Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: The normal distribution: properties, applications, approximations
Learning Objective/s:
  • Describe the definition, mean, standard deviation, and symmetry of the normal distribution.
  • Apply the Empirical Rule to estimate probabilities within 1, 2, and 3 standard deviations.
  • Use Z‑tables to find tail and two‑tailed probabilities and to determine percentiles.
  • Approximate a binomial distribution with a normal distribution, including continuity correction.
  • Solve A‑Level style problems involving probability calculations and inverse normal calculations.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed handouts of Z‑table
  • Calculator (or graphing calculator)
  • Worksheet with practice problems (including binomial approximation)
  • Whiteboard and markers
  • Sample data set (e.g., heights) for real‑world example
 Introduction:
Begin with a quick recall of the Empirical Rule and ask students where they have seen bell‑shaped curves in real life. Build on their understanding of mean and standard deviation from previous lessons. Today they will be able to standardise any normal variable, use a Z‑table to find probabilities and percentiles, and apply the normal approximation to binomial problems.
Lesson Structure:
  1. Do‑now (5’) – Short quiz on mean, SD, and symmetry of the normal curve.
  2. Direct instruction (10’) – Define normal distribution, introduce the standard normal and Z‑transformation; demonstrate on projector.
  3. Guided practice (12’) – Read a Z‑table and compute probabilities for given intervals; teacher circulates.
  4. Empirical Rule activity (8’) – Quick estimation tasks using the 68‑95‑99.7% rule; discuss answers.
  5. Binomial approximation (15’) – Explain conditions, continuity correction, then solve the example B~Bin(40,0.3) together.
  6. Independent practice (10’) – Worksheet: find percentiles, compute tail probabilities, apply normal approximation.
  7. Exit ticket (5’) – Each student writes one correct statement about when the normal approximation is appropriate and one step of the Z‑conversion.
Conclusion:
Review the key steps: identify μ and σ, standardise, use the Z‑table, and apply continuity correction when approximating a binomial. For the exit ticket, each student recorded the appropriate use of the normal approximation. Assign homework: a set of A‑Level style questions requiring probability calculations, percentile finding, and a binomial‑to‑normal approximation.