Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Apply differentiation and integration to kinematics of a particle moving in a straight line, relating displacement, velocity and acceleration for constant or variable acceleration
Learning Objective/s:
  • Describe the relationship between displacement, velocity, and acceleration using calculus.
  • Differentiate a given displacement function to obtain velocity and acceleration.
  • Integrate a given acceleration function to obtain velocity and displacement, applying initial conditions.
  • Apply the constant‑acceleration equations derived from calculus to solve kinematic problems.
  • Solve variable‑acceleration problems by successive integration and interpret the results.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice questions
  • Graphing calculator or computer algebra system
  • Prepared example slides (PDF)
  • Ruler and graph paper for motion diagrams
  • Student notebooks and pens
 Introduction:
Begin with a quick recall of the definitions of displacement, velocity and acceleration. Connect these ideas to students’ prior experience with motion graphs. State the success criteria: students will be able to move between s(t), v(t) and a(t) using differentiation and integration, and apply the results to constant and variable acceleration problems.
Lesson Structure:
  1. Do‑now (5'): Answer three short questions on the meanings of s, v, a; teacher reviews answers.
  2. Mini‑lecture (10'): Review differentiation from s(t) to v(t) and a(t) with a worked example (s(t)=5t²+3t+2).
  3. Guided practice (12'): Integrate a(t)=6t to obtain v(t) and s(t), emphasizing the use of v₀ and s₀.
  4. Constant‑acceleration activity (10'): Derive the three classic kinematic equations via integration; students complete a brief worksheet.
  5. Variable‑acceleration exploration (12'): Solve the problem a(t)=4t, find v(t) and s(t) at t=3 s, using calculators for verification.
  6. Collaborative problem set (8'): Groups tackle practice questions 1‑4 from the source notes while the teacher circulates.
  7. Exit ticket (3'): Each student writes one key step for converting a variable acceleration function into a displacement expression.
Conclusion:
Recap the chain of relationships s → v → a and the reverse process using integration, highlighting the role of initial conditions. Collect exit tickets to gauge understanding, and assign homework: complete two additional kinematics problems (one constant‑acceleration, one variable‑acceleration) from the textbook.