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Q&A #650


Practical application for algebra

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From: Claudia (for Teacher2Teacher Service)
Date: Oct 13, 1998 at 21:39:08
Subject: Re: Practical application for algebra

There are many ways to make a lesson interesting! You can involve students in
a game. You can choose information to make the lesson pertinent and
meaningful!  I take it that you want this to happen with systems of linear
equations!  Is there a particular way that you have to solve them?

Sometimes, systems can be easier to solve by intuition than by using
equations!  (As my algebra II class has pointed out to me recently, since the
topic of systems is what we are currently studying.)

One major application is to physics. They use systems of 3 equations with
hideous scientific notation type coefficients! One of the biggest
applications of systems with 3 unknowns is the inventory kind of problems. I
have an article I share with my students about a gentleman who worked for
Bell Laboratories who solved a system with 800,000 variables!  They find that
mind-boggling. Yet when you think about it, the real world requires a lot
more than 2 unknowns at the time.

Anyway, one thing would be to create a uniquely attractive story about
several students, who took a trip and the numbers and weights of various
pieces of luggage.  You can give different groups different parts of the trip
to determine what kind and how many of each piece of luggage made it through
the various airports along the trip.  I don't know if this is totally
appropriate for an Honors class, but it is fun.  They give the students graph
paper and two pieces of uncooked spaghetti. (Linguini might be better as it
does not  roll as easily). Have them plot two possible answers for each of
two equations. The place where the spaghetti intersects is the solution! You
can make it more of a mental math activity that way.  (for example, Sally has
24 coins, all dimes and nickels. She has $2.00 in all. How many of each coin
does she have? Students fix a piece of spaghetti on say (12, 12) and (24, 0)
for the first equation. Perhaps (20,10) and (0,20) for the second.

There is always great fun with matrix solutions.  Did you know that the US
government used matrices in the past as a form of cryptography to send secret
messages?

 Good luck
 -Claudia, for the Teacher2Teacher service

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