Demystifying Variables

Demystifying Variables (Part 1)

What are “variables” and why are they called variables?  Why do we need them and how are they used? Students often get very confused when the topic of a variable is introduced.  As the excellent math teacher that you are, it is very important that this concept is introduced in simple terms.  Here are some key points to consider sharing with your students. Variable comes from the word “vary”, which essentially means “changeable”. Something that is changeable can take on different values or quantities depending on other values associated with the calculation (we will look at an example soon).  On the contrary, something that is not changeable cannot take on different values and is thus fixed.  Something that is not changeable is called a constant.  Variables in mathematics are usually denoted with the use of a letter from the English alphabet.  In other advanced math subjects, letters from the Greek alphabet are used, and in some early math subjects symbols (such as a box or square) are used to simplify the concept of a variable.  

In math, another name for variable is “unknown”, “unknown value”, or “unknown variable”. All of these terms refer to the same concept of a “variable”.  The reason these different terms are sometimes used is because when a variable is presented to us in a math problem, it is in the form of a letter, and we therefore do not know what the value or quantity the letter (variable) represents.  In most cases, the objective of a math problem is to “find the value” of the unknown or to “solve” for the unknown variable.

Let’s look at an example of an equation with no variables:

2 + 3 = 5

In the above equation, we have no variables because each value shown is known to us.  Therefore from the above equation, we see that 2 plus 3 is indeed equal to 5 and thus the equation is a true a equation.  A “true” equation is one where the left side of the equation is equal to the right side of the equation.  

Here is an example of an equation WITH a variable:

2 + X = 5

The letter denotes a value that can change depending on the other known values on the left and right of the equation.

If X is equal to 3, then the equation is true.  Let’s say we had a similar looking problem like

2 + X = 8.  

Now, to make the equation true, x has to be equal to 6.  Notice how ‘x’ changed from being 3 in the first equation, to now being 6 in the second equation.  X is the variable that varied from 3 to 6.