Introduction

The words "problem solving" may have a different definition, meaning and interpretation to different people. Some describe problem solving as: "Engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings." Other have the more traditional view that requires students to "translate" or solve a problem through a direct computational method. Most problems in algebra can be categorized by type. Either way, there are seven basic questions that you want to keep in mind when you are faced with a word problem:

This problem solving unit will demonstrate how to tackle algebra word problems by interpreting and translating relationship into algebraic expressions, formulating equations and interpreting the appropriate solutions.

Mathematics is a language; it is the language of quantity. It is logically structured; its study helps to introduce you to abstract and analytical thinking. Its focus in understanding concepts, not memorizing algorithms.

Mathematics is the exploration of patterns and relationships. Patterns and relationships can be numerical, geometrical, spatial, logical, linguistic, pictorial and perhaps many other things. Doing math is figuring out some of those relationships. This process does involve computations, procedures, and algorithms, but these make up only part of the picture. The whole point of learning about these activities is to facilitate the discovery of relationships.

A thorough understanding of a problem means you must know what each term in the problem means. Each problem may contain several different types of information -- descriptive, procedural, geometric, relational, spatial, conceptual, and so on. Descriptive information describes the kind of numbers or geometrical figure you are dealing with. For example, consecutive, integer, and prime describe specific sets of numbers; right, adjacent, and supplementary describe angles or angle relationships. Procedural information indicates which mathematical operation is to be performed -- sum, product, difference, half, twice, three times. Relational information indicates how two or more quantities are related -- greater than, less than, more, equal. A more detailed account of the different kinds of information you might encounter is found below. Keep in mind that the information that follows is not exhaustive.

*descriptive:*	consecutive, integer, prime, right, adjacent, supplementary, rectangular, odd, quadratic, linear,
*procedural:*	sum, product, difference, quotient, half, twice, square, cube, three times, less than, greater than, more, increase, minus
*geometric:*	Polygon, radius, segment, matrix, hypotenuse, circle, sphere
*relational:*	greater than, less than, more, most, greatest, equal, shorter, same as, between, equal to, before
*spatial:*	vertical, horizontal, adjacent, next to, beneath, farther, between, inside
*conceptual:*	probability, proportion, area, diameter, altitude, base, profit, average, function, equation, base, length, quadratic, linear, distance, variable, perimeter, speed, rate, diagonal, ratio, side, reciprocal