Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Apply differentiation to connected rates of change, small increments and approximations
Learning Objective/s:
  • Describe the concept of related rates and how differentiation links variable changes.
  • Apply the chain rule to derive formulas for connected rates of change.
  • Use linearisation to estimate small increments in functions.
  • Construct and use tangent‑line approximations for quick evaluations.
  • Solve typical IGCSE Additional Mathematics problems involving rates, increments, and approximations.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice questions
  • Graph paper and calculators
  • Prepared diagrams (expanding circle, ladder, sphere)
  • Whiteboard markers
  • Formula summary handout
 Introduction:
Begin with a quick real‑world scenario of an oil spill expanding to capture students' interest. Review the derivative as a rate of change and recall the chain rule from previous lessons. Explain that by the end of the lesson they will be able to model and solve related‑rate problems and make accurate approximations.
Lesson Structure:
  1. Do‑now (5') – Estimate √26 using known squares; discuss answers.
  2. Mini‑lecture (10') – Present key concepts of related rates, small increments, and linear approximation; highlight formulas.
  3. Guided example (15') – Work through the expanding‑circle problem, prompting students to write the relationship, differentiate, and substitute.
  4. Collaborative practice (20') – In pairs, solve the ladder and temperature‑rate problems while the teacher circulates.
  5. Approximation activity (10') – Demonstrate linear approximation for ln(1.05) and volume change; students complete a short worksheet.
  6. Check for understanding (5') – Quick quiz on selecting the appropriate formula for a given scenario.
  7. Summary & reflection (5') – Review objectives, clarify misconceptions, and collect exit tickets.
Conclusion:
Summarise how differentiation connects changing quantities and enables quick estimates. Ask students to write one takeaway on an exit ticket. Assign homework: complete the remaining practice questions and prepare a short explanation of a real‑world related‑rate situation.