AOPS Algebra experience needed

[jennynd]

What is the pacing, how long for a chapter?

Do u split sections? Or finish a section in one setting? Knowing it might be different for each section, please give example. Like.....Finish 3.1 in 1 day, 5.3 in 2 days... How muCh time for 1 day?

Do you supplement anything?

How long take u to go through Algebra 1 part? (chapter 13)

[Luckymama]

Last year dd did all of AoPS prealgebra and the first four chapters of Intro to Algebra.

 

Some sections took one day, sone two days. It depended on the topic and on the length of the section. I made very loose plans for math only a week at a time and constantly adjusted (you should see all the arrows and cross-outs in last year's planner :lol:) I allowed two days for the end-of-chapter review and challenge problems. Sometimes she only needed one day.

[Diviya]

My dd started the algebra book in mid-April and just about finished chapter 5 at the end of May. She started this book right after finishing the AoPS Prealgebra book, so she had some momentum, and familiarity with the method. Also, it is important to note that she spent up to 2 hours or more on math per day (not every day), by her choice. Pacing has been about one section per day, with the exercises, and 2-3 days for the chapter ends. If I were just starting out with AoPS, I would assume two days per section (one day for the new material and one day for the exercises), and 3-5 days for chapter ends. Or, two hours per section, and 5-7 hours per chapter end. Of course, some chapters will go more quickly than others. Her pacing was about the same for the Prealgebra book, after about chapter 3. But like I said, she spends a lot of time on math. Got sucked in. I love it!

 

Hope that helps a little.

[Luckymama]

My dd started the algebra book in mid-April and just about finished chapter 5 at the end of May. She started this book right after finishing the AoPS Prealgebra book, so she had some momentum, and familiarity with the method. Also, it is important to note that she spent up to 2 hours or more on math per day (not every day), by her choice. Pacing has been about one section per day, with the exercises, and 2-3 days for the chapter ends. If I were just starting out with AoPS, I would assume two days per section (one day for the new material and one day for the exercises), and 3-5 days for chapter ends. Or, two hours per section, and 5-7 hours per chapter end. Of course, some chapters will go more quickly than others. Her pacing was about the same for the Prealgebra book, after about chapter 3. But like I said, she spends a lot of time on math. Got sucked in. I love it!

 

Hope that helps a little.

 

Yeah, dd spent about 60-90 minutes daily on math. Math is her second-favorite subject after science.

[jennynd]

That is about the speed DS is going, 1section/day. I originally planned 2 days for section and want to know if 1day/section is general pace through the book.

Now, so far he doesn't seem need explanation in the excercises at all to solve the problem. The excercise question itself gave enough clue for him to solve it and use same method to solve the other questions. Will u still have him go through the wordy explanation? Right now, if he can solve it, I let it go.. Will I miss anything?

Another concern I have right now is the word problems, after the section, reviews, challenge, although he did solve the problem, but I don't feel he have the "proficient" I like. Somebody suggested alcumus. will that have question corresponding to the chapters?

Edited September 3, 2012 by jennynd

[snowbeltmom]

Somebody suggested alcumus. will that have question corresponding to the chapters?

Yes. You can set Alcumus to follow the chapters in the algebra book, or you can choose what topic you would like Alcumus to focus on. Alcumus is free. You would just need to setup an account.

[fractalgal]

What is the pacing, how long for a chapter?

Do u split sections? Or finish a section in one setting? Knowing it might be different for each section, please give example. Like.....Finish 3.1 in 1 day, 5.3 in 2 days... How muCh time for 1 day?

Do you supplement anything?

How long take u to go through Algebra 1 part? (chapter 13)

 

In my daughter's experience, the earlier chapters went more quickly. She daughter did at most two sections per day, but it was usually only one section once we got past Chapter 6. She spent one day on the Review Sections, and one day on the Challenge sections immediately after the Review sections at the end of a chapter.

 

As for a range of how much time for one day, I remember one time she was done with a lesson in less than 20 minutes (just a basic non-Review section), and another day she spent about 90 minutes (a Challenge section). So it can vary greatly with the Challenge sections taking the longest amount of time - especially Chapter 7 and later.

 

I did not supplement anything, but she reads Life of Fred books on her own for enrichment. If you wanted to supplement, I see nothing wrong with that. Sometimes its helpful for a student to see that you can approach a math concept/problem from a different perspective and still get the correct answer - one of the beauties of Mathematics.

 

For the Algebra I (first 13 chapters) it took her approximately five months, but I made her take tests (and an extra review day) every six chapters. She did not like to review for the tests, though I still made her do it.

[jennynd]

In my daughter's experience, the earlier chapters went more quickly. She daughter did at most two sections per day, but it was usually only one section once we got past Chapter 6. She spent one day on the Review Sections, and one day on the Challenge sections immediately after the Review sections at the end of a chapter.

 

 

That's good to know. We finished chapter 4, and some sections he did took around 20 mins to go through excercise and problems , many questions, he didn't use pencil/papers and he was there laughing and said hie 4 yr old sister can do it. (no, she can't).. And I was like... Now what?! So, chapter 6 is where is start gets interesting?.... Good to know...

[Luckymama]

That's good to know. We finished chapter 4, and some sections he did took around 20 mins to go through excercise and problems , many questions, he didn't use pencil/papers and he was there laughing and said hie 4 yr old sister can do it. (no, she can't).. And I was like... Now what?! So, chapter 6 is where is start gets interesting?.... Good to know...

 

 

There were some sections that were soooooo easy for dd too. I had her do alcumus on those days, or work through an old AMC8 test.

[Diviya]

That is about the speed DS is going, 1section/day. I originally planned 2 days for section and want to know if 1day/section is general pace through the book.

Now, so far he doesn't seem need explanation in the excercises at all to solve the problem. The excercise question itself gave enough clue for him to solve it and use same method to solve the other questions. Will u still have him go through the wordy explanation? Right now, if he can solve it, I let it go.. Will I miss anything?

 

when my daughter went through the sections, I checked her answers and eyeballed the "wordy explanations.". If I saw something interesting, I either had her read it ,or we read it together. If it was straightforward, or she solved it the same way they did, we skipped it. Sometimes their solutions are really cool, and totally different from how we solved it.

[regentrude]

I would highly recommend against any scheduling. The difficulty of the chapters is very uneven; some are easy, some are harder, and even for a person with a strong math background, it is often impossible to predict which problems will take particularly long for the student. (For everybody who used it: remember the linear optimization problem with Farmer Fred? That single problem easily took more than one hour.) We have progressed at whatever pace necessary for mastery. The kids work, and pick up the next day where they stopped.

 

DD finished the whole book in 7th grade in one school year, with working through the summer; she spent 220 hours on math that year.

DS worked through the algebra 1 portion (through chapter 12) in 6th grade in one school year; he did math daily for 45 to 60 minutes. We spent another semester on chapters 13 through 15, took a semester break for Counting and Probability, and are currently finishing chapters 16-22 and hope to be done after Christmas.

Edited September 3, 2012 by regentrude

[regentrude]

Now, so far he doesn't seem need explanation in the excercises at all to solve the problem. The excercise question itself gave enough clue for him to solve it and use same method to solve the other questions. Will u still have him go through the wordy explanation? Right now, if he can solve it, I let it go.. Will I miss anything?

 

 

Yes, he will miss a lot. The explanation to the problems contains the teaching: not only the solution, but a discussion why the method works, where common pitfalls and misconceptions are, what possible extensions there are. The explanation on how to use the book particularly recommends that the student read the solutions thoroughly even if he was able to solve the problems. Also, sometimes the student's way of solving is different from the solution presented in the book; it is very valuable to study alternative solutions. (Some people complain about the book being wordy; well , it is written towards the student to be used without a teacher, so everything a teacher would explain is in the text.)

 

Another concern I have right now is the word problems, after the section, reviews, challenge, although he did solve the problem, but I don't feel he have the "proficient" I like. Somebody suggested alcumus. will that have question corresponding to the chapters?

I am not sure I understand your concern. If he is able to solve all problems at the end of the section, including the challenge problems, he should be fine.

The one area we needed some supplementation was in chapter 2, practicing simplifying expressions, because my kids ended up making careless mistakes, mostly signs. We just wrote a few more problems and had them practice until it became automatic. This was the only chapter where AoPS did not give us enough practice.

 

ETA: You mention in one post that your son did not use pencil and paper to solve the problems. The easier chapters are the time to teach him how to write out solutions completely and clearly so that somebody else is able to understand what was going on (or he himself in a year). This is a very important skill that needs to be learned and practiced.

Edited September 3, 2012 by regentrude

[jennynd]

I am not sure I understand your concern. If he is able to solve all problems at the end of the section, including the challenge problems, he should be fine.

The one area we needed some supplementation was in chapter 2, practicing simplifying expressions, because my kids ended up making careless mistakes, mostly signs. We just wrote a few more problems and had them practice until it became automatic. This was the only chapter where AoPS did not give us enough practice.

 

because he still has to work it through.. If that make any sense. He didn't solved it like I do. I look at the problem, I immediately know what the question is asking, what to do. He is not like that. He will eventually figure it out, maybe 10-15 mins on a harder question. but not like how I solve it... And I don't feel he is proficient until he can solve it like I do.... am I expect too much..?.

[regentrude]

because he still has to work it through.. If that make any sense. He didn't solved it like I do. I look at the problem, I immediately know what the question is asking, what to do. He is not like that. He will eventually figure it out, maybe 10-15 mins on a harder question. but not like how I solve it... And I don't feel he is proficient until he can solve it like I do.... am I expect too much..?.

 

Not sure I understand- can you give me an example what you mean?

It is also normal that a learner has to do all the steps, one by one - where an experienced person sees the answer.

Also remember the AoPS philosophy: if the student can answer every problem correctly right away every time, he is using material that is too easy. The goal is to learn to wrestle with the problem and figure it out.

[jennynd]

Not sure I understand- can you give me an example what you mean?

It is also normal that a learner has to do all the steps, one by one - where an experienced person sees the answer.

Also remember the AoPS philosophy: if the student can answer every problem correctly right away every time, he is using material that is too easy. The goal is to learn to wrestle with the problem and figure it out.

 

Chapter 3 is the part i am referring.

For example, one question says 5 consecutive integers , the sum is 6 more than the last number. He wrote out 5 numbers quickly, x, x+1...., he quickly start one side of equation for one side is x+10=... But it took him good 10 mins to realize that the other side is just adding x,x+1,x+2....,

Conversation..

DS, mom, I am stuck

Me, looking over, what is the first sentence says

DS, 5 consecutive number adding together

Me, where is that?

DS, that is x+10.....

Me.. Think again..:glare:

DS, it is x+10..

Me, that's right, but where is the other side

DS, you are not helping.. Leave me alone....

Me:glare::banghead:

5 mins later.....

He figured it out, it simply just adding 5 number :001_huh:

I don't get it, it is not even what I will think is a hard question. For a kid went through SM 6 cwp, IP, question like this should be apiece of cake..but after he fail to put that 5 consecutive number together , I feel he is still shaky on word problems. There is another word problem in review he asked for help. The grandpa is 5 times age...... Challenge side ,he did fine, but that was only 2 word problems...

We went on with chapter 4 which is quite straight forward, but this one section just really bugs me

[regentrude]

Chapter 3 is the part i am referring.

For example, one question says 5 consecutive integers , the sum is 6 more than the last number. He wrote out 5 numbers quickly, x, x+1...., he quickly start one side of equation for one side is x+10=... But it took him good 10 mins to realize that the other side is just adding x,x+1,x+2....,

 

 

This is not something I would be concerned about if it was my child. The important thing is that he sits through it and eventually does figure it out.

One a great strength of AoPS is that every problem is a bit different and forces the student to think and not just repeat a drilled procedure. It is the cumulative effect of all the thinking about all the different problems that teaches the problem solving. Eventually, the student will get good at it and recognize what to do with an unfamiliar problem. The goal is not, IMO, to instantly recognize a problem type and see the answer - that comes with experience.

[kiana]

This is not something I would be concerned about if it was my child. The important thing is that he sits through it and eventually does figure it out.

One a great strength of AoPS is that every problem is a bit different and forces the student to think and not just repeat a drilled procedure. It is the cumulative effect of all the thinking about all the different problems that teaches the problem solving. Eventually, the student will get good at it and recognize what to do with an unfamiliar problem. The goal is not, IMO, to instantly recognize a problem type and see the answer - that comes with experience.

 

Yes. Agree 100%.

 

If he gets there with a bit of thought, for word problems, that's fine. I wouldn't stop and dwell on word problems until he instantly recognizes how to solve every one.

[jennynd]

I am so glad I asked. It really is a mind set shift for me. Growing up in Taiwan have to compete for high school entry exam. You almost required to do every question exists multiple times until it become you can answer the question as soon as you see it. You really do not have time to think.

But what you say make sense. At this stage, the problem solving skill should be what I care about. But not solving problem instantly when he see a question.

 

Thank you...

[lewelma]

Someone mentioned that the review questions and challengers took a day each. We have not found this to be true. I don't remember about the first 1/2 of the Algebra book because it was a while ago, but in general AoPS reviews take my son about 3 hours, and he can finish only 1/2 of the challengers in 3 hours. So I schedule 4 days for Review and Challengers and have him do as many challengers as he can get done in 2 days. Some times if he really loves a topic he will spend an additional day on challengers. As Regentrude explained, AoPS is not easy to schedule, so we set some goals but then allow for flexibility.

 

Ruth in NZ

[fractalgal]

That's good to know. We finished chapter 4, and some sections he did took around 20 mins to go through excercise and problems , many questions, he didn't use pencil/papers and he was there laughing and said hie 4 yr old sister can do it. (no, she can't).. And I was like... Now what?! So, chapter 6 is where is start gets interesting?.... Good to know...

 

Yes, overall the problems get more difficult as the chapters increase, and they will likely take longer. I think the fact that your son has done the IP and CWP from Singapore will be helpful to him. My daughter has told me that she has used the bar diagram method she learned in Singapore to help her solve some of the Challenge problems.

[Sebastian (a lady)]

Yes, he will miss a lot. The explanation to the problems contains the teaching: not only the solution, but a discussion why the method works, where common pitfalls and misconceptions are, what possible extensions there are. The explanation on how to use the book particularly recommends that the student read the solutions thoroughly even if he was able to solve the problems. Also, sometimes the student's way of solving is different from the solution presented in the book; it is very valuable to study alternative solutions. (Some people complain about the book being wordy; well , it is written towards the student to be used without a teacher, so everything a teacher would explain is in the text.)

 

I am not sure I understand your concern. If he is able to solve all problems at the end of the section, including the challenge problems, he should be fine.

The one area we needed some supplementation was in chapter 2, practicing simplifying expressions, because my kids ended up making careless mistakes, mostly signs. We just wrote a few more problems and had them practice until it became automatic. This was the only chapter where AoPS did not give us enough practice.

 

ETA: You mention in one post that your son did not use pencil and paper to solve the problems. The easier chapters are the time to teach him how to write out solutions completely and clearly so that somebody else is able to understand what was going on (or he himself in a year). This is a very important skill that needs to be learned and practiced.

 

An area where I ended up supplementing was working with polynomials. What I found was that they generally understood what they were doing, until it was time to factor trinomials. Then I found that they just hadn't handled enough polynomial multiplication problems to have developed a good feel for what was happening.

 

If you will, they knew that 4, 5 and 20 were a multiplication/division fact family; but didn't have a corresponding feel for (a+1) (a-1) = a^2 -1

We spent much of the summer working through a couple chapters of an older Dolciani Algebra 1 book. Lots of working with the polynomial expressions until it was more comfortable.

[jennynd]

An area where I ended up supplementing was working with polynomials. What I found was that they generally understood what they were doing, until it was time to factor trinomials. Then I found that they just hadn't handled enough polynomial multiplication problems to have developed a good feel for what was happening.

 

If you will, they knew that 4, 5 and 20 were a multiplication/division fact family; but didn't have a corresponding feel for (a+1) (a-1) = a^2 -1

We spent much of the summer working through a couple chapters of an older Dolciani Algebra 1 book. Lots of working with the polynomial expressions until it was more comfortable.

 

The boy actually went through key to algebra already. So he already quite proficient with multiplying polynomial, factoring polynomial

Edited September 5, 2012 by jennynd