Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Form and use composite functions, understanding that the order of composition is important
Learning Objective/s:
  • Describe the definition of a composite function and the notation $f\circ g$.
  • Explain why the order of composition affects the result and identify when functions commute.
  • Apply the step‑by‑step procedure to form and simplify composite functions.
  • Determine the domain of a composite function based on the inner and outer functions.
  • Solve practice problems involving composite functions and avoid common errors.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheets with practice questions
  • Graphing calculator or algebra software
  • Whiteboard markers and erasers
  • Set of function cards for a quick activity
 Introduction:
Begin with a quick real‑world example, such as applying a tax calculation after a discount, to highlight why the order matters. Review the definition of a function and remind students of substitution skills from previous lessons. State that by the end of the lesson they will be able to correctly form, simplify and state the domain of composite functions.
Lesson Structure:
  1. Do‑now (5'): Students identify inner and outer functions from a short worksheet.
  2. Mini‑lecture (10'): Define composite functions, notation, and illustrate order importance with a flowchart.
  3. Guided practice (15'): Work through the example $f(x)=2x+3$, $g(x)=x^{2}-1$ to form $(f\circ g)(x)$ and $(g\circ f)(x)$ step‑by‑step.
  4. Independent practice (15'): Students solve the four practice questions while the teacher circulates.
  5. Common pitfalls check (5'): Class discussion using the checklist of typical errors.
  6. Exit ticket (5'): Write one correct composite function with its domain and note one mistake to avoid.
Conclusion:
Summarise that the order of composition changes the resulting expression and domain, reinforcing the step‑by‑step method. Collect exit tickets as a quick retrieval check. Assign homework: complete two additional composite‑function problems from the textbook and prepare a short explanation of why $f\circ g \neq g\circ f$ for non‑commuting functions.