Lesson Plan

• Apply basic differentiation rules to obtain f '(x) for a given function.
• Determine the gradient of a curve at a specified point by evaluating f '(x).
• Construct the equation of the tangent line using point‑slope form.
• Derive the normal line equation as the negative reciprocal of the tangent gradient.
• Identify and handle special cases (horizontal/vertical tangents) and simplify final equations.

• Projector and screen
• Whiteboard and coloured markers
• Graphing calculators (or Desmos access)
• Worksheet with practice questions and worked examples
• Printed handout of basic differentiation rules
• Rulers and graph paper for sketching curves
• Student notebooks

Begin with a short video showing how engineers use tangents to design roads, linking the concept to real‑world problems. Review that the derivative gives the instantaneous gradient of a curve, which they have already used for simple functions. State that by the end of the lesson they will be able to find and write the equations of both tangent and normal lines for any curve. Success criteria: correct derivative, accurate gradient at the point, and properly formatted line equations.

1. Do‑now (5') – Quick quiz on basic differentiation rules (constants, powers, trig).
2. Mini‑lecture (10') – Introduce gradient function, tangent/normal formulas, and special cases (vertical/horizontal).
3. Guided Example 1 (15') – Work through the cubic curve y = 2x³‑3x²+x‑5 at x=2, modelling each step on the board.
4. Guided Example 2 (15') – Implicit differentiation for the circle x²+y²=25 at (3,4); students complete in pairs.
5. Independent Practice (15') – Students solve 3 practice questions from the worksheet while teacher circulates.
6. Check for Understanding (5') – Exit ticket: give a function and point, write the gradient and tangent equation.
7. Summary (5') – Recap the four‑step procedure and highlight common pitfalls.

Review the key steps: differentiate, evaluate at the point, use point‑slope for the tangent, then take the negative reciprocal for the normal. Collect exit tickets to gauge understanding and address any lingering errors. For homework, assign the remaining practice questions from the worksheet, encouraging students to check their work against the summary checklist.