AoPS progression question - what next?

[chocolate-chip chooky]

We've powered our way through the pre-algebra text and I'm at the point of ordering more.

It takes a while to get here, so I need to be organised.

 

My daughter (11) hasn't needed to work that much of pre-algebra and I'm hoping I've done the right thing in allowing that.

 

For much of the book we've gone straight to challenge problems and she loves those and asks for more. If she can do the challenge problems, is it okay to move on? Or is there merit to working through the chapters step by step? I find it hard to imagine her enjoying having to do it all. The challenge problems give her real joy though.

 

Is Intro to Algebra the best book to head to next?

 

And are there any others that would sit well beside it? Geometry maybe?

 

We work from a range of texts for variety (AoPS pre-alg, Zaccaro, LoF and also an Australian grade 10 maths textbook) and her progression overall probably isn't linear.

 

To give an idea of her level, she's mastered most of Australian Grade 10 curriculum. We don't separate out into algebra, trig, geometry, calc etc here. It's all mixed up into overall maths courses/grades.

She has also mastered LoF Beginning Algebra and is looking for more challenge.

 

Oh, and this time around, I'm not even concerned about the cost to get the books here. Last time I agonised over it. But I now know that it is worth it.

 

I'd appreciate your thoughts and advice.

 

Thank you!

 

 

[snowbeltmom]

We've powered our way through the pre-algebra text and I'm at the point of ordering more.

It takes a while to get here, so I need to be organised.

 

My daughter (11) hasn't needed to work that much of pre-algebra and I'm hoping I've done the right thing in allowing that.

 

For much of the book we've gone straight to challenge problems and she loves those and asks for more. If she can do the challenge problems, is it okay to move on? Or is there merit to working through the chapters step by step? I find it hard to imagine her enjoying having to do it all. The challenge problems give her real joy though.

 

Is Intro to Algebra the best book to head to next?

 

And are there any others that would sit well beside it? Geometry maybe?

 

We work from a range of texts for variety (AoPS pre-alg, Zaccaro, LoF and also an Australian grade 10 maths textbook) and her progression overall probably isn't linear.

 

To give an idea of her level, she's mastered most of Australian Grade 10 curriculum. We don't separate out into algebra, trig, geometry, calc etc here. It's all mixed up into overall maths courses/grades.

She has also mastered LoF Beginning Algebra and is looking for more challenge.

 

Oh, and this time around, I'm not even concerned about the cost to get the books here. Last time I agonised over it. But I now know that it is worth it.

 

I'd appreciate your thoughts and advice.

 

Thank you!

 

It sounds like the Intro to Algebra book would be a good fit.  Imo, the other books that would sit well beside the Intro to Alg would be the Number Theory and Intro to C&P.  The Geometry book is considered to be the most challenging of the intro books.

 

I would not worry about not finishing the pre-algebra book.  (The pre-algebra book wasn't even available for two of my kids and they did just fine jumping into the Intro to Algebra book.)

 

 

 

[kiana]

If she can go straight to the challengers and do fine on them I would absolutely not go through the regular ones. Since she's already gone through LOF algebra and grade 10 aussie maths she should be fine with any of the intro series and will probably find the most new material in NT/CP although all of them would still be very much worth doing. 

[Mike in SA]

If you are using multiple sources, you don't need to do all the regular problems - you're bringing in lots of practice already.  There is value in doing the derivations and examples alongside the book, though.  You might have a different approach, but the process is valuable.

 

I would go straight to the Intro to Algebra book, and look to take a break before Intermediate Algebra, possibly by using the C&P and NT texts.

 

For shipping, can you save by ordering multiple books at once?

[regentrude]

If she knows prealgebra (whether form th challenge problems of AoPS pre-A or any other source), you can go straight into Intro to Algebra.

I would not recommend attempting to do Intro to Geometry in parallel. The geometry text requires mastery of algebra through quadratics. Also, we found it more abstract and a much higher level of challenge than the Algebra text.

[chocolate-chip chooky]

If she knows prealgebra (whether form th challenge problems of AoPS pre-A or any other source), you can go straight into Intro to Algebra.

I would not recommend attempting to do Intro to Geometry in parallel. The geometry text requires mastery of algebra through quadratics. Also, we found it more abstract and a much higher level of challenge than the Algebra text.

 

She is actually very comfortable with quadratics and all methods of factoristion (much of it is covered in LoF Beginning Algebra and Aus Grade 10 maths). 

 

She can factorise in her head, and she uses the quadratic formula easily. She's also had a crack at deriving it from scratch. That was a challenge!

She's also done a bit of applied stuff too, like graphing parabolas.

 

She actually loves to have good meaty word problems that end up with quadratics in simultaneous equations. Good fun!

 

She is really confident in this stuff, probably partly due to the mixed curricula approach I've used (and also her genuine enjoyment of it all and natural maths ability).

 

So, maybe AoPS Geometry would be okay?

 

The reason I keep coming back to geometry is that she loves it and I can't get my hands on enough problems that are just right for her current level.

I don't want to rush straight in to Aus Grade 11 maths texts. I think we should go broader and/or deeper for a while.

 

Her eyes lit up when I told her I was asking my online community about new AoPS books  :001_smile:

Edited May 29, 2017 by chocolate-chip chooky

[Arcadia]

My kids have no problems with intro to geometry concurrent with intro to algebra because of this. We are used to mixed curricula and concurrent tracks.

[chocolate-chip chooky]

If you are using multiple sources, you don't need to do all the regular problems - you're bringing in lots of practice already.  There is value in doing the derivations and examples alongside the book, though.  You might have a different approach, but the process is valuable.

 

I would go straight to the Intro to Algebra book, and look to take a break before Intermediate Algebra, possibly by using the C&P and NT texts.

 

For shipping, can you save by ordering multiple books at once?

 

If I get just the Intro to Algebra set, the postage is US$35.

 

If I get the Intro to Alg + Intro to Geometry set, the postage is US$58.

(These prices are from Rainbow Resources. Buying straight from AoPS is much higher postage cost. It's US$47 for just one and US$64 for two).

 

 

So, it's definitely worthwhile for me to order two at once, even if we don't use them concurrently.

 

 

While the postage costs are eye-wateringly high either way, I try to view the overall cost as the cost for the book. And like I've said, I now know it's well worth it.

[Arcadia]

If you don't mind the price tag, I would actually be aiming for the volume 1 and volume 2 books instead of or in addition to the intro books as those are mixed topics books.

 

https://artofproblemsolving.com/store/item/aops-vol1

[Pegs]

If I get just the Intro to Algebra set, the postage is US$35.

 

If I get the Intro to Alg + Intro to Geometry set, the postage is US$58.

(These prices are from Rainbow Resources. Buying straight from AoPS is much higher postage cost. It's US$47 for just one and US$64 for two).

 

 

So, it's definitely worthwhile for me to order two at once, even if we don't use them concurrently.

 

 

While the postage costs are eye-wateringly high either way, I try to view the overall cost as the cost for the book. And like I've said, I now know it's well worth it.

 

Hey Chooky,

 

I have all of the intro books and their solutions manuals, and I'm happy to offer you an extended loan of them if you'd like. I'm not using them myself any more, and DS is still a few years off.

 

PM me if you're interested. :)

[Julie of KY]

I think you could do any or all of the INTRO books. I did them concurrently by one week we'd do a chapter of algebra, next week we'd do geometry, 3rd week we'd do counting and probability, 4th week we'd do number theory. The review problems at the end of the chapter would go into the next week so that we'd be doing some review problems of one book and a new chapter of another. 

 

Pick whichever sounds good to you.... and yes, I think you could move on to geometry and it would likely be a good challenge.

[chocolate-chip chooky]

Thank you, everyone, for your input. It is all much appreciated.

 

Wow, Pegs, that is incredibly generous of you!

I'll PM you.