2.2 Algebraic Thinking

Algebraic thinking involves recognizing patterns, using variables, and understanding relationships. This section covers about 30% of the Mathematics subtest.

Patterns and Sequences

Arithmetic sequences: Add the same number each time

• Example: 2, 5, 8, 11, 14... (add 3)
• Rule: Start at 2, add 3

Geometric sequences: Multiply by the same number each time

• Example: 2, 6, 18, 54... (multiply by 3)
• Rule: Start at 2, multiply by 3

Variables and Expressions

Variable: A letter that represents an unknown value

Expression: A mathematical phrase with numbers, variables, and operations

• Example: 3x + 5

Translating words to expressions:

Equations and Inequalities

Equation: Mathematical sentence showing two expressions are equal

• Example: 3x + 5 = 14

Solving one-step equations:

• x + 5 = 12 → x = 12 - 5 → x = 7
• 3x = 15 → x = 15 ÷ 3 → x = 5

Inequalities: Use <, >, ≤, ≥, ≠

• Example: x + 3 > 7 → x > 4

Input/Output Tables (Function Tables)

Finding the rule:

Strategy: Look at how each input relates to its output.

Coordinate Plane

Components:

• X-axis (horizontal)
• Y-axis (vertical)
• Origin (0, 0)
• Ordered pairs (x, y)

Quadrants:

• Quadrant I: (+, +)
• Quadrant II: (-, +)
• Quadrant III: (-, -)
• Quadrant IV: (+, -)

For the Exam: Elementary math focuses on Quadrant I (positive x and y values).