The idea of over-the-fence-change-sign certainly can serve as a powerful heuristic, and I know that many people think that way, so I appreciate that (see Dave Lundy's work). At the same time, the idea of balance, unlike the idea of over-the-fence-switch-sign, might be better grounded in the very idea of what an equation is about. That is, the idea of a scale emanates from a real world experience of balance, whereas the fence metaphor seems to rely on a somewhat brittle metaphor. My 2 cents :-)
(4x^2 - x^2) + (3x + x) + (2 - 3) = 0 parenthesis so you can see how they combine. So 4x^2 -X^2 = 3x^2 the exponents don't change. Just the numbers. and the result is 3x^2 + 4X -1 = 0.
@lewis2670 so for 4x^2 + 3x + 2 = x^2 – x + 3 you bring the right side over the fence or equal sing and change the sign getting: 4x^2 + 3x + 2 - x^2 + x -3 = 0 and since you moved everything just make it equal to 0 (zero). Now you group like terms for easier understanding: 4x^2 - x^2 + 3x + x + 2 - 3 = 0. Now you can see that these numbers can combine. You have +14X^2 and -X^2 since positive and Negative You subtract. Do the same for the rest of the eq. U end up with...
I think it's easier to think of it as bringing sings over the fence. The fence you are jumping is the ' = ' sign. So if you have an equation like the one you gave you can to bring all the numbers over to one side.
Usually bring them over to which ever side requires you to move less numbers over that fence. In this case if the same number of variables so i chose move to the left. When you move items over the equal sign you just change their sign to the opposite of what they were.
Think of the equation as a scale: stuff to the left and right of the "=" sign are balanced. Now, we want always to keep it balanced no matter what we do. So if we remove (subtract) stuff from one side, we must remove exactly as much stuff from the other side, or otherwise it will no longer be balanced. This holds both for numbers, such as 3, and or variables, such as x^2.
I agree with you take on teaching, Kinetic learning helps make the sometimes abstract nature of mathematics come alive. The elegance of numbers can unlock so many things! Great work and my best regards :)
no matter what, math is not meaningful.
TehJimmyman 3 months ago
@TehJimmyman retard ^^
humanmatti 2 months ago
jk
set8100 4 months ago
im only 11...i dont get dis... D:
set8100 4 months ago
@set8100 IM 9 AND I GET IT.
aznmisscupcakes 4 months ago
@aznmisscupcakes he was jk
EliteBoner 4 months ago
The idea of over-the-fence-change-sign certainly can serve as a powerful heuristic, and I know that many people think that way, so I appreciate that (see Dave Lundy's work). At the same time, the idea of balance, unlike the idea of over-the-fence-switch-sign, might be better grounded in the very idea of what an equation is about. That is, the idea of a scale emanates from a real world experience of balance, whereas the fence metaphor seems to rely on a somewhat brittle metaphor. My 2 cents :-)
gabr67 4 months ago
(4x^2 - x^2) + (3x + x) + (2 - 3) = 0 parenthesis so you can see how they combine. So 4x^2 -X^2 = 3x^2 the exponents don't change. Just the numbers. and the result is 3x^2 + 4X -1 = 0.
ufkinloveit 4 months ago
@lewis2670 so for 4x^2 + 3x + 2 = x^2 – x + 3 you bring the right side over the fence or equal sing and change the sign getting: 4x^2 + 3x + 2 - x^2 + x -3 = 0 and since you moved everything just make it equal to 0 (zero). Now you group like terms for easier understanding: 4x^2 - x^2 + 3x + x + 2 - 3 = 0. Now you can see that these numbers can combine. You have +14X^2 and -X^2 since positive and Negative You subtract. Do the same for the rest of the eq. U end up with...
ufkinloveit 4 months ago
@lewis2670
I think it's easier to think of it as bringing sings over the fence. The fence you are jumping is the ' = ' sign. So if you have an equation like the one you gave you can to bring all the numbers over to one side.
Usually bring them over to which ever side requires you to move less numbers over that fence. In this case if the same number of variables so i chose move to the left. When you move items over the equal sign you just change their sign to the opposite of what they were.
ufkinloveit 4 months ago
stumped why does x2 get subtracted 4x2 + 3x + 2 = x2 – x + 3
4x2 – x2 + 3x + x = 3 – 2
LEWIS2670 4 months ago
@LEWIS2670
Think of the equation as a scale: stuff to the left and right of the "=" sign are balanced. Now, we want always to keep it balanced no matter what we do. So if we remove (subtract) stuff from one side, we must remove exactly as much stuff from the other side, or otherwise it will no longer be balanced. This holds both for numbers, such as 3, and or variables, such as x^2.
gabr67 4 months ago
I agree with you take on teaching, Kinetic learning helps make the sometimes abstract nature of mathematics come alive. The elegance of numbers can unlock so many things! Great work and my best regards :)
circledancer 4 months ago
Makes sense, doesn't it!
Sharmiep1 4 months ago
Found this about teaching math......
fiegent 4 months ago