In implementing the Geometry process and content performance indicators, it is expected that students will identify and justify geometric relationships, formally and informally. For example, students will begin with a definition of a figure and from that definition, students will be expected to develop a list of conjectured properties of the figure and to justify each conjecture informally or with formal proof. Students will also be expected to list the assumptions that are needed in order to justify each conjectured property and present their findings in an organized manner.

The intent of both process and content performance indicators is to provide a variety of ways for students to acquire and demonstrate mathematical reasoning ability when solving problems. The variety of approaches to verification and proof is what gives curriculum developers and teachers the flexibility to adapt strategies to address these performance indicators in a manner that meets the diverse needs of out students. Local curriculum and local/state assessments must support and allow students to use any mathematically correct method when solving a problem.

Throughout this document the performance indicators use the words investigate, explore, discover, conjecture, reasoning, argument, justify, explain, proof, and apply. Each of these terms is an important component in developing a student's mathematical reasoning ability. It is therefore important that a clear and common definition of these terms be understood. The order of these terms reflects different stages of the reasoning process.

Investigate/Explore - Students will be given situations in which they will be asked to look for patterns or relationships between elements within the setting.

Discover - Students will make note of possible relationships of perpendicularity, parallelism, congruence, and/or similarity after investigation/exploration.

Conjecture - Students will make an overall statement, thought to be true, about the new discovery.

Reasoning - Students will engage in a process that leads to knowing something to be true or false.

Argument - Students will communicate, in verbal or written form, the reasoning process that leads to a conclusion. A valid argument is the end result of the conjecture/reasoning process.

Justify/Explain - Students will provide an argument for a mathematical conjecture. It may be an intuitive argument or a set of examples that support the conjecture. the argument may include, but is not limited to, a written paragraph, measurement using appropriate tools, the use of dynamic software, or a written proof.

Proof - Students will present a valid argument, expressed in written form, justified by axioms, definitions, and theorem using properties of perpendicularity, parallelism, congr