Friday, January 6, 2012

Solving Word Equations with a Spy

 Word problems are a perfect example of how students, especially visual learners, can not  solve equations without background stories or a math foundation. 

Example one: One of two numbers is five more than the other.  The sum of the numbers is 17.  Find the numbers.

Step one:  Remind students that there will always be an x in these types of equations.  Their first decision is to figure out who the x is.  Compare this idea to finding the SPY (x).  Since it is now a story, they will probably be more interested.  Before solving algebra equations, give them LOTS of problems to find the spy or x in.  That's all they have to do is find the x.  In the problem above x is just "one of the two numbers."  If they start with this, then they know the other number is x + 5.  So the equation looks like the one below:
                      x + x + 5 = 17
You can NOT put parentheses around the second number to separate it.  If you use (  ) a whole new operation (distributive power) is required.

Step two:  Add up your x's.  Remind kids that there is ALWAYS an UNDERSTOOD number 1 in front of every variable.  Multiplying 1 by anything never changes it.  This is a VERY IMPORTANT concept in algebra that comes in very handy.  Another handy concept is that you can divide any number or variable by 1 and it won't change anything.  So the new equation is like the one below:

  1x + 1x + 5 = 17           or           2x + 5 = 17

Step three:  If you go back to my Tagalong blog, you will remember that the 2x is a married couple on a date with a "tag-a-long" chaperone, little brother, someone you don't want on a date.  So that tagalong must be moved.  If you continue with the SPY THEME, you could tell the kids that the 5 is someone who is following them, and must be avoided.

In this example, since the number five is positive, we will add his opposite (-5) to both sides of the equation.  The new equation looks like the one below:
    2x + 5 -5 = 17 -5    or   2x = 12

Here is where I tell the kids we are going to Divorce Court (see blog).  You MUST DIVIDE EQUALLY ON BOTH SIDES OF THE EQUATION.  In the spy themed math lesson, I would tell the kids we must separate the spy from the numbers.  The result is the equation below:
  2x  = 12     or   x = 6   and     x +5 = 11
  2        2

I'm stopping this blog here.  Tomorrow I will add two more word problems to show you how important it is to make sure the kids really understand and remember the rules.  If spys themselves forgot the rules, our world would be in anarchy. 


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