Elementary
Entry-Level Math
The very first steps, for grades 1–3. Counting, adding and taking away, place value, money and time, and shapes — taught with pictures and tiny steps.
- 1. Counting & Number Sense
- 2. Addition to 20
- 3. Subtraction to 20
- 4. Place Value to 1,000
- 5. Two- & Three-Digit Addition
- 6. Two- & Three-Digit Subtraction
- 7. Money — Coins, Bills & Making Change
- 8. Time, Calendar & Measurement
- 9. Shapes, Patterns & Groups
Elementary
Basic Math
The grade 4–6 foundations. Multi-digit multiplication and division, factors, fractions, decimals, percents, and multi-step word problems.
- 1. Place Value & Whole-Number Operations
- 2. Multiplication
- 3. Division
- 4. Factors, Multiples, GCF & LCM
- 5. Fractions — Meaning & Equivalence
- 6. Fraction Operations
- 7. Decimals
- 8. Ratios, Rates & Percents
- 9. Measurement, Geometry & Word Problems
Foundations
Pre-Algebra
The on-ramp. Number sense, fractions, decimals, percents, and negative numbers — the pieces that make or break algebra later.
- 1. Number Sense & Order of Operations
- 2. Factors, Multiples & Primes
- 3. Integers & Negative Numbers
- 4. Fractions
- 5. Decimals
- 6. Ratios, Rates & Proportions
- 7. Percents
- 8. Measurement & Geometry Basics
- 9. Variables & Expressions
High School
Algebra I
The core of high-school math: equations, functions, lines, systems, exponents, polynomials, and quadratics — taught for understanding.
- 1. Foundations & Expressions
- 2. Linear Equations & Inequalities
- 3. Functions & Notation
- 4. Linear Functions & Graphs
- 5. Systems of Equations
- 6. Exponents & Exponential Functions
- 7. Polynomials & Factoring
- 8. Quadratic Functions
- 9. Data & Statistics
High School
Geometry
Shapes, proofs, and spatial reasoning — angles through circles and solids, with the whiteboard drawing every figure.
- 1. Foundations & Constructions
- 2. Transformations & Symmetry
- 3. Congruence & Triangle Proofs
- 4. Similarity & Dilations
- 5. Right Triangles & Trigonometry
- 6. Circles
- 7. Coordinate Geometry
- 8. Area, Surface Area & Volume
- 9. Probability
High School
Algebra II
Where algebra grows up: complex numbers, logarithms, rational and radical functions, sequences, and conics.
- 1. Foundations & Systems
- 2. Quadratic Functions & Complex Numbers
- 3. Polynomial Functions
- 4. Rational Expressions & Functions
- 5. Radicals & Rational Exponents
- 6. Exponential & Logarithmic Functions
- 7. Sequences & Series
- 8. Trigonometric Functions
- 9. Statistics & Probability
High School
Trig / Pre-Calc
The bridge to calculus: trigonometry on the unit circle, identities, vectors, matrices, and polar coordinates.
- 1. Functions & Their Graphs
- 2. Polynomial & Rational Functions
- 3. Exponential & Logarithmic Functions
- 4. Trigonometric Functions
- 5. Analytic Trigonometry
- 6. Applications of Trigonometry
- 7. Conic Sections & Parametric Equations
- 8. Sequences, Series & the Binomial Theorem
- 9. Introduction to Limits
College level
Calculus
Limits, derivatives, and integrals — the ideas explained out loud, one honest step at a time.
- 1. Limits & Continuity
- 2. The Derivative: Definition & Basic Rules
- 3. Product, Quotient & Chain Rules
- 4. Applications of Derivatives
- 5. Curve Sketching & Optimization
- 6. Antiderivatives & Indefinite Integrals
- 7. The Definite Integral & the Fundamental Theorem
- 8. Applications of Integration
- 9. Introduction to Differential Equations
College level
Differential Equations
For the student racing ahead: first- and second-order equations, slope fields, systems, and Laplace transforms.
- 1. Introduction, Classification & Slope Fields
- 2. First-Order Equations: Separable & Linear
- 3. Qualitative Analysis: Equilibria & Stability
- 4. Numerical Methods: Euler & Runge-Kutta
- 5. Second-Order Linear: Homogeneous
- 6. Second-Order: Nonhomogeneous, Vibrations & Resonance
- 7. Laplace Transforms
- 8. Linear Systems & the Phase Plane
- 9. Nonlinear Systems & Stability
High School
Probability & Statistics
Reading data honestly: distributions, probability, inference, and why correlation isn't cause.
- 1. Exploring Data
- 2. Describing Distributions
- 3. Scatterplots & Correlation
- 4. Collecting Data
- 5. Probability Basics
- 6. Conditional Probability & Independence
- 7. Random Variables & Expected Value
- 8. The Normal Distribution
- 9. Sampling & Inference