermediate C&P and Number Theory

Precalculus

Calculus

 

And I agree with the others that it's probably not feasible unless you're absolutely devoted... and the books would be easier to keep up with than the courses.

 

The way we have done it, not with that same goal, was to do Algebra and Geometry with other curricula, C&P and Number Theory classes simultaneously (which was a LOT of work - I don't really recommend that, although the topics match up extremely well), and then we switched to the Problem Solving books, which do a very nice overview of a lot of the topics in the Intro and Intermediate serieses, but trimmed down quite a bit. DS is doing Calculus with another curriculum, but if we were continuing to homeschool after this year I'd switch him back to AoPS and maybe back him up to Precalculus. The calculus he's doing is definitely calculus in the service of engineering and not calculus for the sake of math. In the meantime he's working on the USAMTS problems to keep up his problem solving skills.

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I've run out of Singapore Math and have to jump ship in midstream so I've decided Pre-Calculus in 10th grader, Calculus in 11th and then something else which may or may not be AoPS in 12th. Maybe continue calculus in a local college, maybe statistics, maybe one of the numerous AoPS alternatives.

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We have been pleased with A Beka high school math & science, but I can't imagine it would give the brainpower that AoPS gives you in math.

 

AoPS does not "give the brainpower." The student needs to have that brainpower already.

 

If your student has been "pleased" with A Beka, rather than "starving for more challenging math", then the plan you have listed is probably not appropriate.

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I changed the sequence a tiny bit.

I put the Number Theory Seminar in 12th grade, and also took off the

question marks and modified the post a bit to focus on the AoPS question.

 

I emailed AoPS last night after posting , and they do indeed offer Algebra 2 and Precalculus over the summers.

 

Thank you to everyone for your input! I would also like to hear from anyone who has taken AoPS online courses and maybe followed this sequence. How did it go?

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I would also like to hear from anyone who has taken AoPS online courses and maybe followed this sequence. How did it go?

My son has taken all of AoPS online classes except for their calculus class to date. He followed a sequence similar to the one you are proposing for your child.

 

The online classes move extremely quicky and he needed to devote a lot of time each day to math. He never took a class over the summer.

 

Unless your child wants to devote hours a day to math over the summer, I don't think your schedule is realistic - especially the precalc, and the C&P and NT combo.

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I think it is probably unreasonable unless you live and breathe math. Online classes move faster than many people want to go.

Doing intro counting and prob with intro number theory in one summer is ambitious.

Beware their summer schedule does not always stay the same from year to year. Also, the int. number theory seminar does not get scheduled very often.

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You don't have to do every single course they offer to get the benefit of the program.

 

Going from algebra in 8th grade to calculus in 11th is challenging with any curriculum. Jumping the curriculum level up a notch AND starting to move faster AND throwing in a bunch of electives(number theory, c + p) is extraordinarily challenging and probably not a good idea.

 

See how algebra 1 goes and modify thereafter, based on availability of courses and how your student responded.

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I'm going to be honest: I think to get that much done, you would have to have started sooner. I think the reason AOPS has the extras (Number Theiry, etc.) is for students who are ahead in the sequence.

 

I think this would be better:

 

8th grade: Algebra 1

Summer before 9th grade: some of the Intro to Number Theory

Summer before 9th grade: some of the Intro to Counting and Probability

9th grade: Intro to Geometry

Summer before 10th grade: more of the two intro books

10th grade: Algebra 2

Summer before 11th grade: some of Algebra 3

11th grade: Precalculus

Summer before 12th: some of Algebra 3 or Intermediate books

12th grade: Calculus

 

All of the summer work could be done at the student's own pacing, and it would not be crucial to the sequence.

 

Disclaimer: We will start our first AOPS online class next week (and it's a math contest course;) we have used the books on our own up to this point.

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You don't have to do every single course they offer to get the benefit of the program.

 

Going from algebra in 8th grade to calculus in 11th is challenging with any curriculum. Jumping the curriculum level up a notch AND starting to move faster AND throwing in a bunch of electives(number theory, c + p) is extraordinarily challenging and probably not a good idea.

 

See how algebra 1 goes and modify thereafter, based on availability of courses and how your student responded.

 

I agree with all three points.

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You don't have to do every single course they offer to get the benefit of the program.

 

This! I wonder if there's anyone who has actually done every single book as you are hoping to do - I'd guess not many, as most AoPS students attend PS. At this stage, starting alg in 8th, I'd guess that's too much.

 

I think the reason AOPS has the extras (Number Theiry, etc.) is for students who are ahead in the sequence.

 

This too - many AoPS students are doing Algebra 1 in 7th grade or earlier, so they have time for the extras.

 

What I would do: plan out the schedule for the core math courses (algebra, geometry, precalc, calc) with summers off and add in the electives (C&P, NT) only as time and desire permit.

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