On their calculators students each control a point.  Projected upfront are the locations of all the points.  As the students move their points, the screen upfront updates.  Students can be given a rule like, "Move until your y-value is two times your x-value."  A function appears in the upfront space.  In addition, all the points from all of the calculators can be passed back to the calculators.  This allows students to "shoot" analytic expressions through this collection of points (e.g. find five equivalent functions that go through these points).  Students' analytic expressions can also be collected and then redistributed to the class for further analysis.  

 

  

All files can be downloaded here.

Launch NetLogo activity (PC users only)

Download Function Activity models self-extracting archive

Launch a variant of this with half-integer positions
 

Click to view in-depth unit created for this activity