What is a variable?
A variable is a symbol for an unknown quantity. It is a number we don't know yet. It can also represent a range of numbers.
For example, I may want to make sure I have extra favors at my birthday party just in case I have unexpected guests. It's still a month before the party and I don't know how many people are coming. I write a note to myself to purchase 2 extra favors. I could write that in an expression:
Number of favors = ? + 2
Where ? is the number of people attending the party. The value of the ? varies and is called a variable. You can use any symbol to represent the number of people attending the party, but typically a variable is usually a letter like x or y (not a ?).
So let's say 10 people come to my birthday party, then I'll have to purchase 12 favors. If 20 people come, then I'll have to purchase 22 favors. The numbers 12 and 20 are called constants. These are numbers whose values stay the same. When I replace a variable with a constant, I am substituting that number for the variable. So in the first case I am substituting the constant 10 for the variable ?. 
Why do we use letters? Take a look at this video with Jesse Roe and Sal Khan to find out why.
Here's a video that describes what a variable is:

Examples
Here are some "real world" examples of when we use variables:
Example 1
If I give you 3 more pennies, you'll have 10 cents. The number of pennies that you started with can be represented by a fixed variable that we'll call x. Here is the expression to represent this: x+3=10

Example 2
I really want your candy bar. If you give it to me, I'll pay you two times what you paid for it. In this example, I don't know how much you paid for it, but I'm willing to double it. The price of the candy is the variable that we'll call p. So if you paid 25 cents, then I'll pay you 50 cents. If you paid 1 dollar, then I'll pay you 2 dollars. Here is the expression to represent this: What I pay you for the candy bar = 2p

Example 3
I think we need to have at least 2 cupcakes per guest at your birthday party. The number of guests at your birthday party can be represented by a variable that we'll call g. Here is the expression to represent this:
The number of cupcakes = 2g

Expressions
According to Math is Fun the definition of a mathematical expression is: numbers, symbols and operators (such as + and ×) grouped together that show the value of something. If our goal is to put real life problems into equations and then solving them, it is important to know how to translate words into algebraic expressions.
When writing expressions, it is important to first start with a common language of both words and symbols. Take a look at the Terms & Symbols page to get started.
When writing expressions, it is important to first start with a common language of both words and symbols. Take a look at the Terms & Symbols page to get started.
Many times writing an expression is the same as translating a word problem. The folks at Purple Math have done a nice job explaining how to approach Translating a Word Problem. Make sure you don't miss that second page where you'll find some excellent examples!
@HomeTutor  This provides a stepbystep explanation on Writing Expressions with online exercises to check for understanding.
@HomeTutor  This provides a stepbystep explanation on Problem Solving Skills with online exercises to check for understanding.


Video Tutorials
Here is a series of excellent videos that show how real world problems can be turned into equations and then solved. Click on the image to the left and then select the appropriate video from the pulldown menu.
1.1 Variables and Expressions  Which movie theater is less expensive?
1.3 Writing Algebraic Expressions  How many text messages can my daughter send based on her allowance?
1.4 Equations and Mental Math  How many packs of hamburgers do I need for the barbecue?
1.4 Write Equations  How much does the cat weigh?
1.5 Problem Solving Plan  Traffic jam  how many cars between me and the exit?

Online Activities
Here is a visual version of the Problem Solving Plan problem.

Practice Worksheets
Use these for practice. Some of the sites allow you to print the questions. Others are online only. In either case, you should systematically work through the problems on paper and then double check to make sure your answers are correct.
Evaluating Algebraic Expressions  This site has a lot of worksheets. Click on "Evaluating Algebraic Expressions Worksheets" and then select the type of problem you want to work on. Then click a letter to the right to select a worksheet.
