The Mathematics of a Pattern

What can a folded piece of paper reveal about infinity? Grade 9 Geometry students recently explored tessellations—repeating patterns of shapes that can cover a plane completely, without gaps or overlaps. Through mathematician and artist Chaim Goodman-Strauss’ Tooti Tooti activity.

Starting with an ordinary piece of paper folded in half, and edges taped, students cut and transformed their paper into tiles that could be repeated to create increasingly complex patterns. But creating something visually interesting was only part of the challenge. Students investigated the mathematics hidden within their designs, looking for rotational symmetry and examining how a shape can be turned 180 degrees around particular points while leaving the overall pattern unchanged. 

There is also a special Thaden connection to the lesson: Goodman-Strauss, a University of Arkansas mathematician and artist, tested and refined Tooti Tooti with Thaden students as he developed the activity. It later earned first place in the National Museum of Mathematics’ 2021 Rosenthal Prize for Innovation and Inspiration in Math Teaching. 

Through cutting, folding, arranging, and questioning, students were able to make an abstract geometric idea tangible art, discovering that behind an intricate pattern is a surprisingly precise mathematical structure.