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Q&A #9409

Teachers' Lounge Discussion: Solving algebraic equations

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From: Em <magnegrad@hotmail.com>
To: Teacher2Teacher Public Discussion
Date: 2006032419:46:29
Subject: Back to the original question!

	The original question for this particular forum asked how to solve a
problem where there is a variable on both sides of the equation.  For
example, 3x + 5 = 2x - 7

Of course, you would only teach this type of problem solving after
students had learned how to solve one step equations, and two step
equations.  The skills must build before you can teach problems with
variables on both sides.  So allow me to elaborate a little on how I
teach two step equations before I tackle that problem up there!  Some
math teachers probably think that this whole idea is totally crazy but
it works with my students!

Let's use the problem 5x - 8 = 38
I try to make math fun by telling my students stories.  When I teach
them to solve two step equations I explain that 5 and x are best
friends, only they have a problem x's little brother 8 is always
hanging around.  So in order for them to have a good time, they need
to get rid of the tag along little brother.  (We have already learned
how to solve one step equations, so the students understand the idea
of equation solving being a lot like balancing on a seesaw and that
you do the opposite (inverse) to get "rid" of something.)

So the students get "rid" of little brother by adding him to both
sides.  This leaves 5 and x alone so now they can have some fun, only
now 5 and x get in a fight.  Now 5 decides to go home.  So you divide
him out of the equation.  This leaves x alone!  I know that this
little story does not include the 38 as a character, but students get
the idea.  

The best things is that once I've taught this concept... they
understand that you must get "rid" of the tag along first then break
up the friends.   If a student is struggling to understand what to do
next, I say who do we get rid of first?  They usually respond... "the
tag along little brother..." or "oh yeah, now the friends split up."  

So when teaching students to solve problems like 3x + 5 = 2x - 7 I
simply add to this concept.  I have learned over time that students
are much more comfortable if the variables are all on the left, and
the numbers are all on the right.  So I always start by moving 2x to
the left side.  Then I move 5 to the right side, and continue solving
until the problem is completed.  

I hope that this is helpful to someone!  I try to make math fun, it's
very hard to make algebra something that is not boring and tedious!

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