Algebra Grade 9. Fundamentals of combinatorics, probability theory and statistics. Collection 1

Embark on an exciting journey through algebra! Our "Algebra Grade 9. Fundamentals of combinatorics, probability theory and statistics" course offers a dynamic learning experience that brings the principles of combinatorics, probability, and statistics to life. Through interactive lessons, quizzes, and engaging activities, students will gain a deep understanding of fundamental concepts.

Why choose our course:

• Interactive quizzes and tests: Test your knowledge and reinforce learning with engaging and challenging quizzes.
• Expertly crafted content: Developed by experienced educators to ensure high-quality and effective learning.
• Focus on analytical thinking: Encourage students to analyze combinatorial problems, apply probability theory, and develop statistical reasoning.

Course Module

Module 1: Fundamentals of combinatorics, probability theory and statistics

• Lesson 20: Combinatorial problems. Sum and product rules.
• Practice exercises.
• Practice exercises.
• Lesson 21: Random events. Frequency and probability.
• Practice exercises.
• Practice exercises.
• Lesson 22: Classical definition of probability.
• Practice exercises.
• Practice exercises.
• Lesson 23: Introduction to statistics. Statistical data representation and processing.
• Practice exercises.
• Practice exercises.
• Independent Homework №5
• Knowledge assessment tasks for §§ 21-24
• Review exercises for Module 4
• Key Takeaways from Module 4
• Final algebra course assessment tasks
• Advanced-level exercises
• Sample variant of the final written mathematics assessment

Expected Learning Outcomes

• Identifies combinatorial problems.
• Provides examples of:
  • Situations where the sum or product rule applies.
  • Random events.
  • Certain, impossible, and equally probable events.
  • Real-life scenarios involving probability-based decision-making.
  • Statistical data representation using tables, charts, and graphs.
• Explains concepts such as:
  • Event frequency, relative frequency, and probability.
  • Sampling.
  • Range, mode, median, and mean of a sample.
• Understands:
  • Conditions under which relative frequency estimates probability.
  • Situations where the classical definition of probability is applicable.
  • The stages of statistical research.
• Finds, organizes, and presents information using graphs and charts.
• Reads, compares, and analyzes statistical data in tables, diagrams, and graphs.
• Solves problems involving:
  • Combinatorial sum and product rules.
  • Frequency and relative frequency calculations.
  • Probability calculations using the classical definition.
  • Statistical data representation.
  • Sample numerical characteristics calculation.

By the end of this course, students will have a thorough understanding of combinatorics, probability theory, and statistics, their applications, and problem-solving methods.