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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 solve puzzles by dragging independent variables while observing the behavior of dependent variables.Each page contains four functions, and students use their observations of behavior to determine which function belongs to a different family from the other three. 


In this activity students will:

  • Drag independent variables and observe and describe the behavior of dependent variables. (Use the drag test.)
  • Distinguish between functions based on the shapes traced by the variables.
  • Distinguish between functions based on the relative speed and direction of the variables.
  • Distinguish between functions based on the presence and pattern of fixed points.
  • Describe several function families (such as translations, rotations, dilations, reflections, and glide reflections) based on the similarities and differences of their behaviors.
  • Formulate a working definition of a function family.
  • Determine whether a function belongs to a particular family.
  • Use function notation appropriately to refer to a function and to a dependent variable.
  • Construct new functions belonging to particular families (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; (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.