Models & Representations

By Levi Clancy for Student Reader on
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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 electron.

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