## Sunday, March 17, 2013

### Algebra

I wrote a little algebra song, its basically just about the steps you use to solve an equation. Here are the lyrics  if you don't understand what I'm singing hopefully this makes much more sense.

Algebra Song

This is a song on how to multiply, two step equation and even on how to divide
I'm also gonna show you distributive property, and vocabulary there's such a wide variety
Like coefficient, variable and constant too
I'll even show you one day that your dreams will come true
Haha, I'm just kidding about the whole dreams part

To multiply you isolate the variable, it's sorta like this thing we call a symbol
It's a letter that represents an unknown number
Don't worry now this wont get any tougher
Then you cancel the constant, a number that doesn't change
You balance both sides, this order wont rearrange
Simplify, then cancel the coefficient, have I told you what that is? I don't think I have yet
It's the number that's being multiplied, then you balance both sides and you simplify
There very last step is to verify
If I can say one thing, this is easy as pie

This is a song on how to multiply, two step equations and even how to divide
I'm also gonna show you distributive property, and vocabulary there's such a wide variety
Like coefficient, variable and constant too
I'll even show you one day that your dreams will come true
I'm still kidding

To divide you isolate the variable, 0 pair the constant, this should be real simple
You balance both sides and you don't simplify,
Cancel the coefficient, in this case you multiply
Balance both sides once again, then you simplify now
I hope this is all making sense
The very last step is to verify, just like I said this is easy as pie

This is a song on how to multiply, two step equations and even on how to divide
I'm also gonna show you distributive property, and vocabulary there's such a wide variety
Like coefficient, variable and constant too
I'll even show you one day that your dreams will come true
Seriously, I'm not gonna do that

The last thing left is distributive property
There's a simple technique and it's very easy
You multiply the constant with the coefficient
Now the constant's changed and its something different
You still have to multiply using the variable, like I said it is a symbol
Follow all the steps for multiplication
When you do that there'll be no complication

This was my song on how to multiply, two step equations and even on how to divide
I showed you distributive property, and vocabulary with such a wide variety

#### Multiplying

The first thing you have to do is isolate the variable so you get rid of the +2 by adding -2. Also do that to the right side, 11-2. That's canceling the constant, the number that doesn't change. Which is why there is an X over it. Now the equation is balanced, well it always has been. When you finish that you're left with 3x=9.

Next you simplify by getting the variable by itself. You cancel the coefficient, the number that is being multiplied. You do that by dividing the number by itself, 3 divided by 3. Don't forget to do the same thing to your right side, 9 divided by 3. You now have x=3.

You balance by now using the value of x in the equation. Which is 3. You simplify by doing the first operation, which is multiplication so 3x3=9. Now you use that for the equation. So now you have 9+2=11. The last thing left is to verify, you do it to prove that the answer is right and both sides are equal, 11=11.

#### Dividing

The first thing you do is isolate the variable so you get rid of the +3 by adding -3. Also do it to the right side. You then balance by multiplying x over 2 by 2 because 2 is the number being divided by. Don't forget to do it to the other side as well, 4x2=8. You cancel the coefficient, using multiplying like I said and then you are left with x=8.

You balance by using the value of x in the equation which is 8. Then you simplify by doing the first operation which is dividing 8 by 2. Now you use that answer for the equation. So now you have 4+3=7. The last thing left is to verify, you do it to prove that the answer is right and both sides are equal, 7=7.

#### Distributive Property

You multiply the coefficient with constant, 3x-2. I showed 3 groups of x (the unknown number (variable)) -2 which is -6. Now the constant is -6, making the equation 3x-6=9. You do all the steps for multiplication since the equation is changed into a multiplication one.

Now you follow the multiplication steps. Isolate the variable by adding +6 since you need to get rid of -6. Remember to also do that on your right side. Cancel the constant by putting an X over it. The balanced equation is now 3x=15. You simplify by getting the variable by itself. Cancel the coefficient so you divide it by itself, 3 divided by 3. Also do that to your other side. You are now left with x=5.
You balance by using the value of the variable in the equation, which is 5. You then simplify by doing the first operation, which is multiplication, 3x5=15. So now you have 15-6=9. The last thing you have to do is to verify your answer. You do it to prove that the answer is right and both sides are equal, 9=9.

#### Modeling

This modeled equation is 2x-2=6
The two red rectangles represent 2x
The two white circles represent -2
The six black circles represent -6

You have to get rid of -2 by adding +2
Remember that whatever you do the left side, you must do to the right
Now you are left with 2x=8 since you added +2 to the right side also

You share the 8 black circles between the 2 red rectangles and you circle the group so you show what each rectangle is worth
So now you know that one rectangle (x) = +4