• proofs NOT be limited to the two column proof style
• analysis and conjectures related to spatial puzzles and games be incorporated throughout the course.

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

Provide examples of how inductive reasoning might lead to false conclusions.

Critique the following statement “Decisions can be made and actions taken based upon inductive reasoning”.

Identify situations relevant to self, family, or community involving inductive and/or deductive reasoning.

Prove algebraic number relationships, such as divisibility rules, number properties, mental mathematics strategies, or algebraic number tricks using deductive reasoning.

Prove conjectures using deductive reasoning.

Analyze an argument for its validity.

Identify errors in proofs that lead to incorrect conclusions (e.g., a proof that ends with 2 = 1).

Solve situational questions that involve inductive or deductive reasoning.

Determine, explain, and verify strategies for solving puzzles or winning games, such as:

• guess and check
• analyze a pattern
• make a systematic list
• create a drawing or model
• eliminate possibilities
• solve simpler problems
• work backward.

Create a variation of a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.