Lesson 3 Flashcards
What is inductive reasoning?
Inductive reasoning is forming a general conclusion based on specific observations. It is often used to identify patterns and make conjectures.
Example: Observing that the sun rises in the east every day and concluding that it will rise in the east tomorrow.
What is deductive reasoning?
Deductive reasoning is drawing conclusions based on general principles or accepted facts. It is used to prove statements logically.
Example: All mammals have lungs; a dog is a mammal; therefore, a dog has lungs.
What is a conjecture?
A conjecture is a statement believed to be true based on observations.
What is a counterexample?
A counterexample is an example that disproves a conjecture, showing that it does not hold in all cases.
What are Polya’s Four Steps for Problem Solving?
- Understand the Problem: Identify what is known, unknown, and what is being asked.
- Devise a Plan: Decide on a strategy to solve the problem.
- Carry Out the Plan: Execute the chosen strategy step by step.
- Look Back: Review the solution for correctness and consider improvements.
What is one problem-solving strategy?
Draw a Diagram: Visualizing the problem can simplify complex relationships.
What is another problem-solving strategy?
Solve a Simpler Problem: Breaking down a problem into easier, smaller parts.
What is a third problem-solving strategy?
Make a Table or Chart: Organizing information systematically to reveal patterns.
What is a fourth problem-solving strategy?
Work Backwards: Start from the desired outcome and reverse the steps to find the starting conditions.
What is a fifth problem-solving strategy?
Guess and Check: Test possible solutions and refine guesses based on feedback.
What is a sixth problem-solving strategy?
Look for Patterns: Identifying recurring elements that can suggest solutions.
What is a seventh problem-solving strategy?
Use Logical Reasoning: Apply principles of logic to infer solutions.
How many handshakes take place if 20 students each shake hands with every other student exactly once?
Use a systematic approach to solve the problem, such as making a simpler version with fewer students.
Prove or disprove the conjecture: For any positive integer, adding the next consecutive integer results in an odd number.
Apply deductive reasoning to prove or disprove this conjecture.
Choose the most appropriate problem-solving strategy for arranging four different-colored blocks.
Identify the strategy that best applies to solving for the number of arrangements.
