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2-1 Using Inductive Reasoning to Make Conjectures

2-1 Using Inductive Reasoning to Make Conjectures. Lesson Objectives. Use inductive reasoning to identify patterns and make conjectures Find counterexamples to disprove conjectures. Vocabulary. inductive reasoning: using specific cases to prove that a rule or statement is true

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2-1 Using Inductive Reasoning to Make Conjectures

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  1. 2-1 Using Inductive Reasoningto Make Conjectures

  2. Lesson Objectives • Use inductive reasoning to identify patterns and make conjectures • Find counterexamples to disprove conjectures

  3. Vocabulary • inductive reasoning: using specific cases to prove that a rule or statement is true • conjecture: a statement based on inductive reasoning that is believed to be true • counterexample: an example that shows a conjecture is NOT true

  4. Steps of Inductive Reasoning FIRST Identify a pattern SECOND Make a conjecture LASTLY Prove the conjecture as true or find a counterexample

  5. Example: Identifying a Pattern Find the next item in each pattern. • January, March, May, … Pattern: every other month (odd months) Next item: July B. 7, 14, 21, 28, … Pattern: multiples of 7 Next item: 35

  6. Example: Making a Conjecture Complete each conjecture. • The sum of two positive numbers is ____. List some examples and look for a pattern. The sum of two positive numbers is positive. • The area of a square with side length greater than 4 is _____ (greater/less) than its perimeter. Example: s = 5, A = 52 = 25, P = 4(5) = 20 The area of such a square is greater than its perimeter.

  7. Example: Making a Conjecture The heights of eight students in a class are recorded below. Make a conjecture based on the data.

  8. Example: Finding a Counterexample Show that each conjecture is false by finding a counterexample. • For every integer n, n3is positive. n = -3 (-3)3 = (-3)(-3)(-3) = -27 • Two complimentary angles are not congruent. 45 + 45 = 90 Two 45˚ angles are complimentary and congruent

  9. Example: Finding a Counterexample • Based on the data of students’ heights, every boy is at least 3 inches taller than the tallest girl.

  10. HW #10: p.77 #11-33 odd

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