Small Group Activity: Surfaces Intro

Problem-Solving 2023

An introduction to the use of the Raising Calculus surfaces.

Students have to match their surface with the appropriate contour map.

What students learn Students are gently introduced to the relationship between contour maps and surfaces.

Your surface represents the town of Granite Falls, a \(\hbox{10 km}\times\hbox{10 km}\) town located in Rock County, which measures \(\hbox{15.5 km}\times\hbox{21.5 km}\).

The state records office has mixed up its county maps. Find the map of Rock County, and determine the location of Granite Falls on this map.


A good introduction to this activity is a SWBQ asking about representations of functions of several variables. Among the desired responses: graphs, level sets, tables of data, symbolic representations.

Student Conversations

Some students will wonder where to put the surface on their contour map, and how to orient it. That's the point!


This activity leads naturally into the Park activity, especially if the last part (“Go”) is omitted. An introduction to densities and possibly integration may be appropriate prior to the Park activity.

Author Information
Raising Calculus team
Learning Outcomes