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AOPS Prealgebra after Singapore 5?


happypamama
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Since it looks like they've made some changes to the Singapore program, I was thinking about being done with Singapore after my son finishes Singapore 5 during fifth grade. Could I move him to AoPS Prealgebra for sixth grade, or is that asking for too much? We could take it slowly if need be and do it over two years if need be.

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We've done exactly that, twice - both were eventually successful, but with somewhat different paths.

 

DS cruised along in AoPS PreAlg till Ch 5...then hit the wall for months.  Tried different curriculums (didn't help), tried different daily schedules (no effect), tried having both of us yell more (negative effect you'd expect).  Eventually he decided he should just start over at Ch 1 and take another run at it - which worked.

 

DD finished SM 5B in June of this year and decided she wanted to complete PreAlg before the AMC8.  She'll finish the last chapter next week.  It's been a lot of work but she has sailed through in <4 months with a chipper attitude and picked everything up very well.  I couldn't be happier for her or more proud.

 

Between the two of them, I'd have said DS was the better math student as of the end of the SM sequence.  The difference, I think, has mostly been attitude and interest.  That said, I don't know that continuing on through SM6 would have helped DS, except that perhaps he'd have been 9 months older.  None of his struggles were really about his prior math background.  SM5 was plenty of prep.

 

 

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We have also just transitioned from Singapore 5 (Standards ) to AoSP Prealgrebra. My daughter also did Life of Fred Fractions and Decimals and Percents as a supplement while doing Singapore. 

 

So far we have done only chapter 1. She is not working as independently as I would like, but with some hints she is seeing how to approach the problems using the AoSP approach. So far I judge it a success. 

 

Learning how to write down the style of proofs that AoSP wants in chapter 1 (demonstrating basic arithmetical principles like the communicative, associative, and distribution properties and applying the definition of subtraction, negation, reciprocals) is new to her. The Singapore approach emphasizing mental math has left her wanting to write down just a final answer. I am using AoSP to train her to show the key steps of her thinking. 

 

I am eager to see how chapter 2 (exponents) goes. I have read that chapter 2 is the hardest in the book. The advanced topics relating to exponents covered in that chapter will be completely new to her. 

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Thanks, everyone!  Okay, I think we will go with AoPS next year in sixth grade.  We can take it slowly and do it over two years if that works best, or we can drop it and try something else if he needs another year for his brain to be ready.  Or if he takes to it readily and flies through it, then he can move on to algebra in seventh, and that'll be okay too.

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I am eager to see how chapter 2 (exponents) goes. I have read that chapter 2 is the hardest in the book. The advanced topics relating to exponents covered in that chapter will be completely new to her. 

 

2 is challenging, as is 5 for some.  Most of the middle was pretty smooth sailing - some kids seem to struggle with the geometry sections (10-13) if they struggle to visualize and the bit about counting and probability is totally new for most.  Be prepared and don't let the kiddo get discouraged if they get a bit stuck on the tricky bits.

 

I had one that worked through AoPS pretty independently, and on that did not at all.  It is what it is, and you should just find what works best, IMO.

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I am eager to see how chapter 2 (exponents) goes. I have read that chapter 2 is the hardest in the book. The advanced topics relating to exponents covered in that chapter will be completely new to her. 

 

I think the most important thing wrt exponents is to not memorize.  If your student forgets what x^(-2) is, they need to run through a little derivation:

 

3^2 = 9

3^1 = 3

3^0 = 1

3^(-1) = ... what's the pattern?

3^(-2) = ... continue the pattern...

 

If your student forgets what x^(a+b) means, don't just tell them but lead them socratically through basic principles:

 

x^a = x*x*x*...*x (a times)

 

x^b = x*x*...*x (b times)

 

x^a * x^b = (x*x*...*x)*(x*x*...*x) a times and then b times for a total of a+b times.  That is, you have a+b x's being multiplied by each other.  

 

I think it's very important to be able to do a quickie derivation of these principles, because you never know when you'll be in a situation where you'll forget and won't have the internet handy.  

 

Or as my math teacher used to say, "Mere memorization is a mathematical malpractice."  

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I think the most important thing wrt exponents is to not memorize.  If your student forgets what x^(-2) is, they need to run through a little derivation:

 

3^2 = 9

3^1 = 3

3^0 = 1

3^(-1) = ... what's the pattern?

3^(-2) = ... continue the pattern...

 

If your student forgets what x^(a+b) means, don't just tell them but lead them socratically through basic principles:

 

x^a = x*x*x*...*x (a times)

 

x^b = x*x*...*x (b times)

 

x^a * x^b = (x*x*...*x)*(x*x*...*x) a times and then b times for a total of a+b times.  That is, you have a+b x's being multiplied by each other.  

 

I think it's very important to be able to do a quickie derivation of these principles, because you never know when you'll be in a situation where you'll forget and won't have the internet handy.  

 

Or as my math teacher used to say, "Mere memorization is a mathematical malpractice."  

 

Yes! DS did this often. It's a good practice for any basic principle in arithmetic.

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