Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Sequences: patterns, nth term, recurrence relations
Learning Objective/s:
  • Identify the pattern of a given sequence (arithmetic, geometric, quadratic, or recursive).
  • Derive and write the explicit nth‑term formula for arithmetic, geometric and quadratic sequences.
  • Formulate and use recurrence relations to generate sequences and convert between explicit and recursive forms.
  • Check and verify formulas by substituting values and using a checklist.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with assorted sequences
  • Graph paper and calculators
  • Whiteboard markers
  • Index cards with sequence examples
  • Access to an online graphing tool (optional)
 Introduction:
Begin with a quick visual puzzle that shows a hidden pattern in a number line to spark curiosity. Recall the previous lesson’s work on arithmetic and geometric sequences. Explain that today students will extend this knowledge to quadratic patterns and recurrence relations, and they will be able to write both explicit and recursive formulas by the end of the lesson.
Lesson Structure:
  1. Do‑now (5'): Quick quiz on identifying arithmetic and geometric patterns from the previous lesson.
  2. Mini‑lecture (10'): Review pattern identification, introduce quadratic sequences and the concept of recurrence relations with board examples.
  3. Guided practice (15'): Solve Example 1 (arithmetic) and Example 2 (geometric) together, students record each step.
  4. Collaborative activity (15'): In pairs, analyse new sequences, determine the type, write the explicit nth‑term and an appropriate recurrence; teacher circulates for support.
  5. Check for understanding (5'): Exit ticket – write the nth‑term for a given sequence and state whether it is explicit or recursive.
  6. Summary & homework (5'): Recap the checklist, assign a worksheet with mixed sequence problems for reinforcement.
Conclusion:
Review the key steps of identifying patterns, deriving formulas, and converting between explicit and recursive forms. Collect exit tickets to gauge understanding and address any lingering misconceptions. For homework, students complete the worksheet that includes arithmetic, geometric, quadratic, and Fibonacci‑type sequences.