# The Craft of Word Problems

## Word Problems Dealing with Ratio and Proportion

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## Narrative

Many of my Middle School students have a limited understanding as to how vastly important Mathematics is to their lives. They have yet to recognize the importance and the necessity of learning math for the “long run,” and how it can help them for the “future.” They have yet to comprehend that math is not so much a subject one learns in school as it is a life skill that they will call upon every day of their lives. Oh, they can
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repeat
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by rote what previous teachers might have told them about computation and other forms of mathematics, and even how they know that math is beneficial because teachers have communicated those ideas, but they generally have not seen the benefit for themselves.

They do not see that throughout their lives they will find themselves in situations where they will be called upon to solve a problem and that they will make the attempt at solving it without even considering that they are “doing math.” They do not recognize that every time they go shopping there are some really practical applications of mathematics that are occurring. Obviously, addition, subtraction, multiplication, and division are happening, but there are ratios, percents, proportions, integers, real numbers, and fractions that are also part of the practice, especially when the individual is accessing whether or not to buy an item that is on sale for 25% off. Each of these aspects of math is part of the Middle School curricula.

The problem is clear. There needs to be a conscious effort made at making math not only more accessible as a life skill, but more practical to their thinking. I am not saying that educators need to make math more fun by utilizing and implementing newer strategies for teaching math by using multi-colored manipulatives and other
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nouveau
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devices, although that is a custom that should be a part of any math teachers bag of tricks, however
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something
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radical must be done. We need to illustrate the fact that math is a vital part of their lives that is utilized on a consistent basis, not only during the most obvious times, but also in the innocuous times when math is not quite so overt, such as when we weigh ourselves, when we calculate calories, and when we watch television.

Popular shows like
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American Idol,
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TRL
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(
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Total Request Live
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)
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,
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and
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Who Wants to Be a Millionaire
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all require some knowledge of Mathematics. Every sport: baseball, football, basketball, and soccer require math as a vital aspect of function. Each of these television programs can be used as a form of enrichment. What student is going to balk at watching television for homework! The math educator must ask him/herself how to keep math away from the impractical, while at the same time conveying theoretical concepts that gear more toward teaching method, less toward busy work, and the conveying of ideas that do not work because they make math complicated, boring, and tedious. Television as math is just one of the methods that can be used to make math less boring.

I freely admit that math
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can
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be tedious, but it is tedious because by its very nature, it is a process of building a skill. One can not just do something once well, and then make the assumption that somehow in the doing one has acquired the full range of skills that one will need to employ in order to duplicate the feat. Repetition is required. Alternative values and situations need to be postulated. Variations need to be addressed. Distinctions in situation need to be made. Accordingly, one requires repetition. That is how process is typically taught, and hence learned.

The more repetition one employs the quicker the skill is learned, but it is learned with the unfortunate side effect that eviscerates the enthusiasm that students have for learning the skill. With every similar problem tedium sets in, and the avid desire our students have for learning is sapped. Where can be found the happy medium between building mathematical life skills, while simultaneously keeping the meaning and theoretical aspect in such a way as to promote their importance to the everyday vicissitudes of life? What tool can be utilized that can set math squarely in the practical, while striving to educate in the realm of the theoretical? More importantly, how do we “do math,” and still remain “real?”

Problem Solving seems to be a catchphrase that has been proposed as a method of resolving the seeming dichotomy that exists between trying to make math relevant, and the teaching of theoretical concepts that will provide the apparatus that allows a person to figure out the hows and whys of math. Although I agree with the proposition that Problem Solving can bridge the chasm between the real and the theoretical aspects of math, I think we need to go a step further. Before one can promote problem solving as the end all and be all for bridging the dichotomy between theory and praxis one must teach a common language that will help the individual student recognize the process that must be followed to ascertain the result of a given problem. In providing students with a common math-speak, the teacher is providing the
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language
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necessary for students to identify
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what
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they are doing, and
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why
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they are doing it.

I believe that the gap between theory and praxis can only be united by the use of a common terminology that is exercised, and then verbalized repeatedly. Although the proposition seems pedantic, it is a far more complicated prospect. The reason for this is that middle school students are just beginning to become comfortable with the grammar of language in itself, let alone with the academic aspects of mathematical vocabulary. Some other challenges are obvious. Some students have difficulty reading. Other students lack the confidence necessary for tackling math problems directly. Still others see little value in learning algebra, geometry, and trigonometry. Not to mention the fact that many of our students in New Haven have the added burden of being students that speak English in school, while speaking an alternative language at home. In my particular situation, as a teacher of Bilingual Latino students, I am often called upon to spend such a great deal of time teaching a sufficient amount of English to get to the basics of a problem that math instruction suffers. Yet with all these seemingly unassailable difficulties, I still believe that word problems are the most valuable asset to the instruction of a middle school student. Here is why.

Word problems are not just a contrivance that can reinforce the language of mathematics. It is by the oral working through of word problems that students fortify their language skills, verbalize process and theory, and only then put into practice the necessary computations required to achieve a specified result. Word problems train the student to be aware of the specific grammar of word problems. There is not only a specific word usage but also number usage. However, there is one further requirement. In order to do math in the precise way I will suggest, one must employ specific procedures that will assist the student in this practice of math. Further, the student will need certain materials that will be found useful both by the teacher and the student.