Lesson Plan

Resources → Subject Notes → Additional Mathematics → Notes
Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Use standard differentiation notation including first and second derivatives
Learning Objective/s:
  • Identify and write first and second derivatives using Leibniz and prime notation.
  • Explain the geometric meaning of f'(x) and f''(x) as gradient and curvature.
  • Apply differentiation rules (power, product, quotient, chain) to compute first and second derivatives of algebraic and trigonometric functions.
  • Check work by verifying consistency of notation and by differentiating again to obtain the second derivative.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with notation table and practice questions
  • Graph‑sketching handouts
  • Calculator (optional)
  • Whiteboard markers and erasers
 Introduction:
Begin with a quick visual of a curve and its tangent to spark curiosity about rates of change. Review that students already know the basic power rule and the concept of a derivative as a slope. Explain that today they will master standard notation for first and second derivatives and learn to choose the most efficient form for exam answers. Success will be measured by correctly writing notation and solving a set of practice problems.
Lesson Structure:
  1. Do‑now (5') – Students match derivative symbols to their meanings on a short worksheet.
  2. Mini‑lecture (10') – Demonstrate Leibniz vs. prime notation and show geometric interpretation with the suggested diagram.
  3. Guided practice (15') – Work through Example 1 and Example 2 together, emphasizing rule selection and notation consistency.
  4. Collaborative activity (10') – Pairs solve Example 3 (chain rule) on the whiteboard and peer‑check each other’s work.
  5. Differentiation rules drill (10') – Quick quiz on power, product, quotient, and chain rules using a clicker or Kahoot.
  6. Independent practice (15') – Students attempt the five practice questions, noting which notation they use.
  7. Exit ticket (5') – Write one correct first‑derivative notation and one second‑derivative notation for a given function.
Conclusion:
Summarise that correct notation not only earns marks but also clarifies the mathematical process. Invite a few volunteers to share their exit‑ticket answers and correct any lingering notation errors. Assign homework: complete a worksheet with additional differentiation problems, including both first and second derivatives. Remind students to check their work by differentiating again.