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| Module 1: Polynomial, Rational, and Radical Relationships |
| Lesson 1: Successive Differences in Polynomials |
| Lesson 2: The Multiplication of Polynomials |
| Lesson 3: The Division of Polynomials |
| Lesson 4: Comparing Methods – Long Division, Again? |
| Lesson 5: Putting It All Together |
| Lesson 6: Dividing by x – a and x + a |
| Lesson 7: Mental Math |
| Lesson 8: The Power of Algebra – Finding Primes |
| Lesson 9: Radicals and Conjugates |
| Lesson 10: The Power of Algebra – Finding Pythagorean Triples |
| Lesson 11: The Special Role of Zero in Factoring |
| Lesson 12: Overcoming Obstacles in Factoring |
| Lesson 13: Mastering Factoring |
| Lesson 14: Graphing Factored Polynomials |
| Lesson 15: Structure in Graphs of Polynomial Functions |
| Lessons 16 & 17: Modeling with Polynomials – An Introduction |
| Lesson 18: Overcoming a Second Obstacle in Factoring – What If There Is a Remainder? |
| Lesson 19: The Remainder Theorem |
| Lessons 20 & 21: Modeling Riverbeds with Polynomials |
| Lesson 22: Equivalent Rational Expressions |
| Lesson 23: Comparing Rational Expressions |
| Lesson 24: Multiplying and Dividing Rational Expressions |
| Lesson 25: Adding and Subtracting Rational Expressions |
| Lesson 26: Solving Rational Equations |
| Lesson 27: Word Problems Leading to Rational Equations |
| Lesson 28: A Focus on Square Roots |
| Lesson 29: Solving Radical Equations |
| Lesson 30: Linear Systems in Three Variables |
| Lesson 31: Systems of Equations |
| Lesson 32: Graphing Systems of Equations |
| Lesson 33: The Definition of a Parabola |
| Lesson 34: Are All Parabolas Congruent? |
| Lesson 35: Are All Parabolas Similar? |
| Lesson 36: Overcoming a Third Obstacle to Factoring – What If There Are No Real Number Solutions? |
| Lesson 37: A Surprising Boost from Geometry |
| Lesson 38: Complex Numbers as Solutions to Equations |
| Lesson 39: Factoring Extended to the Complex Realm |
| Lesson 40: Obstacles Resolved – A Surprising Result |
| Module 2: Trigonometric Functions |
| Lesson 1: Ferris Wheels – Tracking the Height of a Passenger Car |
| Lesson 2: The Height and Co-Height Functions of a Ferris Wheel |
| Lesson 3: The Motion of the Moon, Sun, and Stars – Motivating Mathematics |
| Lesson 4: From Circle-ometry to Trigonometry |
| Lesson 5: Extending the Domain of Sine and Cosine to All Real Numbers |
| Lesson 6: Why Call It Tangent? |
| Lesson 7: Secant and the Co-Functions |
| Lesson 8: Graphing the Sine and Cosine Functions |
| Lesson 9: Awkward! Who Chose the Number 360, Anyway? |
| Lesson 10: Basic Trigonometric Identities from Graphs |
| Lesson 11: Transforming the Graph of the Sine Function |
| Lesson 12: Ferris Wheels – Using Trigonometric Functions to Model Cyclical Behavior |
| Lesson 13: Tides, Sound Waves, and Stock Markets |
| Lesson 14: Graphing the Tangent Function |
| Lesson 15: What Is a Trigonometric Identity? |
| Lesson 16: Proving Trigonometric Identities |
| Lesson 17: Trigonometric Identity Proofs |
| Module 3: Exponential and Logarithmic Functions |
| Lesson 1: Integer Exponents |
| Lesson 2: Base 10 and Scientific Notation |
| Lesson 3: Rational Exponents – What are 2½ and 2⅓ ? |
| Lesson 4: Properties of Exponents and Radicals |
| Lesson 5: Irrational Exponents – What are 2√2 and 2𝜋 ? |
| Lesson 6: Euler’s Number, e |
| Lesson 7: Bacteria and Exponential Growth |
| Lesson 8: The “WhatPower” Function |
| Lesson 9: Logarithms – How Many Digits Do You Need? |
| Lesson 10: Building Logarithmic Tables |
| Lesson 11: The Most Important Property of Logarithms |
| Lesson 12: Properties of Logarithms |
| Lesson 13: Changing the Base |
| Lesson 14: Solving Logarithmic Equations |
| Lesson 15: Why Were Logarithms Developed? |
| Lesson 16: Rational and Irrational Numbers |
| Lesson 17: Graphing the Logarithm Function |
| Lesson 18: Graphs of Exponential Functions and Logarithmic Functions |
| Lesson 19: The Inverse Relationship Between Logarithmic and Exponential Functions |
| Lesson 20: Transformations of the Graphs of Logarithmic and Exponential Functions |
| Lesson 21: The Graph of the Natural Logarithm Function |
| Lesson 22: Choosing a Model |
| Lesson 23: Bean Counting |
| Lesson 24: Solving Exponential Equations |
| Lesson 25: Geometric Sequences and Exponential Growth and Decay |
| Lesson 26: Percent Rate of Change |
| Lesson 27: Modeling with Exponential Functions |
| Lesson 28: Newton’s Law of Cooling, Revisited |
| Lesson 29: The Mathematics Behind a Structured Savings Plan |
| Lesson 30: Buying a Car |
| Lesson 31: Credit Cards |
| Lesson 32: Buying a House |
| Lesson 33: The Million Dollar Problem |
| Module 4: Inferences and Conclusions from Data |
| Lesson 1: Chance Experiments, Sample Spaces, and Events |
| Lesson 2: Calculating Probabilities of Events Using Two-Way Tables |
| Lessons 3 & 4: Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables |
| Lesson 5: Events and Venn Diagrams |
| Lessons 6 & 7: Probability Rules |
| Lesson 8: Distributions – Center, Shape, and Spread |
| Lesson 9: Using a Curve to Model a Data Distribution |
| Lessons 10 & 11: Normal Distributions |
| Lesson 12: Types of Statistical Studies |
| Lesson 13: Using Sample Data to Estimate a Population Characteristic |
| Lessons 14 & 15: Sampling Variability in the Sample Proportion |
| Lessons 16 & 17: Margin of Error When Estimating a Population Proportion |
| Lessons 18 & 19: Sampling Variability in the Sample Mean |
| Lessons 20 & 21: Margin of Error When Estimating a Population Mean |
| Lesson 22: Evaluating Reports Based on Data from a Sample |
| Lesson 23: Experiments and the Role of Random Assignment |
| Lesson 24: Differences Due to Random Assignment Alone |
| Lessons 25–27: Ruling Out Chance |
| Lessons 28 & 29: Drawing a Conclusion from an Experiment |
| Lesson 30: Evaluating Reports Based on Data from an Experiment |