Intermediate Algebra and Functions

          Module 1: Foundations of Algebraic Expressions

Section 1: Introduction to Variables and Constants  
- Lesson 1: Understanding Variables  
  - Module 1, Section 1, Lesson 1: Exploring what variables are and how they represent unknown values  
- Lesson 2: Recognizing Constants  
  - Module 1, Section 1, Lesson 2: Learning the role of constants and their fixed values

Section 2: Simplifying Algebraic Expressions  
- Lesson 1: Combining Like Terms  
  - Module 1, Section 2, Lesson 1: Techniques to identify and combine like terms in expressions  
- Lesson 2: Applying the Distributive Property  
  - Module 1, Section 2, Lesson 2: Using the distributive property to expand and simplify expressions

Section 3: Order of Operations  
- Lesson 1: Understanding PEMDAS  
  - Module 1, Section 3, Lesson 1: Breaking down the order of operations using PEMDAS rules  
- Lesson 2: Evaluating Expressions Step-by-Step  
  - Module 1, Section 3, Lesson 2: Practicing step-by-step evaluation of complex expressions

Section 4: Introduction to Exponents  
- Lesson 1: Basic Exponent Rules  
  - Module 1, Section 4, Lesson 1: Learning the fundamental rules of exponents  
- Lesson 2: Working with Powers  
  - Module 1, Section 4, Lesson 2: Exploring how to calculate and simplify powers

Section 5: Algebraic Vocabulary Essentials  
- Lesson 1: Key Algebra Terms  
  - Module 1, Section 5, Lesson 1: Familiarizing with essential algebra terminology  
- Lesson 2: Forming Expressions from Words  
  - Module 1, Section 5, Lesson 2: Translating verbal descriptions into algebraic expressions

Module 2: Solving Equations and Inequalities

Section 1: One-Step Equations  
- Lesson 1: Solving Addition and Subtraction Equations  
  - Module 2, Section 1, Lesson 1: Methods for solving simple one-step equations using addition and subtraction  
- Lesson 2: Solving Multiplication and Division Equations  
  - Module 2, Section 1, Lesson 2: Applying inverse operations to solve equations with multiplication or division

Section 2: Two-Step Equations  
- Lesson 1: Balancing Equations  
  - Module 2, Section 2, Lesson 1: Strategies to maintain balance while solving two-step equations  
- Lesson 2: Isolating the Variable  
  - Module 2, Section 2, Lesson 2: Steps for isolating variables in two-step problem-solving

Section 3: Multi-Step Equations  
- Lesson 1: Combining Like Terms in Equations  
  - Module 2, Section 3, Lesson 1: Simplifying equations by combining like terms  
- Lesson 2: Solving Equations with Variables on Both Sides  
  - Module 2, Section 3, Lesson 2: Techniques for moving terms and solving balanced equations

Section 4: Introduction to Inequalities  
- Lesson 1: Understanding Inequality Symbols  
  - Module 2, Section 4, Lesson 1: Learning the meaning of inequality symbols and their usage  
- Lesson 2: Graphing Simple Inequalities on a Number Line  
  - Module 2, Section 4, Lesson 2: Visualizing inequality solutions on a number line

Section 5: Solving Inequalities  
- Lesson 1: One-Step Inequalities  
  - Module 2, Section 5, Lesson 1: Solving basic one-step inequalities using inverse operations  
- Lesson 2: Multi-Step Inequalities  
  - Module 2, Section 5, Lesson 2: Approaching more complex inequalities with multiple steps

Module 3: Functions and Graphing Fundamentals

Section 1: Introduction to Functions  
- Lesson 1: Defining a Function  
  - Module 3, Section 1, Lesson 1: Understanding what makes a function and how it differs from a relation  
- Lesson 2: Domain and Range Basics  
  - Module 3, Section 1, Lesson 2: Identifying possible inputs (domain) and outputs (range) of functions

Section 2: Function Notation and Evaluation  
- Lesson 1: Understanding Function Notation (f(x))  
  - Module 3, Section 2, Lesson 1: Learning the meaning and usage of function notation  
- Lesson 2: Evaluating a Function at a Given Value  
  - Module 3, Section 2, Lesson 2: Practice substituting values to determine function outputs

Section 3: Graphing Linear Functions  
- Lesson 1: Plotting Points on the Coordinate Plane  
  - Module 3, Section 3, Lesson 1: Fundamentals of the coordinate plane and point plotting  
- Lesson 2: Drawing Straight Lines and Identifying Slope  
  - Module 3, Section 3, Lesson 2: Connecting points and interpreting slope and y-intercept

Section 4: Understanding Slope and Intercept  
- Lesson 1: Calculating Slope  
  - Module 3, Section 4, Lesson 1: Step-by-step instructions for calculating the slope between two points  
- Lesson 2: Interpreting the Y-Intercept  
  - Module 3, Section 4, Lesson 2: Analyzing the significance of the y-intercept in a linear equation

Section 5: Real‑World Applications of Functions  
- Lesson 1: Modeling Real‑Life Situations with Linear Functions  
  - Module 3, Section 5, Lesson 1: Translating daily problems into linear function models  
- Lesson 2: Analyzing Graphs to Interpret Information  
  - Module 3, Section 5, Lesson 2: Using graphs to make predictions and draw conclusions from data

Module 4: Polynomials and Factoring Techniques

Section 1: Introduction to Polynomials  
- Lesson 1: What are Polynomials?  
  - Module 4, Section 1, Lesson 1: Defining polynomials and understanding their components  
- Lesson 2: Identifying Degree and Term Structure  
  - Module 4, Section 1, Lesson 2: Learning how to determine the degree and number of terms in a polynomial

Section 2: Adding and Subtracting Polynomials  
- Lesson 1: Techniques for Adding Polynomials  
  - Module 4, Section 2, Lesson 1: Methods to add polynomial expressions together  
- Lesson 2: Techniques for Subtracting Polynomials  
  - Module 4, Section 2, Lesson 2: Approaches to subtract polynomial expressions and simplify the result

Section 3: Multiplying Polynomials  
- Lesson 1: Multiplying Binomials Using the FOIL Method  
  - Module 4, Section 3, Lesson 1: Step-by-step guide to applying FOIL in multiplying binomials  
- Lesson 2: Multiplying Polynomials with More Than Two Terms  
  - Module 4, Section 3, Lesson 2: Extending multiplication techniques to trinomials and larger expressions

Section 4: Factoring Basics  
- Lesson 1: Factoring Out the Greatest Common Factor (GCF)  
  - Module 4, Section 4, Lesson 1: Methods for identifying and factoring the GCF from polynomials  
- Lesson 2: Factoring Quadratic Expressions  
  - Module 4, Section 4, Lesson 2: Techniques for breaking down simple quadratic expressions into factors

Section 5: Advanced Factoring Techniques  
- Lesson 1: Factoring by Grouping  
  - Module 4, Section 5, Lesson 1: Learning to factor expressions by grouping terms  
- Lesson 2: Recognizing Special Products (Difference of Squares and Perfect Square Trinomials)  
  - Module 4, Section 5, Lesson 2: Identifying and factoring special forms in polynomials

Module 5: Real‑World Applications and Problem‑Solving with Functions

Section 1: Modeling Real‑World Situations  
- Lesson 1: Translating Word Problems into Equations  
  - Module 5, Section 1, Lesson 1: Converting real-life scenarios into algebraic expressions and equations  
- Lesson 2: Setting Up Function Models  
  - Module 5, Section 1, Lesson 2: Creating functions that model everyday situations accurately

Section 2: Exploring Data Through Functions  
- Lesson 1: Using Scatter Plots to Visualize Data  
  - Module 5, Section 2, Lesson 1: Learning how to plot and interpret data using scatter plots  
- Lesson 2: Introduction to Linear Regression Concepts  
  - Module 5, Section 2, Lesson 2: Basic overview of regression analysis as a tool for trend prediction

Section 3: Interpreting Graphical Data  
- Lesson 1: Reading and Understanding Graphs  
  - Module 5, Section 3, Lesson 1: Techniques for effectively interpreting data embedded in graphs  
- Lesson 2: Drawing Conclusions from Graph Trends  
  - Module 5, Section 3, Lesson 2: Evaluating trends and making informed predictions based on graph analysis

Section 4: Functions in Economic and Social Contexts  
- Lesson 1: Using Functions for Cost‑Benefit Analysis  
  - Module 5, Section 4, Lesson 1: Applying algebraic functions to basic economic decision scenarios  
- Lesson 2: Modeling Break‑Even and Profit Points  
  - Module 5, Section 4, Lesson 2: Setting up equations and functions to determine break‑even points

Section 5: Integrative Problem‑Solving  
- Lesson 1: Solving Multi‑Concept Word Problems  
  - Module 5, Section 5, Lesson 1: Combining algebraic and function skills to tackle integrative problems  
- Lesson 2: Comprehensive Review and Real‑World Application  
  - Module 5, Section 5, Lesson 2: Reviewing key concepts and applying them to final, real‑life scenarios