Mathematician Sir Roger Penrose was born in 1931.

Roger Penrose, who was knighted in the 1980s for his outstanding contributions to mathematics and received the Wolf prize for contributions to physics in 1988, began “playing” with geometry while working on his Ph.D. at Cambridge University in England. Penrose became fascinated with tessellations—the covering of a surface with a set of tiles of a given shape that usually results in a tile pattern. Penrose wanted to determine whether a surface could be covered with a given set of shapes without creating a pattern. After years of study, Penrose found a solution, but it required thousands of different shapes. Through further study and effort, he eventually reduced the required number to just two. The shapes used in this solution are not common geometrical forms, but rather two unusual parallelograms now called “kites and darts.” Penrose’s work was used in some of the famous creations of M.C. Escher.

Illuminations
Students learn about and experiment with geometrical shapes, especially the triangle, in Building with Triangles (Pre-K–8), a series of activities that include multiple opportunities for students to communicate their findings.

In a nine-lesson unit called Powerful Patterns (Pre-K–2), very young students are introduced to logic as they use logical thinking to create, identify, extend and translate patterns. They make patterns with objects, numbers and shapes. They also explore a variety of patterns in mathematics, in physical education, science and social studies.

In Covering the Plane with Rep-Tiles (3–8), students discover and explore a special kind of tiling of the plane. Rep-tiles are geometric figures such that n copies can fit together to form a larger, similar figure.

ReadWriteThink
Students explore shape and pattern through an adapted sketch-to-stretch strategy and read-alouds of winter-themed books in the lesson Teaching Shapes Using Read-Alouds, Visualization, and Sketch to Stretch (K–2).

Science NetLinks
In A Matter of Pattern (K–2), students concretely experiment with patterns by creating and predicting patterns formed when making paper snowflakes. They then construct understanding that patterns may be predicted based on observation.

One of Sir Roger Penrose’s many contributions to math and science was his work in quantum physics, some of which involved calculating energy in black holes and participating in what some call “the greatest debate in history” when he debated Stephen Hawking over theories of the universe. Use the Science NetLinks lesson Black Holes (9–12) to help students learn about the existence of black holes.