Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Solve graphically or algebraically inequalities involving moduli, including forms such as k|ax + b| > c, k|ax + b| ≤ c, k|ax + b| ≤ |cx + d|, |ax + b| ≤ cx + d and |ax² + bx + c| > or ≤ d
Learning Objective/s:
  • Describe the meaning of absolute value and state its fundamental properties.
  • Apply case‑splitting techniques to solve linear absolute‑value inequalities of the forms k|ax+b| > c and k|ax+b| ≤ c.
  • Solve inequalities that contain two absolute values by squaring and handling the resulting quadratic inequality.
  • Analyse and solve quadratic absolute‑value inequalities and interpret the solutions both algebraically and graphically.
Materials Needed:
  • Projector or interactive whiteboard
  • Whiteboard and markers
  • Graph paper and rulers
  • Worksheet with practice questions (including the examples)
  • Scientific calculators
  • Printed handout summarising case‑splitting rules
 Introduction:
Begin with a quick real‑world hook about measuring distances on a number line. Review the definition and key properties of absolute value that students have already learned. State that by the end of the lesson they will be able to solve a range of absolute‑value inequalities both algebraically and graphically, and demonstrate these solutions clearly.
Lesson Structure:
  1. Do‑now (5') – short quiz on absolute‑value properties and sign interpretation.
  2. Mini‑lecture (10') – introduce the general case‑splitting method for k|ax+b| ⧧ c and discuss sign reversal when k < 0.
  3. Guided practice (15') – work through Example 1 (3|2x‑5| > 9) and Example 2 (|4x+1| ≤ 2x‑3) step‑by‑step, modelling the algebraic process.
  4. Group activity (15') – students solve a set of practice problems (including a quadratic absolute‑value inequality) using both algebraic case‑splitting and a quick sketch on graph paper; teacher circulates to check reasoning.
  5. Whole‑class discussion (10') – share solutions, highlight common errors, demonstrate squaring method for k|ax+b| ≤ |cx+d|, and connect to the graphical approach.
  6. Exit ticket (5') – each student writes one solved inequality and one key tip they will remember for the exam.
Conclusion:
Recap the case‑splitting strategy and the importance of checking the sign conditions for each region. Collect the exit tickets to gauge understanding and assign the worksheet (including a graphical problem) as homework to reinforce the techniques learned today.