# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.05

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

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## II. Making a Plan (Focusing on the Solution)

Students often formulate questions and thus set up different discovery exercises. Although there are always some standard means of solving particular problems, other plans may be much more interesting. Alternative methods may also lead to new discoveries. In any mathematics class it is very probable that more than one solution process will arise from any particular word problem.

Do not let your students think that once they have made a plan, they must stick with it. In order to obtain a true solution, that is accurate, the plan may be revised many times.

We suggest a stimulated discussion to encourage alternative plans to find a solution. Then the students are not ‘’locked in” to one specific plan that they may not have been able to memorize. By stressing alternatives and exploration, they have a chance to continue from one unsuccessful approach to another until they finally do find some comfortable plan of their own’

It is such a joy to watch your students investigate until they find their own paths towards a solution. Heuristic teaching, the discovery method, will be most prevalent in Step Two of our S.M.S. method. Let us also emphasize that a good plan deserves some thought. We should teach the students how to draw a good plan so that the problem will indeed have relevance.

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(Problem Three)’
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Suppose the student is to find the area of the property diagrammed next to purchase fertilizer for the lawn’(figure available in print form)

One student may total the areas of the house and the pool before subtracting them from the overall lot’s area. Another one may subtract the house and the pool immediately, individually, from the overall lot. Alternative methods should also help to approximate an answer. When we approximate, we are tapping the intuitions which are sometimes totally neglected in mathematics.