Inquiry-Based Activity for Spherical Geometry

Spherical Geometry is a topic that I like to share with my Honors Geometry students, but it is very difficult to try to describe when we take notes on a two-dimensional piece of paper.  I found an activity on Twitter a while ago where people used balloons to talk about spherical Geometry.  This activity has quickly become one of my students' favorites.  

For this activity, I have each student blow up a balloon.  I also give each student a marker.  We talk about how lines in spherical geometry are "great circles" that have to pass through two opposite sides of the balloon.  We quickly discover that ALL lines in spherical geometry intersect.  We talk about Euclidean geometry where two points make one distinct line.  We draw out on our balloons how this isn't always the case in spherical geometry.  We also talk about how we can draw a triangle on our balloons that has three right angles.  

Since I had my students start drawing on balloons for this lesson, I can see that their level of understanding has greatly improved.  They also enjoy having a balloon for the rest of the day.