Tuesday, March 22, 2011

Think about the problem before you dive in..

Everyone has experienced or heard a story of the teacher who distributed a 25-question examination with clear instructions to the class to read all of the questions before answering any.  And to make the long story short, question #25 ends up being something like.  "Ignore the first 24 questions and turn in a blank page with only your name on it"..  ha.  Sure enough, at least some of the kids get busy immediately answering questions instead of reading them all first and then look like dummies later..  Good lesson to learn early in life.  Otherwise you might find yourself in a room full of partially assembled IKEA furniture looking at the directions for Step 12 realizing now that you did step 5 wrong.
But my favorite sort of classroom trickery was the math challenges..  The questions you had to think about for a while before diving in.  Hmm.  What's the trick?  Where's the gimmick?  I always wanted to be the first kid with the answer but it was tough competition. 

A good example..  A teacher wants to give a child a tedious math assignment to keep him busy for an hour.  She tells him to add up all the numbers from 1 to 100.  as in 1 + 2 + 3 + 4 +.. all the way to 100.  Have fun kid!  ha.

So the kid comes up to her desk a minute later and says, "Yo teach I get 5,050 is that right?"  To her amazement, he was correct.  So, explain how it is possible for someone to add up 100 numbers so quickly.

 Easy one right.  See the pattern?  0+100 = 100,  1+99=100,  2+98=100, ... 49+51=100.  So that's 50 ways to make 100 and 50 in the middle left over.  5,050.  easy as Pi.

The lesson..  Think about your problem before you dive into the solution.  understand it, draw it, look for patterns, make it simpler.  Laziness is a virtue in math.  And remember my theory for everything..  The more difficult a problem seems, the simpler its solution will be.            

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