Mathematical Reasoning & Proofs

#### Core Ideas

• Employ forms of mathematical reasoning and justification appropriate to the solution of a problem.
• Extract pertinent information from situations and determine what additional information is needed.
• Formulate conjectures and test them for validity.
• Invoke problem-solving strategies.
• Verify and interpret results of a problem.
• Use mathematical language in representations to make complex situations easier to understand.

Picking Apples

• See Related Classroom Video Visit: Comparing Linear Functions
Cecilio Dimas leads students through a lesson asking students to analyze various movie rental pricing options and methods for conducting cost analysis. The multimedia documentation of Dimas's teaching includes a pre-teaching planning conversation between Dimas, Sally Keyes, math coach, and Kamaljit Sangha, another math teacher at Ida Price Middle School. The documentation also includes a follow-up faculty debrief with observing teachers and an interview with participating students. VIDEO >>

 Course 1 (Algebra)

#### Core Ideas

• Employ forms of mathematical reasoning and proof appropriate to the solution of the problem, including deductive and inductive reasoning, making and testing conjectures, and using counterexamples and indirect proof.
• Show mathematical reasoning in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models.
• Explain the logic inherent in a solution process.
• Use induction to make conjectures and use deductive reasoning to prove conclusions.
• Draw reasonable conclusions about a situation being modeled.

 Course 2 (Geometry)

#### Core Ideas

• Employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures and using counter examples and indirect proof.
• Show mathematical reasoning in solutions in a variety of ways, including words, numbers, symbols, pictures, charts, graphs tables, diagrams, and models.
• Explain the logic inherent in a solution process.
• Identify, formulate, and confirm conjectures.
• Use synthetic, coordinate, and /or transformational geometry in direct or indirect proof of geometric relationships.
• Establish the validity of geometric conjectures using deduction; prove theorems, and critique arguments made by others.