# Solve a Math Word Problem

Edited by Jerry Rivers, Lynn, Eng

As a mathematics secondary school teacher, many of our students came to the class expressing they just could not solve a math word problem. By following the steps below, they soon learned to solve the word problems, and gained more confidence in solving not only such problems in the class room, but in their everyday lives. In this tutorial, by following the steps presented, you will learn how to solve a math word problem successively.

## Steps

1. 1
First, to prepare you to solve those math problems that pop up occasionally in everyday life
:

1. Prepare yourself mentally so you will solve the problem successfully.
2. Visualize yourself solving the problem ahead. This is a metacognitive, or "thinking about thinking" step that is helpful in any task, whether it is shooting a basketball, learning a new foreign word, or solving a math problem.
4. Write down the information in a list for understanding. Leave out any info that is not needed to solve the problem.
5. Label all data and variables with proper measurement units, such as minutes, miles, kilometers, etc. Use the conventionally accepted first letter/s of the measurement to keep it associated and organized. Example - "m" for "meter", and "mi" for mile.
6. If you have the problem in metric units, use only metric measurements in the entire problem.
7. Be sure to write down and understand what the problem is asking to be solved.
8. Keep your entire problem solving neat and organized. This ensures that when you look back at the problem steps, they are all legible to you or another person who can possibly assist you.
9. Neatly sketch any pictures or graphs.
10. Find the key words to solve the problem.
11. Very important! Some of the key words will be words that you must convert to one of the four math operations: adding, subtracting, multiplying or dividing. The word "is" or "are" means "=".
1. Keywords for adding are: And, total of, added to, sum of, more than, increased by, added to, and combined. Example - Tom increased savings by \$10. He had \$30. How much does he have now? Just add: 30+10=40.
2. Keywords for subtracting are: Less than, difference of, difference between, decreased by, reduced by, fewer, or fewer than. Example - Jose' is 5 feet tall, and Rebecca is 5 feet and 2 inches tall. What is the difference in their height? 5' 2" - 5' = 2 ".
3. Keywords for multiplying are any words in which a quantity or variable is repeated: Times, find the product of, times more than, or number of times. Example: John has three times more dogs than Bill. Bill has six hunting dogs. So, 3 X 6 = 18 dogs for John. If there is a variable next to a number (constant) or another variable (xy), you must multiply them. I drove my car 60 mph. How long before I travel 120 miles? 60x = 120. Since 60 times 2 equals 120 miles. The variable "x" stands for "2". I drove for two hours at that speed.
4. Keywords for dividing are: Into, how many times into, per, what is the quotient, amount for each, divided by, times less than. Example: How many times less than \$100 is \$20? You simply divide 100 by 20, which is 5. 100/20 = 5.
2. 2
Follow the correct formula if you must find area, volume, or perimeter
.
Keep in mind that area will involve multiplying two dimensions (square units), volume is three dimensions (cubic units) , and perimeter is adding the length (linear units) around any flat area. Example: A box 3 feet wide, 2 feet tall, and 4 feet deep has these measurements: Area of the bottom is 3 X 4 = 12 square units; perimeter of the bottom is 3' + 2' + 4' = 9'; volume is 3 X 4 X 2 = 24 cubic units.
3. 3
Organize information by grouping terms with parentheses and the above-mentioned operation signs as needed
.
To organize in the proper order: Parentheses, Exponents, Multiplying, Dividing, Adding, and Subtracting. For multiplying and dividing, set up and solve left to right. Then, for any adding and subtracting of quantities, set up and solve left to right. The acronym for this is PEMDAS.
4. 4
Example
:
The length of a soccer field is 36 meters more than its width. Since you are not given the width, use "w" for the distance. To express the length you can use (36 + m) as a grouping.
5. 5
You need a plan of action, or strategy to solve a word problem
.
Find one of these strategies to organize or clarify, so that the word problem is easier to solve:
1. Make a pattern. Example: 1, 3, 6, 10, x. What is "x"? The numbers increase by 2, 3, and 4. The "x" must be found by adding now 5. With this pattern the next number must be 15.
2. Work backwards. Example: A zoo has 100 mammals. There are 6 tigers, 6 hyenas, 10 elephants, and 10 wolves. How many other mammals are there? You must start with the total of 100, and work backwards. 100 - 6 - 6 - 10 - 10 = 68 other mammals.
3. Make a chart or table. This is categorizing typically a pattern onto a classification chart for better understanding to solve the problem.
4. Guess and check. Estimating is a big part of mathematics, and will ensure that your answer makes sense. Example: If you sell apples at 25 cents each, and sell 8 apples, you know the total must be around 200 cents, or \$2, and not 20,000 cents, or about \$200. This ensures you have the correct decimal placement in your sales.
5. Draw a graph or picture with labeling. As humans, we are very visually oriented. Drawing a picture especially can make the representations in the word problem more tangible, and make it easier to solve.
6. Use a model. Example: To multiply exponents of a base, do you add them or multiply them? Use a simple problem and check to see what to do if you have forgotten. First try adding the exponents: 3 squared times 3 squared = 3 to the 4th power. This is 81. 3 X 3 X 3 X 3 = 81, so, yes, just add the exponents.
6. 6
7. 7
These strategies will make those word problems that were seemingly overwhelming, now problems that you can solve anytime they appear in your life
.
It will be helpful in solving problems involving many aspects of your life, such as calculating expenses or distances for trips.

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## Article Info

Categories : Communications & Education

Recent edits by: Lynn, Jerry Rivers
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