THE CHALLENGE: Fold your very own Hyperbolic Plane from a simple piece of paper!

*Materials Needed*: A square piece of paper. Youtube instructional video below!*Math Concepts: *Hyperbolic planes, vertices, opposites, exponential functions, reflections, symmetry

*Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments! *

4.) Model with mathematics *Compare this model to a surface with positive curvature (a ball) or zero curvature (a piece of paper) surfaces. This surface has negative curvature. What do you notice about the 3 types of curvature? What’s the same? What’s different? What can you do on this surface that you can/cannot do with the others? *

5.) Use appropriate tools strategically. *As you’re folding this, discuss with students what tools make the folding easier or less easy. What kinds of paper works best? What sizes? *

6.) Attend to precision. *Discuss with students how successful your models are depending on the precision of your folds. *