Differentiation II

Grade 12 · Mathematics

Semester 2 | Period 4 | Week 19

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Subject: Mathematics

Semester: 2

Period: 4

Week: 19

WEEK 19

Class: Grade 12
Age: 17 years
Duration: 40 minutes x 5 periods
Subject: Mathematics
Topic: Differentiation II
Focus: Rules of Differentiation (Sum, Difference, Product, Quotient, Composite Functions), Application of Differentiation (Maxima, Minima, Acceleration, Velocity, Rate of Change)

 

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Apply the rules of differentiation to functions.
  2. Differentiate functions involving sums, differences, products, quotients, and composite functions.
  3. Solve problems using differentiation to determine maximum and minimum points, as well as acceleration, velocity, and rate of change.

 

INSTRUCTIONAL TECHNIQUES:

  • Direct instruction
  • Guided practice
  • Problem-solving
  • Collaborative exercises
  • Real-life applications (e.g., velocity, acceleration, rate of change)

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Standard derivative charts
  • Computer-assisted instructional materials (optional)

 

PERIOD 1 & 2: RULES OF DIFFERENTIATION (SUM, DIFFERENCE, PRODUCT, QUOTIENT, COMPOSITE FUNCTIONS)

PRESENTATION:

 

PRESENTATION:

Step

Teacher's Activity

Student's Activity

Step 1 - Review

Review all the rules of differentiation and their applications. Answer any questions that students have.

Students ask clarifying questions and review important points.

Step 2 - Problem Solving

Provide complex, real-life problems to solve using differentiation. Guide students through the process.

Students work individually or in pairs to solve problems.

Step 3 - Conclusion

Summarize the key points from the lesson. Emphasize the importance of differentiation in solving real-life problems.

Students take final notes and reflect on the applications of differentiation.

 

EVALUATION:

  1. Solve a problem involving velocity and acceleration.
  2. Differentiate a composite function and apply the chain rule.
  3. Find the maximum and minimum points of a quadratic function.