Word Problems: Everybody’s Favorite

Last updated Feb 5, 2021

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Walk into any classroom in Pennsylvania and ask who looks forward to curling up in a comfy chair and doing word problems all night.

Not seeing many hands? Not surprising. Word problems tend to be low on most students’ lists of fun ways to pass an evening.

The math portion of the SAT (or ACT) also tests reading skills. Remembering this point can help with all the questions, but is particularly relevant to deciphering word problems.

Since speed is an issue during testing, you might be tempted to skim the verbal parts of a word problem, “pull out” the numbers, and start manipulating them in whatever way seems most logical. Watch out! This can backfire big time.

It’s true that if you do not perform the correct operations, multiple choice answers can provide a clue that the answer is wrong. However, depending on this safety net is not without its costs. If you redo the problem, you can gain the point—but in the process lose valuable time. If the test requires you to grid in the answer, well whoops, there goes your safety net! No lost time, but possibly no point, either.

Below are a few suggestions to use the ‘word’ part of word problems to your advantage.

Keywords

Some of the most important information embedded in word problems is in the form of keywords. Keywords indicate the correct operation to use with two or more numbers. Consider the following short problems:

What is 20% of 150?

150 is 20% of what?

Although the numbers are the same, proper attention to keywords shows that the questions are, in fact, different. Percent questions contain three important numbers that must be identified: the percent, the whole, and the part (the fourth number, 100%, is a constant). In a math problem one of the three is always missing. But which one? Both problems above include the percentage, easily identified by its sign. However, the first question asks the student to find the percentage of the whole. The whole is identified by its key position: directly after the word of. The second question has no number after of, only a question word. Therefore the 150 here is the part, as it cannot be either the percentage or the whole.

Keywords guide, but you should follow thoughtfully, not blindly. You know that getting an average involves adding and dividing. However the word average may be used in a non-mathematical sense:

Jason recorded his running times during an average week. His times were 20 minutes, 25 minutes, 15 minutes, 18 minutes, and 30 minutes. What is the range between Jason’s shortest and longest sessions?

Here the word range is the keyword and supersedes the word average. How can you get better at analyzing keywords? Practice, practice, practice!

Logic

One often overlooked skill is remembering to take the ‘reality’ of the word problem seriously. Word problems always operate by real world logic. There are no half children (as in, no teacher can have a class of 20.5 students). No athlete will ever run 30 miles in 6 minutes. If you calculate that a plumber’s apprentice made $6,000 for 2 hours work, you probably have a decimal out of place somewhere. Consider:

Sondra needs 2 yards of fabric to make a shirt. She finds a remnant of 7 yards on sale. How many shirts will Sondra be able to make from her remnant?

Although 7 divided by 2 is 3 ½, it is highly unlikely that Sondra will expend the time or trouble to make half a shirt. Therefore the answer is that she can make 3 complete shirts.

Labels

One of the trickiest things to watch out for is when word problems use labels to pull what we call “The Ol’ Switcheroo”. For example:

Karen is packing to take a short trip. The airline she plans to use will allow carry-on luggage with a maximum volume of 2,772 cubic inches. Karen’s suitcase measures 22 inches by 1 foot by 14 inches. Will she be able to carry it on the flight?

If you fail to notice that one of the dimensions is recorded in feet (not inches), you will calculate a much smaller volume than the suitcase actually holds (308 cubic inches instead of 3696). This will lead you to conclude that Karen can take the luggage on board with her, when in fact she cannot. Don’t be fooled by this sleight-of-hand!

Practicing with an experienced tutor is the most reliable path to becoming skilled at word problem strategies—which, in turn, is a great way to raise that math score!

At A+ Test Prep and Tutoring, we are here to help make the testing process as productive and stress-free as possible. We match you with tutors who review both content and testing strategies to help you attain your “personal best” score.

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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