Benchmark 11B:
Common Themes - Models
(grades 6-8, page 269)
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
