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Published byTodd Dennis Modified about 1 year ago

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Notes 1.1

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Vocabulary Conjecture: an unproven statement that is based on truths Inductive Reasoning: a process that includes looking for patterns and making conjectures Counterexample: an example that shows that a conjecture is false

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Example 1: Designing a Pattern Sketch the next figure in the pattern

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Example 2: Describing a Number Pattern Describe a pattern in the sequence of numbers. Predict the next two numbers. a.) 5, 3, 1, -1, ___, ___ b.) 1, -4, 9, -16, ___, ___ c.), ___, ___

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Example 3: Make a Conjecture Complete the conjecture. Conjecture: The product of two consecutive even integers is divisible by ___________________.

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Example 4: Finding a Counterexample Show that the conjecture is false by finding a counterexample. Conjecture: All odd numbers are prime.

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Exercises: 1.) Sketch the next figure in the pattern.

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2.) Describe a pattern in the sequence of numbers. Predict the next two numbers. a.) 1, 2, 6, 24, ___, ___ b.) 0, 3, 8, 15, 24, ___, ___

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3.) Show that the conjecture is false by finding a counterexample. Conjecture: The square of the sum of two numbers is equal to the sum of the squares of two numbers. That is, (a + b) 2 = a 2 + b 2

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