Math · Algebraic Thinking

Introduction to Variables

A variable is a letter that stands in for a number you don't know yet — it turns plain arithmetic into a puzzle-solving tool!
🔎A Variable = a Mystery Number
? unknown # name it x the variable
Instead of leaving a blank, we use a letter like x or y to hold the spot of a number we don't know yet. The very same x can be a different number in every new problem!
⚖️Expression vs. Equation
📝 EXPRESSION
x + 5 ✗ no equals sign
A math phrase — numbers, operations, and variables.
It says "an unknown number plus five."
You can evaluate it, but there's nothing to "solve" yet.
🟰 EQUATION
x + 5 = 12 ✓ has an equals sign
A math statement: two expressions are equal.
The = sign balances both sides like a scale.
Now it's a puzzle — solve to find what x must be!
🧩Parts of an Expression
term 1 term 2 3 x + 5 coefficient (times the variable) variable constant (never changes)
Coefficient = 3 Variable = x Constant = 5
✏️Worked Example: Substitution
Evaluate x + 5  when  x = 7
1
Start with the expression x + 5.
2
Substitute: swap the variable x for its value 7  →  (7) + 5.
3
Add to evaluate:   7 + 5 = 12.
⭐ When x = 7,   x + 5 = 12
🔑Key Terms
Variable A letter or symbol that stands for an unknown number.
📝Expression A math phrase with numbers, operations & variables — but NO = sign.
🟰Equation A statement that two expressions are equal (it has an = sign).
✖️Coefficient The number multiplied by a variable (the 3 in 3x).
🔢Constant A number on its own — its value never changes.
🔁Substitution Replacing a variable with its number value to evaluate.
Remember: a variable is just a letter holding the spot of a mystery number — and the moment you add an = sign, an expression becomes an equation you can solve!
✏️ Math Anchor Chart · Introduction to Variables
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