Math Competitions and Olympiad Training

          Module 1: Mathematical Foundations

Section 1: Arithmetic and Number Sense  
- Lesson 1: Introduction to Whole Numbers  
  Module 1, Section 1, Lesson 1: Introduction to Whole Numbers  
- Lesson 2: Basic Operations and Mental Math  
  Module 1, Section 1, Lesson 2: Basic Operations and Mental Math  

Section 2: Fractions, Decimals, and Percentages  
- Lesson 1: Understanding Fractions and Decimals  
  Module 1, Section 2, Lesson 1: Understanding Fractions and Decimals  
- Lesson 2: Real-World Applications of Percentages  
  Module 1, Section 2, Lesson 2: Real-World Applications of Percentages  

Section 3: Introduction to Ratios and Proportions  
- Lesson 1: Basic Concepts of Ratios  
  Module 1, Section 3, Lesson 1: Basic Concepts of Ratios  
- Lesson 2: Solving Proportions in Everyday Problems  
  Module 1, Section 3, Lesson 2: Solving Proportions in Everyday Problems  

Section 4: Fundamentals of Algebra  
- Lesson 1: Variables, Expressions, and Simple Equations  
  Module 1, Section 4, Lesson 1: Variables, Expressions, and Simple Equations  
- Lesson 2: Techniques for Solving Basic Equations  
  Module 1, Section 4, Lesson 2: Techniques for Solving Basic Equations  

Section 5: Logical Thinking and Basic Problem-Solving  
- Lesson 1: Developing Logical Reasoning Skills  
  Module 1, Section 5, Lesson 1: Developing Logical Reasoning Skills  
- Lesson 2: Step-by-Step Approaches to Problem Solving  
  Module 1, Section 5, Lesson 2: Step-by-Step Approaches to Problem Solving


Module 2: Number Theory and Algebraic Reasoning

Section 1: Prime Numbers and Divisibility  
- Lesson 1: Fundamentals of Prime Numbers  
  Module 2, Section 1, Lesson 1: Fundamentals of Prime Numbers  
- Lesson 2: Basic Divisibility Rules and Their Applications  
  Module 2, Section 1, Lesson 2: Basic Divisibility Rules and Their Applications  

Section 2: Factors, Multiples, and Exponents  
- Lesson 1: Understanding Factors and Multiples  
  Module 2, Section 2, Lesson 1: Understanding Factors and Multiples  
- Lesson 2: Introduction to Exponents as Repeated Multiplication  
  Module 2, Section 2, Lesson 2: Introduction to Exponents as Repeated Multiplication  

Section 3: Introduction to Modular Arithmetic  
- Lesson 1: Understanding Remainders in Division  
  Module 2, Section 3, Lesson 1: Understanding Remainders in Division  
- Lesson 2: Simple Problems Using Modular Concepts  
  Module 2, Section 3, Lesson 2: Simple Problems Using Modular Concepts  

Section 4: Algebraic Manipulation Techniques  
- Lesson 1: Simplifying Expressions  
  Module 2, Section 4, Lesson 1: Simplifying Expressions  
- Lesson 2: Basic Factoring Methods  
  Module 2, Section 4, Lesson 2: Basic Factoring Methods  

Section 5: Equations and Inequalities Fundamentals  
- Lesson 1: Solving Basic Linear Equations  
  Module 2, Section 5, Lesson 1: Solving Basic Linear Equations  
- Lesson 2: Understanding and Solving Simple Inequalities  
  Module 2, Section 5, Lesson 2: Understanding and Solving Simple Inequalities 


Module 3: Combinatorics and Probability

Section 1: Basic Counting Principles  
- Lesson 1: Introduction to Counting Techniques  
  Module 3, Section 1, Lesson 1: Introduction to Counting Techniques  
- Lesson 2: The Concept of Permutations in Simple Scenarios  
  Module 3, Section 1, Lesson 2: The Concept of Permutations in Simple Scenarios  

Section 2: Combinations and Arrangements  
- Lesson 1: Understanding Combinations and When to Use Them  
  Module 3, Section 2, Lesson 1: Understanding Combinations and When to Use Them  
- Lesson 2: Solving Simple Arrangement Problems  
  Module 3, Section 2, Lesson 2: Solving Simple Arrangement Problems  

Section 3: Fundamentals of Probability  
- Lesson 1: Basic Concepts and Definitions of Probability  
  Module 3, Section 3, Lesson 1: Basic Concepts and Definitions of Probability  
- Lesson 2: Calculating Probabilities in Everyday Situations  
  Module 3, Section 3, Lesson 2: Calculating Probabilities in Everyday Situations  

Section 4: Counting Puzzles and Logical Challenges  
- Lesson 1: Introduction to Counting-Based Puzzles  
  Module 3, Section 4, Lesson 1: Introduction to Counting-Based Puzzles  
- Lesson 2: Strategies for Tackling Logical Counting Problems  
  Module 3, Section 4, Lesson 2: Strategies for Tackling Logical Counting Problems  

Section 5: Data Interpretation and Basic Statistics  
- Lesson 1: Reading and Interpreting Graphs  
  Module 3, Section 5, Lesson 1: Reading and Interpreting Graphs  
- Lesson 2: Introduction to Mean, Median, and Mode  
  Module 3, Section 5, Lesson 2: Introduction to Mean, Median, and Mode


Module 4: Geometry and Spatial Reasoning

Section 1: Basics of Euclidean Geometry  
- Lesson 1: Understanding Points, Lines, and Angles  
  Module 4, Section 1, Lesson 1: Understanding Points, Lines, and Angles  
- Lesson 2: Basic Geometric Constructions and Diagrams  
  Module 4, Section 1, Lesson 2: Basic Geometric Constructions and Diagrams  

Section 2: Triangles and Polygons  
- Lesson 1: Properties and Types of Triangles  
  Module 4, Section 2, Lesson 1: Properties and Types of Triangles  
- Lesson 2: Exploring Regular and Irregular Polygons  
  Module 4, Section 2, Lesson 2: Exploring Regular and Irregular Polygons  

Section 3: Circle Fundamentals  
- Lesson 1: Introduction to Circles and Arcs  
  Module 4, Section 3, Lesson 1: Introduction to Circles and Arcs  
- Lesson 2: Basic Properties and Measurements in Circles  
  Module 4, Section 3, Lesson 2: Basic Properties and Measurements in Circles  

Section 4: Geometric Transformations  
- Lesson 1: Understanding Symmetry and Reflection  
  Module 4, Section 4, Lesson 1: Understanding Symmetry and Reflection  
- Lesson 2: Introduction to Rotations and Translations  
  Module 4, Section 4, Lesson 2: Introduction to Rotations and Translations  

Section 5: Problem-Solving with Geometry  
- Lesson 1: Visualizing and Analyzing Geometric Problems  
  Module 4, Section 5, Lesson 1: Visualizing and Analyzing Geometric Problems  
- Lesson 2: Developing Strategies for Geometry Competitions  
  Module 4, Section 5, Lesson 2: Developing Strategies for Geometry Competitions


Module 5: Problem Solving Strategies and Competition Preparation

Section 1: Reading and Analyzing Problems  
- Lesson 1: Techniques for Understanding Problem Statements  
  Module 5, Section 1, Lesson 1: Techniques for Understanding Problem Statements  
- Lesson 2: Identifying Key Information and Clues  
  Module 5, Section 1, Lesson 2: Identifying Key Information and Clues  

Section 2: Time Management and Strategic Approaches  
- Lesson 1: Managing Time During Competitions Effectively  
  Module 5, Section 2, Lesson 1: Managing Time During Competitions Effectively  
- Lesson 2: Quick Decision Making and Prioritizing Problems  
  Module 5, Section 2, Lesson 2: Quick Decision Making and Prioritizing Problems  

Section 3: Practical Exercises with Past Olympiad Problems  
- Lesson 1: Solving Basic-Level Past Olympiad Problems  
  Module 5, Section 3, Lesson 1: Solving Basic-Level Past Olympiad Problems  
- Lesson 2: Group Discussion and Step-by-Step Solution Analysis  
  Module 5, Section 3, Lesson 2: Group Discussion and Step-by-Step Solution Analysis  

Section 4: Strategies for Multiple Choice and Short Answer Questions  
- Lesson 1: Approaches and Techniques for Multiple Choice Problems  
  Module 5, Section 4, Lesson 1: Approaches and Techniques for Multiple Choice Problems  
- Lesson 2: Developing Precision in Short Answer Responses  
  Module 5, Section 4, Lesson 2: Developing Precision in Short Answer Responses  

Section 5: Review, Test-Taking Tactics, and Mental Preparation  
- Lesson 1: Revisiting Key Concepts and Techniques  
  Module 5, Section 5, Lesson 1: Revisiting Key Concepts and Techniques  
- Lesson 2: Final Strategies for Test-Taking and Competition Mindset  
  Module 5, Section 5, Lesson 2: Final Strategies for Test-Taking and Competition Mindset