Variables
A letter sits where a number should be. What is it allowed to mean, and how do you read and write the expressions it lives in?
Where you are 5 inside
What this area is about
A variable is a letter that stands for a number: one number you have not found yet, an amount that changes, or a slot in a rule meant for many numbers. This area is about reading that letter correctly and naming the pieces of the expressions built around it, so that 3(n + 2) and n + 5 = 12 mean exactly one thing to everyone.
How these fit together
A first step. Using a letter for the unknown number replaces the box in an equation such as 8 \times \square = 64 with a letter, to write a story as one equation.
Definitions. What a letter stands for tells its three jobs apart: an unknown, as in n + 5 = 12, a quantity that changes, and a placeholder in a general rule. Terms, coefficients and constants names the parts of an expression such as 5x^2 - 3x + 7. Expression, equation and inequality tells a quantity apart from a claim that can be true or false.
A procedure. Translating between words and expressions turns “five less than a number” into n - 5, and back.
A path through it
Using a letter for the unknown stands on its own as the first step. Then what a letter stands for. After it, terms, coefficients and constants, then expressions versus equations; translating between words and expressions also follows what a letter stands for.
Next: substituting a value, combining like terms and what a solution is.