In Lesson


Example Lesson: Year 12 Advanced Mathematics – Learning the Chain Rule

Objective: By the end of this lesson, students will be able to understand and apply the chain rule in differentiation.

Lesson Plan

1. Revise Homework and Previous Concepts (15 minutes)

  • Activity: Go over select problems from the previous homework set, such as questions from textbooks or provided worksheets.
  • Example Problem: Differentiate 𝑓(π‘₯)=sin⁑(π‘₯)π‘₯2+1
  • Solution: Using the quotient rule: 𝑓′(π‘₯)=cos⁑(π‘₯)(π‘₯2+1)βˆ’sin⁑(π‘₯)(2π‘₯)(π‘₯2+1)2
  • Purpose: Reinforce understanding of the quotient rule and ensure students have mastered previous concepts.

2. Learning New Material (45 minutes)

  • Concepts Covered:
    • Introduction to the chain rule of differentiation.
    • Theoretical perspective and practical applications.
  • Rule: The chain rule states that for a function 𝑦=𝑓(𝑒(π‘₯)), 𝑑𝑦𝑑π‘₯=𝑑𝑦𝑑𝑒⋅𝑑𝑒𝑑π‘₯
  • Example Problem: Differentiate 𝑦=sin⁑(3π‘₯2)
    • Solution: 𝑒(π‘₯)=3π‘₯2β€…β€ŠβŸΉβ€…β€Šπ‘‘π‘’π‘‘π‘₯=6π‘₯ 𝑦=sin⁑(𝑒)β€…β€ŠβŸΉβ€…β€Šπ‘‘π‘¦π‘‘π‘’=cos⁑(𝑒) 𝑑𝑦𝑑π‘₯=cos⁑(3π‘₯2)β‹…6π‘₯=6π‘₯cos⁑(3π‘₯2)
  • Interactive Discussion: Work through the theory and applications, with the tutor providing examples and guiding students through problems.

3. Applying and Practicing New Material (30 minutes)

  • Activity: Students practice the chain rule with a broader problem set.
  • Problems:
    • Differentiate 𝑦=(2π‘₯2+π‘₯βˆ’5)3
    • Differentiate 𝑦=sin⁑(3π‘₯2)
    • Differentiate 𝑦=(4π‘₯3βˆ’2π‘₯2+π‘₯βˆ’5)4
  • Purpose: Build and test competency in applying the chain rule.

4. Review of Topics (15 minutes)

  • Activity: Summarize key points and create annotated notes for review.
  • Discussion: Encourage students to ask questions and clarify doubts.
  • Purpose: Consolidate learning and ensure students understand the material.

5. Homework Assignment (10 minutes)

  • Assignment: Complete remaining problems from the worksheet and additional textbook exercises.
  • Problems:
    • Differentiate 𝑦=sin⁑((π‘₯2βˆ’3π‘₯)5)
    • Differentiate 𝑦=cos⁑(sin⁑(𝑒π‘₯2))
  • Purpose: Reinforce learning and prepare for the next lesson.

6. Goal Setting and Feedback (5 minutes)

  • Activity: Set learning goals for the next session and provide feedback.
  • Discussion: Reflect on the lesson, discuss challenges, and identify areas for improvement.
  • Purpose: Tailor future lessons to student needs and ensure continuous improvement.