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.

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. 
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. 
