Inductivereasoning and deductive 2013

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Inductivereasoning and deductive 2013

  1. 1. GT Geometry Drill10/3/13 1. What are the next two terms in the sequence? 1, 4, 9, 16... 2. Write a counterexample for the following statement: For any number m, 3m is odd.
  2. 2. Accept the two statements as given information. State the conclusion based on the information. • 1. AB is longer than BC; BC is longer than CD • 2. 12 is greater than integer M. M is greater than 8 • 3. 4x + 6 = 14, then x =?
  3. 3. Use inductive and deductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures. Objectives
  4. 4. Find the next item in the pattern. Example 1A: Identifying a Pattern January, March, May, ... The next month is July. Alternating months of the year make up the pattern.
  5. 5. Find the next item in the pattern. Example 1B: Identifying a Pattern 7, 14, 21, 28, … The next multiple is 35. Multiples of 7 make up the pattern.
  6. 6. Find the next item in the pattern. Example 1C: Identifying a Pattern In this pattern, the figure rotates 90° counter- clockwise each time. The next figure is .
  7. 7. Check It Out! Example 1 Find the next item in the pattern 0.4, 0.04, 0.004, … When reading the pattern from left to right, the next item in the pattern has one more zero after the decimal point. The next item would have 3 zeros after the decimal point, or 0.0004.
  8. 8. When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true. You may use inductive reasoning to draw a conclusion from a pattern. A statement you believe to be true based on inductive reasoning is called a conjecture.
  9. 9. Deductive reasoning is the process of using logic to draw conclusions from given facts, definitions, and properties.

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