Solving Reading/Story/Word Problems

Students (and others) frequently have an aversion to reading/story/word problems; that is, to problems that are expressed in story form rather than as definite mathematical equations and expressions that need to be solved. However, most math problems that are presented to us in the real world environment come to us in the form of prose, or in the form of a story or verbal description of some kind. Seldom are we given "a straight up math problem" to solve, where the equation (or equations) is already written out for us so that all we must do is apply the mechanical methods of mathematics that we have learned to solve the problem. To solve problems of this type, we need to learn to apply some logical thinking to the problem, converting some of the words that describe the problem into mathematical symbols and/or operations that can be manipulated to come up with an answer.

To solve problems of this kind, we need to learn to convert the words of the problem into mathematical symbols, expressions, and operations that represent the problem description. For example, the word(s) ‘is/are’ generally translate(s) to the mathematical ‘=’ sign and logically represent the concept of equality. The words ‘and’ and ‘sum’ imply or translate to the operation of addition (+). The words ‘double’ or ‘triple’ imply the operation of multiplying by 2 or 3, respectively. Something that is ‘squared’ or ‘cubed’ is raised to the second or third power, respectively. Use symbols/letters such as ‘x’ and ‘y’ to represent quantities in the problem that are not known. And so on. In this way we can translate the words into one or more mathematical expressions that we can solve.

The following Web site offers additional insights into solving word/story problems:

http://www.purplemath.com/modules/translat.htm

The following are examples of using the approaches described above to solving word/story problems.

Example 1

Problem: The sum of two numbers is 15, and the ratio of the first number to the second number is two-thirds. What are the two numbers?

Solution:

Example 2

Problem: To earn an A in a course, Mary must have an average score of at least 90 on five tests. If her first four test scores are 92, 86, 79, and 96, what score does she need on the fifth test to obtain a 90 average?

Solution:

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