Geometric transformations, Frieze patterns, & Pysanky Eggs
For the past couple of units in middle school mathematics, students have been learning a lot about geometric transformations on the coordinate plane and how to both identify and create sequences of transformations in various contexts. Two learning objectives they were expected to master were TSW #5: “I can describe and perform a sequence of transformations.” and TSW #6: “I can solve real-world problems by using sequences of transformations.”
At the end of Unit 7, students took time to explore ways in which sequences of geometric transformations are used in different areas such as art, graphic design, architecture, and even archaeology. After being introduced to the many ways in which geometric transformations are used in various real-world settings, we focused on a particular class of geometric transformations called frieze patterns which have been used for centuries by various civilizations all over the world. Frieze patterns are a special class of geometric transformations which consist of all the geometric transformations students learned in class while mastering their TSWs for Unit 7, including horizontal translations, 180o rotations, reflections about horizontal and vertical lines, and combinations of transformations called “glides”. These special patterns can be found in ancient Greek architecture, dollar bills, Native American pottery, Japanese Kimonos, automobile tire treads, traditional African and Arabic clothing designs, and even Ukrainian pysanky eggs.
Since the Easter holiday had just passed and several of our students are Ukrainian themselves, this was a perfect opportunity for students to see connections between the mathematics they were learning in class with their own culture and holiday traditions. To guide students through this authentic learning experience, LIS invited Ms. Olyana Karpus to lead a workshop on how to paint these special decorative eggs. Not only did students have the opportunity to create their own pysanky eggs, but Ms. Karpus also spent a lot of time teaching the students about the rich history of this special tradition and the symbolism behind all the patterns and colors used when decorating the eggs. It was an amazing experience for all involved and I would like to give a special thanks
both Ms. Olyana Karpus and Mrs. Yuliya Bastien for organizing and hosting such a meaningful and enriching learning activity for our students.
