Mathematics word problems

The chapters in this part help you find your way through the maze of mythical mathematical word problems. No more anxiety attacks — in this part, I show you how to move through the problems with confidence. 

Am classic type of mathematical word problem is the mixture problem. v " But mixture problems go beyond just mixing up antifreeze with water or chocolate syrup with milk. Mixture problems involve all sorts of situations where you combine so much of one thing that has a certain amount of worth or density with so much of something else that has more worth or more density. 

Venezky, R. L. Bregar, W. S. (1988). Different levels of ability in solving mathematical word problems. Journal of Mathematical Behavior, 7, 111-134. 

It is just a few weeks, perhaps even just a few days, from now. You haven t begun to study. Perhaps you just haven t had the time. We are all faced with full schedules and many demands on our time, including work, family, and other obligations. Or perhaps you have had the time, but procrastinated topics in mathematics are topics that you would rather avoid at all costs. Computation and word problems have never been your strong suit. It is possible that you have waited until the last minute because you feel rather confident in your mathematical skills, and just want a quick refresher on the major topics. Maybe you just realized that your test included a mathematics section, and now you have only a short time to prepare. 

If any of these scenarios sound familiar, then Just in Time Math is the right book for you. Designed specifically for last-minute test preparation, Just in Time Math is a fast, accurate way to build your essential computational and word problem skills. This book includes nine chapters of common mathematical topics, with an additional chapter on study skills to make your time effective. In just ten short chapters, you will get the essentials—just in time for passing your big test. 

Chapter 10 Word Problems covers processes and strategies used to solve mathematics in context. 

A math word problem presents challenges in understanding, organization, and launching the mathematical problem to be solved. To illustrate all these steps (and more), consider a problem involving two friends and their walking adventure. They both leave the same place at the same time one walks north and the other walks east. One walks faster than the other. And, for some reason known only to them, they can determine how far apart they are after a period of time. 

The easiest arithmetic operation you encounter is addition. The first things that kids master in school are addition rules and addition tables. So it s always comforting to find a word problem that involves the operation of addition. A big clue that you re probably dealing with an addition problem is the word and. (See Chapter 1 for more on the mathematical meanings of everyday words.)... 

You get that feeling of satisfaction when an algebraic equation or inequality works out and you get one or more solutions. The next step in word problems is then, of course, to see if the solution of the equation or inequality is an answer to the problem. If the solution doesn t work, then you go back to see if you ve done some miscomputation. But sometimes, no amount of good mathematics is going to get you an answer. It could be that the question just doesn t have an answer. 

The hardest part of any word problem is translating the text into math. When you read a problem, you can frequently translate it word for word from text statements into mathematical statements. At other times, however, a key word in the problem hints at the mathematical operation to be performed. Here are some translation rules ... 

The Quantitative section measures your general understanding of basic high school mathematical concepts. You will not need to know any advanced mathematics. This test is a simple measure of your availability to reason clearly in a quantitative setting. Therefore, you will not be allowed to use a calculator on this exam. Many of the questions are posed as word problems relating to real-life situations. The quantitative information is given in the text of the questions, in tables and graphs, or in coordinate systems. 

The most important skill needed for word problems is being able to translate words into mathematical operations. The following list will give you some common examples of English phrases and their mathematical equivalents. 

This is very similar to creating and assigning variables, as addressed earlier in the word-problem section. In addition to identifying what is known and unknown, also take time to translate operation words into actual symbols. It is best when working with a word problem to represent every part of it, phrase by phrase, in mathematical language. 

To solve word problems, you must be able to translate words into mathematical operations. You must analyze the language of the question and determine what the question is asking you to do. 

The following list presents phrases commonly found in word problems along with their mathematical equivalents ... 

The inverse problem in this case is formulated as recovery of the unknown coefficient 7 of the elliptic operator from the known values of the field p(r, u>) in some domain or in the boundary of observations. In a number of brilliant mathematical papers the corresponding uniqueness theorems for this mathematical inverse problem have been formulated and proved The key result is that the unknown coefficient 7 (r) of an elliptic differential operator can be determined uniquely from the boundary measurements of the field, if 7 (r) is a real-analytical function, or a piecewise real-analytical function. In other words, from the physical point of view we assume that 7 (r) is a smooth function in an entire domain, or a piecewise smooth function. Note that this result corresponds well to Wcidelt s and Gusarov s uniqueness theorems for the magnetotelluric inverse problem. I would refer the readers for more details to the papers by Calderon (1980), Kohn and Vogelius (1984, 1985), Sylvester and Uhlmann, (1987), and Isakov (1993). 

De Corte, E., Verschaffel, L. (1985). Beginning first graders initial representation of arithmetic word problems. Journal of Mathematical Behavior, 4, 3-21. 

Nesher, P., 8c Katriel, T. (1977). A semantic analysis of addition and subtraction word problems in arithmetic. Educational Studies in Mathematics, 8, 251-269. 

Psychology of. 4. Word problems (Mathematics) 5. Educational tests and measurements. I. Title. 

Pharmacokinetics concerns itself with a particular set of mathematical problems the so-called "word problems." This type of problem presents additional challenges to the problem solver translating the words and phrases into mathematical symbols and equations, performing the mathematical manipulations and finally translating the result into a clinically meaningful... 

West, B.H., Setting up differential equations from word problems, in Modules in Applied Mathematics, Vol. 1, Differential Equations, Lucas, W.F., Ed., Springer-Verlag, New York, 1983, chap. 1. 

There used to be two realities in the world of physics Experiment and Theory. Now there are three, and the third one is The Computer. In the community of physicists outside of the computer-simulation enclave, there is a good deal of skepticism about computer simulations of many-particle systems. This skepticism is certainly justified at the present time. Nevertheless, in my opinion, computer simulation will affect the progress of physics in a profound way. The many-body problems that we worked on for decades will finally yield to computer simulation. This does not mean that many-body problems will suddenly become simple the complications of these problems will appear in a new form. The question will be, how are computer simulations to be interpreted in terms of the mathematically posed problem, or in terms of physical reality. A computer-generated many-particle process contains an enormous amount of information, and the challenge will be to extract the information we want, leaving computer artifacts behind. In other words, the computer may have the answer, but we will have to figure out the question. 

It is important to remember the presentation of a mathematical problem which affects its process. In recent study, Richter et al.[5] used numerical formulas and numeric embedded in text as two arithmetical types to stimulate participants. Furthermore, we also stated that the process of solving problems was presented as a formula mainly requires attention and memory processes, whereas word problems. 

A word of caution is in order at this point. There is an unrealistic tendency on the part of some to think that once the mathematical solution of a problem has been found the task of the scientist is completed, and that the effort of interpreting and applying the solution is an easy one. We must emphasize the fact that the difficulty of solving an operational problem is really encountered after the mathematical solution has been obtained i.e., in the effective application of the theoretical solution to a specific, physical problem. 

The consequence of all these (conscious and unconscious) simplifications and eliminations might be that some information not present in the process will be included in the model. Conversely, some phenomena occurring in reality are not accounted for in the model. The adjustable parameters in such simplified models will compensate for inadequacy of the model and will not be the true physical coefficients. Accordingly, the usefulness of the model will be limited and risk at scale-up will not be completely eliminated. In general, in mathematical modelling of chemical processes two principles should always be kept in mind. The first was formulated by G.E.P. Box of Wisconsin All models are wrong, some of them are useful . As far as the choice of the best of wrong models is concerned, words of S.M. Wheeler of New York are worthwhile to keep in mind The best model is the simplest one that works . This is usually the model that fits the experimental data well in the statistical sense and contains the smallest number of parameters. The problem at scale-up, however, is that we do not know which of the models works in a full-scale unit until a plant is on stream. 

After all this fancy mathematics, we need a word of caution. It is extremely dangerous to apply the state estimate as presented in this chapter. Why The first hint is in Eq. (9-32). We have assumed perfect knowledge of the plant matrices. Of course, we rarely do. Furthermore, we have omitted actual terms for disturbances, noises, and errors in measurements. Despite these drawbacks, material in this chapter provides the groundwork to attack serious problems in modem control. 

---