Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Understand the idea of a derived function as the rate of change and the link with gradients of curves
Learning Objective/s:
  • Describe the meaning of the derived function as an instantaneous rate of change.
  • Explain the relationship between the derivative and the gradient of a tangent to a curve.
  • Apply basic differentiation rules to find derivatives of common functions.
  • Use the derivative to determine the gradient at a specific point and write the tangent equation.
  • Solve short practice problems involving rates of change and tangent slopes.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice questions
  • Graph paper and rulers
  • Scientific calculators
  • Set of prepared function cards for rule practice
 Introduction:
Begin with a quick real‑world hook: ask students how speed tells us how far a car travels each second. Recall that they have already used average rate of change from linear graphs. Explain that today they will discover the instantaneous version – the derivative – and that success will be shown by correctly finding gradients and tangent equations.
Lesson Structure:
  1. Do‑now (5') – Students complete a short worksheet converting average rates to instantaneous rates from a table of points.
  2. Mini‑lecture (10') – Define derived function, notation, and link to tangent gradient using a diagram.
  3. Guided practice (12') – Work through the example \(y = 3x^{2}-5x+2\), differentiate and find the gradient at \(x=4\) together.
  4. Rule carousel (10') – In groups, each group receives a differentiation‑rule card, practices applying it to a function, then rotates.
  5. Independent practice (15') – Students attempt the five practice questions, checking answers with the answer key.
  6. Check for understanding (8') – Quick quiz on identifying correct derivative notation and writing the tangent equation using point‑slope form.
Conclusion:
Summarise that the derivative gives the instantaneous rate of change and the slope of the tangent. Ask a few students to share one answer from the practice set as a verbal exit ticket. Assign homework to complete a worksheet extending the differentiation rules to composite functions.