Calculus Preparation and Fundamentals

          Module 1: Precalculus Algebra Review

Section 1: Basic Algebra Operations  
- Lesson 1: Key Arithmetic Operations  
  - Module 1, Section 1, Lesson 1 Key Arithmetic Operations  
- Lesson 2: Simplifying Algebraic Expressions  
  - Module 1, Section 1, Lesson 2 Simplifying Algebraic Expressions  

Section 2: Solving Equations  
- Lesson 1: Understanding Linear Equations  
  - Module 1, Section 2, Lesson 1 Understanding Linear Equations  
- Lesson 2: Techniques to Isolate the Variable  
  - Module 1, Section 2, Lesson 2 Techniques to Isolate the Variable  

Section 3: Factoring and Exponents  
- Lesson 1: Introduction to Factoring Polynomials  
  - Module 1, Section 3, Lesson 1 Introduction to Factoring Polynomials  
- Lesson 2: Rules of Exponents  
  - Module 1, Section 3, Lesson 2 Rules of Exponents  

Section 4: Functions as a Concept  
- Lesson 1: Defining a Function  
  - Module 1, Section 4, Lesson 1 Defining a Function  
- Lesson 2: Understanding Domain and Range  
  - Module 1, Section 4, Lesson 2 Understanding Domain and Range  

Section 5: Interactive Algebra Experiments  
- Lesson 1: Hands-on Equation Exploration  
  - Module 1, Section 5, Lesson 1 Hands-on Equation Exploration  
- Lesson 2: Group Problem-Solving with Algebra  
  - Module 1, Section 5, Lesson 2 Group Problem-Solving with Algebra  

Module 2: Exploring Functions

Section 1: Introduction to Functions  
- Lesson 1: What Is a Function?  
  - Module 2, Section 1, Lesson 1 What Is a Function?  
- Lesson 2: Everyday Examples of Functions  
  - Module 2, Section 1, Lesson 2 Everyday Examples of Functions  

Section 2: Function Notation  
- Lesson 1: Understanding f(x) Notation  
  - Module 2, Section 2, Lesson 1 Understanding f(x) Notation  
- Lesson 2: Evaluating Functions at Given Inputs  
  - Module 2, Section 2, Lesson 2 Evaluating Functions at Given Inputs  

Section 3: Linear Functions  
- Lesson 1: Characteristics of Linear Functions  
  - Module 2, Section 3, Lesson 1 Characteristics of Linear Functions  
- Lesson 2: Graphing Straight Lines  
  - Module 2, Section 3, Lesson 2 Graphing Straight Lines  

Section 4: Quadratic Functions  
- Lesson 1: Features of Quadratic Functions  
  - Module 2, Section 4, Lesson 1 Features of Quadratic Functions  
- Lesson 2: Visualizing Parabolas  
  - Module 2, Section 4, Lesson 2 Visualizing Parabolas  

Section 5: Interactive Function Activities  
- Lesson 1: Matching Functions to Graphs  
  - Module 2, Section 5, Lesson 1 Matching Functions to Graphs  
- Lesson 2: Collaborative Graph Sketching  
  - Module 2, Section 5, Lesson 2 Collaborative Graph Sketching  

Module 3: Introduction to Graphs and Behavior

Section 1: Graph Basics  
- Lesson 1: Understanding the Coordinate Plane  
  - Module 3, Section 1, Lesson 1 Understanding the Coordinate Plane  
- Lesson 2: Plotting Points Accurately  
  - Module 3, Section 1, Lesson 2 Plotting Points Accurately  

Section 2: Graphing Different Types of Functions  
- Lesson 1: Revisiting Graphs of Linear Functions  
  - Module 3, Section 2, Lesson 1 Revisiting Graphs of Linear Functions  
- Lesson 2: Plotting Simple Quadratic Graphs  
  - Module 3, Section 2, Lesson 2 Plotting Simple Quadratic Graphs  

Section 3: Behavior of Functions  
- Lesson 1: Identifying Increasing and Decreasing Trends  
  - Module 3, Section 3, Lesson 1 Identifying Increasing and Decreasing Trends  
- Lesson 2: Recognizing Constant Function Behavior  
  - Module 3, Section 3, Lesson 2 Recognizing Constant Function Behavior  

Section 4: Interpreting Data from Graphs  
- Lesson 1: Reading Graphical Information  
  - Module 3, Section 4, Lesson 1 Reading Graphical Information  
- Lesson 2: Analyzing Trends in Graphs  
  - Module 3, Section 4, Lesson 2 Analyzing Trends in Graphs  

Section 5: Collaborative Graph Project  
- Lesson 1: Conducting a Hands-on Graphing Experiment  
  - Module 3, Section 5, Lesson 1 Conducting a Hands-on Graphing Experiment  
- Lesson 2: Group Analysis of Graph Results  
  - Module 3, Section 5, Lesson 2 Group Analysis of Graph Results  

Module 4: Fundamentals of Limits

Section 1: Intuitive Understanding of Limits  
- Lesson 1: Introducing the Concept of Approaching Values  
  - Module 4, Section 1, Lesson 1 Introducing the Concept of Approaching Values  
- Lesson 2: Exploring Sequences That Approach a Limit  
  - Module 4, Section 1, Lesson 2 Exploring Sequences That Approach a Limit  

Section 2: Limits Through Graphs  
- Lesson 1: Visualizing Limits on Graphs  
  - Module 4, Section 2, Lesson 1 Visualizing Limits on Graphs  
- Lesson 2: Recognizing Limit Behavior in Plotted Functions  
  - Module 4, Section 2, Lesson 2 Recognizing Limit Behavior in Plotted Functions  

Section 3: Interactivity with Limits  
- Lesson 1: Demonstrating Limits Through Experiments  
  - Module 4, Section 3, Lesson 1 Demonstrating Limits Through Experiments  
- Lesson 2: Group Discussion on Limit Concepts  
  - Module 4, Section 3, Lesson 2 Group Discussion on Limit Concepts  

Section 4: Algebraic Approach to Limits  
- Lesson 1: Using Substitution Techniques to Approach Limits  
  - Module 4, Section 4, Lesson 1 Using Substitution Techniques to Approach Limits  
- Lesson 2: Recognizing Patterns That Indicate Limits  
  - Module 4, Section 4, Lesson 2 Recognizing Patterns That Indicate Limits  

Section 5: Problem-Solving with Limits  
- Lesson 1: Solving Simple Limit Problems  
  - Module 4, Section 5, Lesson 1 Solving Simple Limit Problems  
- Lesson 2: Collaborative Exercises in Computing Limits  
  - Module 4, Section 5, Lesson 2 Collaborative Exercises in Computing Limits  

Module 5: Preparing for Calculus: Synthesis and Applications

Section 1: Review of Key Concepts  
- Lesson 1: Recap of Foundational Algebra  
  - Module 5, Section 1, Lesson 1 Recap of Foundational Algebra  
- Lesson 2: Recap of Basic Function Concepts  
  - Module 5, Section 1, Lesson 2 Recap of Basic Function Concepts  

Section 2: Connecting Functions and Limits  
- Lesson 1: Integrating Function Behavior with Limit Ideas  
  - Module 5, Section 2, Lesson 1 Integrating Function Behavior with Limit Ideas  
- Lesson 2: Practical Experiments Linking Concepts  
  - Module 5, Section 2, Lesson 2 Practical Experiments Linking Concepts  

Section 3: Real-life Applications  
- Lesson 1: Informal Exploration of Rates of Change  
  - Module 5, Section 3, Lesson 1 Informal Exploration of Rates of Change  
- Lesson 2: Modeling Everyday Phenomena with Mathematical Concepts  
  - Module 5, Section 3, Lesson 2 Modeling Everyday Phenomena with Mathematical Concepts  

Section 4: Interactive Review Session  
- Lesson 1: Group Discussion on Learned Concepts  
  - Module 5, Section 4, Lesson 1 Group Discussion on Learned Concepts  
- Lesson 2: Problem-Solving Workshop for Concept Reinforcement  
  - Module 5, Section 4, Lesson 2 Problem-Solving Workshop for Concept Reinforcement  

Section 5: Preparing for the Next Step  
- Lesson 1: Assessment of Readiness for Calculus  
  - Module 5, Section 5, Lesson 1 Assessment of Readiness for Calculus  
- Lesson 2: Preview of Future Calculus Concepts  
  - Module 5, Section 5, Lesson 2 Preview of Future Calculus Concepts