S/O Integrated Math: Integrated AoPS in particular

[go_go_gadget]

I know there are at least several posters who have worked AoPS topics concurrently, and I think we're going to do the same. I was just thinking that I should spend a weekend carefully planning this out, but realized I'd be reinventing this wheel. I'm in a pure math grad program so I'm perfectly confident in my ability to sort this out on my own, but I'd love to hear from BTDT people about what their progressions have looked like with regard to, say, which chapters from Geometry are best worked after xyz chapters of Intro. to Alg., and the like. My son will finish Pre-A this year and I have the Intro. to Alg. and Counting books, but won't be buying the Geometry and Intro. to Number Theory books for a couple of months yet, so my recreational planning drive is getting twitchy. :D I'd love to have some ideas while I'm waiting!

[wapiti]

My dd is just coming to the end of the geometry online class but did not use aops for algebra (B&M school).  There was a small number of problems throughout the course that involved solving quadratics.  It would be simplest to start Geometry after getting through quadratics (say, ch 13?) in the Intro to Algebra text.

[Julie of KY]

My oldest did all four Intro books concurrently. He'd work through the exercises in one book in about a week and then do the review problems the next week, Meanwhile he'd start a new chapter in a different book while doing the review problems. (He did about one chapter out of each of the four books every month). I'd say you need some algebra before really getting into the geometry book. While a few of the problems involved quadratics, I don't think you are losing anything by starting geometry before quadratics. Just be aware that a couple of problems (not many) might be overly frustrating as you haven't covered quadratics yet. Same with the Counting and Probability book - generally it's easier than algebra, but a few problems involve more advanced algebra like quadratics. Currently he's finishing AoPS Precalc.

 

If you are starting the Number Theory book later, then you might find the beginning repetitive of prealgebra and algebra, but it is useful and gets into many topics not covered elsewhere.

 

My second son started both algebra and geometry after the AoPS prealgebra book. He's running a little ahead in chapters in algebra, but alternates the two -- he does about one chapter out of each of two books every month. (Though he's good at math, he doesn't like it and therefore is not doing counting and prob nor number theory. I'll probably move him to something else instead of going to the Int. AoPS series.)

 

Generally, I say you have to keep doing math, but I give them some say as to which book next at the end of each chapter.

[go_go_gadget]

 

My dd is just coming to the end of the geometry online class but did not use aops for algebra (B&M school).  There was a small number of problems throughout the course that involved solving quadratics.  It would be simplest to start Geometry after getting through quadratics (say, ch 13?) in the Intro to Algebra text.

 

Right, I know the standard recommendation is to leave the Algebra for a bit and do Geometry after Ch.11, then go back after the Geometry book is finished and finish Algebra, but I'm wondering if the Geometry book can be started sooner. Just from looking at the TOC, it looks like it should be possible, but sometimes there are subtleties that are easier to pick up on after actually going through. Do the problems with quadratrics start right away in the Geometry book, or could you start the geometry book at an earlier point in the Algebra book to work it alongside Algebra, making sure that you'd passed quadratics in Algebra by the time you would need it in Geometry? And has anyone found a particularly good sequence for working all four books (including the Intro. to Counting and Number Theory books) together, or does it not matter much? 

 

AoPS should make a dependency tree by chapter for each book. They almost have it on Alcumus, but not quite.

[go_go_gadget]

My oldest did all four Intro books concurrently. He'd work through the exercises in one book in about a week and then do the review problems the next week, Meanwhile he'd start a new chapter in a different book while doing the review problems. (He did about one chapter out of each of the four books every month). I'd say you need some algebra before really getting into the geometry book. While a few of the problems involved quadratics, I don't think you are losing anything by starting geometry before quadratics. Just be aware that a couple of problems (not many) might be overly frustrating as you haven't covered quadratics yet. Same with the Counting and Probability book - generally it's easier than algebra, but a few problems involve more advanced algebra like quadratics. Currently he's finishing AoPS Precalc.

 

If you are starting the Number Theory book later, then you might find the beginning repetitive of prealgebra and algebra, but it is useful and gets into many topics not covered elsewhere.

 

My second son started both algebra and geometry after the AoPS prealgebra book. He's running a little ahead in chapters in algebra, but alternates the two -- he does about one chapter out of each of two books every month. (Though he's good at math, he doesn't like it and therefore is not doing counting and prob nor number theory. I'll probably move him to something else instead of going to the Int. AoPS series.)

 

Generally, I say you have to keep doing math, but I give them some say as to which book next at the end of each chapter.

 

Thanks! This is exactly the kind of detail I need.

[wapiti]

I had to hop in the car after I posted and realized that I am more familiar with the online problems than the book ones. Naturally there is plenty of general equation-solving in geometry but I can't really remember where two-variable equations showed up or how often, just that they were there.

[regentrude]

 

Right, I know the standard recommendation is to leave the Algebra for a bit and do Geometry after Ch.11, then go back after the Geometry book is finished and finish Algebra, but I'm wondering if the Geometry book can be started sooner. Just from looking at the TOC, it looks like it should be possible, but sometimes there are subtleties that are easier to pick up on after actually going through. Do the problems with quadratrics start right away in the Geometry book, or could you start the geometry book at an earlier point in the Algebra book to work it alongside Algebra, making sure that you'd passed quadratics in Algebra by the time you would need it in Geometry?

 

Just browsing through the geometry book: quadratics are needed in chapter 6.

[go_go_gadget]

Just browsing through the geometry book: quadratics are needed in chapter 6.

 

Perfect. Thanks!

[Julie of KY]

I agree, I think the first place you need quadratics is in Chapter 6 (Pythagorean theorem) but most all the chapter can be done without quadratics - I've done it with kids before quadratics and concurrently. I think chapter 7 of geometry is the hardest chapter, also power of point chapter.