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Algebra Textbook for Younger Students

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Do you have an algebra textbook that you like for when you have younger than usual student?

I'll be teaching from and assigning problems from the book, it's not for the student to read and study independently.

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For a first run through, I have used MUS alg and geo.  I follow it with another yr of each.  The MUS book has a lot of white space so it isn't overwhelming with text for a younger student.

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I used Key to Algebra as a first run through, after Hands on Equations, and then moved into AoPS. Key was nice because it moved to doing work on paper, but still was very gentle.

 

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25 minutes ago, Crimson Wife said:

I haven't used them myself but I've always been intrigued by the Arbor Center series.

I agree--I think they would have worked well for my younger son.

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We started AOPS prealgebra with my young son. I taught it to him and he was able to handle it (though, it was real slow going for a couple of years).

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My younger-than-usual student's algebra-related path started with the DragonBox Algebra apps, moved to Algebra Lab Gear (books and blocks), followed by AoPS Prelagebra, then AoPS Intro to Algebra.

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My oldest did/is doing:
1. Hands on Equations (especially the Verbal Problems book), 
2. AOPS Prealgebra (and Alcumus) interspersed with Zaccaro's Becoming a Problem Solving Genius when he needed a break,
3. AOPS Algebra (and Alcumus) interspersed with Zaccaro's Real World Algebra when he needed a break.

We made it through chapter 9 of AOPS Algebra and then DS hit a wall when we got to factoring polynomials, so he is working through the third Arbor Center book, Chuckles the Rocket Dog.  After that we might go back and finish AOPS Algebra chapters 10-13, or he might just reach mastery of those chapters on Alcumus, or we might call it good and move on to AOPS Intro to Counting & Probability.

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We started with AoPS pre-A at a young age.  Kiddo understood the math but paid too little attention to detail so had tons of mistakes (losing exponents and negative signs, etc) because their problems are complicated.  We took a break and did some of the Arbor Press books until kiddo grew up a bit.  We would have probably been OK if we'd moved more slowly - I should have set a time limit early on.  We've continued with the routine of doing AoPS a couple of days each week and then doing Life of Fred on any busy days and not worrying too much about how quickly we finish the book - we spent 1.5 years each on pre-A and Alg.  For geometry, we did that a couple of days each week and continued on with LOF algebra as a weekly review of algebra concepts.  We also took some time to do number theory and introductory probability, which kiddo found to be fun.  Now in the second AoPS algebra book, we still do LOF on busy days, usually around once/week.  Kiddo has found it to be useful to see the same concept presented 2 different ways and see different types of problems for the same material.  

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I think that's a tricky one, because kids at this age, kids can manage SOME of the things but not others. And most textbooks aren't really designed for that, since they are meant for older kids. 

Personally, I'm currently working on algebraic manipulations with my daughter -- so far, we've done both linear equations and quadratics. The idea of doing the same thing to both sides of an equation seems to make total sense to her, so that's gone well. She's had no trouble with expanding and factoring quadratics, either, but then I've basically spent all of our arithmetic years working on the properties of the operations, so it's all well-integrated for her. 

We've also been working on functions which, again, has been pretty intuitive and easy. But we aren't doing anything like domain and range yet -- just defining functions and calculating them. 

I'm also planning to quite a lot of graphing with her -- kids not understanding graphs is a pretty big problem, so I think it's a good idea to graph lots of fun functions. I personally think it's a good idea to start by graphing all sorts of functions, instead of focusing on lines to the exclusion of everything else. I'll let this Math with Bad Drawings post speak for me: 

https://mathwithbaddrawings.com/2017/03/08/lines-beyond-y-mx-b/

Specifically, the following bit: 

"If I were trying to teach you about animals, I might start with cats and dogs. They’re simple, furry, familiar, and lots of people have them lying around the house. But I’d have to show you some other animals first. Otherwise, the first time you meet an alligator, you’re gonna be like, “That wet green dog is so ugly I want to hate it.”

Anyway, I'm not really helping with the question, and I apologize for that! But I do think it's a hard problem, because if you go through a textbook, you'll run into things that will be too hard for no reason other than age, and then you'll have to slow down on going through concepts in order to beat your head against a wall that may very well turn out to be a door in a few years, anyway. And I personally prefer grabbing the concepts first while keeping the material age-appropriate :-). 

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On 3/9/2020 at 11:32 PM, square_25 said:

I think that's a tricky one, because kids at this age, kids can manage SOME of the things but not others. And most textbooks aren't really designed for that, since they are meant for older kids. 

Personally, I'm currently working on algebraic manipulations with my daughter -- so far, we've done both linear equations and quadratics. The idea of doing the same thing to both sides of an equation seems to make total sense to her, so that's gone well. She's had no trouble with expanding and factoring quadratics, either, but then I've basically spent all of our arithmetic years working on the properties of the operations, so it's all well-integrated for her. 

We've also been working on functions which, again, has been pretty intuitive and easy. But we aren't doing anything like domain and range yet -- just defining functions and calculating them. 

I'm also planning to quite a lot of graphing with her -- kids not understanding graphs is a pretty big problem, so I think it's a good idea to graph lots of fun functions. I personally think it's a good idea to start by graphing all sorts of functions, instead of focusing on lines to the exclusion of everything else. I'll let this Math with Bad Drawings post speak for me: 

https://mathwithbaddrawings.com/2017/03/08/lines-beyond-y-mx-b/

Specifically, the following bit: 

"If I were trying to teach you about animals, I might start with cats and dogs. They’re simple, furry, familiar, and lots of people have them lying around the house. But I’d have to show you some other animals first. Otherwise, the first time you meet an alligator, you’re gonna be like, “That wet green dog is so ugly I want to hate it.”

Anyway, I'm not really helping with the question, and I apologize for that! But I do think it's a hard problem, because if you go through a textbook, you'll run into things that will be too hard for no reason other than age, and then you'll have to slow down on going through concepts in order to beat your head against a wall that may very well turn out to be a door in a few years, anyway. And I personally prefer grabbing the concepts first while keeping the material age-appropriate :-). 

Thanks.

We've also done arithmetic from a properties first point of view and he's easily branching into algebraic concepts as well. I'm fairly confident in directing his math education, but I don't want to write out all the problem sets myself all the time.


He is already doing a great deal of algebraic skills. He graphs (and transforms) curves in 2d and is learning to graph 3d curves, he plays with functions, solve equations, manipulates and simplify expressions etc. He can work with quadratic equations and expressions as well.

I want a book that will help me consolidate and solidify his ability to use algebra in a real world sense of the word.

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So I picked up a copy of 2nd edition Foerster Algebra 1 and Algebra 2 for a good price locally.
The Algebra 1 guides the students in how to write expressions for specific situations and it's exercises for word problems.
Exercises for proofs are written out and required to be fully explained by the student, which is an excellent exercises for building those math skills.

Foerster uses bar-models in the early chapters then weans the kids off of them so that they can write expressions intelligently and includes diagrams throughout for word problems.
Chapter 7 is solving and evaluating equations with BASIC programming which is a little obsolete-but over all it seems like a solid text. I like that by Chapter 8 it's expected that students are able to read and work the text independently, because Ch1-6 are building them up to that skill. There is oral drill in each section and even in Algebra 2 there are Do These Quickly drills for each (most) section?

It seems like a well put together book. It's not flashy or cute, but I like it. Unfortunately the texts are thick and heavy, but I think that we can work with that fairly well.

I will keep my eyes out for something better, but I really like these Foerster books. I may pick up a copy of his Precalculus with Trigonometry text to see how the whole series reads.

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47 minutes ago, mathmarm said:

I want a book that will help me consolidate and solidify his ability to use algebra in a real world sense of the word.

Hmmmm, OK. I'm not sure what algebra in a real world sense of the world means. You mean doing word problems? I think what he's doing sounds like algebra already :-). How do you graph 3D curves, by the way? Do you use a computer program? 

Let us know how Foerster's goes! I'm always interested in gathering reviews :-). 

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40 minutes ago, square_25 said:

Hmmmm, OK. I'm not sure what algebra in a real world sense of the world means. You mean doing word problems? I think what he's doing sounds like algebra already :-). How do you graph 3D curves, by the way? Do you use a computer program?

No, I'm am old fuddy-duddy. We do all our graphing by hand. We graph on a XYZ coordinate plane that we draw on the board.

We are holding off on introducing technology beyond pencil and paper for the majority of elementary. I want him to go through calculus and differential equations by hand first.

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9 minutes ago, mathmarm said:

No, I'm am old fuddy-duddy. We do all our graphing by hand. We graph on a XYZ coordinate plane that we draw on the board.

We are holding off on introducing technology beyond pencil and paper for the majority of elementary. I want him to go through calculus and differential equations by hand first.

Yeah, same! I haven't thought about doing 3D graphs.. that's tricky! 

Have you tried parametric graphs? Those are fun, too, if you're getting bored with normal ones :-). 

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4 hours ago, mathmarm said:

So I picked up a copy of 2nd edition Foerster Algebra 1 and Algebra 2 for a good price locally.
The Algebra 1 guides the students in how to write expressions for specific situations and it's exercises for word problems.
Exercises for proofs are written out and required to be fully explained by the student, which is an excellent exercises for building those math skills.

Foerster uses bar-models in the early chapters then weans the kids off of them so that they can write expressions intelligently and includes diagrams throughout for word problems.
Chapter 7 is solving and evaluating equations with BASIC programming which is a little obsolete-but over all it seems like a solid text. I like that by Chapter 8 it's expected that students are able to read and work the text independently, because Ch1-6 are building them up to that skill. There is oral drill in each section and even in Algebra 2 there are Do These Quickly drills for each (most) section?

It seems like a well put together book. It's not flashy or cute, but I like it. Unfortunately the texts are thick and heavy, but I think that we can work with that fairly well.

I will keep my eyes out for something better, but I really like these Foerster books. I may pick up a copy of his Precalculus with Trigonometry text to see how the whole series reads.

What yr is the copyright of your alg 1 book? Mine are 1994.  Chpt 7 in my book covers expressions and equations containing 2 variable. Chpt 8 is linear functions, scattered data and probability. (a few word problems scattered throughout the book are still BASIC problems, but only a handful.

20200318_135114.jpg

Edited by 8FillTheHeart

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5 hours ago, square_25 said:

I think what he's doing sounds like algebra already :-).
Let us know how Foerster's goes! I'm always interested in gathering reviews :-). 

Yes, he's definitely doing algebra already.

1 hour ago, 8FillTheHeart said:

What yr is the copyright of your alg 1 book? Mine are 1994.  Chpt 7 in my book covers expressions and equations containing 2 variable. Chpt 8 is linear functions, scattered data and probability. (a few word problems scattered throughout the book are still BASIC problems, but only a handful.

20200318_135114.jpg

 

Mine is second edition, copyrighted 1990. It says second edition on the cover and on the title page There are 14 chapters and a Final Exam, on 679 pages not counting the indices, tables, etc.
01-Expressions and Equations
02-Operations with Negative Numbers
03-Distributing: Axioms and Other Properties
04-Harder Equations
05-Some Operations with Polynomials and Radical
06-Quadratic Equations
07-Evaluating Expressions by Computer
08-Expressions and Equations Containing Two Variables
09-Properties of Exponents
10-More Operations With Polynomials
11-Rational Algebraic Expressions
12-Radical Algebraic Expressions
13-Inequalities
14-Functions and Advanced Topics
---Final Examination

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48 minutes ago, mathmarm said:

Yes, he's definitely doing algebra already.

 

Mine is second edition, copyrighted 1990. It says second edition on the cover and on the title page There are 14 chapters and a Final Exam, on 679 pages not counting the indices, tables, etc.
01-Expressions and Equations
02-Operations with Negative Numbers
03-Distributing: Axioms and Other Properties
04-Harder Equations
05-Some Operations with Polynomials and Radical
06-Quadratic Equations
07-Evaluating Expressions by Computer
08-Expressions and Equations Containing Two Variables
09-Properties of Exponents
10-More Operations With Polynomials
11-Rational Algebraic Expressions
12-Radical Algebraic Expressions
13-Inequalities
14-Functions and Advanced Topics
---Final Examination

Looks like the 94 ed removes chpt 7, makes chpt 8 chpt 7, and adds a new chpt 8 on probability.  The 94 addition includes all of the other chpts/exams.

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7 hours ago, mathmarm said:

No, I'm am old fuddy-duddy. We do all our graphing by hand. We graph on a XYZ coordinate plane that we draw on the board.

We are holding off on introducing technology beyond pencil and paper for the majority of elementary. I want him to go through calculus and differential equations by hand first.

By the middle of the book, Foerster does assume calculator usage on most word problems.  It sort of comes and goes, but there are going to be many problems that would be a royal pain without a calculator.  It sort of bothered me with an older kid who is solid on arithmetic, but I would find it even more troublesome for a younger child.  I liked the text well enough to get over it, but thought I would share.

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22 minutes ago, Mom2mthj said:

By the middle of the book, Foerster does assume calculator usage on most word problems.  It sort of comes and goes, but there are going to be many problems that would be a royal pain without a calculator.  It sort of bothered me with an older kid who is solid on arithmetic, but I would find it even more troublesome for a younger child.  I liked the text well enough to get over it, but thought I would share.

I look through the answers to determine which ones I allow the calculator for.  Mostly the cumbersome radical problems.  

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On 3/18/2020 at 7:02 PM, Mom2mthj said:

By the middle of the book, Foerster does assume calculator usage on most word problems.  It sort of comes and goes, but there are going to be many problems that would be a royal pain without a calculator.  It sort of bothered me with an older kid who is solid on arithmetic, but I would find it even more troublesome for a younger child.  I liked the text well enough to get over it, but thought I would share.

Yep, that's right.
The author states in the Foreword to the Teacher:
"...The first part of the book is carefully sequenced to lead to the Quadratic Formula by mid-year. This departure from the more traditional sequence of topics is made possible by technology, specifically the use of a calculators to evaluate radicals. As a result, students are able to work more realistic word problems in which answers are decimals. Students must check their answers based on whether or not they are reasonable, not because they came out as small, whole numbers."

 For now, I plan for him to do everything by hand. It will keep his arithmetic and mental calculation skills razor sharp. 🙂  The book includes Table of Square Roots and a Table of Trigonometric Functions in the back, and some of the examples say "by calculator or by tables" when they explain a step, so I'll be photocopying and laminating those tables for easy and continual reference throughout.

I haven't gotten a chance to look through the whole book yet, but I do anticipate skipping 12-8 and 12-9, and adjusting the 12-Test accordingly by removing that material from the exam because the higher powers chapter would require another chart, or a calculator and I'm okay not getting that deep into the weeds on it with this first pass since it'll come back around in the Algebra and Trigonometry book.

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On 3/18/2020 at 10:40 AM, square_25 said:

Let us know how Foerster's goes! I'm always interested in gathering reviews :-). 

It's not a review YET, but here's where my thinking is. I'm planning to read through chapters 1-6 more closely this week. Honestly he can do most of the calculation or manipulation type stuff in ch1 - ch4 now, and is learning the ch5 and 6 material already so I expect we'll get through the first few chapters easily. The learning objective for him during the early chapters will be:

  • reading a textbook correctly
  • identifying the important stuff
  • taking notes from a textbook
  • copying problems from a book to a paper and
  • showing his work

We tend to do school sessions 2x a day, and my thinking is that for the first part of the book, we'll work by the timer for about 20 minutes, then have him do 5-15 minutes of table time. I am thinking it'll look something like:

Session 1: I'll sit with him on the couch and we'll buddy-read through the lesson and work the examples on a mini-whiteboard (if needed.) I'll  have him do the oral practice immediately. He'll use a sticky-note to mark something he feels is important information. Then his table work will be to write down 1-3 important things from the lesson. (this can be an example, a definition, whatever he determines is important from that lesson)

Session 2:, I'll sit with him on the couch and he'll work the straight-forward exercise problems on the mini-whiteboard (if needed) or orally for about 20 minutes. I'll assign 3-5 problems for him to do during his table time. So he'll do 3-5 problems on a sheet of notebook paper.

I think we'll be able to get through most lessons in a day with this approach, but
I plan to spend 2 days on
1-8, 1-9, 2-8, 4-3,
and I think we'll spend 3 days on
3-5, 3-6, 4-6
This way he's able to work through all or nearly all of those exercises. Especially 3-5 and 3-6 which gets him started with simple proofs. (I intend to come back around to his list the steps and justification proofs later and show him how to write a paragraph-proof at the end of the year, so I want to be able to use his earlier work for this)

 Chapter 5 has 528 polynomial drills grouped in 10 sections and organized according to pattern and arranged so that you learn to factor them in your head by the time that you're done.  Chapter 6 has 299 quadratic drills grouped across 8 sections before you get to word problems in 6-9 and 6-10. 
I want him to do all the drill in Ch 5 and 6, but not in a way that it creates a bottle neck or becomes a drudgery. Since he's familiar with but not fluent with polynomials and quadratics, I'm thinking that I may start him on chapter 5 and 6 at the same time that we start Ch 1. Then when we finish Ch4. He should be able to smoothly run through Ch 5 and Ch6, and the math-sessions should stay short and fun, because there should be minimal struggle with the math itself, but in being careful with his reading, copying, etc.
 

There is a test for each chapter, and a cumulative test for Ch 1-6. I haven't worked the tests myself, so I don't know if I'll assign them or not. I don't plan to skip much in the first half of the book, but plan to skip Ch 7 (BASIC) entirely. So I will be looking at Ch8-14 within the first weeks of April, and I will re-visit them probably at the beginning of May as well to come up with a plan for those chapters.

 

I'm thinking we'll be able to do almost a lesson a day for CH1-4, so we'll get through most of Ch4 before May
 I think that he'll finish Ch 5 and 6 at a steady pace once we get to them in early-or-mid April, but if he's needing to slow down and spread the drill out then I may start Ch 8 while he works on those chapters to keep him engaged. But I'm not sure. For now, I'd like to focus on getting through 1-6.

Edited by mathmarm
correcting the April -- > May
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I'm curious how he'll do using a textbook! We haven't tried that experiment :-). 

DD7 has become way more able to show her work this year, although personally, I would rather have work on explaining her work in words (that is, writing proofs) rather than showing mechanical calculations. And that one is definitely dependent on her ability to write, which is really coming along, but still needs work. 

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1 hour ago, mathmarm said:

 Chapter 5 has 528 polynomial drills grouped in 10 sections and organized according to pattern and arranged so that you learn to factor them in your head by the time that you're done.  Chapter 6 has 299 quadratic drills grouped across 8 sections before you get to word problems in 6-9 and 6-10. 

What degree polynomials are they factoring and what are they using to factor? Since I'm not using a program, I could probably stand a reminder of what we're supposed to be doing 😉.

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24 minutes ago, square_25 said:

What degree polynomials are they factoring and what are they using to factor? Since I'm not using a program, I could probably stand a reminder of what we're supposed to be doing 😉.

Given that it's at the beginning of an Algebra 1 text, I'm certain that they're just second-degree trinomials. That's pretty standard for first year algebra in the US. Typically you don't get into the factor theorem until the 2nd year Algebra (or at least the end of Algebra 1)

  

1 hour ago, square_25 said:

I'm curious how he'll do using a textbook! We haven't tried that experiment :-). 

DD7 has become way more able to show her work this year, although personally, I would rather have work on explaining her work in words (that is, writing proofs) rather than showing mechanical calculations. And that one is definitely dependent on her ability to write, which is really coming along, but still needs work. 

As I said, I'll be helping him through it step by step, so I'm expecting that he'll do great using a textbook. No way am I going to set my 1st grade Big Boy in front of an Algebra text all by himself. We're going to sit on the couch, buddy-read it, discuss it together, etc. I'll be supporting and scaffolding him all the way. He'll only have table tasks when I feel certain that he can do the work successfully.

As for formal proofs written paragraph style, yes, that's the end-goal.  As I mentioned, we'll loop back around to paragraph proofs later on this year. But he's not ready to successfully write paragraph proofs on his own so I'm not going to ask him too.

Math is a secondary subject for Jr at this time, Hubby and I prefer that his main academic focus remain on writing, drawing, geography and music.

We'd start the book, not so much for the math, but for all the other skills that I already listed.

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Ah, OK, I see. Has he worked with other textbooks? Even as a math person, I find math textbooks about the least pleasant textbooks out there -- math tends to be much denser to read than lots of other subjects. We've started taking notes on textbooks this year, and it's been pretty fun. But we haven't tried a math text yet. Would you work towards taking notes after you work through buddy-style? 

10 minutes ago, mathmarm said:

Given that it's at the beginning of an Algebra 1 text, I'm certain that they're just second-degree trinomials. That's pretty standard for first year algebra in the US. Typically you don't get into the factor theorem until the 2nd year Algebra (or at least the end of Algebra 1)

Oh, got it! For what it's worth, DD7 seems to have just intuited Vieta's formulas and is factoring random monic quadratics without any drill, so he may not need that much, either. (I didn't really expect her to, but she surprised me.) 

I'm not really familiar with the US algebra sequence... for one thing, I took math in Canada, and for another, I pretty much knew most of it by the time I got to Canada in grade 6 (it was taught way earlier in Ukraine, and my grandmother is a math teacher, anyway). So I apologize for the clueless questions :-). 

10 minutes ago, mathmarm said:

Math is a secondary subject for Jr at this time, Hubby and I prefer that his main academic focus remain on writing, drawing, geography and music.

 

What do you guys do for geography? I'm pretty bad at geography, so we haven't started doing anything for it, really. We've been doing reading, writing, music (piano), math, and recently Russian. Everything else is pretty unschooled. 

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10 minutes ago, square_25 said:

Ah, OK, I see. Has he worked with other textbooks? No. Even as a math person, I find math textbooks about the least pleasant textbooks out there -- math tends to be much denser to read than lots of other subjects. We've started taking notes on textbooks this year, and it's been pretty fun. But we haven't tried a math text yet. Would you work towards taking notes after you work through buddy-style? Yes, as I outlined this in my earlier post. Go back and read where I describe how I would like each session to go and you should notice that my thinking is that after we've read the lesson, done the examples, and he's identified something important, he'll take a few notes on it during his table time. 

Oh, got it! For what it's worth, DD7 seems to have just intuited Vieta's formulas and is factoring random monic quadratics without any drill, so he may not need that much, either. (I didn't really expect her to, but she surprised me.)  I'm looking for him to build speed and fluency so even though he's able to factor polynomials, it takes him a little bit of time. My hope is that some concentrated drill will get him to go build speed and fluency.

I'm not really familiar with the US algebra sequence... for one thing, I took math in Canada, and for another, I pretty much knew most of it by the time I got to Canada in grade 6 (it was taught way earlier in Ukraine, and my grandmother is a math teacher, anyway). So I apologize for the clueless questions :-). 

What do you guys do for geography? I'm pretty bad at geography, so we haven't started doing anything for it, really. We've been doing reading, writing, music (piano), math, and recently Russian. Everything else is pretty unschooled.

Quote

Geography: learning about the worlds physical geography using a Read-Draw-Write learning pattern. This study will culminate in creating a hand-drawn world atlas.
    Read - he'll read daily about a specific continent for a week.
    Draw - each day he'll draw a map of the world, and he'll draw the continent of the week 3x. Which brings me to the
    Write - I'll make a photocopy of his best continent map and he'll write geography-themed copywork on it.
    Write - Beginning in the 3rd cycle through the continents, he'll take 2-column notes on his reading and use them to write a paragraph in later cycles.
The focus is mostly on the 6 permanently inhabited continents but Antartica will be included too. For the 3rd cycle through the continents we're shortening the time we focus on a continent to 2 to 3 days at a time. After he's got each map down solid, we're going to make an atlas by compiling his best maps, copywork and paragraphs into a book.

 

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7 minutes ago, mathmarm said:

Ah, OK, I see. Has he worked with other textbooks? No. Even as a math person, I find math textbooks about the least pleasant textbooks out there -- math tends to be much denser to read than lots of other subjects. We've started taking notes on textbooks this year, and it's been pretty fun. But we haven't tried a math text yet. Would you work towards taking notes after you work through buddy-style? Yes, as I outlined this in my earlier post. Go back and read where I describe how I would like each session to go and you should notice that my thinking is that after we've read the lesson, done the examples, and he's identified something important, he'll take a few notes on it during his table time. 

Oh, got it! For what it's worth, DD7 seems to have just intuited Vieta's formulas and is factoring random monic quadratics without any drill, so he may not need that much, either. (I didn't really expect her to, but she surprised me.)  I'm looking for him to build speed and fluency so even though he's able to factor polynomials, it takes him a little bit of time. My hope is that some concentrated drill will get him to go build speed and fluency.

Got it. Yes, sorry, I didn't see that bit. That makes sense :-). 

I'm sure drill will help! I guess it drills the same kinds of skills as long division, maybe? That is, knowing how to factor an integer. Or do they also do things like completing the square for factoring? 

7 minutes ago, mathmarm said:

Geography: learning about the worlds physical geography using a Read-Draw-Write learning pattern. This study will culminate in creating a hand-drawn world atlas.
    Read - he'll read daily about a specific continent for a week.
    Draw - each day he'll draw a map of the world, and he'll draw the continent of the week 3x. Which brings me to the
    Write - I'll make a photocopy of his best continent map and he'll write geography-themed copywork on it.
    Write - Beginning in the 3rd cycle through the continents, he'll take 2-column notes on his reading and use them to write a paragraph in later cycles.
The focus is mostly on the 6 permanently inhabited continents but Antartica will be included too. For the 3rd cycle through the continents we're shortening the time we focus on a continent to 2 to 3 days at a time. After he's got each map down solid, we're going to make an atlas by compiling his best maps, copywork and paragraphs into a book.

 

Cool! DD7 has been playing with her interactive globe a lot recently, lol, which is about the sum total of our geography studies. We should do something more serious at some point. Thanks for the ideas!

Do you wind up integrating some history into the geography? My problem with geography, personally, was that it was so dry that it wouldn't stick in my head... But then I'm not very motivated by facts. I know some people are. 

Edited by square_25

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I was going to suggest Foerster! I presented it a little differently - I don’t think she ever even saw the book. I presented the lesson on a big whiteboard and then wrote some of the exercises in a notebook for her to solve. While I agree that learning to take notes from a textbook is important, I didn’t want to ruin DD’s zeal for math by trying to impose note taking or other executive function skills on her in that subject. We’ll do that in some other subject. (I should add that she did write down geometry formulas in a small formula notebook during geometry - she was fine with that and found it fun.)

we are now in Precalculus with Trigonometry and it is by far my favorite of the 3 Foerster books we have used so far. It is so clearly written! There are little explorations in most sections that act kind of like the discovery method or at least a hands on way to experience the topic.
 

i love Foerster for a young student because it’s deep but not weedsy, if you know what I mean. (DD has done AOPS summer camps and I have personally worked through all of AOPS PreA - that approach is not for her.  At least not yet.)

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8 hours ago, bensonduck said:

I was going to suggest Foerster! I presented it a little differently - I don’t think she ever even saw the book. I presented the lesson on a big whiteboard and then wrote some of the exercises in a notebook for her to solve. While I agree that learning to take notes from a textbook is important, I didn’t want to ruin DD’s zeal for math by trying to impose note taking or other executive function skills on her in that subject. We’ll do that in some other subject. (I should add that she did write down geometry formulas in a small formula notebook during geometry - she was fine with that and found it fun.)

we are now in Precalculus with Trigonometry and it is by far my favorite of the 3 Foerster books we have used so far. It is so clearly written! There are little explorations in most sections that act kind of like the discovery method or at least a hands on way to experience the topic.
 

i love Foerster for a young student because it’s deep but not weedsy, if you know what I mean. (DD has done AOPS summer camps and I have personally worked through all of AOPS PreA - that approach is not for her.  At least not yet.)

Yes! Deep, but not weedsy! I love how it scaffolds and guides so neatly. The problem sets are well designed and the explanations and the text is readable--I honestly feel like Jr. can read it and follow what he's reading. The more I read these 2 books, the more I want to buy the precalculus and calculus books.

There are a couple of (probably nit-picky) things that I don't like, but I'm more than willing to supplement and scaffold around them. Over all, this seems a really well built series. I have to read Algebra 1 and Algebra 2 more carefully, but so far I like what I'm seeing pretty well.

I wasn't going to start him with the book until 2nd grade started, but he's been dying to have a math book and when he saw it he wanted to start right away and to have a math book. :wink:. I'm a mean-mom because I told him he has to wait until April 1 to start.

As for taking notes, that's probably the part he's most looking forward too. We lucked out in that we have a little boy who loves to write and is always asking for "writing homework" so we've bought a special notebook for him to use when he writes math notes and he's so excited.

This isn't exactly what I'd planned, or exactly as I'd prefer it, but it is what it is.

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If you decide you want the precal book, let me know. I have a copy and solutions manual that are like brand new that I would be happy to sell after the  current crazy. I cant teach precal (beyond my abilities). Only 1 of my kids used it with Kathy in Richmond as her teacher.

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5 hours ago, 8FillTheHeart said:

If you decide you want the precal book, let me know. I have a copy and solutions manual that are like brand new that I would be happy to sell after the  current crazy. I cant teach precal (beyond my abilities). Only 1 of my kids used it with Kathy in Richmond as her teacher.

Excellent! What is the copyright or publication date on your edition?

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1 hour ago, mathmarm said:

Excellent! What is the copyright or publication date on your edition?

I'm not sure and it is in a moving box in my closet (we moved this summer and I didn't have room to unpack all of my boxes.  I bought it new when my 25 yr old dd was in 11th grade, so I bought somewhere around 2010 or 2011.

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I'm super curious how your DS likes it -- keep us updated! I may very well get a textbook someday, so reviews with little kids are helpful :-). 

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2 minutes ago, square_25 said:

I'm super curious how your DS likes it -- keep us updated! I may very well get a textbook someday, so reviews with little kids are helpful :-). 

If you wind up getting a textbook, I recommend that you import one from Eastern Europe or a country with a similar approach to mathematics. You won't like most of the texts designed on this continent.

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1 hour ago, mathmarm said:

If you wind up getting a textbook, I recommend that you import one from Eastern Europe or a country with a similar approach to mathematics. You won't like most of the texts designed on this continent.

Oh yeah, why? 

ETA: that's a serious question. I haven't used an Eastern European textbook since I was 10... I've spent the vast majority of my life in North America. 

Edited by square_25

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11 minutes ago, mathmarm said:

Just a suggestion.

 

Could you please explain where you're coming from? I think you must be misinterpreting my background. I haven't worked with Eastern European textbooks since I was in elementary school and am not biased towards them. 

Edited by square_25

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6 hours ago, square_25 said:

Could you please explain where you're coming from? I think you must be misinterpreting my background. I haven't worked with Eastern European textbooks since I was in elementary school and am not biased towards them. 

Oh, maybe I have you confused with another poster.

What do you want out of a math textbook for your young child?

What would be the benefit of using one in your homeschool given that you reject the Standard Scope and Sequence and prefer to create their worksheets and problem sets on demand, by hand for what interests them/you?

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6 minutes ago, mathmarm said:

Oh, maybe I have you confused with another poster.

What do you want out of a math textbook for your young child?

What would be the benefit of using one in your homeschool given that you reject the Standard Scope and Sequence and prefer to create their worksheets and problem sets on demand, by hand for what interests them/you?

Really, mostly to have example problems and make sure I’m covering everything? I don’t reject the standard topics, I just tend to like covering them in a different order!! But I’d absolutely want to make sure I covered the standard stuff in an algebra text. I teach online at AoPS, but even though DD7 is ready for the material their textbooks cover, I doubt she’s ready for the format... so I like hearing reviews of other books!

We use BA occasionally and I like using old Math Kangaroos for word problems, so it’s not like we never use outside sources :-). 

I hope I haven’t offended you with my suggestions!! 

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On 3/23/2020 at 10:32 PM, square_25 said:

Really, mostly to have example problems and make sure I’m covering everything? I don’t reject the standard topics, I just tend to like covering them in a different order!! But I’d absolutely want to make sure I covered the standard stuff in an algebra text. I teach online at AoPS, but even though DD7 is ready for the material their textbooks cover, I doubt she’s ready for the format... so I like hearing reviews of other books!

We use BA occasionally and I like using old Math Kangaroos for word problems, so it’s not like we never use outside sources :-). 

I hope I haven’t offended you with my suggestions!! 

Yes, I said:  you reject the standard scope and sequence. I did not say that you reject standard topics. What I mean is that you go through material to a different depth-level (scope) and you go through material in a wildly different order (sequence) than is typical.

That's super common among mathematically inclined parents, as far as I know. It isn't a weird or bad thing in my opinion--it's natural. Bookworm Parents that love to read share more books and share books differently than parents who are literate but indifferent to reading. Athletic parents share their love of sport differently. They interact with their kids and sports in a way that is inherently more focused and intent than most other parents are when they're playing catch with their kids. It's not weird or unusual that a mathematician engages their kids mathematically in a different way than is standard. At least I don't think so.

If you just need a scope and sequence to make sure that you're covering everything then a Table of Contents will do just fine (and take up a lot less space). You can view many of them online for free or download a counties scope and sequence. If you want a few example problems, then yeah maybe invest in a text but not always. I have found many textbooks for the elementary crowd to be...really generic.

Also, you haven't offended me--Too me personally, you're posts have --at times-- come across as braggy or boastful, which is a bit...much?, The boastful tone of your posts sometimes makes it awkward to read and know how to respond to but I have realized that that's more to do with the way you talk, and less to do with your actual intent. You're very passionate about math education and very outspoken, and that's just your personality.

That's not something to be offended by. Honestly,  you seem to be doing a pretty good job teaching your young daughter mathematics. You're documenting and publishing details about your approach. Such data is always something too celebrate and nothing to be offended by. 

I have a colleague who is a linguist. She's raising her kids in 5 different languages just because she can. She teaches her kids to read and write 3 other languages outside of their spoken languages. She documents her kids language acquisition quite closely and takes extensive notes on their development.

I have another acquaintance who is a high performance athlete and her daughter is being raised exceedingly physical. She's got all sorts of charts, alarms, timers and stats on her girl.

Several of the mathematicians that I know of have taught mathematics in wildly different ways to their kids and many of their kids are advanced well and above what is typically expected of their age/grade. Some of them share their experiences openly, others guard their "trade secrets" fiercely, lol.

It's just natural to many parents (especially those in Academia, I think) to include their kids in their world view and their specialties.

Edited by mathmarm
ordering paragraphs for clarity

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4 minutes ago, mathmarm said:

Also, you haven't offended me--Too me personally, you're posts have --at times-- come across as braggy or boastful, which is a bit...much?, The boastful tone of your posts sometimes makes it awkward to read and know how to respond to but I have realized that that's more to do with the way you talk, and less to do with your actual intent. You're very passionate about math education and very outspoken, and that's just your personality.

 

Hmmmm, I'm sorry if it comes out that way. Braggy about DD7's accomplishments? I'm proud of her, of course, but I actually don't feel that boastful about them -- they are about who she is, not about me. I'm actually much more interested in pedagogy and how to teach math generically. Since you have a very advanced kid, I was assuming you'd just take them as description :-). For me, it's actually somewhat more interesting to think about kids who don't connect the dots that easily. As you say, I'm pretty passionate about math education. And I've been interested in the experiments I've made, but especially experiments I've made with kids that are bright but not super accelerated. She's become a bad subject for my experiments, alas -- way too intuitive!! 

6 minutes ago, mathmarm said:

I have a colleague who is a linguist. She's raising her kids in 5 different languages just because she can. She teaches her kids to read and write 3 other languages outside of their spoken languages. She documents her kids language acquisition quite closely and takes extensive notes on their development.

I have another acquaintance who is a high performance athlete and her daughter is being raised exceedingly physical. She's got all sorts of charts, alarms, timers and stats on her girl.

Several of the mathematicians that I know of have taught mathematics in wildly different ways to their kids and many of their kids are advanced well and above what is typically expected of their age/grade. Some of them share their experiences openly, others guard their "trade secrets" fiercely, lol.

It's just natural to many parents (especially those in Academia, I think) to include their kids in their world view and their specialties.

 

Yeah, I think that's one of the joys of homeschooling -- to introduce your kid to the thing you're really good at. I'm a much better math teacher than I am a poetry teacher ;-). So it makes sense for me to focus on math. 

11 minutes ago, mathmarm said:

If you just need a scope and sequence to make sure that you're covering everything then a Table of Contents will do just fine (and take up a lot less space). You can view many of them online for free or download a counties scope and sequence. If you want a few example problems, then yeah maybe invest in a text but not always. I have found many textbooks for the elementary crowd to be...really generic.

 

I think, like you, we're mostly done with the elementary textbooks, anyway. That's why I'm curious how this algebra text goes for you -- it's possible it'll be useful for us to get an algebra text at some point, and I don't think DD7 is ready for AoPS. I'm sure I'd still pull the text apart and teach it in a different order, but at some point mathematics becomes a lot more sprawling and it's easier to have a reference and a source of problems. I don't know if that'll be at algebra or later for us (or never), but you're one of the few people who's teaching a kid that young algebra, which is why I'm interested in your experience. 

I apologize again for input you found unhelpful. I was hoping that because we have similar-sounding kiddos, my experiences would perhaps be useful, but it sounds like they probably aren't. I'll moderate my tone :-). 

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7 minutes ago, square_25 said:

 

Hmmmm, I'm sorry if it comes out that way. ..

I apologize again for input you found unhelpful. ...

. I'll moderate my tone :-). 

I don't think you need to apologize or be sorry.

I realize that it's not your intent to boast. You aren't bragging--but if you sensed weirdness in my replies in this thread, it's because I was thrown at first and couldn't determine if you were, but once I determined that it's just your personality, your enthusiasm, your communication style, I realized that you're not bragging. You're just communicating.

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2 minutes ago, mathmarm said:

I don't think you need to apologize or be sorry.

I realize that it's not your intent to boast. You aren't bragging--but if you sensed weirdness in my replies in this thread, it's because I was thrown at first and couldn't determine if you were, but once I determined that it's just your personality, your enthusiasm, your communication style, I realized that you're not bragging. You're just communicating.

We did talk a bunch on your other thread, so I think I was also assuming we would both kind continue that conversation (in which I made an unreasonable number of suggestions, lol.) 

I'm just excited to find someone else doing an algebra experiment with a little kid :-). We weren't even going to start algebra this year, but DD7 pestered me because of her Murderous Math books, so here we are :D. It's been really fun. I don't even know how long we'll spend here, since I feel like we need to circle back to some stuff (like long division, lol. We still haven't done long division!) I hope you enjoy having a structured approach to algebra and that your DS enjoys the book!! I really do want to hear reviews. 

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20 hours ago, square_25 said:

We did talk a bunch on your other thread, so I think I was also assuming we would both kind continue that conversation (in which I made an unreasonable number of suggestions, lol.) 

Ooooohhhhh. That was over a month ago. I haven't re-read that thread and I didn't realize that you were continuing on from then.

I'm just excited to find someone else doing an algebra experiment with a little kid :-). We weren't even going to start algebra this year, but DD7 pestered me because of her Murderous Math books, so here we are :D. It's been really fun. I don't even know how long we'll spend here, since I feel like we need to circle back to some stuff (like long division, lol. We still haven't done long division!) I hope you enjoy having a structured approach to algebra and that your DS enjoys the book!! I really do want to hear reviews. 

I know families in real life who explore algebra or geometry simultaneously (or first) and have met a few others online. It's not unheard of for me. I myself had a very non-standard math education, so doing math according to an alternative scope and sequence with my kids feels like less of an experiment and more of just an experience.

It doesn't feel like this big mysterious unknown to explore geometry and algebra with my young kids (no pun intended). To me, even though I feel uncertain about the exact tools to use on this journey, I feel certain about what I'm doing. It's like solving an equation from a class of equations that you know how to systematically approach. You know some theorems and properties that inform the approach you take to the problem, even if you can't recall a particular algorithm at that instant. You know if you play with the different parts of the equation, something will occur to you.

I will keep my eyes out for interesting math texts that might be fun for or doable by a 5-8yo. From reading through it, there are things that I like about Foerster and things that I don't like about Foerster, but I haven't used it enough to have anything concrete to report. I've already shared the details of how I plan to use it. When we're a month or so in, I'll try and remember to come back and give an update.

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11 minutes ago, mathmarm said:

Ooooohhhhh. That was over a month ago. I haven't re-read that thread and I didn't realize that you were continuing on from then.

Yeah, that makes sense! I think it just stuck in my head because you were one of the only people but me (or maybe the only person!) who was doing harder math with a little kid! 

12 minutes ago, mathmarm said:

I know families in real life who explore algebra or geometry simultaneously (or first) and have met a few others online. It's not unheard of for me. I myself had a very non-standard math education, so doing math according to an alternative scope and sequence with my kids feels like less of an experiment and more of just an experience.

What was your math education like? 🙂I don't know if mine was standard or nonstandard, but it was practically all self-motivated past the age of 10... I was an obsessive math contest kid and I did a TON of math in high school. And then I got a math bachelor's and a math Ph.D, lol. I've always loved it, although I wound up not loving research math enough to do it as a job. 

14 minutes ago, mathmarm said:

It doesn't feel like this big mysterious unknown to explore geometry and algebra with my young kids (no pun intended). To me, even though I feel uncertain about the exact tools to use on this journey, I feel certain about what I'm doing. It's like solving an equation from a class of equations that you know how to systematically approach. You know some theorems and properties that inform the approach you take to the problem, even if you can't recall a particular algorithm at that instant. You know if you play with the different parts of the equation, something will occur to you.

I'd agree with that :-). Like you, I'm comfortable doing nonstandard things, because I'm sure I'd be able to course-correct if it went off the rails. 

Oh, totally random question -- I was looking over the thread, and you said you were doing graph transformations. How are you guys approaching that? How did you introduce them? We haven't done anything like that yet... just barely started graphing. 

15 minutes ago, mathmarm said:

I will keep my eyes out for interesting math texts that might be fun for or doable by a 5-8yo. From reading through it, there are things that I like about Foerster and things that I don't like about Foerster, but I haven't used it enough to have anything concrete to report. I've already shared the details of how I plan to use it. When we're a month or so in, I'll try and remember to come back and give an update.

 

Thank you! Both of those would be appreciated. 

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On 3/26/2020 at 12:27 AM, square_25 said:

What was your math education like? 🙂I don't know if mine was standard or nonstandard, but it was practically all self-motivated past the age of 10... I was an obsessive math contest kid and I did a TON of math in high school. And then I got a math bachelor's and a math Ph.D, lol. I've always loved it, although I wound up not loving research math enough to do it as a job. 
 

My mother was a high school math teacher. She ran a math tutorial and enrichment program as well. She taught her kids math far beyond the depth and pace of the public school schedule. I was exposed to a lot of quality, enrichment math from the beginning. By Jr. High/middle school, I was being exposed to a lot of undergraduate and graduate level math, as well as helping in her Math Program with other kids.

Quote

Oh, totally random question -- I was looking over the thread, and you said you were doing graph transformations. How are you guys approaching that? How did you introduce them? We haven't done anything like that yet... just barely started graphing. 

We played with functions, mathematical curves and reading the coordinate plane as separate and intertwined skills for a couple of months. I don't have time to write up the approach right now, but I'll share more when I can.

 

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Just now, mathmarm said:

My mother was a high school math teacher. She ran a math tutorial and enrichment program as well. She taught her kids math far beyond the depth and pace of the public school schedule. I was exposed to a lot of quality, enrichment math from the beginning. By Jr. High/middle school, I was being exposed to a lot of undergraduate and graduate level math, as well as helping in her Math Program with other kids.

We played with functions, mathematical curves and reading the coordinate plane as separate and intertwined skills for a couple of months. I don't have time to write up the approach right now, but I'll share more when I can.

 

Cool :-). My grandmother was a math teacher as well, so I did get exposed to lots of stuff as a kid... sadly, we didn't live in the same place as her after I was 11, so I didn't get much outside teaching (except for school, which just rehashed things) after that age. But I did get exposed to lots of stuff through contests. 

Yes, please let me know what you did for graphing -- as I said, we're just starting out :-). I'm still trying to figure out if I should make another go over geometry, this time with angles, triangle similarity, and with the Pythagorean theorem, before doing serious graphing. Right now, we're just graphing points and noticing patterns. 

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