Patterns and Inductive Reasoning

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Presentation transcript:

Patterns and Inductive Reasoning Geometry – Lesson 2.1 Patterns and Inductive Reasoning

Geometry 2.1 - Notes Sketch the next figure (4) in the following pattern.

Geometry 2.1 - Notes Sketch the next figure (5) in the following pattern.

Geometry 2.1 - Notes Describe the “pattern” in words. How would you tell a friend how to draw this pattern?

Geometry 2.1 – Vocabulary Conjecture: A conjecture is an unproven statement that is based on observations.

Geometry 2.1 – Vocabulary Inductive Reasoning: The process of looking for a pattern, making a conjecture, and verifying the conjecture is true.

Geometry 2.1 – Notes How do you prove a conjecture is true? We must demonstrate or prove that the statement is true for EVERY case.

Geometry 2.1 – Notes How do you prove a conjecture is false? We must find one example which makes the conjecture false.

Geometry 2.1 – Vocabulary Counterexample: A counterexample is an example which shows the conjecture is false.

Geometry 2.1 – Notes Make a conjecture for the following pattern.

Geometry 2.1 – Notes Patterns may also exist in a sequence of numbers. Can you find a conjecture for each pattern? 3, 6, 12, 24, … 20, 15, 10, 5, … 2, 3, 5, 8, 12 …

Geometry 2.1 – Notes Can you find a counterexample for each conjecture? Squaring a whole number and adding one will always be an even number. For any number x, x2 is always larger than x.

Geometry 2.1 – Notes Check for understanding: Write a conjecture for the TOTAL number of objects in each diagram.