- Subchapter B
- Models
- For Grades: 6-8
- Learning Goal 1
- Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.

- Learning Goal 2
- Mathematical models can be displayed on a computer and then modified to see what happens.

- Learning Goal 3
- Different models can be used to represent the same thing. What model to use depends on its purpose.

- Learning Goal 4
- Simulations are often useful in modeling events and processes.

- Learning Goal 5
- The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.

- Learning Goal 6
- A model can sometimes be used to get ideas about how the thing being modeled actually works, but there is no guarantee that these ideas are correct if they are based on the model alone.

- Learning Goal 1
- For Grades: 9-12
- Learning Goal 1a
- A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

- Learning Goal 1b
- A mathematical model may give insight about how something really works or may fit observations very well without any intuitive meaning.

- Learning Goal 2
- 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 reveal the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and simulated testing of devices and structures and in the simulation of complicated processes.

- Learning Goal 3
- 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 other models would not work equally well or better.

- Learning Goal 4
- Often, a mathematical model may fit a phenomenon over a small range of conditions (such as temperature or time), but it may not fit well over a wider range.

- Learning Goal 5
- The behavior of a physical model cannot ever be expected to represent the full-scale phenomenon with complete accuracy, not even in the limited set of characteristics being studied. The inappropriateness of a model may be related to differences between the model and what is being modeled.

- Learning Goal 1a

- For Grades: 6-8

- Models