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When is a child ready for Algebra?


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Hello all,

 

I wish I had taken advantage of this forum sooner.  This is my third year homeschooling, and I've been swamped ever since I started.  I quit my part-time job which will hopefully help me to not merely survive but actually plan ahead and see the big picture (at least now and then).  =)

 

My oldest is 9 and 1/2 years old and reads at a very high level.  He reads 900-page sci-fi books for fun.  I can't keep up with him!  He scored 12th-grade level on spelling when we did our first standardized test this year.  But my question is about math.  He's been complaining that it's "too easy."

 

We started in 1st grade with a combo of Saxon and Singapore.  We started on first grade materials even though I knew he already knew a lot of it, because I wanted to reinforce facts for him.  By the end of 2nd grade, he had gone through 3 years of both curricula.  This year I decided to switch to RightStart Math, hoping that would help with my second son, who didn't like Saxon at all.  I started my oldest at Level D, based on the brief placement test, but now I realize that level was too low.  I like the Montessori thinking behind RightStart (we're a Montessori family), but it seems like it's not challenging enough.  I'm really running out of steam for this school year, so I'm not going to make any major changes until next school year, but I'll try to supplement with some leftover Challenging Word Problems books from Singapore I have lying around.

 

I have two questions, however, with regard to the future.

 

1) What do I do for next year?  It will be 4th grade for him.  Do I continue with RightStart E and skip over stuff, so we get through it faster?  Does anyone know anything about Level G (it looks like there's no F), in terms of how challenging it is?  Do you have other curriculum recommendations?  I don't want him to miss important skills, but it would be better to be able to move faster.  Also, my time is getting more and more limited, so it would be nice to have a curriculum that he could basically do on his own, rather than depending on me (RS is teacher-heavy).

 

Other question...

 

2) What should be my goal over the next few years?  i.e., when should we start Algebra?  My husband says, "if he's bored, start Algebra."  I know Susan Wise Bauer says that most students aren't ready for the abstract thinking involved in Algebra until at least 7th or 8th grade.  Is this true for all kids, or is it different with accelerated learners?  How can I know when he's ready?  I want him to be engaged and challenged, but not push him before he's ready.  If he's not ready for Algebra, what kind of math can keep him engaged for 5th and 6th (and 7th?) grade in the meantime?

 

 

I wish I had more time to better craft each curriculum choice, but I'm really swamped.  We're adding child #3 to the homeschooling mix in the fall, and child #2 still needs a lot of time with me.  Plus, I need to potty-train my toddler at some point, and every once in awhile do laundry.  =)  I posted the math curriculum question to the K-8 board, but no one replied.  I'd appreciate any input any of you have to offer.

 

Thanks,

 

Erin

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Has he been doing the challenging word problems all along from Singapore? Maybe let him run through those for awhile to see where he is at. There is a huge difference we find between the computational skills of regular Singapore and the thinking skills required to apply those for CWP.

 

Is an online math program an option? A friend used Stanford's epgy math program for her gifted third grader, which frees up her time.

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2) What should be my goal over the next few years?  i.e., when should we start Algebra?  My husband says, "if he's bored, start Algebra."  I know Susan Wise Bauer says that most students aren't ready for the abstract thinking involved in Algebra until at least 7th or 8th grade.  Is this true for all kids, or is it different with accelerated learners?  How can I know when he's ready?  I want him to be engaged and challenged, but not push him before he's ready.  If he's not ready for Algebra, what kind of math can keep him engaged for 5th and 6th (and 7th?) grade in the meantime?

 

Most students does not apply to accelerated learners. If he is not ready, you will know it -- he will start struggling -- and you can drop back to another plan then. There are many people here whose children successfully completed algebra at younger ages than that and went on to do very well. I completed it early myself. 

 

In public school, algebra readiness would be a major, major concern, because a student who is inappropriately placed in algebra cannot just take 2 years to finish the course, but must move at the same pace as everyone else. You may end up with someone who would be a top student, had he started algebra at 13, but struggles in math due to starting too early. This is of far less concern in a homeschool setting where the pace can be slowed to fit the needs of the child. 

 

I would switch him back to Singapore next year, doing CWP as well and compacting as needed. I would not do Saxon as well. When he gets to 6th grade, start investigating samples of algebra/pre-algebra programs to see which ones look like a possibility. 

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I'm surprised you switched from Singapore to Right Start because it's much more common for people to start out with Right Start and then switch to Singapore. Right Start starts off challenging but then slows down in the middle of C. D and E together struck me as having only a single year's worth of material. Singapore, by contrast, starts off slowly but then increases in challenge level. My oldest did RS B & C then Singpapore 3A through 8A (where she is currently). My 2nd child did Singapore 1, then RS B and the first part of C along side Singapore 2, and 3A through 4A along side Beast Academy 3.

 

I plan to take my DS through Singapore 5 and then make a decision about whether to continue on with Singapore or switch to Art of Problem Solving pre-algebra.

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I'm surprised you switched from Singapore to Right Start because it's much more common for people to start out with Right Start and then switch to Singapore. Right Start starts off challenging but then slows down in the middle of C. D and E together struck me as having only a single year's worth of material. Singapore, by contrast, starts off slowly but then increases in challenge level. 

Yeah, I basically did that because I didn't know what I was doing!  Oh well, live and learn.  I should have done more research.  Thanks for the input.

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Thanks for all the suggestions.  It's rather overwhelming looking at all the options out there for math.  There's a lot more out there than the 4 or 5 mentioned in WTM!  I would appreciate it if someone could briefly summarize some of these newer programs and compare them.  (difficulty level, what they cover, supplement or full program, where to start)

 

Could someone comment on the following programs?  I would really appreciate it.  Thanks.

 

Jousting Armadillos

Beast Academy

Art of Problem Solving

Mammoth Math

Hands on Equations

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Has he been doing the challenging word problems all along from Singapore? Maybe let him run through those for awhile to see where he is at. There is a huge difference we find between the computational skills of regular Singapore and the thinking skills required to apply those for CWP.

 

Is an online math program an option? A friend used Stanford's epgy math program for her gifted third grader, which frees up her time.

He did CWP for level 1 & 2 with no problem.  We'll work on CWP 3.

 

I'm interested in online classes.  I don't know anything about Stanford's epgy program, but I'll check it out.  Do you know what course your friend does, or are there other online courses you'd recommend?  Thanks.

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Thanks for all the suggestions.  It's rather overwhelming looking at all the options out there for math.  There's a lot more out there than the 4 or 5 mentioned in WTM!  I would appreciate it if someone could briefly summarize some of these newer programs and compare them.  (difficulty level, what they cover, supplement or full program, where to start)

 

Could someone comment on the following programs?  I would really appreciate it.  Thanks.

 

Jousting Armadillos

Beast Academy

Art of Problem Solving

Mammoth Math

Hands on Equations

 

I've used all of these, so I'm at least nominally qualified to comment.  Caveat, though: my kids are very bright and enjoy math, but they aren't off-the-charts gifted, math accelerated, etc. like a lot of the kids on this board, so take my comments FWTW.  Caveat, of course, is that this is all just one person's experience/opinions:

 

Jousting Armadillos - this is the first of a 3-book series, designed to be used 6th-8th grades, which covers PreAlgebra and Algebra.  It is based on Jacobs Elementary Algebra and Math, a Human Endeavor, and is heavily focused on math problems, puzzles, and the logic and thinking side of math.  JA is the Pre-Algebra portion.  It is totally awesome, we love it.  It is what I would consider "gentle" discovery method - in that you are led to discover and derive the concepts, rather than just being taught them and then given a bunch of practice problems.  But it's not wowza difficult like AoPS can be.  It makes a very nice algebra-portion-of-prelgebra for a kid who is rock solid on arithmetic.  It doesn't cover traditional preA topics like geometry, statistics or probability, though.  We've paired it with Zaccaro's Real World Algebra for a very satisfying PreAlgebra year.

 

Beast Academy - by the makers of AoPS, this is an elementary program (3rd and half of 4th grade are complete at this  point).  It's very heavy on problem solving, understanding the concepts behind the math and being able to apply them creatively,.  I'm just starting to use it with my rising 3rd grader, so I can't say if it will be a core curriculum, or a supplement for us.  I do notice that the difficulty seems to vary considerably from section to section - some of the geometry stuff is incredibly challenging, some sections seem spot on as 3rd grade math.  Looking at the scope & sequence, it looks like it will contain a lot of topics not normally covered in elementary math.  The biggest downside with this program is its slow release rate - a lot of people are "running out" of BA as the production schedule isn't keeping up with their kids use of it.  I'm starting to worry about this a bit myself, not something I had thought we would have to consider.

 

Art of Problem Solving (AoPS) - a math curriculum for PreAlgebra on up, plus contest prep, that is targeted to gifted students.  very deep, very conceptual, includes a lot of stuff not typically covered - both within the books, and with the inclusion of topics not usually found in the typical s&s.  Very challenging.  very problem solving focused.  Not a fit for every student by a long shot, but those who have used it sucessfully tend to swear by it.  THere are also online classes and a free online math program called Alcumus.  Also free videos available online.

 

Math Mammoth - currently covers K-6, with a 7th grade/prealgebra program in the works.  Also lots of topical books for focused practice.  very solid program, super incremental, with tons of practice.  It's a great spine to make sure you cover everything, there are chapter reviews, tests, end of year tests, etc.  Super step by step, yet also very easy to accelerate.  Some topics are covered better than others: gemoetry isn't its strong suit, but ratios and the connections between decimals, fractions, percents is covered excellentlly well.  It's inexpensive, there is great support from the author.  

 

Hands-on equations - a hands on manipulative based introduction to solving equations, can be used as early as 3rd grade.  The real meat of the program is in the large Verbal Problems Book (not the one that comes with the intro package)  - it has hundreds of challenging algebra word problems at all levels.  I can't imagine ever running out.  This is a great supplement that you could use for multiple years.

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We've used some of the programs you asked about but not all. I know I answered another question recently about Beast Academy but can't figure out what thread it was in so this is probably a repeat answer. For context, I have a daughter who just turned 9 and we use MUS as our spine because it is straight forward and the fact that it is organized by topic made it very easy to accelerate without worrying about skipping concepts. My plan has always been to cover elementary math with MUS and then switch to AOPs. Along the way we've used Life of Fred, Singapore CWP, Beast Academy, Hands on Equations and various other things as supplements. We've completed all the elementary MUS books and have 3 or 4 lessons left in Pre-Algebra before we move on to AOPs.

 

Beast Academy - By the time Beast Academy was introduced we were well past 3rd grade math. I bought it anyway figuring it could be a review/supplement and that dd would like the format. She loves it and it helped (along with Fred) to make math more fun for her. I can't really comment on it as a stand alone curriculum because she already knew how to multiply, divide, etc before starting. The first 2 books had a few problems in each section that required a little extra effort on her part (the ones listed at challenge problems) but she could answer them most of the time. The 3rd book has some problems that are challenging and she requires hints. This is more about problem solving ability than arithmetic. I think the book does a good job of balancing easy problems that build confidence and thinking skills with challenging problems that require more effort and will probably help her to prepare for AOPs pre-algebra. She likes the books so much that will will probably continue with them even though we are starting the pre-algebra book. I plan to rotate between the two to give her some "easy" math days.

 

Hands on Equations - we used the iPad apps a year or so ago and dd liked them and enjoyed playing with it. It is a nice supplement but not a stand alone.

 

AOPs pre-algebra - I've read through the first few chapters and dd will start the book in the next few weeks. It is a good fit for her because she likes to work independently and will not mind that is is wordy. She has played on alcumus a few times and enjoys the explanations and the videos. We will use those as well.

 

I prefer the problem solving solutions in the answer book in AOPs & Beast Academy much more than Singapore CWP. Singapore just isn't the right fit for us. We do the CWP because I like to know that what we are learning translates to other programs but I just don't love the format or approach to problems all the time.

 

 

Edited to add: My dd qualifies as profoundly gifted in the language arts but not necessarily math. She is very accelerated but it is not her favorite or strongest subject. She doesn't require much drill and was bored and frustrated with math for a few years. We moved through arithmetic quickly because I knew she would enjoy problem solving more and she agreed to stop crying all the time if I stopped making her do so many worksheets :)

 

 

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2) What should be my goal over the next few years?  i.e., when should we start Algebra?  My husband says, "if he's bored, start Algebra."  I know Susan Wise Bauer says that most students aren't ready for the abstract thinking involved in Algebra until at least 7th or 8th grade.  Is this true for all kids, or is it different with accelerated learners?  How can I know when he's ready?  I want him to be engaged and challenged, but not push him before he's ready.  If he's not ready for Algebra, what kind of math can keep him engaged for 5th and 6th (and 7th?) grade in the meantime?

 

 

 

Readiness is really student-dependent, particularly with respect to gifted kids.  Having three gifted kids, they are all somewhat different with math.  My oldest daughter completed Algebra I in 4th grade.  She did very well but did not enjoy it at all, so we took 5th grade "off"

 and did AoPS books.  My son was ready for Algebra in 4th grade; however, after a rather interesting time of it with my daughter, I held off until 5th grade.  He breezed through it then and has worked through Geometry this year (6th grade) fairly effortlessly.  My other daughter does not like math at all and will be taking Algebra this fall in 7th grade.  I debated having her take it this year, as she could do the work, but I decided not to because she did not want to do it. 

 

Based on my experience with my kids, I have learned that readiness around here has much more to do with their attitudes than with academic readiness.  I learned that the hard way with my oldest daughter in respect of math.  In any case, I think it's important to consider this aspect of readiness also.  Just my .02

 

Curricula that kept them engaged are Singapore CWP, AoPS, and Hands on Equations.  They went from Singapore 6 to HS math with Foerster Algebra.

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In order to start Algebra arithmetic needs to be solid (addition, subtraction, multiplication, and exponents AND using those in the context of fractions, decimals, ratios, proportions, percentages, basic linear equations, graphing, AND a solid understanding of base 10 system), and the student needs to be able to abstract ideas well.  Doing the algorithms in algebra is one thing, but understanding what they represent is another.

 

Now is a great time, while their divergent thinking is still very high, to go into deep concepts.  Study fractals, look at symmetry, puzzle through logic problems and difficult recreational mathematics.  I would do some Challenge Math (Zacarro), CWP, maybe BA, look at all the Martin Gardner books, watch videos from places like numberphile, vi hart, and math munch, and keep a solid arithmetic program going on in the background (SM 4 or 5?).  With gifted kids acceleration is only one aspect of differentiation.  Depth and breadth can be as fulfilling to the highly capable mind.

 

Good luck!

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For fun, you might check out the Dragon Box app, it introduces Algebra in a puzle solving game format.

 

We have used Math Mammoth as our spine, currently working through the sixth grade books and starting Jousting Armadillos alongside. We've done a bit of right start G as well, I would pair it with another program for prealgebra.

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I second the idea of looking into Dragon Box. My kids have loved it and it has introduced Algebra really well.

 

Math Mammoth is a pretty solid program. We are using it as a spine with Beast Academy and Life of Fred as supplements. I'm expecting my oldest to be ready for Algebra by next January although techniquely he'll be in 5th grade. He understands the concepts fairly well, but his fact recall is still really slow and I'd like to see him get his basic math skills a little faster and more solid before moving on. That's what we are focusing on right now otherwise he would've started Algebra halfway through this year (he's in 4th grade now). He is satisfied with adding in Beast Academy as he finds the problems thought provoking and rather fun. So long as there is something math wise to keep him happy, he'll play along with me and keep working on his basics. I have been pretty open with him about what we are doing and where we are going. He likes to be in on the decision making although I don't give him the last say, he knows that I will take his desires seriously.

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2) What should be my goal over the next few years?  i.e., when should we start Algebra?  My husband says, "if he's bored, start Algebra."  I know Susan Wise Bauer says that most students aren't ready for the abstract thinking involved in Algebra until at least 7th or 8th grade.  Is this true for all kids, or is it different with accelerated learners?  How can I know when he's ready?  I want him to be engaged and challenged, but not push him before he's ready.  If he's not ready for Algebra, what kind of math can keep him engaged for 5th and 6th (and 7th?) grade in the meantime?

My vote is start Algebra when he is ready. Offer him algebra gradually and if he eats it up, gets it, wants more, than he is ready. Once you start, go at his pace. I mixed in simple algebra stuff from the time that we did math facts and the boys never had a problem, they ate it up. They could solve simple algebraic equations when they were 3 years old and now at six they can solve rational expressions and graph systems of equations. There have been times when we slowed down and struggled with something but mostly I just let them go at their own pace and keep engaging them.

 

We dabble in other branches of mathematics as well. I'm currently doing even more research and preparation for a sort of gap year--we're going to be doing 2 math books--one that is highschool Algebra and another that is Math Exposure.

 

There is nothing especially magical about Algebra that it can't be began at 3 and must be began at 13. Nothing at all. The difficulty is often in the presentation and the lead-in, Algebra is easy, but many teachers fumble it. You can do Algebraic exercises as an extension of arithmetic to keep them challenged and help them begin making those connections and really help them to own the underlying principles. We used Algebra Readines Made Easy [ARME] Gr. 1-6 and the boys enjoy it, they are also doing Keys to Algebra and like it.

Erin

 

 

Thanks for all the suggestions.  It's rather overwhelming looking at all the options out there for math.  There's a lot more out there than the 4 or 5 mentioned in WTM!  I would appreciate it if someone could briefly summarize some of these newer programs and compare them.  (difficulty level, what they cover, supplement or full program, where to start)

 

Could someone comment on the following programs?  I would really appreciate it.  Thanks.

 

Jousting Armadillos

Beast Academy

Art of Problem Solving

Mammoth Math

This is the only math on your list that we've ever tried. Its been the only one that we needed. Like you, I started my boys at 1st grade level math even though I knew that they were above and beyond it. There were other things for them to learn and practice by starting in MM1a though, so we did. They did MM1 - MM4 within the span of a year. Math Mammoth has excellent coverage of topics, the teaching is excellent, the exercises just the right level.

 

Sometimes there are a lot of problems, but I'm a fan of rote-work. For us drilling to help a skill 'set' and a concept to 'sink in' is effective. So, for our purposes, MM has just the right amount of exercises and I have made my boys do every problem with the exception of a few calculator problems. If I had to list weaknesses for MM I might say reviews and geometry. MM is a mastery based curriculum, but some more frequent cumulative reviews written in the program might be a little nice, ya know? We did a lot of review outside of MM  so it doesn't bother us but it might bother some people. This is easy enough to supplement.

 

Sometimes the boys don't 'get' her geometry explanation on their own so we go over the section together but once they know what she's getting at, they do fine. Some of the word problems are real head scratchers for the boys which I think is good. I like to know that their heads are in the game.

Hands on Equations

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How many levels of Singapore have you done?  In the OP you said you did it for three years, so does that mean that you've done levels 1-3?  If so, I would definitely do Singapore levels 4 and 5 before looking for a solid prealgebra program (such as AoPS).  Be sure to use the CWP and/or IP books with Singapore.  If his arithmetic is extremely solid (particularly fractions, decimals, and percents) at the end of Singapore 5B, you could move into Jacobs Algebra, as it contains all the prealgebra *algebra* that a kid needs. 

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  • 3 weeks later...

Hi! I am so happy to have found this forum and thread as I am similarly looking for math work for my 3rd grade son.

 

I'm new to all this - you all know so much about the choices. I taught my son the concept of Algebra back in first grade. I was stunned. But my husband wants to emphasize the importance of a well rounded child and has asked that we don't focus on math, which is easy for my son, but focus on what he needs to do better at (writing). But now my son is finishing up 3rd grade and after newly finding out of his high IQ from testing, I am wondering if part of his problem in school is boredom, and I am re-opening the idea of letting him excel at math at his pace, b/c I want him to feel the joy of success instead of always focusing on the areas he struggles most in.

 

My question is: I want a math book (not online) that will both teach him the concepts and do quizzes. I checked out Singapore's CWP books but it seems like they are more quizzes than lessons. He doesn't need lengthy lessons, but explaining the concept first (ex: to get the perimeter add the length of all sides) would be helpful. I also don't know if I am looking at the right books so an Amazon link would be much appreciated. I would love to get a book (series_ that just went through the concepts of math from 5th-8th grade. I think he will just absorb it like a sponge and I want him to self-learn as he does very well like that. I am happy to come in and answer questions but he will go thru it much faster if he doesn't have to wait for me to explain each new concept. Thanks!

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I'm not sure what you mean by 'don't focus on math' -- he should be getting math appropriate to his level in math for an age-appropriate amount of time, and writing appropriate to his level in writing for an age-appropriate amount of time. It seems like pure torture to not teach (or spend very little time on) the subjects he's good at to focus on the ones he's not good at. 

 

CWP is intended as a supplement to the Singapore Math curriculum, so it's not a full curriculum itself. I would check out the following:

 

1) Beast Academy -- this would add challenge and algebraic thought. The only problem is that it's only got the third grade and part of 4th, so he'll outgrow it pretty quickly.

 

2) Math mammoth -- I think this would fit your goal of a more independent program that has concept explanations as well as practice problems. I would check out the samples first to make sure he's okay with the format. It's also inexpensive and you can choose between grade-level-oriented and topics-oriented. 

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