Further Mathematics - Senior Secondary 2 - Logical reasoning

Logical reasoning

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TERM: 1ST TERM

WEEK 10
Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Logical Reasoning
Focus:
i. Fundamental issues in intelligent systems
ii. Fundamental definition
iii. Modeling the world

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

  1. Identify and understand the fundamental issues in intelligent systems.
  2. Define logical reasoning in the context of intelligent systems.
  3. Explore how logical reasoning models the world around us.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided discussion
• Demonstration
• Group activities
• Practice exercises

INSTRUCTIONAL MATERIALS:
• Whiteboard and markers
• Charts showing critical issues in intelligent systems
• Flashcards with logical reasoning problems
• Worksheets for modeling exercises

 

PERIOD 1 & 2: Introduction to Logical Reasoning in Intelligent Systems
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Introduces the concept of logical reasoning in intelligent systems. Explains that intelligent systems mimic human reasoning, and logical reasoning is a foundation for problem-solving.

Students listen and ask questions for clarification.

Step 2 - Fundamental Issues in Intelligent Systems

Guides students to identify fundamental issues such as perception, knowledge representation, and decision-making in intelligent systems.

Students identify key issues in intelligent systems and share their thoughts.

Step 3 - Definition of Logical Reasoning

Defines logical reasoning as the process of using facts to draw conclusions. Gives examples of how reasoning is applied in artificial intelligence.

Students listen attentively and discuss the real-world applications of logical reasoning.

Step 4 - Modeling the World

Explains how intelligent systems model the world using logical structures. Demonstrates examples of decision trees, knowledge bases, and reasoning algorithms.

Students observe the examples and participate in modeling exercises.

NOTE ON BOARD:
Logical Reasoning in Intelligent Systems:

  1. Perception: How systems sense and interpret information.
  2. Knowledge Representation: How information is structured and stored.
  3. Decision Making: How systems make informed decisions based on logic.

EVALUATION (5 exercises):

  1. Define logical reasoning in the context of intelligent systems.
  2. What are the fundamental issues in intelligent systems?
  3. Give an example of knowledge representation in artificial intelligence.
  4. Why is logical reasoning important in modeling the world?
  5. Describe one real-world application of intelligent systems using logical reasoning.

CLASSWORK (5 questions):

  1. Identify the fundamental issue in intelligent systems related to perception.
  2. How do intelligent systems model the world?
  3. What is the role of decision-making in intelligent systems?
  4. Provide an example of knowledge representation in AI.
  5. Explain how logical reasoning can solve a problem in intelligent systems.

ASSIGNMENT (5 tasks):

  1. Research an intelligent system and describe its use of logical reasoning.
  2. Explain how decision trees are used in modeling intelligent systems.
  3. Define knowledge representation and provide an example.
  4. Think of a scenario where intelligent systems might face challenges in decision-making.
  5. Write a short essay on the importance of logical reasoning in artificial intelligence.

 

PERIOD 3 & 4: Application of Logical Reasoning to Model the World
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the role of logical reasoning in creating models of real-world situations.

Students engage by providing examples of real-world problems that require modeling.

Step 2 - Guided Practice

Demonstrates how to apply logical reasoning to model problems (e.g., weather prediction, traffic management).

Students follow along and participate in applying logical reasoning to simple problems.

Step 3 - Group Activity

Divides the class into small groups. Each group works on a different problem and applies logical reasoning to model a solution (e.g., traffic flow, decision-making for a store’s inventory).

Students work collaboratively within their groups to solve the problem.

Step 4 - Discussion

Each group presents its solution to the class, discussing the logical reasoning and modeling steps they took.

Students listen to each group's presentation and ask questions.

NOTE ON BOARD:
Modeling the World Using Logical Reasoning:

  1. Identify the problem.
  2. Choose a logical model (e.g., decision trees, algorithms).
  3. Apply the reasoning process to solve the problem.
  4. Present the solution using logical conclusions.

EVALUATION (5 exercises):

  1. How can logical reasoning be used to model real-world problems?
  2. Explain how decision trees are used in traffic management.
  3. Describe a scenario where knowledge representation would help solve a problem.
  4. What are the steps involved in modeling a problem using logical reasoning?
  5. Discuss one challenge in applying logical reasoning to real-world problems.

CLASSWORK (5 questions):

  1. How would you use logical reasoning to solve a weather forecasting problem?
  2. Provide an example of a real-world problem that could be modeled using logical reasoning.
  3. What is the importance of decision-making in intelligent systems?
  4. How does knowledge representation aid in intelligent system development?
  5. Why is logical reasoning important for artificial intelligence development?

ASSIGNMENT (5 tasks):

  1. Research how intelligent systems are used in self-driving cars.
  2. Explain how logical reasoning helps in healthcare decision-making systems.
  3. Write about a scenario where logical reasoning failed in a system.
  4. Provide a real-world example of a problem that could be solved using knowledge representation.
  5. Discuss how artificial intelligence uses logical reasoning to improve its decision-making process.