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## Lesson 1-1

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**Lesson 1-1**Patterns and Inductive Reasoning**Ohio Content Standards:**• Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. -Demonstrate fluency in computations using real numbers. -Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.**Ohio Content Standards:**• Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. -Demonstrate fluency in computations using real numbers. -Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. • Generalize and explain patterns and sequences in order to find the next term and the nth term.**Vocabulary:**• Inductive Reasoning –**Vocabulary:**• Inductive Reasoning – When you make a conclusion based on a pattern of examples or past events.**Find the next three terms of each sequence.**• 11.2, 9.2, 7.2, …**Find the next three terms of each sequence.**• 11.2, 9.2, 7.2, … • 6, 12, 24, …**Find the next three terms of the sequence:**• 101, 102, 105, 110, 117, …**Vocabulary:**• Conjecture –**Vocabulary:**• Conjecture – A conclusion that you reach based on inductive reasoning.**Vocabulary:**• Conjecture – A conclusion that you reach based on inductive reasoning. • Counterexample –**Vocabulary:**• Conjecture – A conclusion that you reach based on inductive reasoning. • Counterexample – an example that does not follow the conjecture, proving the conjecture false.**Jordan studied the data below and made the following**conjecture:**Jordan studied the data below and made the following**conjecture: • Multiplying a number by -1 produces a product that is less than -1.**Jordan studied the data below and made the following**conjecture: • Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1**Jordan studied the data below and made the following**conjecture: • Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1**Jordan studied the data below and made the following**conjecture: • Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1 100(-1) = -100 and -100 < -1**Jordan studied the data below and made the following**conjecture: • Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1 100(-1) = -100 and -100 < -1 300(-1) = -300 and -300 < -1**Jordan studied the data below and made the following**conjecture: • Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1 100(-1) = -100 and -100 < -1 300(-1) = -300 and -300 < -1 Find a counter example for his conjecture.**Assignment:**Pgs. 7 – 9 2 – 34 evens