Jacobs geometry chapter one question

[Phoatogirl]

I sent my son in to work on math the last couple weeks without my oversight because I've been recovering from surgery. He told me that his new geometry course (Jacobs 2nd edition) is boring and not even math. I finally sat down with it and I understand what Jacobs is getting at (logic etc)with the first chapter, although I'm personally not interested in it and do find it more boring than working an algebra problem. I can totally understand why my son said what he did, since he's a "show me the formula and tell menhow to use it" guy. Does he need this first chapter or can it be skipped????

[Julie in MN]

I can't remember chapter 1, but basically, the sad news is that geometry is not algebra, and won't be all year. And Jacobs teaches from a logic perspective, all year.

 

So maybe chapter 1 is where to get used to that?

 

Otherwise, I'd say it's up to you.

Julie

[C_l_e_0..Q_c]

There are no formulas in geometry, or just a few. Jacobs is about proofs, not calculations, at least from what I've seen so far. It's about shaping your mind around a systematic approach to logic. You like or you don't. But either way you have to get through it.

 

It might be the first math program that forces him to think, if he's the type to enjoy plugging formulas. My son is starting chapter 2. so we're also discovering Jacobs Geometry.

 

I used to love Geometry, and got the highest mark in the whole province. It's hard to beat 105% ;-)

[Lori D.]

Yes, I would do chapter 1 because it is foundational to understanding the logic that you'll use in writing proofs throughout most of the rest of the book -- but don't dwell too much on it; just do it at a rapid pace, and move on. :) After chapter 1 you start getting into proofs, which show WHY certain math principles are true; your DS will most likely find that to be a bit more "math-like" and hopefully more enjoyable.

 

About 3/4ths of the textbook is about "plane Geometry" -- points, lines, angles, triangles, and other 2-D figures, their connections, and proving through formal proofs their connections. It is not until the last few chapters of the book that Jacobs gets into the formula aspect of Geometry (calculating area and volume of solids such as cubes, prisms, spheres and cylinders).

 

We really enjoyed Jacobs Geometry (2nd ed.) after we got into it; hope your family will too! About the only chapter I'd say would be okay to skip is towards the end -- the chapter on non-Euclidean forms of geometry -- consider it an "optional extra" chapter. Warmest regards, Lori D.

Edited September 28, 2011 by Lori D.

[jamajo]

I'm an algebra type of gal (As in high school) and Cs in Geometry. I have no idea what you guys are talking about when you say logic regarding Geometry.

 

I remember calculations about shapes. Does this mean I should be looking at something more like BJU Geometry for my 10th grader next year?

 

All Geometry programs are not how you are describing Jacob's to be, is it??

 

sorry .... is this what it means to hijack a post:tongue_smilie:

[TravelingChris]

I am not understanding you, jamajo. All geometry courses that are on a high school level are basically about logic of shapes and angles and that kind of thing. There is very little arithmetic in geometry so if you are talking about things like finding perimeters or areas of certain shapes, that is done in elementary school or middle school, way before geometry. I am sure BJU Geometry does it in a similar way even if there is no specific chapter on logic in the text.

[Lori D.]

The Logic that comes into Geometry is in the writing of Proofs. Euclid, the ancient Greek who first formalized the study of Geometry, did so by starting with just a very few principles given to be true, and then with a series of Logical, step-by-step statements, would then build an argument (called a "proof") showing another more complex truth about geometric shapes (lines, polygons, circles).

 

These Proofs, through a Logic series of statements show why something like why two angles are equal. To actually see what I am trying to explain, check out this explanation and actual examples of Geometry Proofs at Sparknotes, or some of the helpful articles at Ask Dr. Math, or watch some of the free tutorials at Khan Academy.

 

High school Geometry texts vary as to how MUCH the program is about writing proofs (e.g.: Jacobs is about 3/4th on explaining the below topics through writing proofs; MUS was less than 1/5 about proofs), and also vary as to how MUCH they discuss Logic when introducing Proofs. But all high school Geometry programs have *some* exposure to writing proofs. Other topics usually covered in geometry have to do with:

- Lines, Line Segments, and Rays (proofs here)

- Angles (LOTS of proofs here)

- Triangles and other polygons (more proofs here)

- Using a Protractor

- Area and Perimeter

- Circles: Radius, Diameter and Circumference

- Area and volume of solids (circles, cylinders, prisms, etc.)

- The Pythagorean Theorem

 

 

Other Geometry programs begin to include some Trigonometry (problem solving with angles), and Analytical Geometry (mix of formulas (algebra) and coordinate graphing (geometry)).

 

A more simple high school geometry program will mostly focus on lines, angles, circles, area and volume, and just a little coverage of proofs, often done as "fill in the missing steps" of the proof. I would suggest that Math-U-See's Geometry is a more simple Geometry program. Jacob's is more average, with more depth of coverage, and more actual proof-writing. An advanced high school Geometry course would most likely include proofs, beginning trig and problem solving, and would introduce Analytical Geometry concepts (which are typically covered in depth in a high school Algebra 2 course).

 

 

Hope that helps! Warmest regards, Lori D.

Edited September 29, 2011 by Lori D.

[jamajo]

Lori...all the topics you listed that are covered in Geometry I totally remember from 10th grade but I guess the logic and proofs just went over my head. Hmmm.... I suppose I won't worry about it now. I'll be sure to actually look at different texts when the curriculum fairs roll around and choose one that makes sense to me.

 

This post just sort of took me off guard as to what Geometry was all about.

Got a love these forums for bringing up topics you never knew you had to think about.

[FourOaks]

"A more simple high school geometry program will mostly focus on lines, angles, circles, area and volume, and just a little coverage of proofs, often done as "fill in the missing steps" of the proof. I would suggest that Math-U-See's Geometry is a more simple Geometry program. Jacob's is more average, with more depth of coverage, and more actual proof-writing. An advanced high school Geometry course would most likely include proofs, beginning trig and problem solving, and would introduce Analytical Geometry concepts (which are typically covered in depth in a high school Algebra 2 course)."

 

My dd is flying through MUS Geometry, so I am wanting to supplement now with even more geometry for her. If Jacob's is average, can you recommend a curriculum that would be considered advanced? I want to prepare her well if the math/science route is the way she may go, so I really would like something that colleges would look at favorably.

 

Thanks

[Lori D.]

...can you recommend a curriculum that would be considered advanced? I want to prepare her well if the math/science route is the way she may go, so I really would like something that colleges would look at favorably.

 

 

Just an aside: The math courses in which you will ESPECIALLY want advanced/college-favorable programs are the Algebra, Alegebra 2, and Pre-Calc/Trig courses. Geometry, while a required math, is NOT a math topic that is heavily focused on -- in either high school or college. In addition, there are only a very few questions on Geometry on the ACT and SAT tests -- the math sections heavily emphasize the Algebra 1 and 2, so, again those are the math areas you especially want to focus on. (High SAT scores in math translates to college admissions and scholarships later on!)

 

However, in answer to your original question -- no personal experience with other Geometry programs other than Jacobs and MUS -- BUT, one program I hear of on this board a lot did come to mind that would work well as a supplement: The Art of Problem Solving (AoPS): Geometry. Here is a nice review of it by Regentrude from a recent post:

 

"The book [AoPS] is written TO the student and does not really require a teacher. It is a discovery based approach; problems are posed, the student has to try to solve them, THEN the solution is given and the new concept discussed. The book covered proofs and the traditional geometry material, but also a lot more material than the traditional geometry courses, interesting problem solving concepts not normally taught, plus has an introduction to trigonometry. We love AoPS. It works well for students who are good at, and enjoy doing, math. I would not use the program for students who are not excited about math."

 

 

Also, check out this past thread for more ideas: What are you using for college prep geometry?

Hope that helps! Warmest regards, Lori D.

Edited October 1, 2011 by Lori D.