- Arithmetic
- Number Theory
- Commutative Properties of Addition and Multiplication
- Associative Properties of Addition and Multiplication
- Additive and Multiplicative Inverse Properties
- Additive and Multiplicative Identity Properties
- Zero Property of Multiplication
- Distributive Properties (non-algebraic)

- Number Systems
- Definition of Closure
- Whole and Natural Numbers
- Definition
- Arithmetic of Whole and Natural Numbers (retaining closure)
- Prime Factorization
- Exponents on (a.k.a. Powers of) Natural Numbers
- Square Roots of Natural Numbers (retaining closure)
- Natural-numbered Roots of Natural Numbers (retaining closure)
- Order of Operations (retaining closure)
- Estimation Techniques
- Applications

- Integers
- Definition
- Arithmetic of Integers (retaining closure)
- Exponents on Integers (retaining closure)
- Natural-numbered Roots on Integers (retaining closure)
- Definition of Absolute Value
- Absolute Value of Integers
- Estimation Techniques
- Applications

- Rational Numbers
- Definition
- Mixed Numbers, Proper, and Improper Fractions
- Simplification of Rational Numbers
- Arithmetic of Rational Numbers
- Converting Between Mixed and Fractional Form
- Converting Between Decimals and Fractions
- Rounding and Truncation
- Definition and Simplification of Compound Fractions
- Exponents on Rational Numbers
- Natural-numbered Roots of Rational Numbers (retaining closure)
- Rational Exponents (retaining closure)
- Application: Ratios and Proportions
- Application: Percent
- Application: Scientific Notation
- Estimation Techniques

- Irrational Numbers
- Simplification
- The Four Operations
- Rationalizing Numerators and Denominators
- Applications
- Pythagorean Theorem
- pi: Area and Circumference of a Circle
- Real Numbers
- Complex Numbers
- i
- The Four Operations
- Units of Measurement
- Unit Conversion
- Unit Analysis
- Finance
- Simple Interest
- Compound Interest
- Statistics
- Mean, Median, and Mode
- Geometry
- Lines and Angles
- Points
- Lines
- Rays
- Line Segments
- Triangles
- Angles and Angle Sums
- Perimeter and Area
- Similar Triangles
- Quadrilaterals
- Perimeter and Area
- Circles
- Circumference and Area
- Combined Figures
- Perimeter and Area
- Set Theory
- Standard Set Notation
- Set-builder Notation
- Intervals
- Algebraic Expressions
- Variables
- Addition and Subtraction
- Like Terms
- Review: Distributive Property
- Multiplication and Division
- Review: Order of Operations
- Evaluation for Given Values
- Exponents
- Whole Number Exponents
- Laws of Exponents - Product with Same Base
- Laws of Exponents - Quotient with Same Base
- Laws of Exponents - Quotient to a Power
- Laws of Exponents - Negative Powers
- Laws of Exponents - Power to a Power
- Laws of Exponents - Product to a Power
- Laws of Exponents - Zero Power
- Laws of Exponents - Quotient with a Negative Power
- Review: Order of Operations
- Formulas
- Distance, Rate, and Time
- Profit, Cost, and Revenue
- Review: Geometry
- Polynomials
- Review: The Four Operations
- Review: The Distributive Property
- Division by a Monomial
- Long Division
- Synthetic Division
- Factoring
- GCF
- Difference of Squares
- Grouping
- Sums and Differences of Cubes
- Trinomials with Unit Lead Coefficient
- Trinomials with Non-unit Lead Coefficient
- Rational Expressions
- Determine Undefined Values
- Simplify
- Multiplication and Division
- Addition and Subtraction of Rational Expressions
- Like and unlike denominators
- Finding the LCD
- Simplifying Complex Fractions
- Radical Expressions
- Simplifying Square Roots of Variables
- Simplifying nth Roots of Variables
- Simplifying nth Roots of a Variable Raised to the nth Power
- Review: The Four Operations
- Review: Rationalizing Numerators and Denominators
- Functions
- Definition of a Function
- Function Notation
- Point-plotting
- Determining the Domain of a Function
- Determining the Range of a Function
- The Arithmetic of Functions
- Composition of Functions
- Inverse Functions
- Algebraic Equations
- Linear
- Equality Property of Arithmetic
- Solving Linear Equations in One Variable
- Solving Absolute Value Equations
- Applications
- Identities and Contradictions
- Solving Linear Equations in Two Variables
- Point-plotting
- Tables
- Slope
- Intercepts
- Graphing: The Intercept Method
- Graphing: The Slope-intercept Form
- Standard Form
- Point-slope Form
- Parallel and Perpendicular Lines
- Linear Functions: Domain and Range
- Formulas
- Review: Evaluate for a Given Set of Variables
- Solve for a Given Variable
- Mixture Problems
- Investment Problems
- Quadratic
- Graphing Using Point-plotting
- Tables
- Solving by Factoring
- Solving by Extraction of Roots
- Solve by Completing the Square
- Solve Using the Quadratic Formula
- Solve Quadratic-like Equations
- Graph Using Completing the Square and Vertex Form
- Graph Using Intercepts
- Optimization Problems
- Quadratic Functions: Domain and Range
- Rational
- Solve Rational Equations
- Applications
- Variation
- Direct
- Inverse
- Joint
- Rational Functions: Domain and Range
- Radical
- Solve Radical Equations Involving One Radical Expression
- Solve Radical Equations Involving More Than One Radical Expression
- Radical Functions: Domain and Range
- Exponentials and Logarithms
- Definitions
- Graphs
- Properties of Exponentials and Logarithms
- Solving Exponential and Logarithmic Equations
- Applications
- Algebraic Inequalities
- Linear
- One Variable
- Solve and Graph Simple Inequalities
- Solve and Graph Compound Inequalities
- Solve and Graph Absolute Value Inequalities
- Two Variables
- Solve and Graph
- Systems
- 2x2
- Geometric Method
- Substitution Method
- Elimination Method
- Inconsistent and Dependent Systems
- 3x3
- See above
- Inequalities
- Conic Sections
- Graphing Circles
- Distance and Midpoint Formulas
- Graphing Parabolas
- Ellipses
- Hyperbolas
- Translation of Axes

- Number Theory