Review and 1.1 Patterns and Inductive Reasoning

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Presentation transcript:

Review and 1.1 Patterns and Inductive Reasoning “Our character is basically a composite of our habits. Because they are consistent, often unconscious patterns, they constantly, daily, express our character…” -Stephen R. Covey

Inductive reasoning is reasoning based on patterns you observe. Examples: Find the pattern of the sequence and show the next two terms or symbols. 2, 4, 8, 16, … 1, 3, 7, 13, 21, …

Using Inductive Reasoning A conjecture is a conclusion you reach using inductive reasoning. Example: Sum of odd numbers. 1 1 + 3 1 + 3 + 5 1 + 3 + 5 + 7 = 1 = 4 = 9 = 16 = 12 = 22 = 32 = 42 What is the sum of the first 30 odd numbers? The first 35 odd numbers? Conjecture:

Using Inductive Reasoning A conjecture is a conclusion you reach using inductive reasoning. Example: Sum of even numbers. 2 2 + 4 2 + 4 + 6 2 + 4 + 6 + 8 = 2 = 6 = 12 = 20 = 1(1 +1) = 2(2+1) = 3(3+1) = 4(4+1) What is the sum of the first 30 even numbers? The first 35 even numbers? Conjecture:

Using Inductive Reasoning A counterexample to a conjecture is an example where the conjecture does not work. Example: Find a counterexample to the statements. “If a number is divisible by 2, then it is also divisible by 6.” “You can connect any three points to form a triangle.”

Practice: Inductive Reasoning Worksheet 1.1 Patterns and Inductive Reasoning Practice: Inductive Reasoning Worksheet Terms: inductive reasoning, conjecture, counterexample “Our character is basically a composite of our habits. Because they are consistent, often unconscious patterns, they constantly, daily, express our character…” -Stephen R. Covey

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