LR01 Students will be expected to analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.

• LR01.01 Make conjectures by observing patterns and identifying properties, and justify the reasoning. 

• LR01.02 Explain why inductive reasoning may lead to a false conjecture. 

• LR01.03 Compare, using examples, inductive and deductive reasoning. 

• LR01.04 Provide and explain a counterexample to disprove a given conjecture. 

• LR01.05 Prove algebraic and number relationships, such as divisibility rules, number properties, mental mathematics strategies, or algebraic number puzzles. 

• LR01.06 Prove a conjecture, using deductive reasoning (not limited to two column proofs). 

• LR01.07 Determine if an argument is valid and justify the reasoning. 

• LR01.08 Identify errors in a given proof. 

• LR01.09 Solve a contextual problem involving inductive or deductive reasoning. 

LR02 Students will be expected to analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

• LR02.01 Determine, explain and verify a strategy to solve a puzzle or to win a game; for example, 

  • • 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 

• LR02.02 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game. 

• LR02.03 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.