## Word Problems

One of the most common forms of problems in mathematics are word problems.  They are essentially mathematical exercises presented in the form of a hypothetical situation that requires an equation to solve.  They are usually expressed in a narrative form.   I consider this a verbal (literary) form of expressing math (See the blog “Expressing Mathematically”).  There are two insights I want to share with you about word problems:

Hypothetical Situations
First, when I solve word problems, I am actually executing at most five steps, not necessarily in the order given: (1) I translate the hypothetical situation into a visual expression, like a diagram using geometric concepts, or straight into an equation or expression. (2) I find the values that we are given in the  word problem, and (3) I find the variable(s) we need to solve for (the “unknown”) to find the solution to the hypothetical situation. (4) I then decide which concepts and/or equations we need to apply to the hypothetical situation. (5) Finally, I apply the proper skills from our math toolbox to find the solution to the word problem.

Actual Situations
Second, a traditional word problem explicitly supplies the students all the necessary information to do steps (1),(2),and (3).  When I am presented with  a problem in a real-world situation, I usually have to define the situation in a way that I can solve it mathematically and express it as a word problem, or a labeled diagram.  Many times, I have to conduct measurements in order to establish the “given” values.  Usually, the “unknown(s)” end up being those values I need to know that I cannot measure in a practical or direct way.  It usually takes some work to properly define the situation that is usually given in a classroom-type word problem.

Word problems are one of many ways we can test the competency of a math student.  They are also effectively used to help the math student achieve mastery in applying certain skills.  I understand that it is impractical to consistently present students with real-world situations to solve.  However, it is just as important for students to know how to properly generate a problem as it is to solve it.