Both scientists and engineers use models. Physical models show how things look or work in the real world. Conceptual models represent relationships and describe how things work or fit together. Mathematical models use mathematical equations, theories, formulas, and proofs. Simulations allow for the control of variables and mimic real-world processes. Models are used to make predictions about the behavior of a system, and examples include sketches, diagrams, mathematical relationships, simulations, physical models, and prototypes.

Scientists perform investigations within systems. Systems have boundaries, components, resources, flow, and feedback. Examples of systems include organisms, machines, galaxies, ideas, and numbers. In laboratory or field research, an essential element affecting the design of an investigation and the interpretation of results is the extent to which the system can be physically isolated or the external conditions controlled.

Engineers predict a system’s behaviors and diagnose problems or failures in system functioning. For example, in a simple mechanical system, interactions among the parts are described in terms of forces that cause changes in motion or physical stresses. A crucial element of system design is considering flows into and out of a system. Systems thinking and system models support critical steps in developing, sharing, testing, and refining design ideas.