Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Numerical methods: numerical solutions of equations, iterative methods
Learning Objective/s:
  • Describe the concept of root‑finding and why numerical methods are required.
  • Explain the principles and convergence criteria of bisection, Newton‑Raphson, secant, and fixed‑point iteration.
  • Apply each method to approximate a root of a given function to a specified tolerance.
  • Compare the efficiency and suitability of the methods for different problem conditions.
  • Evaluate the accuracy of obtained approximations using appropriate stopping criteria.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with example problems
  • Graphing calculator or computer with spreadsheet/IDE (e.g., Python)
  • Whiteboard and markers
  • Handout summarising algorithms and convergence tables
 Introduction:
Many real‑world equations cannot be solved exactly, so we turn to numerical techniques. Students should recall continuity, differentiability, and basic algebraic manipulation. By the end of the lesson they will be able to select an appropriate root‑finding method, execute it, and justify its convergence.
Lesson Structure:
  1. Do‑now (5'): Quick quiz on definitions of a root and continuity.
  2. Mini‑lecture (10'): Overview of the root‑finding problem and convergence criteria.
  3. Demonstration (10'): Teacher models the bisection method on the board with a sample function.
  4. Guided practice (15'): Pairs apply bisection to a new function and verify results with calculators.
  5. Newton‑Raphson tutorial (10'): Derive the formula, discuss pitfalls, and compute iterations for a given cubic.
  6. Secant & Fixed‑point stations (10'): Small groups rotate through worksheets applying each method.
  7. Comparison discussion (5'): Class summarises advantages/disadvantages using a comparison chart.
  8. Exit ticket (5'): Students write which method they would choose for a specified scenario and why.
Conclusion:
We recap the key ideas of each iterative method and emphasise checking convergence criteria before accepting a result. The exit ticket provides a quick retrieval check, and for homework students will solve a root‑finding problem using two different methods and reflect on the accuracy achieved.