Pre-geometry?

[MamaSprout]

We're doing a mash-up of MM6/7 along with Real World Algebra for PreAlgebra this year (and maybe into next year).

 

I want to skip the Geometry chapters in Math Mammoth, partially to mix things up, and partially because I'd like to do something more fun/ rigorous for a geometry- loving math kid who's done Singapore up to 5b.

 

I had thought Patty Paper Geometry, but it seems fussy... Hands on stuff doesn't always get done unless it's on her terms.

 

I'm having a hard time getting a feel for CTC Understanding Geometry. I assume we would continue this into the first part of Algebra?

 

I'm not sure if Key To Geometry would be interesting enough... I haven't looked closely, though.

 

Have I missed anything? I saw the James Tanton stuff in the Epic Geometry thread, but I think that's high school, and there does not seem to be any samples of the books.

[Chris in VA]

Key to Geo is basically a lot of constructions. We used it to supplement a bit. It might be a fun intro, but it is a little dry, imo.

 

I'd just wait until Algebra 1 is completed, and then jump in full-force with a standard curriculum.

[maize]

We are in about the same place as you and looking at similar options. Dd11 like Righstart Geometry, we've done a bit of that but not enough to really review it. So far mostly constructions, though I've always sound those fascinating.

[Farrar]

:bigear:

 

If you haven't played Dragonbox Elements yet, that's great for teaching geometry. The Murderous Maths book Savage Shapes has some cool pre-geometry stuff in there and so does The Perfect Sausage about three dimensional geometry, though that one has other topics as well like about distance and speed and force. Agreed that Key to is dry. This is in my plans for next year as well, so I'm curious what else is out there.

[maize]

:bigear:

 

If you haven't played Dragonbox Elements yet, that's great for teaching geometry. The Murderous Maths book Savage Shapes has some cool pre-geometry stuff in there and so does The Perfect Sausage about three dimensional geometry, though that one has other topics as well like about distance and speed and force. Agreed that Key to is dry. This is in my plans for next year as well, so I'm curious what else is out there.

Thanks for the reminder about the Dragonbox app, we have it but haven't tried it out yet. My kids enjoyed the algebra one, so hopefully Elements will be a hit as well.

[MamaSprout]

:bigear:

 

If you haven't played Dragonbox Elements yet, that's great for teaching geometry. The Murderous Maths book Savage Shapes has some cool pre-geometry stuff in there and so does The Perfect Sausage about three dimensional geometry, though that one has other topics as well like about distance and speed and force. Agreed that Key to is dry. This is in my plans for next year as well, so I'm curious what else is out there.

 

I forgot- She's done Dragonbox Elements, and has read and reread both Murderous Maths books. Loved them all.

[kiana]

PM loesje about CTC geometry -- she's using it in middle school and could probably give you more details. 

[Chrysalis Academy]

Well, we did pretty much exactly what you are describing last year, down to wanting to skip the geometry in MM.  We have the CTC Understanding Geometry book.  Ch. 1-7 covers everything you'd need for "pre-geometry" - everything AoPS covers in the PreA book, plus more on some topics, and it's an easier to use, less wordy, more colorful, but still very deep-thinking kind of book.  We're just starting with it and will be alternating chapters between this and Alg 1 - kind of our own integrated math - but after looking at a bunch of things this looks like it will work very well.  Feel free to ask me if you have any specific questions about the book.

[maize]

Well, we did pretty much exactly what you are describing last year, down to wanting to skip the geometry in MM. We have the CTC Understanding Geometry book. Ch. 1-7 covers everything you'd need for "pre-geometry" - everything AoPS covers in the PreA book, plus more on some topics, and it's an easier to use, less wordy, more colorful, but still very deep-thinking kind of book. We're just starting with it and will be alternating chapters between this and Alg 1 - kind of our own integrated math - but after looking at a bunch of things this looks like it will work very well. Feel free to ask me if you have any specific questions about the book.

Is this the book you are talking about?

 

http://www.criticalthinking.com/understanding-geometry.html

[Chrysalis Academy]

Yes, that's the one.

[MamaSprout]

Well, we did pretty much exactly what you are describing last year, down to wanting to skip the geometry in MM.  We have the CTC Understanding Geometry book.  Ch. 1-7 covers everything you'd need for "pre-geometry" - everything AoPS covers in the PreA book, plus more on some topics, and it's an easier to use, less wordy, more colorful, but still very deep-thinking kind of book.  We're just starting with it and will be alternating chapters between this and Alg 1 - kind of our own integrated math - but after looking at a bunch of things this looks like it will work very well.  Feel free to ask me if you have any specific questions about the book.

 

Do you think this work? It's kind of rough. My goal is to not duplicate anything in MM. If a subject is covered in 6, then reviewed in 7, we will only need to do it in 7. There's a certain amount of guessing here b/c MM7b won't be out until January. I estimate we should finish this in 2 school years (counting this one)

 

MM6-

Do all of chapters 1-3; Review of Operations, Expressions and Equations and Decimals.

Chapter 4-5 are to be reviewed in MM 7b. (Ratios and Percents), so cover them quickly, or wait until 7b comes out.

Chapter 6 (prime factorization)- Skip. Do chapter 1 in Russian Math 6 instead since MM coverage is similar to what we've  seen in Singapore.

Chapter 7- (fractions) do whole chapter. Basically, begin MM7a and Exploring Geometry after this chapter

Chapter 8 (Integers) Skip: Do MM7a Chapters 1 and 2 instead. (Language of Algebra & Integers)

Chapter 9 (Geometry) Skip: Begin CTC Exploring Geometry one day/ week

Chapter 10 (Statistics) Skip- Do Statistics from 7b

 

MM7-

Chapters 1 and 2; (Language of Algebra & Integers)

Begin Real World Algebra one day per week. Continue MM7 3 days/ week and Exploring Geometry 1 day/ week.

Finish MM7 as follows

Chapt 3: One Step Equations- all

Chap 4: Rational Numbers- all

Chapter 5 Equations and Inequalities- all

7b (projected chapters- taken from Forward in 7a)

Chapter 6 Ratios: Do all

Chapter 7 Proportions: Do all

Chapter 8 Percent: Do all

Chapter 9 (skip) Geometry and Pythagorean Theorem)

Chapter 10 Statistics and Probability: Do all

 

When Math Mammoth is finished, finish Real World Algebra 3 days a week, switch Exploring Geometry to 2 days a week. Probably will finish out second school year.

 

After Real World Algebra is completed (probably year 3), begin AoPS Intro to Algebra 4 days per week/ and drop Exploring Geometry back to 1.

 

Putting this down helps me "see" it, and I welcome any comments.

 

Thanks!

[Chrysalis Academy]

I think that sounds like a really great plan.  Of course you'll tweak it as you go, but I'm the same way, I like to see it all planned out like that.  MM7 wasn't out last year, of course, so mine was a bit more cobbled together, but I think your plan looks totally solid.  We skipped parts of MM6 that I planned to cover using other things, and for the rest, we accelerated through the chapters -  rather than skipping entirely, I would have her do the chapter test, and then pull out the lesson on any topic she missed.

[zoobie]

Do you think this work? It's kind of rough. My goal is to not duplicate anything in MM. If a subject is covered in 6, then reviewed in 7, we will only need to do it in 7. There's a certain amount of guessing here b/c MM7b won't be out until January. I estimate we should finish this in 2 school years (counting this one)

 

MM6-

Do all of chapters 1-3; Review of Operations, Expressions and Equations and Decimals.

Chapter 4-5 are to be reviewed in MM 7b. (Ratios and Percents), so cover them quickly, or wait until 7b comes out.

Chapter 6 (prime factorization)- Skip. Do chapter 1 in Russian Math 6 instead since MM coverage is similar to what we've  seen in Singapore.

Chapter 7- (fractions) do whole chapter. Basically, begin MM7a and Exploring Geometry after this chapter

Chapter 8 (Integers) Skip: Do MM7a Chapters 1 and 2 instead. (Language of Algebra & Integers)

Chapter 9 (Geometry) Skip: Begin CTC Exploring Geometry one day/ week

Chapter 10 (Statistics) Skip- Do Statistics from 7b

 

MM7-

Chapters 1 and 2; (Language of Algebra & Integers)

Begin Real World Algebra one day per week. Continue MM7 3 days/ week and Exploring Geometry 1 day/ week.

Finish MM7 as follows

Chapt 3: One Step Equations- all

Chap 4: Rational Numbers- all

Chapter 5 Equations and Inequalities- all

7b (projected chapters- taken from Forward in 7a)

Chapter 6 Ratios: Do all

Chapter 7 Proportions: Do all

Chapter 8 Percent: Do all

Chapter 9 (skip) Geometry and Pythagorean Theorem)

Chapter 10 Statistics and Probability: Do all

 

When Math Mammoth is finished, finish Real World Algebra 3 days a week, switch Exploring Geometry to 2 days a week. Probably will finish out second school year.

 

After Real World Algebra is completed (probably year 3), begin AoPS Intro to Algebra 4 days per week/ and drop Exploring Geometry back to 1.

 

Putting this down helps me "see" it, and I welcome any comments.

 

Thanks!

 

Bumping an older thread, but I'm wondering how this has been working for you. I'm about to start MM6 with DD in a week or so... :)

[Chrysalis Academy]

Since this thread just reappeared, I'll add another pre-Geometry resource:  The EdX  Geometry class.  Its syllabus covers the content of a high school geometry course; I think of it as Pre-Geometry, because I don't think there are enough problems for full mastery, and it doesn't include writing proofs, but I'm super impressed with the instruction - very clear, interactive, short lessons, adaptive.  My 7th grader is doing it right now, and I think that she will find both the CTC book and the Geometry portion of Alcumus (at least the Pre-A bits) much more manageable after this introduction.

[MamaSprout]

Bumping an older thread, but I'm wondering how this has been working for you. I'm about to start MM6 with DD in a week or so... :)

I think this probably would have worked, but we ran out of time to use the MM7b chapters before a test we wanted her to see those topics before taking.

 

We ended up only skipping the geometry chapter in MM 6, only doing 1 and 2 in MM7, dropping Real World Algebra and doing more in Understanding Geometry. We did a few odd weeks of Russain Math 6, and gave Derek Owens PreA a spin.

 

I tried to pick back up a MOEMs book we have after the test, but it just wasn't fun anymore. DD asked if she could try Algebra and I had her take the placement test for Jacobs. We've moved on to that, although I do like the way MM 7 presents things. We will probably use it as back up, extra practice, and out of the house work while she transitions over to working into a notebook.

 

She's used an assortment of PreA materials for a while, and I think she was ready to move on. HTH!

[Professormom]

The CTC book looks interesting. Is there a solutions guide? Thx:-)

[Professormom]

Nm. I just read the Critical Thinking description more closely, and it says student book with answers.

[Loesje22000]

Yes just plain answers, not nice step by step solutions as in AoPS.

We are almost done with the book.

Now we are preparing the grade 8 math exam

 

ETA:

We don't have 'pre-geometry' here, it is just part of the college bound middle school track here.

Understanding geometry covered what we needed.

The vocational track has different math.

[Chrysalis Academy]

Yep, just answers.  Which makes it tricky if you are geometry-challenged yourself - my dd and I tend to get the exact same questions wrong, and sometimes we don't know why!

[dereksurfs]

I wanted to give another perspective on this for those considering their options.  We were in the same boat last year before starting Geometry.  After AoPS Intro to Algebra we really wanted to do a pre-geometry.  We have Patty Paper and were also planning on purchasing CTC's Understanding Geometry.  We were going to do it last Summer before Jurgensen Geometry which was starting in the Fall at WHA.  I knew it was a rigorous course and wanted some conceptual development and practice beforehand.  Well, as things sometimes happen in homeschooling, ds13 felt he needed more practice with algebraic fundamentals after AoPS.  He had the concepts, he just needed more practice.  So, instead of working on pre-geometry we ended up working through parts of TabletClass Algebra to solidify his skills.  

 

Now, as he approaches the end of Jurgensen Geometry I am happy to see that he has excelled in the course and really does enjoy it.  This isn't to say a pre-geometry would have been a bad idea.  Rather, for those who may run out of time, it may not be as critical to your dc's success as you might imagine.  I definitely see it as an enrichment opportunity if time permits.  Just don't feel too bad if you do not dedicate enough time or rigor toward pre-geometry before starting full geometry.  That said, all of our kids have had introductions to some 'basic' geometric concepts throughout their math training.  They love DragonBox Elements and our son's favorite hobby is Origami.  There were some intro concepts in their curriculum, but beyond that we did nothing else to prepare and were fine. Solid algebra and problem solving skills were really key for ds13.

 

ETA: One last caveat, I know all kids are different and for ds13 these concepts including constructing logical proofs comes relatively naturally.  The fact that he has scored highly with no formal prior training may not be the same for other children including our younger dds.  I'm just not sure how one could measure the effectiveness of taking extra pre-geometry vs. not.  Maybe it falls into the category of better to error on the side of more preparation than less if given the opportunity?

[MamaSprout]

Good points, Derek.

 

My original thought with the pre-geometry was kind of pre-AOPS geometry, or getting enough geometry to get by until a later, harder geometry class. I'm happy she likes it, and I'm kind of rolling with whatever works at the moment. I don't even want to think about real geometry for a while. Algebra snuck up on me though, so maybe I should.

[SparklyUnicorn]

Didn't read the other responses.  We used this:

 

http://www.criticalthinking.com/understanding-geometry.html

[dereksurfs]

Good points, Derek.

 

My original thought with the pre-geometry was kind of pre-AOPS geometry, or getting enough geometry to get by until a later, harder geometry class. I'm happy she likes it, and I'm kind of rolling with whatever works at the moment. I don't even want to think about real geometry for a while. Algebra snuck up on me though, so maybe I should.

 

Yeah, I just re-read your update and its funny how our plans change, especially when using a variety of sources.  We had something similar occur reminding me of 'the best laid plans of mice and men.' ;)

 

I think you really hit the nail on the head though when focusing on something which works.  Nowhere does it say that getting from point A (primary math) to point B (secondary math) has to be a straight line.  I really like that you are flexible enough to be tailoring things as you go.  

 

Now that Algebra with Jacobs snuck up and you are heading down that road are you still considering AoPS (algebra or geometry) for the future?  The reason I ask is that it is also my opinion that taking two passes through Algebra is perfectly fine, especially if dealing with super challenging material such as AoPS.  In addition, AoPS Geometry is reported to be one of their most challenging courses.  So maybe something else would help first before that.  Although some AoPS seems to be the best prep for more AoPS.  

 

We decided to go with Jugensen for Geometry at WHA instead, primarily because I wanted someone else to grade the proofs.  What I found was that it was not only helpful having an instructor grade the proofs but to instruct in good form as well.  For example, a proof could be terribly verbose yet logically correct.  The instructor would then demonstrate how to write proofs more efficiently, which I really love.  I see this same thing in my profession as a software engineer.  Someone can write a program which might 'work' yet is horribly inefficient.

[MamaSprout]

Now that Algebra with Jacobs snuck up and you are heading down that road are you still considering AoPS (algebra or geometry) for the future? The reason I ask is that it is also my opinion that taking two passes through Algebra is perfectly fine, especially if dealing with super challenging material such as AoPS. In addition, AoPS Geometry is reported to be one of their most challenging courses. So maybe something else would help first before that. Although some AoPS seems to be the best prep for more AoPS.

 

We decided to go with Jugensen for Geometry at WHA instead, primarily because I wanted someone else to grade the proofs. What I found was that it was not only helpful having an instructor grade the proofs but to instruct in good form as well. For example, a proof could be terribly verbose yet logically correct. The instructor would then demonstrate how to write proofs more efficiently, which I really love. I see this same thing in my profession as a software engineer. Someone can write a program which might 'work' yet is horribly inefficient.

Currently Plan A is to finish Jacobs then move on to AOPS Number Theory and Counting and Probability, probably one with a class. From there maybe the Intro Algebra B and see where we are before deciding on Geometry.

 

I guess I don't have Plan B yet, but rather vague ideas involving a tutor or online classes.

 

I agree with your efficiency comment. I see the same thing in college and professional writing. I know I cannot teach those little efficiencies in mathematics and think I would do DC a disservice if I tried to teach it.