Mathematical Communication
 Elementary School The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student: a Uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work. b Shows mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models. c Explains solutions to problems clearly and logically, and supports solutions with evidence, in both oral and written work. d Considers purpose and audience when communicating about mathematics. e Comprehends mathematics from reading assignments and from other sources.

 Middle School The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student: a Uses mathematical language and representations with appropriate accuracy, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagrams. b Organizes work, explains facets of a solution orally and in writing, labels drawings, and uses other techniques to make meaning clear to the audience. c Uses mathematical language to make complex situations easier to understand. d Exhibits developing reasoning abilities by justifying statements and defending work. e Shows understanding of concepts by explaining ideas not only to teachers and assessors but to fellow students or younger children. f Comprehends mathematics from reading assignments and from other sources.

 High School The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student: a Is familiar with basic mathematical terminology, standard notation and use of symbols, common conventions for graphing, and general features of effective mathematical communication styles. b Uses mathematical representations with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams. c Organizes work and presents mathematical procedures and results clearly, systematically, succinctly, and correctly. d Communicates logical arguments clearly, showing why a result makes sense and why the reasoning is valid. e Presents mathematical ideas effectively both orally and in writing. f Explains mathematical concepts clearly enough to be of assistance to those who may be having difficulty with them. g Writes narrative accounts of the history and process of work on a mathematical problem or extended project. h Writes succinct accounts of the mathematical results obtained in a mathematical problem or extended project, with diagrams, graphs, tables, and formulas integrated into the text. i Keeps narrative accounts of process separate from succinct accounts of results, and realizes that doing so can enhance the effectiveness of each. j Reads mathematics texts and other writing about mathematics with understanding.