Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Sketch graphs of cubic polynomials and their moduli when given as a product of three linear factors, clearly showing intercepts
Learning Objective/s:
  • Describe how the leading coefficient determines the end‑behaviour of a cubic expressed as three linear factors.
  • Explain how to construct a sign chart to identify intervals where the cubic is positive or negative.
  • Apply the sign chart to sketch the cubic, marking all x‑ and y‑intercepts and estimating turning points.
  • Create the graph of the modulus function |f(x)| by reflecting any negative portions and labeling the resulting cusps.
Materials Needed:
  • Graph paper or digital graphing tool
  • Scientific calculators
  • Whiteboard and markers
  • Projector with slide set of examples
  • Worksheet containing practice cubic expressions
  • Rulers for neat sketches
 Introduction:
Begin with a quick recall of how the roots of a polynomial give the x‑intercepts and how the leading coefficient controls end‑behaviour. Prompt students to predict the shape of a cubic when its factors are shown. Explain that today they will sketch both the cubic and its modulus, and will be assessed on correctly labeling all intercepts and cusps.
Lesson Structure:
  1. Do‑now (5') – Students list the x‑ and y‑intercepts for a given cubic on mini‑whiteboards.
  2. Mini‑lecture (10') – Review the factor form f(x)=a(x‑p)(x‑q)(x‑r), discuss the role of a in end‑behaviour, and illustrate sign‑chart concept.
  3. Guided practice (15') – Whole‑class work through steps: identify factors, compute intercepts, build sign chart, sketch the basic cubic on the board.
  4. Paired activity (10') – Each pair selects a new cubic, constructs its sign chart, sketches the cubic and then the modulus |f(x)|, labeling cusps.
  5. Class check (10') – Pairs display sketches; teacher highlights common pitfalls (ordering roots, forgetting reflection, missing y‑intercept).
  6. Exit ticket (5') – Students write the three essential steps needed to sketch |f(x)| for any cubic.
Conclusion:
Recap the sequence: factor identification, intercept calculation, sign‑chart creation, cubic sketch, and modulus reflection with cusps. Collect exit tickets to gauge understanding, and assign the worksheet for homework, requiring students to complete three additional cubics and produce both graphs.