A model is a simplified substitute for the real problem, allowing us to solve the problem in a relatively simple way.
- Analysis models are previously solved problems that describe either (a) the behavior of some physical entity or (b) the interaction between that entity and the environment.
- Geometric models form geometric constructions of real situations. We then analyze the geometric construction. These are commonly used in trigonometry.
- Simplification models ignore insignificant details.
- Structural models make it easier to understand concepts which are relatively abstract. For example, thinking of an election as a cloud of electron density is a structural model of an electroon.
Thinking of problems from different perspectives will oftentimes help you figure things out.
- Mental representations occur when you imagine a scene based on a description in a word problem. You envision a sequence of events and can predict what will occur in the future.
- Pictorial representations occur when you draw your mental representaition. The drawing describes what you would see if you were observing the situation in the problem.
- Simplified pictorial representations are pictorial representations to which a simplification model has been applied.
- Graphic representations are graphs which represent situations in problems