Algebraic Thinking

Variables & Expressions

A variable (usually a letter like x or n) stands for an unknown number.

An expression combines numbers and variables: 3x + 5 means "3 times a number plus 5".

Evaluating expressions: If x = 4, then 3x + 5 = 3(4) + 5 = 12 + 5 = 17.

Solving One-Step Equations

To solve for x, undo what was done to it using inverse operations:

• x + 7 = 12 → subtract 7 from both sides → x = 5
• x − 3 = 9 → add 3 to both sides → x = 12
• 4x = 20 → divide both sides by 4 → x = 5
• x/3 = 6 → multiply both sides by 3 → x = 18

Golden rule: Whatever you do to one side, do the same to the other side.

Function Tables (Input–Output)

A function table shows pairs of inputs and outputs following a rule.

Check differences: output increases by 6 when input increases by 3 → ratio 2:1. Try rule y = 2x + 3: 2(2)+3=7 ✓, 2(5)+3=13 ✓. Rule confirmed.