Lesson Plan

• Describe factorial notation and its role in counting.
• Distinguish between permutations and combinations and state when order matters.
• Apply formulas for permutations (with/without repetition) and combinations (including stars‑and‑bars) to solve problems.
• Solve multi‑step counting scenarios such as password creation.
• Identify common pitfalls and check solutions for consistency.

• Projector or interactive whiteboard
• Printed worksheet with practice questions
• Calculator (optional)
• Index cards or tiles for hands‑on arranging activity
• Formula summary handout
• Whiteboard markers

Begin with a quick brain‑teaser: “How many different 3‑letter codes can be made from the letters A‑F?” This activates prior knowledge of counting and highlights the importance of order. Review the factorial concept from previous lessons. State that by the end of the lesson students will be able to choose and arrange objects correctly and spot common errors.

1. Do‑now (5') – Mini‑whiteboard task on a simple permutation; teacher circulates for immediate feedback.
2. Mini‑lecture (10') – Introduce/refresh factorial notation, then present permutation formulas (no repetition, with repetition, repeated objects) with brief examples.
3. Guided practice (12') – Demonstrate combination formulas and stars‑and‑bars on the projector; students complete guided notes.
4. Collaborative activity (15') – Groups use index cards to model arrangements and selections, record counts, and discuss why order matters.
5. Worked example (8') – Solve the password problem step‑by‑step, emphasizing breaking a problem into independent stages.
6. Check for understanding (5') – Exit‑ticket quiz: one permutation question and one combination question.
7. Summary & reflection (5') – Review objectives, students self‑assess mastery, teacher clarifies any lingering doubts.

Recap the key formulas and the distinction between ordered and unordered selections. Collect exit tickets to gauge individual understanding and assign a short homework set of mixed permutation/combination problems for reinforcement.