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===== Total Differentials on a Surface: Instructor's Guide =====

==== Main Ideas ====

==== Students' Task ====
//Estimated Time: 10 min//

==== Prerequisite Knowledge ====
==== Props/Equipment ====

  * [[:Props:start#whiteboards|Tabletop Whiteboard]] with markers
  * [[:Props:start#surface|Plastic Surface]]  

==== Activity: Introduction ====

Students should be introduced to the ideas of differentials using a one-dimensional graph and the corresponding symbolic relationship.  Then, give each group a plastic surface representing a function $f(x,y)$ and ask them to sketch $df$, $dx$, and $dy$ on the surface and to relate these differentials geometrically and then symbolically.

==== Activity: Student Conversations ====
==== Activity: Wrap-up ====
==== Extensions ====