AoPS - Intro to Probability or Intro to Number Theory?

[kohlby]

My oldest is doing the first 12 chapters of Intro to Algebra as Algebra I. We're going to then switch books for either Introl to Probability or Number Theory and then go back to Intro to Algebra for the remaining chapters for Algebra II. Which do you think is a better pick?

 

*He's in chapter 10 currently in the Intro to Algebra. He has struggled in three sections so far, but we got through them. In every case, it was a situation of math maturity which is why I'm doing a different course before finishing the book. Though in every case, it was also sections that are not covered in any high school Alg I nor even Alg II course that I've ever seen! (I'm a former high school math teacher and also tutored high school math so I've seen many public school math books). He's 9 years old and in 4th grade so no rush to get to Geometry before S.A.T.'s at this point.

[regentrude]

I would say it depends entirely on his interests.

For my son, we were in a similar situation of wanting a break after the algebra 1 portion. He was interested in probabilities and did Intro to C&P for a semester. We then returned to algebra.

With your son being so young, you have so much time that I would plan for BOTH books as a nice interesting detour from the main sequence.

[kohlby]

I'm not sure which he would be more interested in. However, as a former teacher, I found that students really enjoyed probability and statistics because it's very relatable with it's applications. So, my hunch is that may be the safer choice. But I still want reviews of both! I have at least another month before I need to order the next book.

[quark]

My son loves number theory but funnily enough, he preferred the Counting and Probability book, possibly because he does lots of number theory in his free time and probability was still a little new to him. Both books should be great for a math-loving younger kid but perhaps you might want to go with one he hasn't had much exposure with just to keep things new and interesting.

[mathwonk]

well you might ask him questions like "which prime numbers are sums of two squares?" [e.g. 5 = 1^2 + 2^2, 17 = 1^2 + 4^2, 97 = 4^2 + 9^2,......., " which is number theory,

 

 

or " which is more likely to get when you throw two dice, spots adding up to 6, or 7?", which is probability.

 

or a basic counting question, like: "everyone at xmas dinner clinked glasses once with everyone else. with 12 dinner guests,

 

how many clinks was that?"

 

 

and see which ones he likes best.

[Belacqua]

well you might ask him questions like "which prime numbers are sums of two squares?" [e.g. 5 = 1^2 + 2^2, 17 = 1^2 + 4^2, 97 = 4^2 + 9^2,......., " which is number theory,

 

 

or " which is more likely to get when you throw two dice, spots adding up to 6, or 7?", which is probability.

 

or a basic counting question, like: "everyone at xmas dinner clinked glasses once with everyone else. with 12 dinner guests,

 

how many clinks was that?"

 

 

and see which ones he likes best.

 

 

Aw, that's like asking a mom which of her children she loves best! :) Good advice, though. I think playing a few rounds of FTW at the AoPS site would also help clarify which kind of problem he finds more appealing.

[jennynd]

Think we are on the same boat. DS is a bit younger and we are on aops algebra ch9. We plan to use counting and probability simply because I worked as statistician for few years and I feel this skill is important not only to math but also science.

[Mukmuk]

Hi Kohlby! You gave me good advise a few months ago when ds was starting off on AoPS. Would it make sense to order the *2* books early? This way, you can have a better idea. We plan to do both eventually. My son asked for C&P first because he loves card games and has always liked the idea of probability. We will do this after Alg1 as well.

[Julie of KY]

My son liked the Intro to Counting and Probability book much more than Number Theory. It really depends on interests.

We would do an algebra chapter and then while working on the review problems, either do a chapter in Counting and Probablity or Number Theory (his choice). We alternated the books at random as long as he was progressing in math, I wasn't too concerned about which book he was working in.

[KAR120C]

Just to throw in another option.... DS really liked how Counting & Probability meshed with Number Theory. We did them simultaneously. I wouldn't try to match them up, but if you have both going at the same time, you'll find that each one is enriched by the other at different points.