# How to Overcome Word-Problem Dread

After teaching SAT math for a while, one learns where students are likely to stumble. Some students are confounded by inequalities and absolute values. Others are confused by “circle problems” where you have to draw in extra lines to find the measures of sides, angles, or arcs. And then there are those students who are convinced they can’t do word problems.

Of course, a big part of the game here is mental. Henry Ford summed this up well when he said: “Whether you think you can or think you can’t – you’re right.” Students who fear specific types of math problems are likely to fail at solving them.

We all have fears. I imagine that a fear of word problems is like trying to find your way out of a forest where everything looks, feels, sounds, and smells the same in every direction. Students that get psyched out just thinking about word problems can’t see their way through the mathematical forest; the jumble of English words are like trees that paralyze their senses.

We introduce kids to word problems in elementary school with mathematically straightforward questions, like: “Sally has 2 apples, James gives her 3 pears, how many pieces of fruit does Sally have?” Such problems are not really just about math, but also integrate practice in reading and writing as well.

By the time students get to high school, word problems are tailored to prepare students for the SAT. The SAT is designed to assess mastery of high school mathematics and related concepts. SAT word problems can be intentionally misleading, confusing, and downright sneaky. The correct answer to a multiple-choice question appears in plain sight, hidden among the most common wrong ones. The essential facts needed to solve the problem can be buried in spurious details. Some questions actually have obvious answers requiring no calculation, but you have to see the trick. Many test mathematical proficiency with proportions, percentages, rates of change, and unit conversions. Others evaluate understanding of concepts like “interest”, “tax” and “profit”.

My job is to help these students overcome their defeatist mindsets about word problems, and to achieve mathematical self-sufficiency. I do this by teaching them reproducible recipes for solution. Oftentimes, it’s as easy as showing the student how to translate the English words into mathematical expressions, the so-called “setting up” of the problem. I demonstrate the same reproducible technique on successive problems until we’ve repeated the process enough times that the student starts believing that maybe, just maybe, she can tackle one on her own. I know I’ve been successful when I see her solve a word problem herself, and a broad smile of self-confidence and accomplishment washes across her face!

Let’s illustrate this process with an example:

The toll rates for crossing a bridge are $6.50 for a car and $10 for a truck. On Tuesday, a total of 187 cars and trucks crossed the bridge, and the total collected in tolls was $1,338. What system of equations will describe how many cars and how many trucks crossed the bridge that day?

The recipe for solution is as follows:

1. Read the whole question. Stop and think. Do you see a shortcut or an easy answer? No.

2. Is there any irrelevant information? The day of the week is irrelevant.

3. How can you express the total number of vehicles in terms of C and T? C + T = 187.

4. How can you describe the total toll collected in terms of C and T? 6.5C + 10T = 1338.

5. Read the question again to remind yourself what you are looking for. You are looking for the system of equations, not C or T. You’re done. The system of equations is

C + T = 187

6.5C + 10T = 1338.

I believe in all my students. I believe that they can all master SAT mathematics, even word problems. It is my job as a teacher to help them get there, and I happily acknowledge and accept that responsibility. Whether I have to explain the answer to a math problem once or a dozen times, I always try to demonstrate an unshakeable faith in my students’ abilities, a faith I hope my students will internalize as positive mindsets for themselves. Only then can I stand back, and let them fly.