Algebraic Structures and Equations

          Module 1: Foundations of Algebraic Structures

Section 1: Introduction to Algebraic Concepts
- Lesson 1: What Is Algebra?
  Module 1, Section 1, Lesson 1 What Is Algebra?
- Lesson 2: The Evolution of Algebra
  Module 1, Section 1, Lesson 2 The Evolution of Algebra

Section 2: Variables and Constants
- Lesson 1: Identifying Variables
  Module 1, Section 2, Lesson 1 Identifying Variables
- Lesson 2: Recognizing Constants
  Module 1, Section 2, Lesson 2 Recognizing Constants

Section 3: Basic Arithmetic in Algebra
- Lesson 1: Revisiting Arithmetic Operations
  Module 1, Section 3, Lesson 1 Revisiting Arithmetic Operations
- Lesson 2: Understanding Order of Operations
  Module 1, Section 3, Lesson 2 Understanding Order of Operations

Section 4: Understanding Algebraic Expressions
- Lesson 1: Constructing Simple Expressions
  Module 1, Section 4, Lesson 1 Constructing Simple Expressions
- Lesson 2: Simplifying Basic Expressions
  Module 1, Section 4, Lesson 2 Simplifying Basic Expressions

Section 5: Foundational Symbols and Notations
- Lesson 1: Common Algebraic Symbols
  Module 1, Section 5, Lesson 1 Common Algebraic Symbols
- Lesson 2: Notation in Equations
  Module 1, Section 5, Lesson 2 Notation in Equations


Module 2: Fundamentals of Equation Manipulation

Section 1: Understanding Equations
- Lesson 1: What Is an Equation?
  Module 2, Section 1, Lesson 1 What Is an Equation?
- Lesson 2: Parts of an Equation
  Module 2, Section 1, Lesson 2 Parts of an Equation

Section 2: The Balance Principle
- Lesson 1: Maintaining Equality in Equations
  Module 2, Section 2, Lesson 1 Maintaining Equality in Equations
- Lesson 2: The Concept of Balancing Both Sides
  Module 2, Section 2, Lesson 2 The Concept of Balancing Both Sides

Section 3: Transposition of Terms
- Lesson 1: Moving Terms Across the Equal Sign
  Module 2, Section 3, Lesson 1 Moving Terms Across the Equal Sign
- Lesson 2: Combining Like Terms
  Module 2, Section 3, Lesson 2 Combining Like Terms

Section 4: Working with Coefficients and Constants
- Lesson 1: Understanding and Using Coefficients
  Module 2, Section 4, Lesson 1 Understanding and Using Coefficients
- Lesson 2: Adjusting Constants to Simplify Equations
  Module 2, Section 4, Lesson 2 Adjusting Constants to Simplify Equations

Section 5: Introduction to Equation Properties
- Lesson 1: The Properties of Equality
  Module 2, Section 5, Lesson 1 The Properties of Equality
- Lesson 2: Applying Properties in Simplification
  Module 2, Section 5, Lesson 2 Applying Properties in Simplification


Module 3: Relationships Between Variables and Expressions

Section 1: Exploring Variables
- Lesson 1: Defining a Variable
  Module 3, Section 1, Lesson 1 Defining a Variable
- Lesson 2: How Variables Represent Quantities
  Module 3, Section 1, Lesson 2 How Variables Represent Quantities

Section 2: Components of Algebraic Expressions
- Lesson 1: Terms, Coefficients, and Constants
  Module 3, Section 2, Lesson 1 Terms, Coefficients, and Constants
- Lesson 2: Building and Interpreting Expressions
  Module 3, Section 2, Lesson 2 Building and Interpreting Expressions

Section 3: The Role of Parameters
- Lesson 1: Introduction to Parameters
  Module 3, Section 3, Lesson 1 Introduction to Parameters
- Lesson 2: Differentiating Parameters from Variables
  Module 3, Section 3, Lesson 2 Differentiating Parameters from Variables

Section 4: Substitution Fundamentals
- Lesson 1: Basic Substitution Techniques
  Module 3, Section 4, Lesson 1 Basic Substitution Techniques
- Lesson 2: Substituting in Simple Expressions
  Module 3, Section 4, Lesson 2 Substituting in Simple Expressions

Section 5: Expression Transformation
- Lesson 1: Rewriting Expressions in Different Forms
  Module 3, Section 5, Lesson 1 Rewriting Expressions in Different Forms
- Lesson 2: Identifying Equivalent Expressions
  Module 3, Section 5, Lesson 2 Identifying Equivalent Expressions


Module 4: Solving Linear Equations

Section 1: Linear Equation Basics
- Lesson 1: Recognizing Linear Equations
  Module 4, Section 1, Lesson 1 Recognizing Linear Equations
- Lesson 2: Identifying the Structure of Linear Equations
  Module 4, Section 1, Lesson 2 Identifying the Structure of Linear Equations

Section 2: One-Step Equations
- Lesson 1: Solving Equations by Addition/Subtraction
  Module 4, Section 2, Lesson 1 Solving Equations by Addition/Subtraction
- Lesson 2: Solving Equations by Multiplication/Division
  Module 4, Section 2, Lesson 2 Solving Equations by Multiplication/Division

Section 3: Two-Step Equations
- Lesson 1: Combining Operations for Two-Step Equations
  Module 4, Section 3, Lesson 1 Combining Operations for Two-Step Equations
- Lesson 2: Simplifying Equations Prior to Solving
  Module 4, Section 3, Lesson 2 Simplifying Equations Prior to Solving

Section 4: Multi-Step Equation Strategies
- Lesson 1: Planning the Sequence of Steps
  Module 4, Section 4, Lesson 1 Planning the Sequence of Steps
- Lesson 2: Working Symmetrically on Both Sides
  Module 4, Section 4, Lesson 2 Working Symmetrically on Both Sides

Section 5: Word Problems and Equations
- Lesson 1: Translating Word Problems into Equations
  Module 4, Section 5, Lesson 1 Translating Word Problems into Equations
- Lesson 2: Setting Up and Solving Contextual Equations
  Module 4, Section 5, Lesson 2 Setting Up and Solving Contextual Equations


Module 5: Applications of Algebraic Structures in Real-World Problems

Section 1: Algebra in Daily Life
- Lesson 1: Recognizing Algebra Around Us
  Module 5, Section 1, Lesson 1 Recognizing Algebra Around Us
- Lesson 2: Everyday Examples of Equations
  Module 5, Section 1, Lesson 2 Everyday Examples of Equations

Section 2: Interpreting Data with Equations
- Lesson 1: Reading Data and Identifying Trends
  Module 5, Section 2, Lesson 1 Reading Data and Identifying Trends
- Lesson 2: Creating Equations from Data Observations
  Module 5, Section 2, Lesson 2 Creating Equations from Data Observations

Section 3: Designing Simple Mathematical Models
- Lesson 1: Building Models from Real Scenarios
  Module 5, Section 3, Lesson 1 Building Models from Real Scenarios
- Lesson 2: Evaluating the Accuracy of Models
  Module 5, Section 3, Lesson 2 Evaluating the Accuracy of Models

Section 4: Scaling and Proportions
- Lesson 1: Understanding Ratios and Proportions
  Module 5, Section 4, Lesson 1 Understanding Ratios and Proportions
- Lesson 2: Using Equations in Scaling Techniques
  Module 5, Section 4, Lesson 2 Using Equations in Scaling Techniques

Section 5: Problem-Solving Approaches in Algebra
- Lesson 1: Developing Strategies for Solving Problems
  Module 5, Section 5, Lesson 1 Developing Strategies for Solving Problems
- Lesson 2: Review, Self-Assessment, and Reflection
  Module 5, Section 5, Lesson 2 Review, Self-Assessment, and Reflection