Unit 6 - Reasoning

Number and Logic

It is expected that students will: Develop number sense and logical reasoning.

1. I can analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.

• Make conjectures by observing patterns and identifying properties, and justify the reasoning.
• Explain why inductive reasoning may lead to a false conjecture.
• Compare, using examples, inductive and deductive reasoning.
• Provide and explain a counterexample to disprove a given conjecture.
• Prove algebraic and number relationships such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks.
• Prove a conjecture, using deductive reasoning (not limited to two column proofs).
• Determine if a given argument is valid, and justify the reasoning.
• Identify errors in a given proof; e.g., a proof that ends with 2 = 1.
• Solve a contextual problem that involves inductive or deductive reasoning

2. I can analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

• Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,
  • guess and check
  • look for a pattern
  • make a systematic list
  • draw or model
  • eliminate possibilities
  • simplify the original problem
  • work backward
  • develop alternative approaches.
• Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.
• Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.