**Benchmark
11B: Common Themes - Models**
**(grades 9-12, page 270)**
The basic idea of mathematical modeling is to find a mathematical relationship
that behaves in the same ways as the objects or processes under investigation.
A mathematical model may give insight about how something really works
or may fit observations very well without any intuitive meaning. (1 of
3)
Standard 1-4 page 137, Grades 9-12

Apply the process of mathematical modeling to real-world problem situations
Standard 4-2 page 146, Grades 9-12

Relate procedures in one representation to procedures in an equivalent
representation

Computers have greatly improved the power and use of mathematical models
by performing computations that are very long, very complicated, or repetitive.
Therefore computers can show the consequences of applying complex rules
or of changing he rules. The graphic capabilities of computers make them
useful in the design and testing of devices and structures and in the simulation
of complicated processes. (2 of 3)
Standard 1-4 page 137, Grades 9-12

Apply the process of mathematical modeling to real-world problem situations
The usefulness of a model can be tested by comparing its predictions to
actual observations in the real world. But a close match does not necessarily
mean that the model in the only "true" model or the only one that would
work. (3 of 3)
Standard 1-4 page 137, Grades 9-12

Apply the process of mathematical modeling to real-world problem situations
Standard 4-2 page 146, Grades 9-12

Relate procedures in one representation to procedures in an equivalent
representation