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Great question Vickie. As far as I can tell you are in grade K-3 at Page county High school. If you are interested in more advanced information, please contact me.
I will begin with some background information and end with a direct answer to your question.
Math is strange and wonderful. Sometimes it is useful to use words instead of numbers. We let the words stand for numbers. A good example of this is speed. How fast can the cat run? What is the cat's top speed? The answer to this can be a number or a word. Let's use the word speed. Even though I don't know how fast the cat runs, I say that the cat runs with speed. Since the speed of the cat changes, and the word variable has the same meaning as change, we say that the cat's speed is variable. Speed is a variable. That's where the word comes from.
There are two kinds of math words. Constants and Variables. A Constant is a word used for a number that never changes -- the value is constant. A variable is a word used for a number that does change -- the value is variable, it changes.
Is the cat's speed a constant or a variable?
What about your bed? How fast can your bed run? The speed of your bed is a constant. It doesn't move at all! Constants never change.
Constants are very simple, but variables are more tricky. When a variable changes, we want to know how it changes. Some variables change on their own. It doesn't matter what else is going on, the variable still changes. These are independent variables because they don't depend on anything else.
Can you guess what dependent variables are? Dependent variables are variables that rely on other variables. This is a tough thing to understand. Dependent variables rely on other variables. A dependent variable may rely directly on an independent variable, or it may rely on another dependent variable.
OK, let's get to some examples:
Time. Is time a variable or a constant? Right, variable. Time is a variable because it changes. Time is an independent variable because it changes on its own. The time is shown on a clock and does not depend on any other variables. Prove this to yourself. You can change other variables by changing what you are doing. Can you do anything that will actually affect the time? (Not just the time on your clock!)
Speed. Speed can change and so speed is a variable. Is speed a dependent variable or an independent variable? Right, dependant -- usually. The speed depends on something. If you drop a ball it gets faster and faster as it falls. The speed depends on the time that has gone by since you dropped it. More time = more speed. Less time = less speed. The speed depends on time and so speed is a dependent variable. Of course, speed can also depend on a lot of other things too. This is what makes dependent variables so hard to understand. You must figure out what they depend on. In some special situations, speed may not be a dependent variable. Light moves at a constant speed. The speed of light is a constant. It is not even a variable!
These examples are boring, but there are many funny things you could imagine. Imagine a magician who put a spell on you so that the faster you run, the bigger your shoes get. Imagine that! You can change your speed so speed is a variable, and your shoes can magically change size so your shoe size is a variable. One variable depends on the other variable, but do you know which variable is the dependent variable? Right, your shoe size is the dependent variable because it depends on your speed. Speed is the independent variable because we never said it depends on anything. Your speed changes over time, but it doesn't depend on anything because you can run how you like. Your speed is not dependent on anything, but your shoe-size is dependent on your speed. Magic!
Usually, people will tell you that Time is the independent variable. This is true, but it is important to understand the difference, not just to memorize one example. I am happy that you already knew the importance of this.
Definition: Independent variables can be given without knowing other variables. The value of a dependant variables depends on the value of another variable.
It is often useful to make a graph of two variables. Just to make things simple, everybody puts the independent variable on the bottom. Make a graph of the temperature every day for one week. Which variable should go on the bottom? Which variable is the independent variable?
A lot of this may seem arbitrary. Why is temperature dependent on time? There isn't really a direct relation here ... is there? Sure there is. It is often colder at night than it is during the day. Temperature is more complicated, but it depends on time. Temperature is a function of time.
I hope I have answered your question Vickie. If you are in high school, I may not have answered all that you hoped to understand. Please email me. If you are in grade K-3, you might ask somebody to erase the hard parts.
neale@innocent.com
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