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“How many ways can you represent a function of several variables?”

Simpler prompts such as “What is a surface?” are not as effective because they lead students to use non-mathematical language.


This SWBQ probes students' notions about surfaces.

Wrap Up

Work with students to create as long a list as possible of representations of functions of several variables. Possible representations include:

  • graphs (surfaces);
  • tables;
  • equations ($x^2+y^2+z^2=4$);
  • functions ($f(x,y)=x^2+y^2$);
  • level sets (contour maps);
  • geometric objects (spheres).

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