Classroom Kits for Raising Calculus

Instructors who participate in professional development workshops for Raising Calculus to the Surface are able to purchase classroom sets for use at their institution.  Kits are composed of 4, 8, 12, or 16 surface models and the associated tools.  When used in a group setting, each surface serves three students - so a set of 12 surfaces works well for a classroom of 36 students.


Click Here to order Classroom Kits

Each kit includes the following materials:

Surfaces Choose from six different surfaces.  Each surface measures 10" x 10" on top, with a height ranging from approximately 0.5" to 6" tall.  The surfaces have a dry erase finish and contain special points marked for use with the activities.  The vertical sides of each surface are painted with transparent paint.  The surfaces were constructed to avoid global symmetry, making it more likely that students discover mathematical relationships which hold for arbitrary multivariable functions.

A Kit of 12 surfaces will contain two surfaces of each color.  If ordering 4, 8, or 16, please contact Aaron Wangberg ( to specify the models desired.  Subtle differences in the surfaces may be useful for different applications.  For example, the Orange, Green, and Blue surfaces have their global maximums and minimums on the surface's boundary, while the global extrema occur on the interior for the others (Red, Yellow, and Purple).

Contour Maps A double-sided 16" x 22" dry-erasable contour map accompanies each surface. The contours on the light green map correspond to a change in height of 1/4" on the surface, and this map also contains a rectangular coordinate grid as well as specially marked points matching those on the surface.  The contours on the light red map represent 1/2" change in height for the surface, is free from a specified coordinate system.  The contour maps are larger than the surfaces to provide a workspace for students, but are printed to the same scale as the surfaces.

Coordinate Grids Each surface comes with a double-sided 16" x 22" dry-erasable coordinate map.  The orange side contains a rectangular coordinate grid (1" x 1" squares).  The purple side contains a polar coordinate grid with circles increasing by 1" in radius. 

Inclinometers (Slope meters) An Inclinometer allows students to measure the rate of change in almost any direction at points where the surface is concave down

Vertical Rulers and Tangent Planes  A 12" standing ruler allows students to estimate height on the surface, and a square clear piece of dry-erasable plastic can be used to represent a tangent plane at a point on the surface.  Each kit contains one ruler and one tangent plane per surface.

Dry Erase Markers Three LOW ODOR EXPO Markers (e.g. red, blue, and black) accompany each surface.  (Other markers may result in ghosting on the surface or contour maps.)

Instructor's Guide An instructor's guide provides details for using the materials in the classroom.  Specific sections provide information about the tools, strategies for using discovery or inquiry learning in the classroom, and a look at the geometric ideas behind multivariable calculus ideas explored with the materials.  The guide includes Instructor's Notes containing information for integrating each activity into the classroom - including insight into the questions students will raise and how to explore student ideas during small group and whole class discussion.  Some activities contain suggested homework problems.  The guide includes a sample 16-week semester schedule.

Website Access  Instructors using the materials have access to the .tex source for the materials on the website, allowing them to modify notation and tailor the activities for their specific courses.

The kits are sold at cost and includes the cost of shipping throughout the U.S. (international shipping incurs an extra fee).  Each kit of 12 surfaces requires approximately 15 hours of labor by undergraduate engineering students.  Materials and machine maintenance account for 75