01 March 2015
Parallel Line Equation Given 1 Point
(Originally posted to Mom on a Narrow Path blog on Weebly, now deleted.)
27 February 2015
21 February 2015
A Beginning...
(Originally posted to Mom on a Narrow Path blog on Weebly, now deleted.)
To be fair, I am no math genius, but I do so enjoy the subject. Surprising, since I always hated Honors Algebra/Trig in high school. Honors Geometry was a little better, but it seemed easier to deal with math that could be seen in drawings and shapes.
Mathematics at a rudimentary level is black and white to me. Numbers can be manipulated to do some pretty crazy and amazing things, but when you answer a problem, there can be no interpretation like in the humanities, language arts, or social sciences. In math, the answer is what it is and there is really no room for debate when dealing with an equation or formula. Professors, teachers, mathematical geniuses, or a bunch of nerds at a coffee shop can debate the best or quickest or easiest way to arrive at an answer. (Some of the liveliest discussions I've ever heard, ironically!) But it still boils down to the black and white fact: when given an algebraic equation and values for any variables, there is a right answer.
Do you enjoy any aspects of math? If so, what is your favorite (or least dreaded) discipline and why?
To be fair, I am no math genius, but I do so enjoy the subject. Surprising, since I always hated Honors Algebra/Trig in high school. Honors Geometry was a little better, but it seemed easier to deal with math that could be seen in drawings and shapes.
Mathematics at a rudimentary level is black and white to me. Numbers can be manipulated to do some pretty crazy and amazing things, but when you answer a problem, there can be no interpretation like in the humanities, language arts, or social sciences. In math, the answer is what it is and there is really no room for debate when dealing with an equation or formula. Professors, teachers, mathematical geniuses, or a bunch of nerds at a coffee shop can debate the best or quickest or easiest way to arrive at an answer. (Some of the liveliest discussions I've ever heard, ironically!) But it still boils down to the black and white fact: when given an algebraic equation and values for any variables, there is a right answer.
Do you enjoy any aspects of math? If so, what is your favorite (or least dreaded) discipline and why?
19 February 2015
Welcome! & Mathematics
(Originally posted to Mom on a Narrow Path blog on Weebly, now deleted.)
I am trying a new tack with blogging. Simple sharing.
New Weebly site. New look. Just simple sharing.
So without further ado, I'll dive right in.
Right now, I am in the second week of College Mathematics I with University of Phoenix through their online campus. Math has pretty much taken over my brain. I forgot how good it feels to look at a problem, solve it, sit back and just glow.
Last week, our assignment covered maybe 10 topics and should have taken all week to study and complete. Granted, the topics were pre-algebra and designed to be relatively simple so that we were not learning brand new concepts while learning the MyMathLab interface, but this was beyond ridiculous.
When an assignment designed to take several hours a day at the minimum only takes 30 minutes for me to complete, I am shocked I ever had trouble with this stuff in high school. Let alone why I am even taking this class. Why wasn't I able to test out?
We never use algebra in daily life, true. But knowing that my brain can wrap itself around these complicated operations of logic in an insanely quick way after all these years is priceless.
I had not thought of Dear Aunt Sally in nearly two decades, maybe more. I just simply knew that when facing an equation, one must work through anything bracketed first. Inside those brackets, you calculate any exponents, then all multiplication and division from left to right, then all addition and subtraction from left to right. Once the parenthetical calculations are complete, you must move on to exponents from left to right, all multiplication and division from left to right, and finally all addition and subtraction from left to right.
Apparently in grade/elementary school, we learned this as "Please Excuse My Dear Aunt Sally".
Please = Parentheses
Excuse = Exponents
My Dear = Multiplication and Division
Aunt Sally = Addition and Subtraction
While I must have learned it this way as well as it does sound familiar to me, I think I used it for what it was, a neat memorization/learning tool, and then tossed it out once I knew in which order to do the operations.
All those sweet little word games in order to remember things. Ahh. To be a kid again and learning those things for the first time. But again, what true good is algebra anyway if you do not use it in daily life at all? Maybe it is understanding that every action or inaction as an equal action or inaction that must result. Now THAT we deal with every day.
If you have an equation, let's go easy, say ...
5x^2*4=16
... you have to remember that whatever you do to one side of the equation, you have to do to the other side. Of course this is a wonky problem and completely solvable for x, but it is not a clean answer for sure.
5x^2*4/4=16/4
5x^2=4
5x^2/5=4/5
x^2=4/5
Now reverse the exponent of 2 on x by getting the square root of x^2 on one side. This is then x on the left. Then you have to get the square root of 4/5, which is, to say the least, a disastrous, calculator required answer, so the most accurate way to write it would be to leave it be as the square root of 4/5 or the square root of 0.8.
Wow. Knowing how to do the work is half the problem. Frankly, the only problem, which is to remember how to do so.
Now I just have to figure out what "First Outside, Inside Last" was supposed to remind me to do...
~Mom on a Narrow Path
Comment from Carole M. on 2/21/2015 04:15:51 PM
I am trying a new tack with blogging. Simple sharing.
New Weebly site. New look. Just simple sharing.
So without further ado, I'll dive right in.
Right now, I am in the second week of College Mathematics I with University of Phoenix through their online campus. Math has pretty much taken over my brain. I forgot how good it feels to look at a problem, solve it, sit back and just glow.
Last week, our assignment covered maybe 10 topics and should have taken all week to study and complete. Granted, the topics were pre-algebra and designed to be relatively simple so that we were not learning brand new concepts while learning the MyMathLab interface, but this was beyond ridiculous.
When an assignment designed to take several hours a day at the minimum only takes 30 minutes for me to complete, I am shocked I ever had trouble with this stuff in high school. Let alone why I am even taking this class. Why wasn't I able to test out?
We never use algebra in daily life, true. But knowing that my brain can wrap itself around these complicated operations of logic in an insanely quick way after all these years is priceless.
I had not thought of Dear Aunt Sally in nearly two decades, maybe more. I just simply knew that when facing an equation, one must work through anything bracketed first. Inside those brackets, you calculate any exponents, then all multiplication and division from left to right, then all addition and subtraction from left to right. Once the parenthetical calculations are complete, you must move on to exponents from left to right, all multiplication and division from left to right, and finally all addition and subtraction from left to right.
Apparently in grade/elementary school, we learned this as "Please Excuse My Dear Aunt Sally".
Please = Parentheses
Excuse = Exponents
My Dear = Multiplication and Division
Aunt Sally = Addition and Subtraction
While I must have learned it this way as well as it does sound familiar to me, I think I used it for what it was, a neat memorization/learning tool, and then tossed it out once I knew in which order to do the operations.
All those sweet little word games in order to remember things. Ahh. To be a kid again and learning those things for the first time. But again, what true good is algebra anyway if you do not use it in daily life at all? Maybe it is understanding that every action or inaction as an equal action or inaction that must result. Now THAT we deal with every day.
If you have an equation, let's go easy, say ...
5x^2*4=16
... you have to remember that whatever you do to one side of the equation, you have to do to the other side. Of course this is a wonky problem and completely solvable for x, but it is not a clean answer for sure.
5x^2*4/4=16/4
5x^2=4
5x^2/5=4/5
x^2=4/5
Now reverse the exponent of 2 on x by getting the square root of x^2 on one side. This is then x on the left. Then you have to get the square root of 4/5, which is, to say the least, a disastrous, calculator required answer, so the most accurate way to write it would be to leave it be as the square root of 4/5 or the square root of 0.8.
Wow. Knowing how to do the work is half the problem. Frankly, the only problem, which is to remember how to do so.
Now I just have to figure out what "First Outside, Inside Last" was supposed to remind me to do...
~Mom on a Narrow Path
Comment from Carole M. on 2/21/2015 04:15:51 PM
:) good for you for returning to school!! I love math, too... The fact that there's no ambiguity, an answer is correct or incorrect and very little in between. :). And FOIL is for multiplying polynomials. I wouldn't remember myself, but I tutor math and am working with a student on that very topic right now! :)
18 February 2015
Narrow Path is Defunct
(Originally posted to Narrow Path Home Study blog on Weebly, now deleted.)
As much of a great idea as Narrow Path was, the kids just were not receptive. They do not want to learn. In fact, the only reason they learn anything or do any school work is because they are required to. Granted our Home Study was required by the parents, but as far as they are concerned, they can disregard anything parents say is required. It means nothing. It means less than nothing.
So as great as my intentions were, and as much fun as it could have been to have a family learning experience, I have found that in blended families where behavioral and learning problems abound, the sooner a home learning initiative is started the better.
I keep meaning to get back here and attempt to integrate my Narrow Path plans into their INCA school work, or I should say integrate the INCA into Narrow Path in order to make their learning experience more fun and engaging with better results, time gets away from me and between my own college education and my full time work schedule, it has been impossible.
They say life is what happens while you make plans, and the best laid plans... What is the rest of that quote anyway?
In the end, I'm a Mom on a Narrow Path all by myself, without the joy of bringing my children with me for the joyous adventure. So this is why so many learners are solitary creatures!
Respectfully Yours,
Mom on a Narrow Path
As much of a great idea as Narrow Path was, the kids just were not receptive. They do not want to learn. In fact, the only reason they learn anything or do any school work is because they are required to. Granted our Home Study was required by the parents, but as far as they are concerned, they can disregard anything parents say is required. It means nothing. It means less than nothing.
So as great as my intentions were, and as much fun as it could have been to have a family learning experience, I have found that in blended families where behavioral and learning problems abound, the sooner a home learning initiative is started the better.
I keep meaning to get back here and attempt to integrate my Narrow Path plans into their INCA school work, or I should say integrate the INCA into Narrow Path in order to make their learning experience more fun and engaging with better results, time gets away from me and between my own college education and my full time work schedule, it has been impossible.
They say life is what happens while you make plans, and the best laid plans... What is the rest of that quote anyway?
In the end, I'm a Mom on a Narrow Path all by myself, without the joy of bringing my children with me for the joyous adventure. So this is why so many learners are solitary creatures!
Respectfully Yours,
Mom on a Narrow Path
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