Sample Task: Wolves & Sheep

The description below is based on observations by BSME participants enrolled in the course Practicum: Experiencing the Hungarian Approach through Observation and Teaching.

We observed a 5th grade classroom at Fazekas Mihály School in Budapest, taught by Erika Jakucs. The lesson goal was to understand how to find points equidistant from various points in the plane. The teacher began the class by posing the following scenario:

There are wolves and sheep. A sheep is eaten by any wolf that is closest to it. But if there are multiple wolves that are the same distance from a sheep, they do not eat the sheep.


After acting out the problem in class, students gathered in small groups. The teacher gave each group poker chips to symbolize wolves and coins to symbolize sheep. She posed a number of questions for investigation:

  • Where are the sheep safe if three wolves stand at the vertices of a triangle? Try several triangles.
  • Where are the sheep safe if four wolves stand at the vertices of a rectangle?
  • What about a parallelogram? Trapezoid?
  • What if there are two lines of wolves? Where are the sheep safe?
  • What if one wolf stands facing a line of wolves?
  • Find an arrangement of infinitely many wolves in which there is no safe place for sheep. (There are several correct answers.)

After students had time to conduct experiments, look for patterns, make conjectures, and uncover underlying structures, the teacher brought the class together for a whole-class discussion. It was only at this time—after these student explorations—that the teacher introduced the definition and properties of perpendicular bisector. We saw how, in summarizing the work that students had just done, the teacher shed light on important concepts and developed generalizations from their experiments.