Advanced Counting Principles
Application of the Pigeonhole Principle, Inclusion-Exclusion Principle, and permutations or combinations with repetitions.
About This Topic
Application of the Pigeonhole Principle, Inclusion-Exclusion Principle, and permutations or combinations with repetitions.
Key Questions
- How do we count arrangements involving indistinguishable objects?
- When is the Inclusion-Exclusion Principle necessary for accurate counting?
- How can the Pigeonhole Principle be used to prove the existence of a specific outcome?
Active Learning Ideas
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Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.