Word problems are the real heart of any higher-level mathematics. Algebra is no exception! Why would anyone bother to learn how to solve equations, if the goal were not to solve a real problem, i.e. a word problem? To solve a word problem, first identify what the problem is asking you to find. Let that unknown be represented by a variable. If there is more than one unknown, let the unknown that you know the least about be represented by the variable, and the other unknown be in direct relationship to the variable.
OK, take a
deep breath and begin … what is the problem asking you to find? … how much candy
Mary and Tom were given … which do you know the least about? … how much candy Tom
was given (since it says that Mary was given 5 less than twice the amount that Tom was
given) … if we let the amount of candy Tom was given = Amount of candy for Tom =
Amount of candy for Mary = Now it says
that Mother bought a bag of 55 pieces. So the
sum of Tom’s and Mary’s candy must total 55.
We would then build our equation and solve …
Tom = Mary = Now, the
argument with application problems that you may give is that “this
problem could have been figured
that out without algebra!” This may be
true since this problem involved whole numbers. Many
students learned the beginnings of algebra using “guess and test.” In my opinion, this was unfortunate. The world does not operate on whole numbers! Think about the same problem as above, only Mother
purchased 60 candy bars (which could Amount of candy for Tom = Amount of candy for Mary =
Tom = Mary = In any application problem the clue is to read the problem carefully … often several times, so that you can identify what type of problem it is and begin a strategy to solve the problem. Identify what the problem is asking you to find and designate a variable to represent this unknown. If you have two unknowns then you can only have one variable, usually the quantity that you know the least about. Any other unknowns are identified using the variable that you designated for the least known quantity. Next, organize the information that is given to you … diagrams and charts are organizational tools. Set up an equation that represents the problem and then solve the equation. Make sure that you have answered the question or questions posed in the problem including units of measure. The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 09-Jan-2014 |