Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Circular measure: radian measure, arc length, area of sector, small angle approximations
Learning Objective/s:
  • Describe the definition of radian measure and convert between degrees and radians.
  • Apply the formulas s = rθ and A = ½ r²θ to find arc lengths and sector areas.
  • Use small‑angle approximations to estimate trigonometric values and assess their accuracy.
  • Solve contextual problems involving circular measure.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice problems
  • Compass and ruler for sketching circles
  • Scientific calculators
  • Formula cheat‑sheet handout
 Introduction:
Begin with a quick visual of a circle on the board and ask students how they would measure the angle formed by a slice of pizza. Recall that degrees are familiar, but introduce the radian as the natural unit linked to arc length. Explain that today’s success criteria are to convert between units, compute arc lengths and sector areas, and use small‑angle approximations accurately.
Lesson Structure:
  1. Do‑Now (5') – Students complete a short conversion table from degrees to radians on the worksheet.
  2. Direct instruction (10') – Explain radian definition, relationship to arc length, and derive s = rθ and A = ½ r²θ with examples.
  3. Guided practice (12') – Work through the two example problems together, using calculators for verification.
  4. Small‑angle activity (8') – Demonstrate sin≈θ, tan≈θ, cos≈1‑θ²/2; students estimate sin 0.05 and compare with calculator.
  5. Collaborative problem solving (10') – In pairs, students solve mixed problems (conversion, arc length, sector area, approximation) and check answers with peers.
  6. Exit ticket (5') – Each student writes one correct formula and one real‑world application of radian measure.
Conclusion:
Summarise the key formulas and why radians simplify calculations involving circles. Ask a few students to share their approximation results and discuss error bounds. For homework, assign a set of problems requiring conversion, arc‑length, sector‑area, and small‑angle calculations.