NSES Content Standard Unifying Concepts and Processes:   Evidence, models and explanation  Grades K-12, page 117  Models are tentative schemes or structures that correspond to real objects, events, or classes of events, and that have explanatory power. Models help scientists and engineers understand how things work. Models take many forms, including physical objects, plans, mental constructs, mathematical equations, and computer simulations.

 
Benchmark 2C The Nature of Mathematics: Mathematical Inquiry
Grades 9-12, page 38
Much of the work of mathematicians involves a modeling cycle, which consists of three steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas. If the match is not considered good enough, a new round of abstraction and manipulation may begin. The actual thinking need not go through these processes in logical order but may shift from one to another in any order.

Benchmark 8E The Designed World: Information Processing
Grades 9-12, page 203
Computer modeling explores the logical consequences of a set of instructions and a set of data. The instructions and data input of a computer model try to represent the real world so the computer can show what would actually happen. In this way, computers assist people in making decisions by simulating the consequences of different possible decisions.

Benchmark 9B The Mathematical World: Symbolic Relationships
Grades 9-12, page 220
Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation.

Benchmark 9E The Mathematical World: Reasoning
Grades 3-5, page 232
One way to make sense of something is to think how it is like something more familiar.

Benchmark 9E The Mathematical World: Reasoning
Grades 6-8, page 233
An analogy has some likenesses to but also some differences from the real thing.

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.

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.

Benchmark 11B Common Themes: Models
Grades 9-12, page 270
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 the 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.

Benchmark 11B Common Themes: Models
Grades 9-12, page 270
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 is the only "true" model or the only one that would work.

See also Chapter 11 Common Themes, Section B: Models, for precursor ideas.