2 1 Patterns and Inductive Reasoning Inductive Reasoning

Inductive Reasoning: reasoning based on patterns you observe

Problem 1: Finding and Using a Pattern Look for a pattern. What are the

Conjecture: A conclusion you reach using inductive reasoning.

Problem 2: Using Inductive Reasoning Look at the circles. What conjecture can you make

Problem 2: Using Inductive Reasoning What conjecture can you make about the twenty-first term

Problem 3: Collecting Information to Make a Conjecture What conjecture can you make about

Problem 4: Making a Prediction Sales of backpacks at a nationwide company decreased over

Counterexample: an example that shows that a conjecture is incorrect. You can prove a

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • If

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • You

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • When

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • One

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2 -1 Patterns and Inductive Reasoning

Inductive Reasoning: reasoning based on patterns you observe

Problem 1: Finding and Using a Pattern Look for a pattern. What are the next two terms in the sequence? 3, 9, 27, 81, …

Problem 1: Finding and Using a Pattern Look for a pattern. What are the next two terms in the sequence?

Conjecture: A conclusion you reach using inductive reasoning.

Problem 2: Using Inductive Reasoning Look at the circles. What conjecture can you make about the number of regions 20 diameters form?

Problem 2: Using Inductive Reasoning What conjecture can you make about the twenty-first term in R, W, B, …

Problem 3: Collecting Information to Make a Conjecture What conjecture can you make about the sum of the first 30 even numbers?

Problem 3: Collecting Information to Make a Conjecture What conjecture can you make about the sum of the first 30 odd numbers?

Problem 4: Making a Prediction Sales of backpacks at a nationwide company decreased over a period of six consecutive months. What conjecture can you make about the number of backpacks the company will sell in May?

Counterexample: an example that shows that a conjecture is incorrect. You can prove a conjecture is wrong by finding one counterexample

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • If the name of a month starts with the letter J, it is a summer month.

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • You can connect any three points to form a triangle

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • When you multiply by 2, the product is greater than the original number

Problem 5: Finding a Counterexample What is a counterexample for each conjecture? • One and only one plane exists through any three points.