Unit 3070: Comprehensive Mathematics Foundations

1. Introduction to Number Systems

• Types of Number Systems
  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational Numbers
  • Irrational Numbers
  • Real Numbers
• Properties and Relationships
  • Subsets and Supersets
  • Number Line Representation
  • Density of Rational and Irrational Numbers

2. Basic Arithmetic Operations

• Addition, Subtraction, Multiplication, Division
• Operations with Integers
• Operations with Fractions
  • Simplifying Fractions
  • Common Denominators
• Operations with Decimals
  • Decimal Place Value
  • Rounding and Precision

3. Properties of Numbers

• Commutative Property
• Associative Property
• Distributive Property
• Identity Property
• Inverse Property
• Application of Properties in Simplifying Expressions

4. Prime Numbers and Factorization

• Definitions: Prime vs Composite Numbers
• Methods to Identify Prime Numbers
• Prime Factorization Techniques
  • Factor Trees
  • Division Method
• Applications of Factorization
  • Simplifying Expressions
  • Solving Problems

5. Introduction to Algebra

• Variables and Algebraic Expressions
• Writing and Interpreting Expressions
• Equations and Inequalities
  • Linear Equations
  • Inequalities and their Solutions
• Solving Equations and Inequalities
  • Addition/Subtraction and Multiplication/Division Methods
  • Using Substitution

6. Linear Equations and Graphing

• Forms of Linear Equations
  • Slope-Intercept Form (y = mx + b)
  • Standard Form
• Graphing Linear Equations
  • Plotting Points
  • Understanding Slope and Intercept
• Systems of Linear Equations
  • Graphical Method
  • Substitution and Elimination Methods

7. Exponents and Radicals

• Understanding Exponents
  • Definition and Notation
  • Laws of Exponents (Product, Quotient, Power Rules)
• Roots and Radicals
  • Square Roots, Cube Roots
  • Simplifying Radical Expressions
• Solving Equations Involving Exponents and Radicals

8. Introduction to Geometry

• Basic Concepts
  • Points, Lines, Line Segments, Rays
  • Angles (Types and Measurement)
  • Polygons and Circles
• Measuring Perimeter, Area, and Volume
  • Formulas for Common Shapes
  • Units of Measurement

9. Properties of Geometric Shapes

• Triangles
  • Types (Equilateral, Isosceles, Scalene)
  • Angle Sum Property
• Quadrilaterals
  • Types (Square, Rectangle, Parallelogram, Rhombus, Trapezoid)
• Circles
  • Radius, Diameter, Circumference
• Polygons
  • Diagonals
  • Interior and Exterior Angles

10. Introduction to Logic and Reasoning

• Principles of Logic
  • Statements and Propositions
  • Logical Operators (AND, OR, NOT)
• Truth Tables
• Conditional Statements
  • If-Then Statements
  • Converse, Inverse, Contrapositive
• Deductive Reasoning
  • Forming Valid Arguments
  • Proof Techniques