Strategies for solving math story problems

The first step is to choose carefully what time and place you are going to do this. Yep. Story problems at 11:30 at night take on a whole new dimension, if you know what I mean. If you're having trouble, you need to start working on them either at school (in class or study hall) when you can find someone to guide you, or at least during the daylight hours. The point is not to put it off until you are totally frustrated or anxious or out of time. I am always amazed when I hear other students say that they could not get to their homework because they ran out of time. You don't run out of time, unless you leave it until too late.

The other part of this is to ask yourself how long you are going to spend on your homework. The answer, of course, is you will spend as long as it takes to get the work done. Your teacher isn't going to be happy if you only do one out of ten assigned homework problems. However, if you're having trouble getting started with your math homework, then divide it into smaller blocks of time. Set yourself the goal of doing one or two problems or working for 15 minutes, whichever takes longer. Then do something else for 15 minutes, like take a walk or clean your room or fold some laundry (you can tell I am someone's mother). Then come back to your homework. Take a look at what you did right with the first two problems and then repeat these steps until you get all the problems done.

You might find:

• you work longer than 15 minutes
• you get more than two problems done
• it is just easier to finish the problems than to keep coming back to them
• your brain works better this way

Wait. Why would your brain work better this way? Well, there's fast thinking (think brilliant lawyers duelling it out in a courtroom battle) and then there is slow contemplative thinking. Some of us learn in a flash, some of us have to practice. If you divide your practice of math into blocks, your mind has a chance to process what you have learned and then when you return to the problems, they start to look eerily familiar.

The second step is to get all your stuff for working on math in one place. This would include your math book, assignment book (so you know what problems to do), good paper (the type you want to turn your assignment on--you may want to use graph paper), scratch paper, pencil, eraser, pencil sharpener, calculator and maybe a ruler. If this step takes a while, organizational skills could be holding you back, leaving you exhausted by the time you get down to actually doing the work. And you will do the work. The third step is to write your name on your first sheet of good paper. No point in turning this assignment in if your name isn't on it.

The fourth step is to work the problem out on your scratch paper. No matter what anybody says, part of what you will get graded on is the appearance of your final draft. Chicken scratches are not legible. Feel free to do all your messy work, erasing, diagram drawing, second tries on your scratch paper. We keep a whole stack of scratch paper for Tad to work on, much of it paper that has one side to draw on or do our calculations on. I use it for making lists. He uses it for math.

Now it's time to get down to brass tacks and take on that problem. First, read the problem out loud, as if you were reading it to someone who knew nothing about it. In fact, you are. That person who knows nothing about the problem is you. All right, if you're in class or study hall or the library, reading aloud might be a problem, but if you read quietly enough, nobody is going to care. Why read out loud? Well, like most people, if you're following directions, there is a tendency to skip to what you know or focus on what you don't know, leading to pointless thoughts like: Gross national product? What is the gross national product of Monaco? Where is Monaco, anyway? I must have missed that day in class and now my life is ruined. Pointless thinking. Admit it and go on. Reading aloud silences the pointless thoughts and engages you, not just your brain, but engages you both as an auditory and a kinesthetic learner. Some students are auditory and learn by hearing, others are kinesthetic and learn by doing. The other thing that's good about reading to yourself is that it helps you focus on what you are doing, not what other people or doing. So you don't have to worry about the math whiz in the seat next to you, working through these problems like there's no tomorrow. Focus on your work, on getting it done, so you can do other stuff. Or even, learn some math and get a good grade.

So keep it simple. Read the question. The whole question. Read it out loud if you can. Next, pick up that pencil and write down two or three things that you do know. Are there variables, usually designated by letter names? How many? Are there numbers? Write down what the problem gives you. Also, write down what you know.

For example, a triangle has three angles, a, b, and c. Angle c is one third angle a, and two times angle a is equal to angle b. How much is two times angle b?

So, you know that you have a triangle. You know that you have variables a, b, and c. You can draw a picture here, if you like. Draw a triangle. Any triangle will do. Why draw? Well, the action helps engage your kinesthetic learner, and seeing the triangle will engage that part of you which is a visual learner. Some people learn best by what they see. Now write down what you know about triangles. Sometimes this is given to you on a test. Now you know why. What you know about triangles is that the sum of their angles adds up to 180 degrees. Oops, maybe you forgot that part. Try reading your notes from class or checking the section of your math book that you are working on. That's right, just like my pastor says at church, don't be afraid, open the book. Are they showing pictures of triangles in this section? Then you might see:

a + b + c = 180

What this means is that the sum of the three angles of a triangle add up to 180 degrees.

You know from the problem that b = 2a. Substitute.

a + 2a + c = 3a + c = 180

Substitution is a big part of story problems. Your goal is to substitute until you can get yourself down to one variable.

You are also given that a = 1/3 c, which means that 3a = c. Substituting c for 3a gives us

3a + c = c + c = 2c = 180; c = 90

At this point, we were able to get to that single variable, c, which will now let us solve for the other two variables. Using this, you solve for a,

a = 1/3c = 1/3*90 = 30

and for b,

b = 2a = 2*30 = 60.

Then, check your work. Does it work out?

a + b + c = 30 + 60 + 90 =180.

So, at this point, you may think that you have solved the problem. But go back and read it--what is the question? The question is, what is two times b? Mathematically, 2b = ? Notice that you had to solve for a, b, and c to get here. If you have shown your work, you stand a very good chance of getting partial credit for your answer. Try to understand that the math teacher wants to see that you are making an effort and wants to see your work.

Now, notice that it's not too hard at this point to go ahead and plug in the answer: 2b = 2*60 = 120. Take all your work and transfer it onto the good sheet of paper. Notice how much neater and more organized your work appears. The first time you do this, it will take more time, but with practice, you'll get much better at it . Make sure you draw a little box around this answer so your teacher, if he or she is in a hurry, knows you solved the problem correctly. Don't be worried about cramming everything onto one piece of paper. I used to drive myself crazy trying to save paper. Just go ahead and use the right amount of paper for the job.

The only other thing I would suggest is that you start to be analytical about the problems. Ask yourself, how many givens do you have, how many things do you have to solve for. Look at the examples in your book and ask yourself, so how would my teacher test me on this concept?

Sometimes, it's not just the math that is the problem with doing story problems. It's working when you are tired, hungry, or haven't left yourself enough time to finish the job. If you're really having trouble, give some thought to working with another student, maybe not doing all the problems with him or her (it can be a real hassle if they aren't doing their share of the work) but doing some of the problems.

Remember, you can do well at story problems and work more efficiently on them if you tackle them with all your math gear handy (you wouldn't climb Everest without your long underwear, would you, honey?), and give yourself a good time of day to tackle them. Engage all aspects of yourself as a learner--auditory, visual and kinesthetic--and remember, story problems are fun!

Also, when you're done with that scratch paper, I would suggest sticking it in a file until the grading period is over. You may lose your notes, or lose your homework or you may have to prove to someone how it was that you suddenly got so good at math. When the grading period is over, and you have that good grade--remember, recycle!