Ask any student what type of math problem he or she finds most challenging and the answer is invariably the same: a groan, followed by “Word problems!” (You may have had this reaction yourself!)
Rarely, if ever, does a student leap to his or her feet declaring that life would be bleak without these mini-mysteries.
The word problem’s negative reputation is interesting for several reasons:
- The math in a word problem is not necessarily any more difficult than that in a straight math problem. In fact, often it is less complex.
- You may have excellent reading skills (and verbal scores), but still encounter difficulties figuring out what the word problem expects you to do.
Enter the keyword. Like footprints, word problem keywords lead you to the detection of the answer. Keywords are clues, not commands; they show you what you probably need to do to get the correct answer to a math problem. They are not magic, but they sure do help!
What is a keyword, exactly? It is a word or phrase in a mathematical word problem that can guide you toward the correct operation(s) to perform: addition, subtraction, multiplication, or division. However, it is possible for the same word to indicate opposite operations (depending on how the question is phrased).
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For example, the words combined and total generally signal that you should add; however, they may appear in problems that require you to perform other calculations as well. “Times” (as in times table) usually indicates multiplication, but the question “How many times does 12 go into 144?” asks you to do the opposite—to divide.
Confused yet? Never fear. Word problem keywords are useful, once you get the hang of them. One of the things to remember is that they rarely point to more than two options (usually multiplication/division or addition/subtraction). The word each for instance, can indicate multiplication or division, as in the following two examples:
Example A
Jeremiah and Susan are getting married. Nine of their friends want to pool their money to get the couple something special. Each friend contributes $30.00. How much will the group have to spend?
In this case we are given the individual amount (smaller) and expected to find the total amount (larger). Multiplication makes the most sense.
Let’s look at the same situation from a different angle.
Example B
Jeremiah and Susan are getting married. Nine of their friends want to get the couple a silver platter for $270.00. They plan to split the cost equally. How much money will each friend contribute?
Here we are given the total (larger) amount and expected to split it into smaller, equal shares. The logic of the problem leads us to identify that each indicates division. The other keywords split and equally reinforce this interpretation.
Parts 2 and 3 of “Cracking the Word Problem” will appear in upcoming issues of our newsletter. In Part 2, we look further into SAT and ACT® math problem logic. Applying common sense to decoding word problems can help you correctly estimate or choose formulas, in addition to helping you with basic operations. In Part 3, we provide a handy list of keywords and their common interpretations. Stay tuned!
At A+ Test Prep and Tutoring, we are here to guide you through the standardized testing process. If you would like more information, our Client Service Directors Anne Stanley and Susan Ware are available to answer questions and provide solutions. You may reach either of them by calling A+ Test Prep and Tutoring at 215-886-9188.
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