Saxon Pre A and Alg 1- To further simplify or not..?

[Cottonwood]

So for 2 yrs now I've been confused about some of the answers in Saxon's Solution's Manuals regarding how far they go to simplify the answer.  Some simplified as far as it will go, but in other places, they do not.  I have been telling the kids to simplify as far as it will go to stay on the safe side, and so that as I check their work, I won't have to do any calculations (hopefully) to see if their fraction matches, in a different way, the answer in the SM.  At first I was doing that but it reallllllllly added to the time I spent correcting.

 

An example would be Pre-A Solutions manual, test 7, number 9....  their answer is 4/3.  My kid's answer was 1 1/3.                                                                                                      

 

Yes that's the same and it's easy enough to breeze through and visually see that's the same.  But then there are these:

 

Pre-A, Lesson 23, practice set, a.)  412 yd

                                                           3

 

DS11 wrote: 137.3 to simplify 'to the end'.  That isn't so easy for me to quickly calculate to see if he's right.  It happens quite often and sometimes it takes considerable time to do the problems myself or I flag it as a loose end and at the end of the day the kids and I go over something like that together b/c I'm unclear and don't want to mark it wrong if it's not. 

 

There have been times where I've marked it wrong b/c, well, it isn't the answer in the SM and it's not obvious to me that it's saying the same thing the kids said.  The kids are required to re-work and correct math mistakes.  So they come to a problem like that, where they know they said what the SM is saying, but a different way.  So then they are frustrated and then I'm frustrated. 

 

I would love to know what Saxon is asking of us in this regard so we can just go on and produce it one way or the other.   Am I missing something as to why it's not consistent?  Or is it consistent and I'm not seeing it.  Is it the type of problem that makes the difference?  I've spent considerable time reading last year and this, trying to see if we missed WHERE Saxon tells us where to stop simplifying or if they do at all..I'm just not making sense of it. 

 

Below are the actual problems that belong to the examples above:

 

 

Pre-A, Test 7, #9:

 

20  .  4  /  3    (that slash is a division symbol LOL) 

24     5     6    

 

= 4

   3  (Saxon's Answer)

 

 

Pre-A, Lesson 23, Practice problem a) Use a unit multiplier to convert 412 ft to yards.

 

There are no 'solutions' for practice problems in the SM but the problem would go something like this:

 

412 ft   .   1  yds    =   412  (Saxon's Answer)     Again, my kid's answer: 137.3

   1           3  ft               3

 

 

 

ETA:  sometimes either/or of the simplifications are in the kids' work, off to the side so I can see the work up, thus either answer.  But, very, very often, the kids do mental math within the problems and the ending answers are very different, and I don't get the benefit of seeing the fractions leading to their answer, thus if their answer is different than the SM, it looks wrong.  I don't want to ask them to write down every single increment of the problem b/c that frustrates them and their supplemental math (AOPS) has encouraged them to do the work conceptually, so often they are making calculations mentally that I can't evaluate on paper.

 

And, these are just examples where Saxon doesn't simplify to the end, but there are many, many examples through each lesson where they DO.

[kiana]

412/3 is NOT the same as 137.3 -- one is exact and one is a decimal approximation. I would mark that wrong with a minor deduction, but if they wrote 137 and 1/3 I would mark it correct. If he wrote 137.3 repeating (with a line over the 3) I would also mark it correct because that is exact, but I would prefer that it be left as a fraction (improper or mixed, no issue either way)

 

There is a difference between giving an alternate exact form of the same answer and giving an approximate form. This is an important difference and worth stressing to your children. 

 

One easy way for YOU to tell if they have given a different exact form of the same answer or an incorrect answer (some exact forms look very different even though they are correct) is to plug the TM answer into a calculator and then subtract your child's answer (do not round at any point). If the difference is 0, they are different exact forms. If the difference is not 0, they are not. For example, if you do 412/3 - 137.3, you will get .0333... This should not actually take too much time. 

 

Now, as for a grading policy when work is not shown and the answer is very different, here is MY policy that I use in classes.

 

If the work is not shown, the answer is correct, and it's something I can do in MY head, I mark it correct.

If the work is not shown, the answer is correct, and it is too complex for me to do in MY head (I teach math so this is a high barrier), I mark it incorrect because I assume an unauthorized aid was used.

If the work is not shown and the answer is incorrect, no partial credit is awarded -- the score is 0. 

[Punks in Ontario]

I've always just kept a calculator nearby to check.  Sometimes we process a question differently than Saxon and I just know I have to spend the time with those.  I just consider it part of the task.

 

ETA I'm pretty confident with math.

[FriedClams]

I do not require my kid in Saxon 1/2 to change reduced fractions to mixed numbers. If the problem states "change fractions to decimals", then they divide out.

[Cottonwood]

 I would not say that I am confident in math, necessarily, so the tip you gave, Kiana, on how to check their work with the calculator is going to save me tons of time, and I don't mind adding that to the task. lol  But reworking some of these problems from the beginning at the end of the day was something I was growing VERY weary of.  Thanks, ladies!!

[K&Rs Mom]

 

    

I would love to know what Saxon is asking of us in this regard so we can just go on and produce it one way or the other.   Am I missing something as to why it's not consistent?  Or is it consistent and I'm not seeing it.  Is it the type of problem that makes the difference?  I've spent considerable time reading last year and this, trying to see if we missed WHERE Saxon tells us where to stop simplifying or if they do at all..I'm just not making sense of it. 

 

 

I would love to know this too!  Our first experience with Saxon is Alg2, and it's the same - I just make sure her answer can convert to match theirs.

[RegularMom]

We've been wondering about this issue as well, specifically when it comes to Pi and unit multiplier problems. I emailed a bit with the saxon homeschool help desk and they said that leaving the symbol for Pi is actually more accurate than doing the calculations, which makes sense to me since 3.14 is a rounded approximation of Pi, but I'm still not clear on why some problems seem to get simplified and some don't. 

 

I've talked this over with my dd14 and told her to not worry so much about doing the calculations for these problems. What's more important is that she sets up the problem properly than gets the calculations right. She was a bit relieved to hear this, actually, because she now finishes faster, not having to do that math.

 

However, I do keep a calculator nearby when grading to make sure, if she does calculate the final answer out of habit, that she's gotten it correct. 

 

 

[Cottonwood]

We've been wondering about this issue as well, specifically when it comes to Pi and unit multiplier problems. I emailed a bit with the saxon homeschool help desk and they said that leaving the symbol for Pi is actually more accurate than doing the calculations, which makes sense to me since 3.14 is a rounded approximation of Pi, but I'm still not clear on why some problems seem to get simplified and some don't. 

 

I've talked this over with my dd14 and told her to not worry so much about doing the calculations for these problems. What's more important is that she sets up the problem properly than gets the calculations right. She was a bit relieved to hear this, actually, because she now finishes faster, not having to do that math.

 

However, I do keep a calculator nearby when grading to make sure, if she does calculate the final answer out of habit, that she's gotten it correct. 

 

The Pi thing came up for the first time today, so thank you for the info on that.  We haven't hit unit multipliers in Alg 1 yet, so I can see we have that to look forward to. lol

 

[EndOfOrdinary]

In many formal math classes the standard is that if a mixed number is used in the problem the answer is to be in mixed number form. If an improper fraction is used, the answer is to be expressed as an improper fraction. Simplify does not refer to converting mixed numbers. Simplify only refers to the act of reducing the fraction. There is nothing simpler about a mixed number.

 

This seems to be what is happening in the problems above. By asking for a unit multiplier they are asking you to directly make an improper fraction, thus the answer is in that form. In the division problem, you must use the reciprocal and thus an improper fraction so you are left with an answer as an improper fraction.

[Omma]

Art Reed, teacher of Saxon Math for 32 years, that it is fine (and even preferred no matter what the Saxon answer key says) if the student leaves an answer as an improper fraction rather than as a mixed number.  He says improper fractions are much easier to work with in algebra than mixed numbers.  Of course, if the book specifically states a way the answer should be given, then go with that!

 

:)

Brenda