Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Coordinate geometry: equations of lines and curves, parametric equations
Learning Objective/s:
  • Derive and apply gradient, intercept, and standard forms of a straight line.
  • Calculate the perpendicular distance from a point to a line using the distance formula.
  • Write and interpret standard Cartesian equations for circles, ellipses, parabolas and hyperbolas.
  • Convert between Cartesian and parametric representations for lines and conic sections.
  • Solve intersection problems between lines and curves by algebraic substitution.
Materials Needed:
  • Whiteboard and markers
  • Projector with slide deck of key formulas
  • Worksheet containing practice problems and a worked example
  • Graph paper or digital geometry app
  • Calculator or graphing calculator
  • Handout of the summary table of equations
 Introduction:
Begin with a quick visual of a line intersecting a circle on the board to spark curiosity. Review the slope‑intercept and standard forms of a line mastered previously, and state that today students will extend this knowledge to conic sections and parametric equations. Explain that success will be measured by correctly deriving equations, converting forms, and solving an intersection problem.
Lesson Structure:
  1. Do‑now (5') – Convert two given points into slope‑intercept and standard form on a short worksheet.
  2. Mini‑lecture (10') – Present gradient, intercept, and general forms; demonstrate the distance‑from‑point formula.
  3. Conic sections overview (12') – Introduce standard Cartesian equations for circles, ellipses, parabolas, and hyperbolas, highlighting key parameters.
  4. Parametric representation (10') – Show parametrisations for lines and each conic; work through a circle example.
  5. Guided practice (15') – Whole‑class walk‑through of the worked example (line‑circle intersection) with students following on their worksheets.
  6. Independent practice (10') – Students solve a similar line‑ellipse intersection and convert a parabola to parametric form.
  7. Check for understanding (5') – Exit ticket: write the parametric equations for a given hyperbola.
Conclusion:
Summarise how the different forms are inter‑related and why parametrisation is useful for solving geometry problems. Collect exit tickets and clarify any lingering misconceptions. Assign homework to complete a set of conversion and intersection problems from the worksheet.