Benchmark 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. (1 of 3)
• Standard 2-1, page 78, Grades 5-8
Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods

Standard 4-4, page 84, Grades 5-8
Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business

Standard 2-1 page 140, Grades 9-12
Reflect on and clarify their own thinking about mathematical ideas and situations

• Mathematical models can be displayed on a computer then modified to see what happens. (2 of 3)
• Standard 11-2 page 171, Grades 9-12
Use simulations to estimate probabilities

Standard 12-3 page 57, Grades K-4
Use models to relate fractions to decimals and to find equivalent fractions

Standard 2-1, page 78, Grades 5-8
Model situations using oral, written, concrete, pictorial, graphical, and algebraic methods

• Different models can be used to represent the same thing. What kind of 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. (3 of 3)
• Standard 4-4 page 32, Grades K-4
Use mathematics in other curriculum areas

Standard 4-4, page 84, Grades 5-8
Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business

Standard 2-2, page 78, Grades 5-8
Reflect on and clarify their own thinking about mathematical ideas and situations