Lesson 2-6

Problem Solving with the 5-Step Method

     A Chemistry student is required to solve many different types of problems.  Despite the variety of problems, some general practices will help you when solving any type of problem.   Good problem solving strategies will allow you to tackle many types of problems, and to develop the confidence that you will need to work at a faster pace.  We will be covering what we call the "5-step method" of problem solving.  There are other methods, but this works as well as any other.

     The steps for the 5-step method are as follows;

1.  Write down the "given" or the known information.  For this step, look over the question and take out the information that has been provided.  This includes any "constants" or information that the problem assumes that you know, or at least know to look up.  For example, you may be asked to solve a problem which involves knowing the density of copper.  The problem may not actually give you the density of copper, but you may have that information on a reference table.  You might think, "how am I supposed to know to look up information that is not mentioned in the problem!?!"  The truth is, it is not as bad as it seems.  When you use the 5-step method, you will realize when you don't have enough information to solve a problem.   That will be your key that you are missing a constant.

2.  Determine and write down the unknown variable.   This is one of the easier steps.  Most people can read a question and determine what the unknown is, or what the question is asking for.

3.  Choose an appropriate equation.  You may or may not have a reference sheet with equations on it when you need to solve a problem.  In certain testing situations, you may have to come up with the equations from memory.  In any case, the process of selecting the appropriate equation involves selecting one that includes some or all of the variables that you have been given, and only contains one unknown.  The unknown is not always the one that you are looking for in your final answer, if the particular problem involves more than one equation.  If you can come up with an equation that contains the variable that your question is asking for, and it is the only unknown in the equation, then the problem can be solved with the one equation.

4.  Isolate the unknown in the equation.  This involves manipulating the equation algebraically, so that the only thing on one side of the equal sign represents the physical quantity that you are solving for.  Do this before substituting values for any of the variables.  If you notice more than one unknown in your equation, go back and look at your reference tables for constants.

5.  Plug the known values into the equation, solve for the unknown, round and add units.  Remember to round your final answer according to the rules of significant digits, and include units.

     Now let us see an example using the 5-step method to solve problems.

Step 1.  Write down the "given" or the known information.

Ah, I see that this is a problem involving the volume, or amount of space occupied by a wooden block.  I will start by writing the word "given" in my word space.  Below this, I will list what I know, assigning appropriate variables to what I have been given.

2.  Determine and write down the unknown variable.

It is easy to determine the unknown variable in this example.  The question clearly states, "What is the length of a wood block?"  To the right of where I wrote the "givens" in my work space, I will write the word "find" and list the appropriate variable for my unknown.

3.  Choose an appropriate equation.

The appropriate equation comes easily to mind.  To find the volume of a rectangle, I need to use:

Volume = Length x Width x Height

or

V = L x W x H

You might notice that the units that come with the values you have been given are often helpful in determining your equation.   The fact that we have cm³ for one value and just cm for two other values suggests that multiplication has occured.

Now I will write the word "formula" to the right of my other work.  Below that, I will write the formula in its standard form.

4.  Isolate the unknown in the equation.

     Avoid the temptation to plug numbers into the equation now, as most Science teachers will probably want you to isolate the unknown first.  Rewrite the equation with the unknown on one side of the equal sign.

5.  Plug the known values into the equation, solve for the unknown, round and add units.

     Let's rewrite the working equation at the top of our workspace, and show all of our work below it.  Remember to work with units.  Once you solve the problem, you must round according to the rules for significant digits.

Note - We rounded our final answer to 3 significant digits because the lowest number of significant digits in the problems was 3.

Now, be sure to check out the worksheets and the online quizzes!

Please forward all questions, comments and criticisms to Gregory L. Curran.
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Last Modified February 07, 2008