Math Discussion - Saxon Algebra 2 & Advanced Math

[Julie in MN]

Algebra II, question 22, lesson 5

The question asks them to "simplify by adding like terms" (as in question 22, lesson 5).
The answer is written without fractions and with negative exponents.

My one daughter thought it was better to not have the negative exponent and put it in the denominator instead. I am wondering if this is actually "wrong." I know there are times where the directions will say to have your answer without negative exponents, so that is clear. But there have been a few problems in lesson 4, 5, and 6 where my child had the answer with a fraction and no negative exponents. Is there a rule that says one is more "simplified" than another way? (a fraction with no negative exponent vs. negative exponent and no fraction)

Lesson 6, #19 my child wrote 1/a5b3c (I don't know how to type exponents on here, so the 5 and 3 are exponents )
Lesson 5, #21 my child wrote -8m2p-7 (the 2 and -7 are exponents)

So, those two answers seem to contractict each other because in lesson 6 the answer key was with negative exponents, and lesson 5 they wanted that as a fraction. So, I am a bit confused! The instructions for both problems were "simplify." So.......is my daughter's answer actually wrong? Is there a rule to follow to know how they should be written. Thanks for taking the time to think this through with me!

We haven't started Algebra 2 yet, but in general, I think "simplify" just means "make it simpler" or sometimes "make it more useful - easier to use in a potential equation." Some things are pretty consistent, like combining all the "X" terms, or all of the known numbers. Another constant is probably reducing fractions to their lowest common denominator. But other things can vary with the particular number, such as whether you get rid of all parentheses (which is normally a good thing but sometimes a factored equation is going to be simpler / easier to use / match a factor in the numerator / etc.). Another variable might be deciding the best spot for the negative or the square root (normally it is better to have those on the top of a fraction, but it seems like occasionally that might complicate rather than simplify things?).

That's my impression, anyways, and I give credit if the student has clearly made some changes and can defend their choices.
Julie

[Julie in MN]

My oldest ds is in 9th grade and is currently using Saxon Algebra 1 this year. If we continue on with MFW's recommended math sequence, this will leave Saxon Advanced Mathematics for his senior year of high school. I've read that it should be done over at least three semesters, if not four. What should I plan for? I don't want him to feel rushed through it, with a mountain of math to do each day, but I also don't want him to have to do another semester to finish up the course after his senior year.

Any advice or words of wisdom are greatly appreciated!
Thanks!

My son did his precalc through dual enrollment, so I don't have personal experience, but Saxon Advanced is typically 3 semesters as you mentioned, so just doing 2/3 of the book is a legit full-year credit. The DIVE CD website gives the whole book 3 semester credits, so you could print out something from them if you worry about "legitimizing" the credit. Of course, you can just see how it goes and move your student forward as he is ready.

Adding: MFW lesson plans schedule 51 weeks, so keeping those will again make it "official" if your student does one year's worth of work (usually 34-36 weeks).

The MFW lesson plans actually schedule 3 lessons each week and with homework that is considered 5 days of work (the tests are included in there, as well). So,your student might of course be able to move forward more quickly at least with some assignments, especially if he is really solid on some skills by then. Some students do finish the book in one year. But no worries if he just follows the schedule.

Does that help?
Julie

[ForByGrace]

Okay, thanks Julie!

I guess I'm mostly just kicking back and forth whether or not to have him take a full year of geometry (with Jacobs) between Alg 1 and 2. I've read about MFW ' S reasoning behind it, but I've also read that many people feel the Saxon sequence is enough without a dedicated year of geometry. If we didn't do Jacob's then he'd have more time for Advanced Math. My son's likely to go into an engineering/mechanical type field. What would be the best preparation for that? Do we spend more time solidifying geometry skills, or advance him further in higher math before college? This is my first high schooler, so I'm still trying to figure it all out. Sorry for all the questions!

This may seem early to ask about this, but he's in Alg 1 now, so I need to decide about what I'm ordering for next year within the next several months.

Thanks for your help!

[TriciaMR]

A friend of mine's daughter did Advanced in 2 semesters by doing math each day.

You could aim for starting early and having summer math and take it as it goes during rest of year. I think you still get a credit if you are diligent and do math most days of your 12th grade year no matter how far you get in that book. When they get to college, more than likely they will take a math placement test and go from there into the proper course.

[Julie in MN]

My son's likely to go into an engineering/mechanical type field. What would be the best preparation for that? Do we spend more time solidifying geometry skills, or advance him further in higher math before college?

It's good you're focusing on math and thinking about the math course, because it's so foundational to engineering-type careers.

I'm not sure there is any one perfect sequence except in general doing a lot of math, and making sure he likes doing all that math. Most of my oldest son's fellow students who dropped out of engineering just weren't ready to spend so many hours doing math. More than what specific courses my son took, I think he was best prepared just by doing a lot of math. He was in a special program where he did both algebra 1 & 2 in the same year. That prepared him for spending college days doing math and math-related things like chemistry and physics. He didn't continue in that program after 8th grade, but it did confirm that he liked math.

I do agree that some exposure to calculus in high school, before it "counts" in college, can be helpful. However, more than that, I'd make sure your student builds up his "math muscles" and ensures that math is the life for him.

As for geometry, my son the engineer was public schooled and for various reasons actually never ended up with a formal geometry course, although he was strong in other areas (such as calculus). He would have liked to have had the geometry course, though. Every bit of math that he knew was helpful to him.

Geometry gives the student two things. First, it cements all those skills in measuring angles and shapes and such. Those are big on the ACT/SAT and they are used in many engineering jobs. Second, geometry teaches a student to think through formal proofs and to absorb all of the theorums and postulates that are foundational to math -- most of the math procedures that are taught in school were originally "proven" before they became standard, so working through that part of geometry helps students understand all of math in an important way. That's the part of geometry that isn't in Saxon.

Personally, I would just keep a student moving through the normal sequence MFW recommends. It's tried and true. Then, if it becomes apparent that the geometry is too easy for him and he's getting everything correct, you can skip through it quickly and maybe just focus on proofs. Or, if he becomes enthused about math, let him double up on lessons and move through math years more quickly. But if the foundation is doing him good, then that is where he should be, I think, rather than way ahead but with a rickety foundation.

HTH,
Julie

[ForByGrace]

A big thank you, Tricia and Julie! I so appreciate your time and helpful information. You've given me much to think on. I do feel very confident in following MFW ' S suggested math sequence. I'd rather he has a rock solid year of geometry, strengthening those skills and getting the instruction on proofs he'll need later. Time will tell how far he gets with the Advanced Math level. That'll be up to him!

Again, thank you so much!

[Julie in MN]

Regarding math tests, specifically an 11th grader in Advanced Math.

I just last year heard the idea of letting students fix problems for half credit and I love using that. Now I'm wondering about other math test details.

In Advanced Math, do you let your student have 3"x 5" equation card or anything? My dd just missed a question that included the surface area of a cone because she couldn't remember the formula. What would you do? Tell her the equation for the 1/2 credit fix, just mark it wrong, or let her have an equation sheet? I remember being allowed equation sheets in lots of classes in college...Physics for sure but I can't remember if Calculus was one of them. How much memorization of geometric formulas do you expect from your students?

Colleen,
I remember that cone formula being hard to remember for some of the kids when my son was in math competitions.

My son did his 11th grade math through dual enrollment, so I didn't have to grade that particular course. But I'd say that professors are all over the board on these types of things. The goal is to get your student to understand and use these formulas quickly and easily, and memorizing truly helps with that. However, some options I can think of:

1. Encourage her to develop a cheat sheet as she goes along, and let her use it all year until select major exam(s).

2. Prep her before tests, especially on the formulas you know she will find hard to remember (teachers often do test prep).

3. Let her review before she does the half credit corrections, re-studying what she knows was hard.

4. Let her do the corrections for half-credit using her notes or a cheat sheet (preferably one that she created during the year), which also encourages her to take good notes/note cards/etc.

5. Just go ahead and let her use a cheat sheet. My son's college algebra 3 class was all on the computer. Thus, students could use their books or anything else during tests. However, tests were very tightly timed (possibly shorter time than classroom exams, not sure), so looking up things could cause you to fail the time limit. So a cheat sheet was a good option for that particular class, although it was up to students to recognize what they would need, and that can be a skill in itself. (I'd have to ask ds whether his later math classes allowed cheat sheets, as they tested in the classroom, but I don't think they did? Of course, some tests could have printed formulas right on the page, not sure on that, either.)

Just brainstorming with you,
Julie