Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Functions: further domain and range, modulus function, sketching graphs
Learning Objective/s:
  • Determine the domain of rational, radical, logarithmic and composite functions using a systematic four‑step procedure.
  • Solve absolute‑value equations and inequalities by splitting into cases.
  • Analyse and sketch the graph of a function by identifying domain, intercepts, symmetry, asymptotes, critical points and behaviour at boundaries.
  • Apply first‑ and second‑derivative tests to locate extrema and points of inflection for graphing purposes.
  • Communicate mathematical reasoning clearly in written work and oral explanations.
Materials Needed:
  • Projector and screen
  • Whiteboard and markers
  • Graphing calculators (or Desmos access)
  • Domain‑range worksheet
  • Absolute‑value practice handout
  • Graph paper and rulers
  • Exit‑ticket slips
 Introduction:
Begin with a quick mental puzzle: “What is the domain of f(x)=1/(x‑2)?” Review that students already know basic domain concepts and the definition of absolute value. Explain that today they will extend domain analysis to more complex expressions, master absolute‑value case work, and learn a systematic checklist for sketching graphs. Success will be shown by completing a worksheet correctly and presenting a clean graph sketch.
Lesson Structure:
  1. Do‑Now (5′): Individual domain‑identification worksheet on simple rational functions.
  2. Mini‑lecture (10′): Review restriction types (denominators, even roots, logs, composites) and model the four‑step domain procedure with f(x)=√(2x‑5)/(x²‑9).
  3. Guided practice (12′): Whole‑class work on similar domain problems; teacher elicits reasoning.
  4. Absolute‑value segment (10′): Define |x|, list key properties, solve |2x‑3|=5 and |x+2|<3 by case splitting; partner practice.
  5. Graph‑sketching checklist (8′): Introduce checklist items (domain, intercepts, symmetry, asymptotes, critical points, inflection points, boundary behaviour) and demonstrate on y=|x‑1|/(x²‑4).
  6. Independent practice (12′): Worksheet requiring domain determination, absolute‑value solution, and a full sketch of a new function; teacher circulates for support.
  7. Exit ticket (3′): Students write one key step they used for today’s problems and any remaining question.
Conclusion:
Recap that finding a domain involves listing all restrictions, solving the resulting inequalities and writing the answer in interval notation, while absolute‑value problems are handled by splitting into cases and graphing follows a structured checklist. Collect exit tickets to gauge understanding and clarify any lingering misconceptions. For homework, assign a set of functions for which students must determine the domain, solve an absolute‑value equation, and produce a neat sketch using the checklist.