Bay 12 Games Forum

Please login or register.

Login with username, password and session length
Advanced search  
Pages: [1] 2

Author Topic: Okay round 2 with college kids worse nightmare!  (Read 2851 times)

3man75

  • Bay Watcher
  • I will fire this rocket
    • View Profile
Okay round 2 with college kids worse nightmare!
« on: April 25, 2014, 10:55:56 pm »

I'm retaking my algebra class this summer with what.people say is the best teacher there is. The last one I had is universally disliked and some say put you down as far as feeling comfortable with algebra.

One kid said it was because she was with a union and only did the minimum.

Anyways what's the kind of logic.one should get into when solving algebra problems in general?
Logged

Vector

  • Bay Watcher
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #1 on: April 26, 2014, 12:58:36 am »

Isolate the variables.
Logged
"The question of the usefulness of poetry arises only in periods of its decline, while in periods of its flowering, no one doubts its total uselessness." - Boris Pasternak

nonbinary/genderfluid/genderqueer renegade mathematician and mafia subforum limpet. please avoid quoting me.

pronouns: prefer neutral ones, others are fine. height: 5'3".

Tiruin

  • Bay Watcher
  • Life is too short for worries
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #2 on: April 26, 2014, 02:33:30 am »

Steps.

Math uses formulas. Formulas are based on parts. Many parts make up the whole.

Deconstruction.

Do not take the problem as a whole if you're finding trouble with it. Single out the values and proceed from there.
Logged

nenjin

  • Bay Watcher
  • Inscrubtable Exhortations of the Soul
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #3 on: April 26, 2014, 04:07:02 pm »

Isolate the variables.

Yep.

My way is not how how you should do it. But I got through early algebra by looking at an equation like 5 + 4(X - 7) = 19 by simply putting numbers in for the value of X until the equation worked. That doesn't scale up to higher level algebra problems and theorems, timed tests, and you'll still have to show your work but it will at least get you through the first week. :P

(I had to retake algebra for college as well, and fucking loathed every minute of it.) 

But yea, as Tiruin said. Always remember your order of operations. Look to see if a problem can be re-written and broken down into its component parts. Simplify a problem down to its most concise statement where you can. Do the calculations inside the parentheses first, then re-write the equation with those calculations filled in. 
Logged
Cautivo del Milagro seamos, Penitente.
Quote from: Viktor Frankl
When we are no longer able to change a situation, we are challenged to change ourselves.
Quote from: Sindain
Its kinda silly to complain that a friendly NPC isn't a well designed boss fight.
Quote from: Eric Blank
How will I cheese now assholes?
Quote from: MrRoboto75
Always spaghetti, never forghetti

Gervassen

  • Bay Watcher
  • Be aggressive.
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #4 on: April 26, 2014, 07:49:51 pm »

Remember the underlying concepts. Those, not formulas, are the real education. Story problems work well for this. You don't know the concept until you know the story problems.

The central concept of algebra is that you can maintain the truth of a mathematical equation by doing the same operation to both sides. The most common reason to change the look of an equation or statement without changing its truth is indeed to isolate and solve for an unknown.

Whenever changing an equation, know why you can do so without breaking its truth. This often because you perform the same operation on the other side, but sometimes the rule of multiplicative identity or other basic rules. Break formulas down to concepts, and steps down to rules. That is your true education.



Logged
The way's paved with knaves that I've horribly slain.
See me coming, better run for them hills.
Listen up now...

             -- Babycakes

gimlet

  • Bay Watcher
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #5 on: April 26, 2014, 08:08:39 pm »

And do LOTS of problems.  Find problem sets on the internet.  Go to the library and see if they have any.  BUY books of problems.  Ask your teacher to loan you books of problems - they get piles of free textbooks.  Keep doing problems until you're getting them all correct, without looking up anything in the textbook.  Then do more tomorrow.   Mix them up so that you don't get a hint from which chapter they come from - that sandbagged me, I thought I was cruising because I could do all the chapter end problems, then the midterm was like a punch in the face because it was a bunch of problems without the context of which chapter they were from.

This lets you analyze where your deficiencies are - If you're repeatedly having trouble with some type of problem, try to figure out why.  How to approach it a different way, in a different order, whatever.  Find different texts from the library that might explain it a different way - not every text is great at explaining every concept.  If you're really stumped after serious work, ask the prof.  Post to one of the online math forums.  Forming a study group can help too, make up problem sets for each other and talk over approaches and reasoning.  Also almost every uni has a tutoring program - if it will help you at all USE IT.  If for some reason they don't, even if you have to put up your own ad and pay a few bucks out of your own pocket for help over something that's blocking you, that is money well spent imho.

Keep up and don't fall behind, later material assumes you know the earlier stuff 100%.  You can get into a world of shit where you have to catch up learning multiple weeks of work with a test looming - been there done that, it SUCKS, don't get into that position...
Logged

3man75

  • Bay Watcher
  • I will fire this rocket
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #6 on: April 27, 2014, 07:17:03 pm »

Okay everyone had a quite a bit to say {which is good thank you all}. Let me see if i can break down your statements so they aren't paragraph long..

Understand formulas {jesus did my last prof kill me there}, understand rules in a formula {already scaring me BUT i can do it!}, figure out the reason said problem is USED {do all formulas actually have a reason?}, and PRACTICE ma butts off until i know everything. Also i agree with learning early material 100% but after my last professor racing across the board in a hour i don't even know if that's possible.

Quick question is it possible to be hard headed like me and get past this or even better learn {learning= actually knowing and only needing periodical brush ups if one hasn't done it in a long time}.
Logged

Vector

  • Bay Watcher
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #7 on: April 27, 2014, 07:32:33 pm »

{do all formulas actually have a reason?}

Yes

Quick question is it possible to be hard headed like me and get past this or even better learn {learning= actually knowing and only needing periodical brush ups if one hasn't done it in a long time}.

Probably? Work hard.
Logged
"The question of the usefulness of poetry arises only in periods of its decline, while in periods of its flowering, no one doubts its total uselessness." - Boris Pasternak

nonbinary/genderfluid/genderqueer renegade mathematician and mafia subforum limpet. please avoid quoting me.

pronouns: prefer neutral ones, others are fine. height: 5'3".

gimlet

  • Bay Watcher
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #8 on: April 27, 2014, 08:17:50 pm »

Yea, I used to have to repeat to myself "MILLIONS of kids got through this material somehow, I am not stupider than every one of them.  I just have to study harder and try different approaches until I get it".  It was especially one class, Linear Algebra, I just was NOT understanding the reasons for the way some of the operations worked.  The class was weeks past it, I had to buckle down and learn how to solve the problems by rote, and I kept doing what I described above - multiple books of problems, doing some every day, reading the chapter in multiple textbooks, 'cause that was what I had to do in Calculus to get over humps, but they were never this bad or this long.

FINALLY something clicked, and I understood *why* it worked - it was actually hugely simpler than I had been making it.  That was one of the most awesome feelings I ever had, I remember it to this day...

Logged

Tiruin

  • Bay Watcher
  • Life is too short for worries
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #9 on: April 27, 2014, 09:06:46 pm »

{do all formulas actually have a reason?}

Yes
They totally do :D

Think of them as plans. Procedures. Methods.
Like blueprints of creating a building--it shows the general outline of how to proceed, and then your mind clicks in after realizing that you're staring at a full fledged building instead of the 2D representation in front of you!

Quick question is it possible to be hard headed like me and get past this or even better learn {learning= actually knowing and only needing periodical brush ups if one hasn't done it in a long time}.

Probably? Work hard.
HECK YES!
Though I'd question you on the interval scale of how hard headed you are :P
See, I believe in the idea of exposure, and understanding. To learn something well, you need to apply your senses to it: hence the idea of Exposure. You should observe and analyze; ponder upon the details you're questioning or confused about, and probably research them yourself if you're confused on specific matters.
Now if you're stubborn about a thing: Try to analyze yourself first. You look at the problem--then you see how you solve it (best to try writing your own way down on paper for posterity), then check if you're right. If not, then check back and ask yourself: What did I do wrong/why did this go wrong?
> Understanding.

...It's hard to explain (on my side because my thoughts are primarily emotion/feeling translated to words and stoofs :v) but I hope I got the basic outline out there.
Logged

3man75

  • Bay Watcher
  • I will fire this rocket
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #10 on: April 28, 2014, 02:28:22 pm »

{do all formulas actually have a reason?}

Yes
They totally do :D

Think of them as plans. Procedures. Methods.
Like blueprints of creating a building--it shows the general outline of how to proceed, and then your mind clicks in after realizing that you're staring at a full fledged building instead of the 2D representation in front of you!

Quick question is it possible to be hard headed like me and get past this or even better learn {learning= actually knowing and only needing periodical brush ups if one hasn't done it in a long time}.

Probably? Work hard.
HECK YES!
Though I'd question you on the interval scale of how hard headed you are :P
See, I believe in the idea of exposure, and understanding. To learn something well, you need to apply your senses to it: hence the idea of Exposure. You should observe and analyze; ponder upon the details you're questioning or confused about, and probably research them yourself if you're confused on specific matters.
Now if you're stubborn about a thing: Try to analyze yourself first. You look at the problem--then you see how you solve it (best to try writing your own way down on paper for posterity), then check if you're right. If not, then check back and ask yourself: What did I do wrong/why did this go wrong?
> Understanding.

...It's hard to explain (on my side because my thoughts are primarily emotion/feeling translated to words and stoofs :v) but I hope I got the basic outline out there.

Hard headed might not be the word. I just hate going into something i hate, being totally lost, and then expected to perform miracles like the returning messiah or something lol.

Umm, my exposure is going to be the math class and the tutoring i take at school {which is FREE so i don't expect much quality  ;)} so i'm not sure how much exposure i need. TBH idk if i passed h.s algebra because the teacher made more sense and the college teacher was in a union that protected her no matter what or if H.S was just made easy and that college is ripping money out of my pocket like a gold digging girlfriend.
Logged

GlyphGryph

  • Bay Watcher
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #11 on: April 29, 2014, 11:00:57 am »

I agree with the person who said it's incredibly important to understand the fundamental concepts of algebra first and foremost - that's how you know which approach to take, and what to do when you don't know of a correct approach.

So, the basics of algebra are roughly:
-Making an identical change to two equal things leaves them equal, but of different value. 5+x = 10 is exactly the same as (5+x)-5 = 10-5.
-Calculating equations, even partially, does not change the value of an equation. For example, for (5+x)-5, you can subtract the five from the five, getting 0+x or simply "x".
-As long as as you apply operations that are equal and opposite, you will not change the value of an equation - but make sure you actually understand your operations! If you have "x", this has exactly the same value as 2*(x/2), 5+x-5, or x+x-x. Not all operations have an inverse that is as equal and opposite as they seem at first glance, though - notably, squareroot(x squared) doesn't necessarily equal 'x', but x^2/x does, since every squareroot operation has two possible answers. -5 and 5, squared, both end up as 25. Square rooting 25 could thus result in either option - however, dividing by "x" which is definitely either -5 or 5 so we know the value won't change).
-Operations are derived from other operations. Changing the way they look doesn't change the value. x+x is the same as 2*x, and 2*x-x is 'x'.
-Any chunk of equation can be treated as a value in it's own right, so long as its a proper chunk (it doesn't violate order of operations) and stuffed into a variable, and variables can be similarly replaced by chunks of equation so long as it has the same value. You can add new equations into the system as needed to keep track of this. 2*(x+4) = 300 can be replaced by 2*y = 300 and y=x+4.

So using earlier rules, we can solve for x above. Take 2*y=300 and realize we can isolate the variable by making an identical change to both sides (with the goal of isolating the variable), and the result will still be equal. So (2*y)/2 = (300)/2. Since we can make calculations without changing the value of either side, we can write that as y=150 without changing any values.  We know that y=x+4, and that y=150, so we can replace y with either chunk (we know it's equal to both) and get either 150=x+4 or x+4=150, which are obviously identical. Then we repeat - do the same thing to each side, with (x+4)-4 = 150-4, which we can then calculate, getting x=146.

Once you've got a solid base there, it's important to start understanding the relationship between different operations. This is where formulas come in! Formulas often provide convenient ways to change complex operations from one form to another without changing the value (or by making identical changes in value to both sides of the equation)

Difficulty operation conversions are where formulas become useful Note that not all formulas are particularly important. Formulas are just rules for replacement, and not all replacements are useful. This doesn't really apply to the ones you are taught though - if a formula gets a name and ends up in a textbook, it's gonna be one of the important ones. Eventually, there's also a good chance you will want to derive some formulas of your own, but those will be the simply type you don't have to bother memorizing.

Important things to remember
Not all equations can be solved exactly - but sometimes you don't need to. If you're working out distance, it doesn't matter if your result could be either 5 OR -5, because either way its 5 units away. Sometimes just knowing the subset of possible answers is enough. Sometimes just knowing the relationship between two values is enough. Knowing that x=2y might be the goal of untangling the equation (2x+42)/2 = 21+(2y^2)/(2y). Oftentimes, finding an understandable relationship is enough.
« Last Edit: May 02, 2014, 09:37:52 am by GlyphGryph »
Logged

3man75

  • Bay Watcher
  • I will fire this rocket
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #12 on: May 01, 2014, 01:43:32 pm »

Glyph i feel stupid for asking this but

(5+x)-5=10-5 An there the same?

instincts tell me to get the -5 on the left and add it to the right making:

(5+x)=10

X=5 Math right?? or a should i give up my dreams of getting a bachelors in economics and stay with psychology?

EDIT: after a 3rd or 4th look this came up in my head.

 "150=x+4 or x+4=150, which are obviously identical. Then we repeat - do the same thing to each side, with (x+4)-4 = 150-4, which we can then calculate, getting x=1"

(x+4)-4=150-4 meaning your subtracting the value "4" from both sides?
« Last Edit: May 01, 2014, 01:52:41 pm by 3man75 »
Logged

GlyphGryph

  • Bay Watcher
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #13 on: May 02, 2014, 09:42:33 am »

Glyph i feel stupid for asking this but
(5+x)-5=10-5 An there the same?
instincts tell me to get the -5 on the left and add it to the right making:
(5+x)=10
X=5 Math right?? or a should i give up my dreams of getting a bachelors in economics and stay with psychology?
The point of adding the "-5" on both sides is that we can actually do the math, giving us (5+x)-5 = x, and 10-5=5, meaning that yes, x=5.

Quote
(x+4)-4=150-4 meaning your subtracting the value "4" from both sides?
Yes, I'm doing the same thing I did above - as long as you do the same thing to both sides of the equation (in this case, subtracting 4), they will remain equal.

It's all about naming, you're equation ends up being "left side = right side", and then you do "left side minus four = right side minus four" which is trivially true because the left side and the right side are the same... you could rephrase is as "left side minus four = left side minus four", since "left side" and "right side" are identical, so you can freely swap them out for each other.
« Last Edit: May 02, 2014, 09:44:15 am by GlyphGryph »
Logged

3man75

  • Bay Watcher
  • I will fire this rocket
    • View Profile
Re: Okay round 2 with college kids worse nightmare!
« Reply #14 on: May 03, 2014, 10:15:01 am »

Glyph i feel stupid for asking this but
(5+x)-5=10-5 An there the same?
instincts tell me to get the -5 on the left and add it to the right making:
(5+x)=10
X=5 Math right?? or a should i give up my dreams of getting a bachelors in economics and stay with psychology?
The point of adding the "-5" on both sides is that we can actually do the math, giving us (5+x)-5 = x, and 10-5=5, meaning that yes, x=5.

Quote
(x+4)-4=150-4 meaning your subtracting the value "4" from both sides?
Yes, I'm doing the same thing I did above - as long as you do the same thing to both sides of the equation (in this case, subtracting 4), they will remain equal.

It's all about naming, you're equation ends up being "left side = right side", and then you do "left side minus four = right side minus four" which is trivially true because the left side and the right side are the same... you could rephrase is as "left side minus four = left side minus four", since "left side" and "right side" are identical, so you can freely swap them out for each other.

So here's another stupid question and i'm sorry if i'm annoying you but...

The basics of Algebra are to keep the left side and right side equal to each other via adding, subtracting, multiplication, and division?
Logged
Pages: [1] 2