How to Solve Mathematic Word Problems

Whether we hate word problems, fear them, or just feel they are sometimes complicated and confusing, if we are to do well in the study of mathematics they need to be dealt with. A clear and organized pattern of attack can take some of the difficulty away. Word problems can be fun, but sometimes intimidating. If we stop for a moment and follow some simple steps to overcome the stumbling blocks that make the problems seem to be difficult, word problem stress can be greatly reduced.

The eight steps we will consider are:

1, Leave plenty of space on your paper

2, Find the main question

3, Write down the information given

4, Assign variables

5, Check units

6, If appropriate, make drawings, graphs, or tables as needed

7, Use the given relationships to generate equations

8, Check equations and their solutions

Before we get into the steps, let’s review a few of those stumbling blocks so that we can recognize them as we approach the problem. Here are my top five major blocks that we should be aware of and avoid:

1.) Past experiences causing anxiety when word problems are encountered

Time is the healer for this type of anxiety; following steps and solution procedures that take the clutter out of the problem and organize it consistently will increase our confidence. Practicing the same pattern every time will eventually leave most of the anxiety in the past.

2.) Impatient analysis getting us off track

Very often when solving homework problems from a textbook we already know what concepts will be used. It can be tempting to look at a word problem and immediately try to see how the current concept or procedure fits the problem. Taking steps out of order may lead to future confusion.

3.) Distractions taking our thinking in directions that don’t help

Sometimes the story line can direct our thinking in directions that are not leading to the solution of the problem. This can be a big problem if we have a natural tendency to let our attention drift. This tendency is not uncommon and needs to be addressed. We need to be focused.

4.) Translation errors

Most people agree that one of the biggest difficulties in word problems is translating the text into equations. Practice makes this easier, but it is still advisable to check the equations to see if they match the given information.

5.) Too much information

Commonly in courses of advanced math and physics the creators of the word problems like to throw in data that is not needed for the solution. Although at first this seems like trickery and somewhat sadistic for the unsuspecting student, it does serve a purpose by teaching the learner how to pick the needed information from a random collection. This provides practice for some real-life problem solving.

The following steps are not meant to help solve any specific problems; in fact, they are not meant to help you with the math skills needed to solve the problem at all. These steps are meant to alleviate some of the added stress that word problems tend to generate. Once equations and graphics are in place, the problem should be solved just like any normal, textbook, non-word problem.

Now that we have pointed out some of the common hurdles we can be afflicted with, let’s get to the process of pulling these word problems apart and put the pieces where they belong. After the problem is properly set up, finding the solution should not be far away.

Step 1

Make sure your pencil is sharp or there is ink in the pen. Also make sure there is plenty of room on the paper. Running out of room will lead to abbreviation of work, which can lead to missing or misusing parts of the math procedure. Write everything out clearly.

Step 2

Before you write anything, look to the question that is being asked, usually at the end of the problem. Write down “Need to Find: [The question being asked]”.

Step 3

Read through the text and write down “Given” followed by the information provided to you.

Step 4

Assign variables to the values given. For example: “Terry is four years older than Bob.”

Terry’s age = T

Bob’s age = (T-4)

Use simple and understandable symbols for the variables, as well as using relationships (like (T-4) for Bob’s age). This makes things easier if one of the things you need to find is Terry’s age. If part of the problem is finding Bob’s age, it might be better to assign this way:

Terry’s age = B+4

Bob’s age = B

Always double check the relationships to make sure they make sense. Use an arbitrary value for the independent variable (the value that the other variables depend on) and see if the results match the text. For example, in the second set of assignments, say Bob’s age is 2, then Terry’s age is 2+4 = 6. Terry is older than Bob, which matches the given text. There is a natural tendency to operate on the wrong variable, so take some time thinking through the assignments.

The relationships are usually signaled using key words, such as “twice as heavy” (multiply), “one third the cost” (divide), “two hours longer” (add), “four apples less” (subtract). When the word problem is a calculus problem at least two more operations may be involved which are differentiating rates of change and integrating summations.

Step 5

Check your units and make them uniform throughout. If it is a calculus problem, change all angles into radians.

Step 6

If possible, make a drawing, graph, or table representing the problem. Make it large enough to be able to identify all the known and unknown variables.

Step 7

Decide on which relationships help you get to a solution. This might take some focused detective work, depending on the complexity. An example of a relationship found in your “given” list is:

“In two years, Terry will be twice as old as Bob.”

You can write that relationship as

2*(B+2) = B+4+2

and then copy the text next to it, or if you are working on a worksheet, just circle the text and draw an arrow to the equation. This way you can remember where you got that relationship. Start putting the pieces together to solve the problem. Watch out for rate problems, since they usually involve multiple units, such as “miles per hour” or “units produced per day.” These problems can be a little tricky, and if the answer you get doesn’t make sense, it could be the rates were not related properly. If this is not a test, review previous problems and examples. If this is on an exam, you should have practiced the procedure plenty of times in your previous assignments and have no problems putting the solution together. If you blew off the assignments… good luck.

Step 8

Check the answer to see if it makes sense. For example, if you are given production rates for two people and the production rate for the two workers working together is lower than one of the workers working alone should indicate an error somewhere.

These steps are considerably basic, but are organized to help declutter the information, clearly define what you are looking for, and make the puzzle easier to solve. The best way to sharpen your skills solving word problems is to put the pencil to the paper and practice, practice, practice. Do the problems assigned, and then look for some more. Do them till you drop, like a professional athlete practicing for a gold medal. Don’t ever give up.