The purpose of this activity is to introduce students to elementary concepts in graph theory in a hands-on, accessible manner. Students will create their own graphs, count certain quantities related to their graphs, make conjectures regarding these quantities, and learn how to explain why their conjecture is true. In the process they will discover the Euler characteristic, a powerful tool for understanding planar graphs.

Combinatorics
Geometry

Problem Posing
Try a Smaller Problem

MP1 - Make sense of problems and persevere in solving them.
MP4 - Model with mathematics.
MP6 - Attend to precision.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated reasoning.