Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Algebra: partial fractions, series, binomial expansion
Learning Objective/s:
  • Describe the method for decomposing rational functions into partial fractions.
  • Apply formulas for arithmetic, geometric, and power series to compute sums and test convergence.
  • Derive and use the binomial theorem and its generalized form for series expansions.
  • Solve problems involving partial fraction decomposition, series summation, and binomial approximations.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with decomposition and series problems
  • Calculator (or graphing calculator)
  • Algebraic formula cards (partial fractions, series sums, binomial coefficients)
  • Whiteboard markers and eraser
 Introduction:
Begin with a quick mental‑math challenge: simplify the rational expression (3x²+5x+2)/((x‑1)(x+2)²) by guessing its decomposition. Review prior work on factoring polynomials and summing series, linking these to today’s objectives. Explain that by the end of the lesson students will be able to decompose fractions, evaluate series, and expand binomials confidently.
Lesson Structure:
  1. Do‑now (5') – short worksheet on factoring denominators and identifying series types; teacher circulates.
  2. Direct instruction – Partial fractions (15') – present the general procedure, work through the example, demonstrate coefficient comparison.
  3. Guided practice – Partial fractions (10') – students pair‑work a new decomposition, share results, teacher feedback.
  4. Mini‑lecture – Series formulas (10') – review arithmetic and geometric series, introduce the Ratio Test with quick examples.
  5. Collaborative activity – Series & binomial expansion (10') – groups expand (1‑x)⁻¹ and (1+2x)^{1/2} using the binomial theorem, check convergence conditions.
  6. Exit ticket (5') – each student writes one correct partial‑fraction decomposition and one series convergence statement.
  7. Homework reminder (5') – assign a worksheet covering all three topics for reinforcement.
Conclusion:
Summarise how partial‑fraction decomposition simplifies integration, how series formulas give quick sums, and how the binomial theorem provides useful approximations. Invite a few students to share one key insight from today’s activities. Collect exit tickets as a retrieval check and assign practice problems for further consolidation.