roguerealitycheck

running-on-rooftops-in-the-rain asked:

Solve each inequality: 1) -4<(2x-2)/(3)<6 2) I1-2xI<1/3

allofthemath answered:

Ok!

Here you go:

roguerealitycheck:

If you do an absolute value problem you can technically leave it as one expression, since |x+1|<1 is the same thing as -1<x+1<1

True! But only if there’s a < rather than a >, or you get some inconsistencies.

mathed-potatoes
thegrumpystudent:

How to ACTUALLY study for Math: Tips to get an A+ 
For the longest time, math has been my complete enemy. Since I was 5 years old, English was always my stronger subject and I hated everything to do with numbers. As I grew up, my test scores were really low, which used to get me so mad considering I could get A’s in other subjects without even trying. Math was the one black spot, but I was too unmotivated to do anything about it. 
Now, I’m got an A+ average in the subject and can safely say that I enjoy doing math. What changed? First, I guess, was my motivation to succeed, but secondly, was I found out how to actually study for it, because you can’t write pages of notes for it like in Biology or something. 
I’m sharing my method because I want to help anyone out there whose really struggling with math! 
Step 1: Do all the exercises your teacher gives you
If your teacher gives you questions to do, you DO them. Don’t be lazy, just get them done because they cover everything that’s going to be on the test and help you strengthen your understanding. I like to purposefully leave doing them till two weeks before the Exam, because then I’m working all the way up to the test so my brain can instantly make connections and I don’t forget things. 
Step 2: Correct your questions
If they have answers at the back of the book, check your answers and see what you got right. It’ll tell you what to study for and what to ask teachers when you come back to school. 
Step 3: Group Study
Everyone has different opinions of group study, but I think that for Math, it’s actually helpful. Even if you only have one good hour of studying, you have that hour to learn how to do any questions you don’t know. For best results, agree to do a certain amount of work before, so you’re both on the same page. 
Step 4: Go over all your answers and make “cheat sheets.” 
Where I’m from, we’re allowed to bring cheat sheets into our maths tests, but even if you’re not allowed, this is a really good way to condense all your information and understanding. Start by writing any formulas that you use. Try not to look at other books while doing this, because it shows if you remember. Once the formulas are done, write out example questions for each chapter. I like to pick a basic question that was covered in a textbook example, a few questions that were repeated a lot during the exercise but with different numbers, and any questions I didn’t understand. Do that with all the chapters you need to study.  
Step 4: Make up your own Practice Questions
This is really important. Write out your own math questions, ranging from easy to hard. If you’re finding it difficult, ask your teacher to make them up or get your friends or older siblings to help you. There’s also the internet, where you can type up what topic you’re doing and get some worksheets that might be what you’re doing in class. This is crucial because it makes sure you just don’t know the information because you’ve unknowingly memorised it, but because you’ve actually learned it. 
—-
So those are my steps to becoming an A+ student. It might not work for some of you, but for others it’ll definitely help their grades. Let me know if you’d like pictures of my math book, because formatting and neatness really helped in the motivation department. 

thegrumpystudent:

How to ACTUALLY study for Math: Tips to get an A+ 

For the longest time, math has been my complete enemy. Since I was 5 years old, English was always my stronger subject and I hated everything to do with numbers. As I grew up, my test scores were really low, which used to get me so mad considering I could get A’s in other subjects without even trying. Math was the one black spot, but I was too unmotivated to do anything about it. 

Now, I’m got an A+ average in the subject and can safely say that I enjoy doing math. What changed? First, I guess, was my motivation to succeed, but secondly, was I found out how to actually study for it, because you can’t write pages of notes for it like in Biology or something. 

I’m sharing my method because I want to help anyone out there whose really struggling with math! 

Step 1: Do all the exercises your teacher gives you

If your teacher gives you questions to do, you DO them. Don’t be lazy, just get them done because they cover everything that’s going to be on the test and help you strengthen your understanding. I like to purposefully leave doing them till two weeks before the Exam, because then I’m working all the way up to the test so my brain can instantly make connections and I don’t forget things. 

Step 2: Correct your questions

If they have answers at the back of the book, check your answers and see what you got right. It’ll tell you what to study for and what to ask teachers when you come back to school. 

Step 3: Group Study

Everyone has different opinions of group study, but I think that for Math, it’s actually helpful. Even if you only have one good hour of studying, you have that hour to learn how to do any questions you don’t know. For best results, agree to do a certain amount of work before, so you’re both on the same page. 

Step 4: Go over all your answers and make “cheat sheets.” 

Where I’m from, we’re allowed to bring cheat sheets into our maths tests, but even if you’re not allowed, this is a really good way to condense all your information and understanding. Start by writing any formulas that you use. Try not to look at other books while doing this, because it shows if you remember. Once the formulas are done, write out example questions for each chapter. I like to pick a basic question that was covered in a textbook example, a few questions that were repeated a lot during the exercise but with different numbers, and any questions I didn’t understand. Do that with all the chapters you need to study.  

Step 4: Make up your own Practice Questions

This is really important. Write out your own math questions, ranging from easy to hard. If you’re finding it difficult, ask your teacher to make them up or get your friends or older siblings to help you. There’s also the internet, where you can type up what topic you’re doing and get some worksheets that might be what you’re doing in class. This is crucial because it makes sure you just don’t know the information because you’ve unknowingly memorised it, but because you’ve actually learned it. 

—-

So those are my steps to becoming an A+ student. It might not work for some of you, but for others it’ll definitely help their grades. Let me know if you’d like pictures of my math book, because formatting and neatness really helped in the motivation department. 

curiosamathematica

Physics minus Mathematics

curiosamathematica:

The great probabilist Mark Kac (1914–1984) once gave a lecture at Caltech, with Richard Feynman in the audience. When Kac finished, Feynman stood up and loudly proclaimed, “If all mathematics disappeared, it would set physics back precisely one week.”

To that outrageous comment, Kac shot back with “Yes, precisely the week in which God created the world.”

An emphasis on practice to reinforce skills proceeds naturally from the assumption that kids primarily need to learn “math facts”: the ability to say “42” as soon as they hear the stimulus “6 x 7,” and a familiarity with step-by-step procedures (sometimes called algorithms) for all kinds of problems — carrying numbers while subtracting, subtracting while dividing, reducing fractions to the lowest common denominator, and so forth. You do one problem after another until you’ve got it down cold. And, as Brownell pointed out, if you have trouble producing the right answer, that’s “taken as evidence only of the need of further drill.”

In reality, it’s the children who don’t understand the underlying concepts who most need an approach to teaching that’s geared to deep understanding. The more they’re given algorithms and told exactly what to do, the farther behind they fall in terms of grasping these concepts. “Mindless mimicry mathematics,” as the National Research Council calls it, is the norm in our schools, from single-digit addition in first grade to trigonometry in high school. Students may memorize the fact that 0.4 = 4/10, or successfully follow a recipe to solve for x, but the traditional approach leaves them clueless about the significance of what they’re doing. Without any feel for the bigger picture, they tend to plug in numbers mechanically while applying the technique they’ve been taught. As a result, they often can’t take these methods and transfer them to problems even slightly different from those they’re used to. Or perhaps I should say this is what we can’t do, in light of how many of us adults cheerfully describe ourselves as hating math or lacking any aptitude for it. (Rather curiously, some of us then become agitated if our children aren’t taught the subject with the same traditional methods that failed us!)

http://www.alfiekohn.org/teaching/practice.htm

I’m feeling very conflicted about homework these days. Most of the students I ask want less, but not none. They seem to feel it helps. When homework dropped off last year, understanding seemed to as well, but of course there are confounds. In short, teaching is hard.

scientiststhesis

curiosity-discoverer-of-worlds:

underthesymmetree:

Fibonacci you crazy bastard….

As seen in the solar system (by no ridiculous coincidence), Earth orbits the Sun 8 times in the same period that Venus orbits the Sun 13 times! Drawing a line between Earth & Venus every week results in a spectacular FIVE side symmetry!!

Lets bring up those Fibonacci numbers again: 1, 1, 2, 3, 5, 8, 13, 21, 34..

So if we imagine planets with Fibonacci orbits, do they create Fibonacci symmetries?!

You bet!! Depicted here is a:

  • 2 sided symmetry (5 orbits x 3 orbits)
  • 3 sided symmetry (8 orbits x 5 orbits)
  • sided symmetry (13 orbits x 8 orbits) - like Earth & Venus
  • sided symmetry (21 orbits x 13 orbits)

I wonder if relationships like this exist somewhere in the universe….

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scientiststhesis