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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.

Students explore and describe relationships between point variables, distinguish between independent and dependent variables, and use examples and non-examples to formulate their own definitions of function.


In this activity students will:

  • Classify points as independent or dependent.
  • Drag independent points and observe and describe the resulting behavior of dependent point(s).
  • Use the drag test to distinguish functions from non-functions.
  • Formulate and discuss their own definition of function.
  • Use the term relation to describe two variables that have a relationship that may or may not be a function.
  • Construct their own examples of functions and non-functions (optional).
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; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure.

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.