Inductive and Deductive Reasoning

Objectives

• Content standards focus on understanding logic and reasoning
• Performance standards focus on communicating mathematical thinking when formulating and analyzing arguments
• Learning objectives for a 45-minute discussion include:
  • Defining inductive and deductive reasoning
  • Applying inductive and deductive reasoning in arguments
  • Appreciating the importance of inductive and deductive reasoning in real life
• The LC code for these objectives is M8GE-IIh-1

Content

• The main topic is using inductive or deductive reasoning in an argument

Learning Resources

• Resources include PowerPoint, IMs, and a laptop
• Teacher material pages are not specified
• Learner's material pages are from the Grade 8 Mathematics Learner’s Material (MELCS), pages 1-13
• Textbook pages are from Mathematics – Grade 8
• Other learning resources include Quarter 2 – Module 13: Using Inductive or Deductive Reasoning in an Argument, First Edition, 2020

Routinary Activities

• Class activities include:
  • Greetings
  • Prayer
  • Checking of Attendance
  • Setting of Standards

Procedures: Review

• The teacher conducts a review/drill of the previous lesson

Establishing Purpose

• Activity called "WHAT'S NEXT?" requires students to identify the next pattern in a sequence

Presentation - Key Terms

• Activity called "ASSEMBLE ME" involves arranging scrambled letters related to the topic
• Key terms include:
  • PATTERN: A sequence of repeating objects, shapes, or numbers
  • CONJECTURE: An educated guess based on observations, which may or may not be true
  • CONCLUSIONS: Statements arrived at by applying logical rules (syllogisms) to premises
  • DEDUCTIVE
  • INDUCTIVE
  • PREMISES: Generally accepted ideas, facts, or rules that lay the groundwork for a theory or general idea
  • ARGUMENT: A collection of statements or propositions that provide support or evidence for a conclusion

Inductive Reasoning

• Specific examples derive general rules, generalizations, or conclusions
• Conclusions are based on observed patterns
• Example:
  • If the sequence is 10, 20, 30, then the next term is 40
  • If the chair in the living room is red and the chair in the dining room is red, then all chairs in the house are red

Deductive Reasoning

• General statements derive a conclusion
• Parts include:
  • Hypothesis: A statement accepted or known at the beginning
  • Conclusion: A statement drawn from the hypothesis
• Example:
  • If Sally does not drink soft drinks, then she does not drink Cola
  • If all mathematics challengers are good in mathematics and Israel, Papasin, Torres, and Lebanon are math challenger contestants, then they are good in mathematics

Abstraction

• Inductive reasoning involves making general conclusions based on specific examples
• Deductive reasoning: Starts with a general rule or fact and applies it to a specific case to reach a certain conclusion

Application

• Inductive and deductive reasoning can be used in everyday life to:
  • See dark clouds every time when it rains, one might conclude that dark clouds mean rain
  • Apply if all dogs bark and Max is a dog, then Max must bark
• Reasoning helps in thinking logically, making decisions, and solving problems

Evaluation

• Identify the type of reasoning used in each situation (Inductive or Deductive)
• Examples include:
  • If the city alarm sounds at 9:00 P.M. every day, then it will sound at 9:00 P.M. (Inductive)
  • If no foreigner can be elected senator in the country and Peter is a foreigner, then Peter cannot be elected senator (Deductive)

Assignment

• Study in advance about the proof