Reasoning In Geometry


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Reasoning In Geometry

  1. 1. Reasoning in Geometry Will Jaramillo
  2. 2.  “Logical Reasoning in Geometry” Project  Mr. Jaramillo  Objectives: Students will use technology to create a presentation on Geometric Reasoning. Students will discuss the significance and difference between inductive and deductive reasoning. In addition, students will explore the four statements (conditional, converse, inverse, and biconditional) to determine the truth value of each statement. Lastly, students must determine whether the conditional statement meets the conditions of a biconditional statement.  TEKS:  G.1.A: Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems.  G.2.B: Make conjectures and determine the validity of the conjectures.  G.3.B: Construct and justify statements about geometric figures, statements, and their properties.  G.3.D: Use inductive reasoning to formulate a conjecture.  G.3.E: Use deductive reasoning to prove a statement.  Criteria:  * Groups of 2  * Construct a PowerPoint Presentation  * Use voice recorder  * Use webcam  *Animations/Slide designs  Slides Must Include, But Not Limited To:  Title slide with names.  Deductive and Inductive Logic  An example, justifying if it is deductive or inductive.  Conditional statement with its converse, inverse, and Contrapositive.  Truth table with descriptions of statement validities.  Webcam, at least for the conclusion  Questions to Consider:  What is the difference between deductive and inductive reasoning?  What are the four types of conditional statements, and how do they relate?  When can a conditional statement also be written as a biconditional statement?  What did you learn from this project in terms of curriculum and technology?  What did you like most about the project? Least?  Grading Outline:  ______ 5 pts. At least 6 slides (MUST USE 6 x 6 RULE)!  ______ 4 pts. Use of voice recorder for at least one minute.  ______ 4 pts. Use of webcam to conclude the presentation.  ______ 5 pts. Conclusion answers questions 4 and 5.  ______ 5 pts. Creative show design.  ______ 8 pts. Deductive and Inductive Reasoning with original example and justifications.  ______ 10 pts. Four conditional statements with truth table and justifications.
  3. 3. Inductive vs. Deductive Reasoning  Inductive Reasoning:  Patterns of observation  Deductive Reasoning:  Logic with facts and properties.
  4. 4. Inductive or Deductive?  There is a myth that bumblebees should not fly because their weight is more than their wings can support. However, if you were to observe bumblebees, you would see that they fly.  Response? (Student’s use record narration, as on this slide) -Inductive Reasoning: observation, without logical facts or properties.
  5. 5. Conditional Statements  Conditional Statement means if p, then q  Converse Statement: if q, then p  Inverse Statement: if not p, then not q  Contrapositive Statement: if not q, then not p  Biconditional Statement: p if and only if q  Can reverse p and q as conditionals
  6. 6. Writing Statements  If it is a tiger, then it has four legs.  Converse Statement:  If it has four legs, then it is a tiger.  Inverse Statement:  If it is not a tiger, then it does not have four legs.  Contrapositive Statement:  If it does not have four legs, then it is not a tiger.
  7. 7. Verifying Validity p →q True p: It is a tiger q →p False q: It has four legs ~p → ~q False ~q → ~p True Since not all statements are true, this is not a tautology. Also, since all statements are not false, this is not a fallacy. This cannot be a biconditional statement (Converse Statement is false).
  8. 8. Project Evaluation