# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.05

## Word Problems Solved By S.M.S.

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We are going to discuss a technique, which we will call The S.M.S. Method (Solutions Made Simple), for use with your problem solving classes. We often get frustrated and seek help in this area of mathematics. Teaching the solving of word problems is not an easy task.

Our unit is designed for many different levels. We plan to use this unit with grades nine and ten in Consumer Mathematics and Basic Algebra. We will use our S.M.S. Method next year as a heuristic approach to the attack of most word problems.

The National Council of Teachers of Mathematics is encouraging a total organization around problem solving as a creative activity. Solving word problems is a thinking process relating past knowledge with a present situation and seeking an outcome; it requires the skills of interpretation, translation, and identification of “key words”. Our Method will look at each of these skills in helping to guide an unorganized thinker.

Mathematics is not just arithmetic and algebraic skills; it is the ability to solve problems. Our method, “Solutions Made Simple”, involves four steps:

1. Knowing the Problem

2. Making a Plan

3. Solving Your Problem

4. Testing Your Solution.

Let us observe and compare the possible techniques used by both unorganized and organized thinkers. Here is an example (Problem One) from an Algebra Class’

There are twice as many boys in the roller skating rink as there are girls. There are 42 people in the rink. How many boys are in the rink?The typical unorganized thinker will see some numbers and merely operate on them. They often make a guess at the solution. The solutions may be’ 21, 40, 44, or 84. Hopefully the word “twice” will not cause a hangup”.”

The organized thinker will read the problem possibly several times and look to see what the question asks. One has to “Know the Problem”. Looking at key words, one must make a plan. The word “twice” means to multiply by 2. One should also recognize that some information is implied: the sum of the boys and girls is 42. The unorganized thinker often ignores this implied information. Next, the organized thinker will write an equation after picking a variable’ x + 2x ~ 42.

The next step is to “Solve Your Problem.” 3x = 42, x = 14. An unorganized thinker might possibly get this far, but a thorough thinker will know that the question was not answered. How many boys are in the rink?

One must analyze the problem again and check whether x or 2x represents the number of boys. Obviously, it is the 2x. The solution, when properly stated, should be: “There are 28 boys in the rink.”

The four steps of the S.M.S. Method can be explained more explicitly as follows: