Introduction to The Steps to Solving Word Problems and Valuable Key Words
If two wrongs don't make a right, try three.
—AUTHOR UNKNOWN
One of the best ways to solve a complicated problem is to break it down into smaller, more manageable pieces. This chapter details the steps to solving math word problems and a fourstep method, along with a discussion of common key words and phrases used in math word problems.
Apply the strategies from this lesson throughout the book and you will be on your way to becoming a successful wordproblem solver.
The Steps to Solving Word Problems
Solving math word problems is a daunting task for some people. However, by having a game plan in mind, even the most difficult problems can be solved.
 The first step is to read and understand the question. For each problem, be sure to carefully read the text the first time through to get the general picture of what the question is asking. At this point, list the information given and summarize the problem in your own words.
 The second step is to make a plan of attack. This will be your approach to solve the problem. In this step, underline any key words, numbers, or phrases you see in the question. This step will assist you in determining the correct operation or operations that should be used. In addition, cross out any extra information that is not necessary to solve the problem.
 The third step is to carry out the plan. In this step, use the plan outlined in step two. This may include strategies such as drawing a picture or diagram, extending a pattern, writing an equation, using a formula, or using guess and check. Each of these strategies will be explained in the various lessons throughout this book. Identify the plan to solve the problem.
 For the final step, check your answer to be sure it is reasonable. Many times, an answer may be the result of an error in setting up the problem, and you may not realize it if the solution is not checked. Review the work done for the problem and the answer reached: does it make sense? If at all possible, check your work in a different way from the way you used to solve the problem. For example, after you have solved an equation, check your work by substituting in the answer and using order of operations to check, instead of simply solving the equation a second time.
Tip:
The problem solving steps can be summarized by the following:
 Read and understand the question.
 Make a plan.
 Carry out the plan.
 Check your work.

To get started, let's practice these steps using an example.
Example
Charlie brought in 3 boxes of cookies to share with his class of 22 students. Chocolate chip cookies are his favorite kind. If there are 18 cookies in each box and each student needs to get the same number of cookies, how many cookies will be left over?
 Read and understand the question. This question asks for the number of cookies left over after they are divided up among students in a class.
 Make up a plan. First, figure out the total number of cookies. Multiply the number of boxes by the number of cookies in each box. Then, divide the total by the number of students in the class. The remainder will represent the number of cookies left over. The question is shown below with important information underlined, and extra information crossed out.
Charlie brought in 3 boxes of cookies to share with his class of 22 students. If there are 18 cookies in each box and each student needs to get the same number of cookies, how many cookies will be left over?
 Carry out the plan. Multiply the number of boxes by the number of cookies in each box to find the total:
Then, divide 54 by the total number of students in the class:
with a remainder of 10. This gives each student 2 cookies, with 10 left over. The solution is that there will be 10 cookies left over.
 Check your work. If each student gets 2 cookies, this is a total of 22 × 2 = 44 cookies to be eaten. Since there were 10 left over, the total number of cookies is 44 + 10 = 54. Because this value is the same as the total number of cookies in the three boxes, the answer is reasonable.
These important steps will be modeled and applied throughout this book to help you solve problems. Use this procedure as a way to tackle any math word problem you may meet on your road to word problem success. Begin your journey by working through the practice set below.
Using Key Words
There are many common key words that appear in math word problems, and using key words and phrases is very helpful when you are deciding on the operation or operations needed. These key words should be underlined or highlighted when you are devising your plan to solve each problem. Here are examples of some frequently used key words and phrases, along with the symbol or operation they represent.
sum, increased, combine, plus, more than, total
difference, decreased, less than, take away
product, times, factor, twice (×2), triple (×3)
quotient, divide, into, out of, split up, break up
is, total, result, same as, equivalent to
is more than, is greater than, is larger than, above
Greater than or equal to ( ≥ )
minimum, at least, is not less than, is not smaller than
is smaller than, is less than, below
Less than or equal to ( ≤)
maximum, at most, is not more than, is not greater than
The key words mentioned in the list are often used in math word problems, so look out for these in the problems in this book, or any other word problems you may come across.
Tip:
Be careful with certain key phrases that are similar.
more than can mean "addition"
is more than can mean "is greater than ( > )"
less than can mean "subtract"
is less than can mean "is less than ( < )"

Translating from Words to Math Symbols
Translating from words into symbols is very much like converting from one language to another. Look for the important vocabulary and use the numbers mentioned in the question to help you write a number sentence. In most cases, the order in which the values and key words are used in the statement is the same as the order in which they will appear in the numerical sentence.
Translate the following examples from words into mathematical symbols:
 Five increased by 10
 The product of 6 and 8
 The quotient of 70 and 7
 The difference of 9 and 4 is the same as 5.
 Five is not greater than 7.
 The sum of 6 and 3 is not less than 8.
 Three less than 11 is equal to 8.
Tip:
The order of the numbers and symbols does not always stay the same for some key words and phrases. In a few cases, the order is reversed.
For example, 6 less than 10 or 6 subtracted from 10 both translate to 10 – 6.

These examples represent a sample of some of the important vocabulary used in many math word problems. Becoming familiar with these words and phrases is a good way to improve your wordproblem solving skills. Work on the following practice problems to see how many of the key words and phrases you have learned.
Find practice problems and solutions for these concepts at The Steps to Solving Word Problems and Valuable Key Words Practice Questions.
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From Math Word Problems in 15 Minutes A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.