What is the best pre-algebra book for a math loving young boy?

[*********]

Ok, so Zee is only six. He's doing CLE Math, which is what we've used from the beginning; he's in level 300 right now, about 1/3 of the way through it.

 

Math is his 'natural' subject. He just gets how it works. There's been only one or two concepts that he didn't get the very first time I explained it to him. He can do two and tree digit addition and subtraction in his head. He can borrow, carry, all that jazz.

 

Last year, in CLE level 200, there were simple algebra problems.

 

Like, if X + 7 = 15, what is X.

 

He loved it. LOVED it. And can I just say, so did I. :D Algebra is probably one of my favorite things to do, school-wise. I have a dss12, and I get excited to help him with his homework. (He's in public school, 7th grade; sadly, a lot of his work is as easy as the things I teach Zee.)

 

So, on to the point; I was wanting to pick up a pre-algebra book to go over with Zee, just for fun. I think he'd enjoy it, and he'd really like the challenge. It wouldn't be any 'official' school work, just for fun.

 

What would you recommend? I know nothing about other math curriculums, so I'm open to all suggestions. I do know that many people do not suggest using CLE math for past the elementary grades. So any links or suggestions? TIA!

[8filltheheart]

I would say there is a huge leap between x + 7 = 15 and pre-algebra. Those type of equations are very typical in 3rd grade math. In order for a child to do pre-algebra, multiplication, division, fractions, and decimals need to be mastered.

 

Have you thought about looking at math programs like Singapore which solve algebraic problems with bar diagrams (not algebra) and are mentally challenging?

 

You could also move on to multiplication/division since he has mastered addition/subtraction.

[SonshineLearner]

I'm going to start on the abacus.... from nurtureminds.com It should be fun... my husband enjoyed "pre-learning" it this last year. Took him a couple of hours to move through the book.

My son also likes learning multiplying and he's talked about dividing/division. He's 6, like your son, so it'll be fun to see what you all do...

Carrie:)

[*********]

I would say there is a huge leap between x + 7 = 15 and pre-algebra. Those type of equations are very typical in 3rd grade math. In order for a child to do pre-algebra, multiplication, division, fractions, and decimals need to be mastered.

 

Have you thought about looking at math programs like Singapore which solve algebraic problems with bar diagrams (not algebra) and are mentally challenging?

 

You could also move on to multiplication/division since he has mastered addition/subtraction.

 

He has done multiplication and division. I don't quite know how to explain him to other people. Frankly, he scares me a little; he just 'gets' math. It's like he already knows it when I 'teach' it to him. I'm worried that I'm not helping him take enough advatage of whatever skill or talent it is that he has in this area. So I thought a 'fun' way to explore it would be to just sit down with a pre-algebra book during quite time and look at it together. But I didn't want to just pick some random book, ya know? What one is good?

 

I'm not trying to brag, or to push ds, or anything. But I sense that he's got some sort of 'gift' when it comes to math; and either way, he REALLY enjoys doing it. So I thought it would be fun for us to do some algebra together, since I really enjoy it, too. (I'm a bit of a math nerd; I got a perfect score on my ACT Math portion, if I recall correctly. I love math. It's kinda weird. :D)

[8filltheheart]

He has done multiplication and division. I don't quite know how to explain him to other people. Frankly, he scares me a little; he just 'gets' math. It's like he already knows it when I 'teach' it to him. I'm worried that I'm not helping him take enough advatage of whatever skill or talent it is that he has in this area. So I thought a 'fun' way to explore it would be to just sit down with a pre-algebra book during quite time and look at it together. But I didn't want to just pick some random book, ya know? What one is good?

 

I'm not trying to brag, or to push ds, or anything. But I sense that he's got some sort of 'gift' when it comes to math; and either way, he REALLY enjoys doing it. So I thought it would be fun for us to do some algebra together, since I really enjoy it, too. (I'm a bit of a math nerd; I got a perfect score on my ACT Math portion, if I recall correctly. I love math. It's kinda weird. :D)

 

I don't think you are bragging or pushing and I can also relate. My 13 yos had mastered multiplication when he was 6 and was doing algebra in 5th grade. That said, unless your ds has mastered all the concepts I listed in my OP, my recommendation would be to look at options that deepen concepts where he is vs. pursuing pre-alg.

 

You might want to look at the Art of Problem Solving's website. This is a site dedicated to developing the skills of gifted math students.

http://www.artofproblemsolving.com/Books/AoPS_B_Rec_Elem.php

 

Even then, I think that Singapore's challenging word problems would be a better route for a 6 yr old b/c AOP is going to expect basic elementary math to be mastered.

[patchfire]

Frankly, he scares me a little; he just 'gets' math. It's like he already knows it when I 'teach' it to him.

 

This describes dd to a T. I knew deep down there was something there when at age two she went around making sets out of everything. It is hard to describe, but I generally tell people that she intuitively understands math.

 

We used Miquon which I think makes a terrific supplement to any math program, and is great for a mathy child. There's also the Zaccaro books - Challenge Math and the like. Those would be fun and enjoyable for the two of you to do together. There's also Math Perplexors - I know Mindware has them, I don't know where else you can purchase them.

 

Finally, on the AoPS website, they have the practice books for the Math Olympiad. Another good source of fun problems. :)

[kiana]

Hands on Equations.

[smrtmama]

The Life of Fred series, hands down.

[HeidiD]

Here's another vote for Hands-On Equations. I got this over the summer to use with my little kids (6 yo included). It takes a concrete approach to algebra - a very accessible method for younger students.

[babysparkler]

He has done multiplication and division. I don't quite know how to explain him to other people. Frankly, he scares me a little; he just 'gets' math. It's like he already knows it when I 'teach' it to him. I'm worried that I'm not helping him take enough advatage of whatever skill or talent it is that he has in this area. So I thought a 'fun' way to explore it would be to just sit down with a pre-algebra book during quite time and look at it together. But I didn't want to just pick some random book, ya know? What one is good?

 

I'm not trying to brag, or to push ds, or anything. But I sense that he's got some sort of 'gift' when it comes to math; and either way, he REALLY enjoys doing it. So I thought it would be fun for us to do some algebra together, since I really enjoy it, too. (I'm a bit of a math nerd; I got a perfect score on my ACT Math portion, if I recall correctly. I love math. It's kinda weird. :D)

 

He sounds just my ds!!! And you sound just like me :)!

 

I wish I had some great advice for you, but I don't... we did Saxon as our "textbook" (skipping the repetition and just working through the "new" materials in it.) I don't necessarily recommend it, but it did give me a good outline on what to "teach" him (thought he always seemed to already know the material and it was mainly a review). Since I love math so much, I tend to use the book for the problems and basic sequential structure, but do all of the lessons with him with paper and pencil on my own. We seem to enjoy that much more, and since I have a good grasp of the math, I can wet his appetite for "deeper" things while covering the "outline" in the book. I do this mainly because the books always seem to be too basic for him, but now that we are moving into algebra, and new things he hasn't yet "seen", I think I may move him more into a textbook approach at some point soon with extra materials for "tangents" that he wants to follow. We plan to do the Art of Problem Solving books next year... I hear they are excellent.

[Storm Bay]

I'd not only do Life of Fred, but I highly recommend doing something like MEP and/or Singapore Math with the IP. In addition, I strongly recommend doing a Russian Math, such as the one at Perpendicular Press http://perpendicularpress.com or Mathematical Circles before getting into Algebra. If you can, do as many of those as you can make time for. Not to rehash the same old same old, but to help develop a deeper understanding of math, to see it different ways, and to help develop the linguistic aspects of math.

 

Singapore Math teaches dc how to solve problems many of us might resort to Algebra to do with simple arithmetic. What it is good for is developing mathematical thinking. The bar diagrams are magnificent, IMO, and I learned all this stuff the old fashioned way at first followed by new Math.

 

Life of Fred pre-Algebra isn't out yet. It may be that your ds is ready for Algebra, as there are some dc who can at young ages, but I'd wait for that book if you can. However, we don't do a pre-Algebra program here since we find that after SM 6 & MUS Zeta we don't need much. Negative numbers come easily to my dc, and they've already been introduced to letters in MUS, and set theory doesn't throw them at all so far. However, my second dd is doing Russian Math first because she doesn't have the focus to do long Algebra problems yet and because she needs to develop her linguistic math abilities (she's highly visual spatial, so tends to solve math without language, and this didn't help her with complex word problems, etc.)

 

How is your ds at logic?

[lgm]

I can relate..optimizing what we did, I'd recommend: get Singapore PM and the Intensive Practice wkbk at whatever level he places in to. It'll take him further than he's worked out in his mind and he'll enjoy multistep problems. He will learn good problem solving techniques, nomenclature, and the properties and algebraic manipulation will become second nature. He'll also gain insight. Get Ed Zaccaro and do the level 3s for warmup and Einstein's for challenge...they are great fun for learning about the world and he'll need the probabilty for any achievement test he's going to take in the future. These two were excellent resources for us at age 6.

 

Also good : zoombinis and pit droids on pc, lego junkbot on the lego website, selected math counts problems, learning to tie knots

 

If you do go to pre-algebra, don't neglect the other strands...bring them up to pre-algebra level before he tests. You may want to consider gifted opportunities in the future and from what I'm reading on other boards, mathy kids that have holes in their knowledge as compared to the usual 'grade levels' don't always get admittance to opportunities they could gain from.

 

Resources for you:

http://www.artofproblemsolving.com/Forum/viewtopic.php?p=33140&highlight=#33140 read Karl Bunday's post (tokenadult)

 

http://www.mathplayground.com/thinkingblocks.html setting up singapore type bar models

 

Enjoy. Our ride has been fun so far. Dolciani is our main pre-algebra pick, with NEM there for fun...I compact by having ds look over a section and work a few selected 'b' and all 'c' problems.

 

P.S. Totally agree with Karin on the verbal....student needs to understand visual, symbol, and verbal and be able to present and explain solution.

Edited September 15, 2009 by lgm

[Capt_Uhura]

Igm, which Dolciani are you using for pre-Algebra?

 

thanks,

Capt_Uhura

[Cindyg]

Hands on Equations.

 

Ditto. This is doable. It doesn't require complex reasoning skill (that even a brilliant 6YO doesn't have yet). It's totally manipulative-based. He'll feel like a genius after the second lesson. It is true pre-algebra (solve for X). This is a winner.

[lgm]

Igm, which Dolciani are you using for pre-Algebra?

 

thanks,

Capt_Uhura

 

Looks like a 1985..isbn 0-395-59123-6

Titled: Pre-Algebra: An Accelerated Course

 

Chosen solely because it was the onlyl version of this title I could find..possibly other years are 'better', but this does it for me. I had excellent math teachers in my time, so I don't need answer keys etc. The big attraction for me is that the child learns to read a math text in both words and symbols. The c problems are icing..it is so sweet to see this kid (at age 10-11) explaining the 'obvious' and enjoying considering cases.

[Rebecca VA]

The Dolciani Pre-Algebra is, sadly, no longer being sold by the publisher. I believe it was written in the early 1980s and revised very little through the years. My daughter used it last year, and we were very pleased with it. It prepared her beautifully for Dolciani Algebra.

[jlovebaker]

would probably be fun with him. Start with the Fractions book - it's the first one and see how he likes it. Also, Mammoth Math does this sort of problem starting in the 4th grade (at least, that's when we started using it and worked with solving for x) - she may start even earlier though. Check out her website ... she has lots of downloads and at a great price. You can even have your son take the placement tests to put him at the right grade level.

 

The beauty of homeschooling is that you can teach at his level no matter his age. Once he really gets the hang of it, I recommend VideoText Algebra. It's pre-Alg plus Alg 1 & 2. I've known kids who have done it by age 10 (very unusual, I think) - my own is in 7th now but started it last year.

[Storm Bay]

The Dolciani Pre-Algebra is, sadly, no longer being sold by the publisher. I believe it was written in the early 1980s and revised very little through the years. My daughter used it last year, and we were very pleased with it. It prepared her beautifully for Dolciani Algebra.

 

 

I would go with LoF pre-Algebra when it comes out, if you really feel you need one, or else that other hands on one mentioned here (but I haven't seen it, so I can't technically recommend it--I've seen enough of LoF to be confident that Dr. Schmidt will do a great job). The best years for Dolciani are 1965-1975, and those have to be bought used. As I suggested earlier, I'd read the Dolciani threads from the high school forum for more on that.

 

fwiw, you never have to state the age of your dc on the high school forum if you ask about Algebra (although the question in this thread was better asked here,) although if you have ages stated in your sig line, I'd take them out before doing that.

[Blessedfamily]

Dd is more gifted in math than I realized, and was going ahead of her Singapore books. Karin is right about being able to see these problems from different perspectives. Even when dd was in the first CWP books, I had her analyze and explain word problem back to after she read them. She would tell me what was there, what was missing, what operations she was going to use to solve them, and why.

 

What I'm doing with the CWP books 4-6 is having her read and think through the problem working it from all angles. She oftens figures it out intinctively, but even so, I have her draw the bar models and she also writes out algebraic equations and solves them to check her work.

 

 

Igm's advice to get the other strands up to par with the algebra is a good reminder for me. I'm trying to make sure not to become unbalanced.

Edited September 20, 2009 by Blessedfamily

[Blessedfamily]

I don't think you are bragging or pushing and I can also relate. My 13 yos had mastered multiplication when he was 6 and was doing algebra in 5th grade. That said, unless your ds has mastered all the concepts I listed in my OP, my recommendation would be to look at options that deepen concepts where he is vs. pursuing pre-alg.

 

You might want to look at the Art of Problem Solving's website. This is a site dedicated to developing the skills of gifted math students.

http://www.artofproblemsolving.com/Books/AoPS_B_Rec_Elem.php

 

Even then, I think that Singapore's challenging word problems would be a better route for a 6 yr old b/c AOP is going to expect basic elementary math to be mastered.

 

It's nice to have a place to ask questions of people who understand you're looking for help and not bragging. To that end, I have a question about determining whether a child is ready for pre-Algebra.

 

If the child has mastered the 4 operations, has a good handle on working the problems in Singapore's CWP with bar models and equations, do you think a full flegged pre-algebra program would then be advisable?

 

For example, a multistep word problem with before and after- Marie and Sharon have the same number of paper clips. When Maries gives 16 paper clips to Sharon, Sharon has three times as many paper clips as Maries. How many paper clips does Sharon have now?

 

So dd did it the Singapore way with bar models, and writes

 

M=S

 

(M-16)= (S+16)x3

 

There are more complex problems, but this is how she "thinks through" problems she has already solved with bar models.

 

Thanks.

 

 

 

 

 

 

I'm watching this thread for pre-algebra rec's, but I'm ordering LOF fractions for now.

[8filltheheart]

It's nice to have a place to ask questions of people who understand you're looking for help and not bragging. To that end, I have a question about determining whether a child is ready for pre-Algebra.

 

If the child has mastered the 4 operations, has a good handle on working the problems in Singapore's CWP with bar models and equations, do you think a full flegged pre-algebra program would then be advisable?

 

For example, a multistep word problem with before and after- Marie and Sharon have the same number of paper clips. When Maries gives 16 paper clips to Sharon, Sharon has three times as many paper clips as Maries. How many paper clips does Sharon have now?

 

So dd did it the Singapore way with bar models, and writes

 

M=S

 

(M-16)= (S+16)x3

 

There are more complex problems, but this is how she "thinks through" problems she has already solved with bar models.

 

Thanks.

 

I'm watching this thread for pre-algebra rec's, but I'm ordering LOF fractions for now.

 

Take what I have to say for what it's worth.....my experience. :D I am not one for rushing through to get to the other side. I have seen it happen to bright kids and the consequences have been there has been excellence in performing operations, but lack of development of understanding concepts.

 

I believe that the leap to pre-alg requires more than a solid grasp of the 4 basic operations. The student must be fully educated on fractions, decimals, order of operations, and ready to deal with the abstractions of negative numbers.

 

If a child is really young, there are better routes to go than pre-alg, alg sequence. Mental math like Singapore (progressing all the way through 6B) and books like the Math Counts books would really stretch the student's math understanding beyond the basic pre-alg manipulations.

 

My kids have never done a "real" pre-alg course b/c they haven't needed to. They have used MUS's alg/geo course as pre-alg/pre-geo (the only MUS course I think has any value and then only as an introduction to the concepts. I picked it b/c my kids have been on the younger side and the pages are not overwhelming and it focuses on the arithmetic side of alg/geo and not theorems/postulates which is good for a basic introduction to the ideas.)

 

FWIW.......my most advanced math student (my 13 yos that is currently taking alg 2) is far more challenged by the art of problem solving books than he is by high school math. He also spends hours on his own tackling the challenges that those books present precisely b/c they are mental challenges and he doesn't like to think he can't do them!!

 

There is simply no reason to rush ahead when there is so many better ways to challenge them. If I had been aware of these resources when he was younger, I would have pursued that route instead of the one that I did. It wasn't until I started to really having to face the realities of where are we going next that I started researching other options.......I now believe they aren't just other options, but realistically better options.

 

Next yr, as a 9th grader, he will doing pre-cal. But, he is simply a kid. I can't manage anything beyond pre-cal myself (and even then that is stretching it. I ended up having to get a tutor for my oldest when he was taking pre-cal b/c I couldn't keep up with him and his questions were deep thought-provoking questions that simply solving the problems in the text wouldn't satisfy. He was way beyond my math abilities.)

 

What will he end up doing? Will he end up being at a disadvantage in the long run by being so far ahead in sequence?? I can't answer those questions b/c we havent' gotten there yet. The problem we are facing is that he is not as advanced in other areas and is a fairly slow reader. He is doing typical high school physics this yr (alg 2 based physics, not cal-based) and is flying through the math. But the reading of a typical 11/12th grade text is slowing him down.

 

I don't want him graduating early b/c they are only kids once. My oldest is extremely mature (to the point of getting married in April with our full blessing. He just turned 20.) However, even with his level of maturity, I wouldn't have wanted him to be out of our home earlier than he was . (He turned 18 after the first few days of university.)

 

So........a very long answer.........look ahead. Try to see where you are going and what you are hoping to accomplish. There is far more to math than progressing through the standard math sequence. Gifted children have the opportunity to explore those areas and end up with far more than having simply moved ahead.

 

HTH

[Blessedfamily]

Thank you, Momof7,

 

I think we'll do a few more programs from different perspectives while finish through Singapore. We always run two math programs at the same time anyway, so I definately want to try LOF's other topics before Algebra.

[Jen500]

Great post, Momof7.

 

My dc are enjoying (along with Singapore) the Creative Problem Solving book (Math Olympiad) and Calculus by and for Young People.

[Blessedfamily]

Great post, Momof7.

 

My dc are enjoying (along with Singapore) the Creative Problem Solving book (Math Olympiad) and Calculus by and for Young People.

 

How do you like the Calculus by and for Young People? I was looking at that this week.

[Jen500]

How do you like the Calculus by and for Young People? I was looking at that this week.

 

This is actually our favorite. We are still working on chapter 1-sums of infinite series. It's really cool to see the kids come up with their own ideas, and we end up spending more time on these than I expected. (In a good way)

I bought the whole package but you really just need the student worksheets. The author is very helpful, and has promptly responded to my emails when I was trying to figure out how to get started.

[Blessedfamily]

This is actually our favorite. We are still working on chapter 1-sums of infinite series. It's really cool to see the kids come up with their own ideas, and we end up spending more time on these than I expected. (In a good way)

I bought the whole package but you really just need the student worksheets. The author is very helpful, and has promptly responded to my emails when I was trying to figure out how to get started.

 

Thanks for the review. :001_smile: I had put it on my wish list, but couldn't find anyone who had used the program.

[Storm Bay]

It's nice to have a place to ask questions of people who understand you're looking for help and not bragging. To that end, I have a question about determining whether a child is ready for pre-Algebra.

 

If the child has mastered the 4 operations, has a good handle on working the problems in Singapore's CWP with bar models and equations, do you think a full flegged pre-algebra program would then be advisable?

 

For example, a multistep word problem with before and after- Marie and Sharon have the same number of paper clips. When Maries gives 16 paper clips to Sharon, Sharon has three times as many paper clips as Maries. How many paper clips does Sharon have now?

 

So dd did it the Singapore way with bar models, and writes

 

M=S

 

(M-16)= (S+16)x3

 

There are more complex problems, but this is how she "thinks through" problems she has already solved with bar models.

 

Thanks.

 

 

 

 

 

 

I'm watching this thread for pre-algebra rec's, but I'm ordering LOF fractions for now.

 

 

We don't do official pre-Algebra programs, but if I were going to do one, I'll wait for the LoF one for my ds. Mine naturally understand negative numbers and are all exposed to learning to substitute letters for numbers in MUS before that level, etc., so we jump right into Algebra. Which one is good is going to depend, in part, on how your dd learns. (I'll put my favourites at the end of this post.)

 

I'm not sure how old your dd is. Some dc are ready for Algebra very young, and some aren't. My eldest started Algebra at 11, but didn't have enough focus, so we went through Algebra 1 over 2 years. However, she needed, IMO, the theory and some proofy Algebra, so we did it again. Bear in mind, though, that my dd hated math. She doesn't hate it as much anymore, but does hate doing assigned work, so it amounts to nearly the same thing. Now she hates writing long geometric proofs.

 

My 11 yo was ready at 10 as far as arithmetic goes, but lacked the maturity to sit and do really long problems, etc. So we are doing a Russian Math first (the one at Perpendicular Press.) I got this suggestion from Myrtle and have been very happy with it. Another great book is Mathematical Circles, and I even have an answer to some questions from the American Mathematical Society that that one is for clever students. These aren't algebra, however. ETA the Russian math from Perpendicular Press does include negative numbers, among other things.

 

The question lies not in arithmetic ability, but in the mental development of logic and reasoning, and it sounds to me like that your dd has that already. The ability to substitute letters is still arithmetic, IMO, and MUS even does this quite early on, before pre-Algebra. There are some gifted dc who are ready very young, particularly profoundly gifted dc, of course. Mine have the ability, but lack the drive to go as fast as they can. Nevertheless, they're all going to start Algebra before 12 based on everything I've seen so far about how they think, reason, etc.

 

We really enjoy LoF, as it's both rigourous and entertaining, a rare combination. It's new to us. The math is taught in the context of a fictional account of a 6 year old genius who is a math professor, and the math is related to real life in humourous ways. But it's also rather rigourous and quite complete. It's also relatively inexpensive. Do get the Home Companion, or whatever that's called, for the answers & for extra cities to do (the problem sets are called cities--6 per chapter, but there are also some in the text that have the answers following as a teacher might do in a classroom.)

 

I do like my dc to do Algebra 1 twice, however, so my 11 yo, once she finishes Russian Math and then LoF, will do at least one other Algebra text. My hands down favourite is Gelfand's Algebra, and I have a copy of the answers (public domain) I could send you if you PM me. However, due to some of the problems being very, very long, most dc aren't ready for this until 13 or so. Also, some of them are very challenging. My eldest has done a good portion of this and we're going to bring it back out when she does Algebra 2. She loves the theory, but doesn't care for the very long problems (but has to do them, bwahahahah. However, she's a teen, so it's a bit different now.)

 

I also like the 1965-1975 Dolciani Structure and Method books for Algebra 1. However, it is difficult to find solution manuals (some have odd answers in the back) and/or teacher's manuals. We were given a copy of the odd answers to the 1965 edition (the only one dd would use, not that she has strong opinions ;)) and finally I put the solutions manual on my Amazon wish list and got a very battered, but usable, copy for more than the text cost (still not expensive.) There are no ISBN numbers for that far back, but if you're interested, I do have ISBN numbers for the 1975 text.

 

My dd liked Lial's Beginning Algebra, but apparently the other Algebra 1 text of Lial's is better, and had I known, I would have used the other one. It's not as good as the older Dolciani, IMO, but many like it.

 

We don't care for TT, and I don't recommend it for mathy students, and certainly not for the mathematically gifted. My dd found it too easy. It's not as rigourous and doesn't teach the theory of it the way that Gelfand's does.

 

Dd found Jacob's Algebra boring, but the first 4 chapters do include pre-Algebra. Many like this text, and I first heard about it on the old AL boards, before there was a LoF and before I heard about Gelfand's or Dolciani.

 

If this doesn't answer your question, please feel free to PM me.

[Blessedfamily]

Very, very helpful. Thank you, Karin.

 

To the OP,

 

Thanks for starting the thread. It brought out some sage advice and opinions on math paths. Have fun with your math kid!:001_smile:

[Storm Bay]

Very, very helpful. Thank you, Karin.

 

To the OP,

 

Thanks for starting the thread. It brought out some sage advice and opinions on math paths. Have fun with your math kid!:001_smile:

 

 

One thing I'd like to add that I've learned recently is that if you do LoF Geometry is that you may wish to add another book along with it. My dd really enjoys it. However, the author has the dc write "Algebra" as the reason for giving a step instead of the actual Algebra Postulate. We're doing a 1973 Dressler Geometry with the LoF, and what I'm going to do is to have dd do the Algebra Postulates in Dressler only (she's 14 so at that age Jane Austen has a character call "that trying age" in Pride and Prejudice. The proofs in Dressler are 2 column and can be rather long. Some argue in favour of other types of proofs, but since we're studying logic as a course on its own, I don't worry about that.

 

Of course, you're still working on figuring out Algebra :).