### Standard 2: Mathematics as Communication

In grades 5-8, the study of mathematics should include opportunities for communication so that students can:
• Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods
Benchmarks 11B (Common Themes: Models)
Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and stories can be used to represent objects, events, and processes in the real world, although such representations can never be exact in every detail.

Benchmarks 11B (Common Themes: Models)
Seeing how a model works after changes are made to it may suggest how the real thing would work if the same thing were done to it.

Benchmarks 11B (Common Themes: Models)
Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly, or that are too vast to be changed deliberately, or that are potentially dangerous.

Benchmarks 11B (Common Themes: Models)
Mathematical models can be displayed on a computer then modified to see what happens.

• Reflect on and clarify their own thinking about mathematical ideas and situations

•   Benchmarks 11B (Common Themes: Models)
Different models can be used to represent the same thing. What kind of a model to use and how complex it should be depends on its purpose. The usefulness of a model may be limited if it is too simple or if it is needlessly complicated. Choosing a useful model is one of the instances in which intuition and creativity come into play in science, mathematics, and engineering.

• Develop common understandings of mathematical ideas, including the role of definitions
• Benchmarks 9E (The Mathematical World: Reasoning)
Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to over generalize, imagining general rules on the basis of only a few observations.

• Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas
• Benchmarks 12D (Habits of Mind: Communication Skills)
Locate information in reference books, back issues of newspapers and magazines, compact disks, and computer databases.

Benchmarks 12D (Habits of Mind: Communication Skills)
Understand writing that incorporates circle charts, bar and line graphs, two-way data tables, diagrams, and symbols.

Benchmarks 12D (Habits of Mind: Communication Skills)
Find and describe locations on maps with rectangular and polar coordinates

• Discuss mathematical ideas and make conjectures and convincing arguments
• Benchmarks 1C (The Nature of Science: The Science Enterprise)
Clear communication is an essential part of doing science. It enables scientists to inform others about their work, expose their ideas to criticism by other scientists, and stay informed about scientific discoveries around the world.

Benchmarks 1B (The Nature of Science: Scientific Inquiry)