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Sunday, October 23, 2011

Solving An Equation with a Tagalong

                                                                                           

                            
  •   Some kids look at their first equations as if they were written in another language.  Well, basically, they are.  So, I explain to the visual learners that it is the LANGUAGE OF LOVE.  That gets their attention (especially high schoolers).  Let's take another look at a problem my way.  In the equation 2x + 4 = 10, they are asked to solve for x.  Believe it or not, this is pretty scary for some kids.  I have tutored high school kids, and I know.   
  • I tell them that the 2x is really a couple who is dating. See how closely attached they are.  They are so in love that no one can probably split them up.  I remind them that in  history, way back in the middle ages (ha ha) when their  great grandparents were young, a couple needed to bring along a chaperone.  Sometimes it was even a younger brother or sister.  I have relabeled this person as a tag-a-long.  We will refer to the picture below as our tag-a-long.

In our equation she represents the +4.

  • So, what would most dating couples want to do with a tag-a-long?  Why-- get rid of her of course.  How can they do that?  Why-- simply subtracting her if she's a positive little thing, or adding her if she's a negative little thing.  We're doing the OPPOSITE of her personality.
  • BUT...there's a rule in algebra that says--- whatever you do to one side of an equation (of the equal sign), you have to do to the other side of an equation.  That seems fair to me.
  • In the equation above, 2x + 4 = 10 , we are going to subtract our positive little tag-a-long  to both sides of the equation.  Here's what that looks like:
                                  2x + 4 - 4 = 10 - 4
  • The fours cancel each other out on the left.  The tag-a-long is sent to the other side of the equation--far away from our dating couple.
  • What we have left on the left side is only 2x.
  • What we have left on the right side is 6.  
  • Our equation is now 2x = 6.  This is still scary for some kids.  See below to how big people solve their problems.
  • They go to DIVORCE COURT.  They split up.  They separate.  They DIVIDE.  Boo hoo. In math we do this with division.  Makes sense, doesn't it.  But, again, whatever you do to one side of the equation, you have to do to the other side.  In math things are fair.  In real divorce court--not so much. (I've watched my share of soap operas).
  •  You divide each side by the number that is in front of the x.  So we are going to divide each side by the number 2.   
  • Our new equation is:      2x = 6      
  •                            2      2                                  
  • I always show them the division like it is set up above because the 2/2 on the left side makes the number 1.  Reminder--any number over itself in a fraction equals 1. That is basically saying 1x is just x.  and 6 divided by 2 is 3.
  • Now our new result after divorcing or spliting up or dividing is X = 3. So, even though our problem is solved, I'm assuming you are as sad as I am that this lovely couple is no longer together.  Especially if you're her mother and had been planning a wedding for a very long time.                                                           
    

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