Geometric Functions
With Technologically Embodied Geometric Functions, students develop conceptual metaphors that directly relate computer-based sensory motor experiences of abstract function concepts. This approach relies on four foundations:
We’re working hard to create the sketches, worksheets, and support materials for these Web Sketchpad activities. Ours is a volunteer effort on the part of everyone involved, both curriculum developers and field testers, and we make these activities freely available for you to download and use with your own students.
As we develop, revise and expand the activities, we need your help. Email your commentary (What worked well? What didn’t?) and your suggested improvements to the webmaster.
The Dynamic Number NSF Project developed 12 Geometric Functions activities designed to help students learn about functions and geometric transformations through direct experiences constructing and manipulating them. (See the four Foundations pages for the mathematical, cognitive science, technology, and pedagogical foundations of this approach.)
All of the activities listed below reside on the Dynamic Number website, and include a student sketch, a student worksheet, and extensive teacher notes. These activities require The Geometer's Sketchpad.
Many of these activities are also available in Web Sketchpad format in the Introducing Transformations unit and the Cartesian Connection unit. Web Sketchpad activities can be used with any modern browser, with no need for students to have access to Sketchpad itself.
Introducing Functions Activities
These activities introduce the function concept and the idea of distinguishing function families based on their behavioral characteristics.
Function Families Activities
These activities acquaint students with the four main geometric function families. They construct and then manipulate members of each family, describe them using function notation, identify the function behavior (particularly relative rate of change) that distinguishes one family from another, and solve interesting challenges related to each of the families.
- The Reflection Family
- The Rotation Family
- The Dilation Family
- The Translation Family
- Rotation, Dilation, and Translation Families (Can replace the three preceding individual activities.)
- Geometric Function Dances
Composition Activities
In these activities students construct two different functions, combine them, and explore the behavior of the resulting composed function.
Advanced Activities
In these activities students create interesting original functions and explore how their new functions transform an entire input domain (in the form of a picture) into an output range.
21 September 2015: Edited to list only activities from the Dynamic Number project.
02 February 2014: Created this page.
This web site is based in part upon work supported by the National Science Foundation under NCSU IUSE award 1712280 (July 2017 through June 2019) and KCP Technologies DRK-12 award ID 0918733 (September 2009 through August 2013). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
We are deeply grateful to McGraw-Hill Education for making Web Sketchpad available for these activities.
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