Define conjecture, inductive reasoning, and counterexample.
Present the stages of reasoning (looking for a pattern, making a conjecture, verifying the conjecture).
Provide examples that demonstrate how to make conjectures from patterns (ex. Describe the pattern in the numbers: 6, 11, 21, 41, 81, 161…).
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.
This video introduces the concept of patterns.
This video introduces the concept of inductive reasoning.
Source: tracyp on Guaranteach
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.
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.
This video shows how to use inductive reasoning to verify a conjecture in mathematics.
Source: Triszan on Guaranteach
This slideshow provides several practice problems learners can use to practice making conjectures from patterns and using counterexamples.