Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Solve problems involving arc length and sector area of a circle using radian measure, including compound shapes
Learning Objective/s:
  • Describe radian measure and convert between degrees and radians.
  • Apply the formulas s = rθ and A = ½ r²θ to find arc lengths and sector areas.
  • Analyze and solve multi‑step problems involving compound shapes by decomposing them into simple circular parts.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with examples and practice questions
  • Ruler and compasses for drawing circles
  • Scientific calculator
  • Coloured markers / highlighters
  • Geometry software (e.g., GeoGebra) – optional
 Introduction:
Begin with a quick visual of a pizza slice to illustrate why radians are useful. Review that a full circle equals 2π rad and recall the degree‑to‑radian conversion. State that by the end of the lesson students will be able to compute arc lengths, sector areas and tackle compound figures.
Lesson Structure:
  1. Do‑now (5'): Students convert a set of angles between degrees and radians on mini‑whiteboards.
  2. Mini‑lecture (10'): Define radian, present conversion formulas, derive s = rθ and A = ½ r²θ with brief examples.
  3. Guided practice (12'): Work through Example 1 (arc length) and Example 2 (sector area) together, checking understanding.
  4. Independent practice (15'): Learners solve Example 3 (finding angle) and Example 4 (compound shape) plus two practice questions while teacher circulates.
  5. Compound‑shape activity (10'): Small groups break a given figure into simple parts, apply the appropriate formulas, combine results, and present their solution.
  6. Exit ticket (3'): Each student writes one key step for solving a compound‑shape problem.
Conclusion:
Summarise the conversion process and the two core formulas for arc length and sector area. Emphasise the strategy of dissecting complex figures into simple sectors or arcs before applying the formulas. Collect exit tickets and assign homework: three additional problems on arc length and sector area, including one compound‑shape question.