Unit 2 Reasoning and Proof Unit 2 Reasoning

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Unit 2 Reasoning and Proof

Unit 2 Reasoning and Proof

Unit 2 - Reasoning and proof Learning Objectives: Learn about reasoning Make logical argument

Unit 2 - Reasoning and proof Learning Objectives: Learn about reasoning Make logical argument and conclusion Justify steps of by postulate or theorem Provide a convincing argument Refine thinking process

Unit 2 - Reasoning and proof 2 -1 Inductive and Deductive reasoning 2 -2

Unit 2 - Reasoning and proof 2 -1 Inductive and Deductive reasoning 2 -2 Conditional statements 2 -3 Postulate and Diagrams 2 -4 Algebraic Reasoning 2 -5 Proving Geometric Relationships

2 -1 Inductive and Deductive Reasoning Key Terms Inductive reasoning: making specific observations and

2 -1 Inductive and Deductive Reasoning Key Terms Inductive reasoning: making specific observations and then drawing broad conclusions or conjecture based on those observations. Deductive reasoning: the reasoning from proven facts, postulates, theorems, definition using logically valid steps to arrive at a conclusion. Postulate: A postulate is a statement that is assumed to be true without a proof. Example: Through any two points in a plane there is exactly one straight line. Theorem: A theorem is a statement that can be proven to be true based upon postulates and previously proven theorems. Example: The measures of the angles of a triangle add to 180 degrees.

2 -1 Inductive and Deductive Reasoning Lesson Aim: ü Define inductive reasoning. ü Define

2 -1 Inductive and Deductive Reasoning Lesson Aim: ü Define inductive reasoning. ü Define deductive reasoning. ü Apply inductive reasoning. ü Use deductive reasoning. ü Understand the difference between inductive and deductive reasoning.

Examples of Inductive Reasoning Question: What is the next term of this sequence? 1,

Examples of Inductive Reasoning Question: What is the next term of this sequence? 1, 3, 5, 7, 9, 11, … Answer: When you look at the pattern in the sequence of numbers, you notice number increased by 2. Therefore by inductive reasoning you can conclude that the next number is 13. Question: What is the next shape ?

Examples of Inductive Reasoning Q: What is the next shape? A: Looking at the

Examples of Inductive Reasoning Q: What is the next shape? A: Looking at the first three shapes with 3, 4, 5 sides leads you to believe that the next shape should have 6 sides. This is a type of logical reasoning called inductive reasoning which is based on studying patterns. Q: What is the next number in the sequence? 1/2, 2/6, 3/18, …. A: Looking at the first numbers leads you to conclude that the next number is 4/54. This is an inductive reasoning because of the pattern.

2 -1 Inductive and Deductive Reasoning

2 -1 Inductive and Deductive Reasoning

2 -1 Inductive and Deductive Reasoning

2 -1 Inductive and Deductive Reasoning

Reasoning and Proof Deductive Reasoning Deductive reasoning DeductiveReasoning and Proof Deductive Reasoning Deductive reasoning Deductive
Proof Techniques and Recursion Proof Techniques Proof byProof Techniques and Recursion Proof Techniques Proof by
Geometry Unit 2 Reasoning and Proof Proof withGeometry Unit 2 Reasoning and Proof Proof with
Proof of Work Proof of Stake Proof ofProof of Work Proof of Stake Proof of
Patterns and Inductive Reasoning Inductive reasoning is reasoningPatterns and Inductive Reasoning Inductive reasoning is reasoning
MOTIVATED REASONING MOTIVATED REASONING What is motivated reasoningMOTIVATED REASONING MOTIVATED REASONING What is motivated reasoning
Reasoning as Search Reasoning We can describe reasoningReasoning as Search Reasoning We can describe reasoning
CaseBased Reasoning CaseBased Reasoning CBR Casebased reasoning CBRCaseBased Reasoning CaseBased Reasoning CBR Casebased reasoning CBR
Inductive Reasoning v Deductive Reasoning Inductive reasoning movesInductive Reasoning v Deductive Reasoning Inductive reasoning moves