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Finding and Describing Patterns

Finding and Describing Patterns

Description:
  1.  

    Define conjecture, inductive reasoning, and counterexample.

  2.  

    Present the stages of reasoning (looking for a pattern, making a conjecture, verifying the conjecture).

  3.  

    Provide examples that demonstrate how to make conjectures from patterns (ex. Describe the pattern in the numbers: 6, 11, 21, 41, 81, 161…).

  4.  

    Provide examples that demonstrate how to use counterexamples to prove a conjecture false. 

 

This packet should help a learner seeking to understand how to use inductive reasoning to find and describe patterns.

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Tutorial

Introduction to Patterns

This video introduces the concept of patterns.

Introduction to Inductive Reasoning

This video introduces the concept of inductive reasoning.

Source: tracyp on Guaranteach

The Stages of Reasoning

This video presents the stages of reasoning: looking for a pattern, making a conjecture, verifying the conjecture. It also introduces the new vocabulary related to finding and describing patterns.

Important Terms

These terms from the previous video are particularly important in finding and describing patterns:

Conjecture: A guess regarding the nature of a pattern.

Inductive Reasoning: Deriving a general rule from specific cases.

Counterexample: An instance in which a conjecture does not hold true, disproving the conjecture.

Using Inductive Reasoning to Prove a Statement

This video shows how to use inductive reasoning to verify a conjecture in mathematics.

Source: Triszan on Guaranteach

Practice Identifying Patterns

This slideshow provides several practice problems learners can use to practice making conjectures from patterns and using counterexamples.