Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Solve problems involving midpoint and length of a line segment and find and use the equation of a perpendicular bisector
Learning Objective/s:
  • Describe how to find the midpoint of a line segment using coordinates.
  • Calculate the length of a line segment with the distance formula.
  • Derive and write the equation of a perpendicular bisector for any segment.
  • Apply these techniques to solve exam‑style geometry problems.
  • Identify and correct common errors related to slopes and vertical/horizontal cases.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice questions
  • Graph paper and rulers
  • Calculator (or graphing calculator)
  • Coordinate‑plane handouts
  • Markers / whiteboard pens
 Introduction:
Begin with a quick visual of two points on a grid and ask students how they could locate the exact centre of the segment. Review the midpoint and distance formulas they have already used in previous lessons. Explain that today they will extend this knowledge to find the equation of a perpendicular bisector, a key skill for IGCSE geometry. Success will be measured by correctly deriving and applying the bisector in practice problems.
Lesson Structure:
  1. Do‑Now (5') – Students complete a short worksheet finding midpoints and lengths of given segments to activate prior knowledge.
  2. Mini‑lecture (10') – Review formulas, demonstrate deriving the slope of a segment and the negative reciprocal, and introduce the point‑slope form for the perpendicular bisector.
  3. Guided practice (12') – Work through Worked Example 2 on the board, prompting students to suggest each step; check understanding with quick questions.
  4. Collaborative activity (15') – In pairs, students plot points, calculate midpoint, slope, and write the perpendicular bisector for a new set of coordinates; teacher circulates to provide feedback.
  5. Whole‑class discussion (5') – Groups share their equations; address common pitfalls such as vertical/horizontal cases.
  6. Exit ticket (3') – Each student writes the three‑step procedure for finding a perpendicular bisector on a sticky note.
Conclusion:
Summarise the three‑step process: midpoint, slope (negative reciprocal), and point‑slope equation. Ask a few students to verbally recap the steps to reinforce retention. Collect the exit tickets as a quick check and assign additional practice questions from the worksheet for homework.