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Grades: 7‒11

In Geometric Functions activities students create, manipulate, and experience function concepts by treating geometric transformations as functions with points as their variables.

In this capstone activity students apply the swirl function from Special Effects—A Swirling Transformation to several pictures. By animating the function through a continuum of members of the swirl family, students create and observe stunning visual effects. Students are challenged to invent new special effects of their own.


In this activity students will:

  • Define a Swirl function using two related variable points.
  • Apply the Swirl function to several geometric objects.
  • Analyze, describe and explain the function by dragging the swirled objects.
  • Compare the user-defined Swirl command, which defines a function, with the built-in Locus command, which constructs the range that corresponds to a given domain.
  • Apply the Swirl function to a picture and describe the results.
  • Describe the connection between the atomic application of a function (to a single point) and the collective application (to an entire set of points).
  • Create a special effect by animating the Swirl function through a continuum of members of the same family.
  • Invent a new special effect function, apply it to a picture, and adjust the function until the desired effect is achieved.

Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure; (8) Look for and express regularity in repeated reasoning.

Content Standards

8.F1,2; 8.G1; F-IF1,2,9; G-CO2; G-SRT1

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This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: If you adapt and/or share this activity, you must attribute it to "KCP Technologies, a McGraw-Hill Education Company." You may distribute it only non-commercially under the same or similar license.

This material is based upon work supported by the National Science Foundation under KCP Technologies Award ID 0918733, with grant period September 1, 2009 through August 31, 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.