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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**

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 = a2 + b2

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