Word problems, solving

Heller, J. I., 8c Greeno, J. G. (1978, April). Semantic processing in arithmetic word problem solving. Paper presented at the meeting of the Midwestern Psychological Association Convention, Chicago. 

Management of technical information required for construction and technical records arising out of construction, and the generation or acquisition of any additional technical information needed for construction (in other words, problem-solving). 

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

The procedure for cross-multiplication is straightforward and relatively easy. The challenge in solving word problems using ratios is in the set-up of the proportion. Take care to keep all terms in order. Remember that two ratios are being compared and that the order of the ratio set-up has meaning. 

When approaching a word problem involving ratios, in addition to a proper set-up, be clear on what the problem is asking for you to solve. Study the next example. 

How did you do on the word problems Benchmark Quiz Check your answers here, and then analyze your results to figure out your plan of attack to master this topic. Keep in mind that there are many ways to solve word... 

If you answered 1-3 questions correctly, you need to make a concentrated effort to practice word problems. Perhaps you become intimidated as soon as you encounter words in a math problem. Read this chapter carefully. There are many suggestions and approaches described to make solving word problems simpler. Practice is the key to success. Pay attention to all tips, rules, and shortcuts and visit the suggested websites for further practice. You may want to refer to Practical Math Success in 2 0 Minutes a Day, published by LearningExpress, which has two Lessons, 15 and 16, devoted to word problems. 

Throughout the course of this book, we have looked at many word problems. Several problems involving distance and speed, percents, simple interest, and ratio and proportions have been reviewed. One other type of word problem not reviewed previously is consecutive integer problems. These problems are relatively easy to solve on multiple-choice tests. 

The four chapters in this part contain general plans of attack — how you approach a word problem and what you do with all those words. I introduce the basic vocabulary of math in word problems, and I outline the steps you use for solving any kind of word problem. You see how to work your way through the various units linear, area, volume, rate. And finally, I use a grand example of handling a math word problem to demonstrate the various techniques you use to solve the rest of the problems in the book. 

A math word problem is full of words — big surprise Word problems really represent the real world. When you have a problem to solve at the office involving ordering new file cabinets, you don t sit down to write out your times tables, and you aren t handed a piece of paper with an algebra problem asking you to solve 2x + 3 = 27. To be successful with a word problem, you... 

No matter how easy or complicated a math word problem, you should always have some guess or inkling or idea as to what the answer may be before you even get started on solving it. Even if you re way off with your guess, this exercise is very useful. You re more apt to check the work if you think that the answer is way out there. Many times, you just find that you didn t do a very good job of guessing. Other times, you find that you made a mistake in the arithmetic and you can go back and correct your error. 

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. 

A math word problem is different from other arithmetic and algebra problems, because you first have to translate from the words to the symbols before you do the operations or solve the equation for the answer. 

Quadratic equations may yield two different answers. Sometimes both answers work in a word problem. But in some instances, only one works or neither of the answers actually answers the question. Just because you can solve a quadratic equation for a correct answer to the equation, it doesn t mean that what you get will solve the original question. The question may be unsolvable. 

This chapter also allows me to cover some word-problem topics that just don t seem to fit anywhere else. You can call this the miscellaneous chapter — it contains word problems that you re likely to come across but that don t have any particular place with all the others. These problems are great for illustrating some more of the techniques that are helpful when solving math word problems. 

Many different types of equations and inequalities are used to solve math word problems. Each type has its own methods for solution, and many have some quirks to watch out for when solving. Here are some more frequently used equations and inequalities ... 

Traditional age word problems use algebraic expressions to write comparisons such as twice the age of or four years older than and then solve for one or more person s age. You ll see lots of parentheses in the equations that are first written so that the meaning is clearly defined and the people s ages are clearly identified. Age problems can get pretty wordy and confusing, so you want to be sure that you ve written something to parallel the wording. 

Many word problems lend themselves to more than one equation with more than one variable. It s easier to write two separate equations, but it takes more work to solve them for the unknowns. And, in order for there to be a solution at all, you have to have at least as many equations as variables. 

The rest of this chapter deals with how to use substitution in systems of equations to solve word problems. 

You re sent out to pick up some refreshments for the guys working on a project. You ve gotten their orders and collected the money, but you ve lost the piece of paper with the exact listing of what everyone wants. Good thing you know how to solve word problems with numbers of items and cost per item. Math saves the day, yet again. 

If a question stumps you, try one of the backdoor approaches explained in the next section. These are particularly useful for solving word problems. 

Remember those word problems you dreaded in high school Many of them are actually easier to solve by backdoor approaches. The two techniques that follow are terrific ways to solve multiple-choice word problems that you don t know how to solve with a straightforward approach. The first technique, nice numbers, is useful when there are unknowns (like x) in the text of the word problem, making the problem too abstract for you. The second technique, working backward, presents a quick way to substitute numeric answer choices back into the problem to see which one works. 

You can frequently solve a word problem by plugging the answer choices back into the text of the problem to see which one fits all the facts stated in the problem. The process is faster than you think because you will probably only have to substitute one or two answers to find the right one. 

Solving a Word Problem Using the Translation Table... 

The second expectation that students with a problem-solving mindset had related to the answers to questions they were asked on homework and exams. These students expected that the answers they obtained as the result of their calculations were the true and correct values. In other words, the equation used during a problem was expected to give a value that exactly corresponded to... 

When solving word problems, look at each phrase individually, then rewrite each in math language. 

Draw Pictures When Solving Word Problems if Needed... 

Pictures are usually helpful when a word problem doesn t have one, especially when the problem is dealing with geometry. Also, many students are better at solving problems when they see a visual representation. But don t waste time making any drawings too elaborate. A simple drawing, labeled correctly, is usually all you need. 

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. 

Chapter 8 reviews problem-solving skills and provides sample SAT word problems with explanations. Chapters 9,10, and 11 are Practice Tests 1,2, and 3. These practice tests are similar to the Math sections of the SAT. Answers and explanations follow the practice tests. 

---