Image of the Week: Patterning in the Real World

Patterning in the Real World

Humans make and seek patterns everywhere we go. Our brains look for pattern and structure in every space as a way of make sense of our world. And mathematics is fundamentally about understanding patterns, making it a fundamental human activity. In the last few weeks, we share patterns that we constructed using dominoes and Geostix, but patterns exist in the real world, too. Wherever humans make their homes, they design spaces with rhythmic structures, embedding patterns in the streets, buildings, and communities. The human world is a rich and authentic source of complex patterns for students of all ages to notice, analyze, and extend. Take a look at our image of the week, taken from apartment buildings in Tribeca in New York City. You’ll find similar structures in many cities around the world. What patterns do you see?

There are dozens of patterns embedded in the façades of these buildings. Notice the rhythm of the stones running across the top of the building. Notice how each floor repeats the same overall structure, which has windows in groups of three. The buildings alternate color, emphasizing the structure of three windows across each building. Each window is, itself, made of a 3 x 4 array of panes, topped with an arch.  And notice the fire escapes, how they zigzag down the face of each building, moving across then diagonally. The horizontal parts of the fire escapes have a repeated pattern – again in threes – of squares with Xs through each. No matter what element you focus your eye on, you’ll see that it is part of a larger structure that repeats:

Often in school we ask students to look for patterns in artificial situations we have constructed, like a string of unifix cubes in alternating colors. We keep the patterns simple in the hopes this will help students identify and extend the pattern. But staying in this patterning space gives students the false impression that patterns are typically simple or only found in carefully curated spaces. In reality, in the real world, patterns overlap and interplay; they are in every space students see each day. Every time your students see a building or walk down a sidewalk, they are confronted with the patterns humans have created, and they can be doing the mathematical work to understand how they organize our world.

Invite your students to examine patterns in the real world with this image of the week, or any of the dozens of other real world patterning activities we have on our website.  After you try this activity with one of our images, take your students on a pattern walk outside your school building! Schools are rich in patterns – in stones and windows like the image of the week – but also plants, sidewalks, doors, trashcans, downspouts, brickwork, roof lines, bike racks, stairs, handrails, and many other features. Students can take photos, draw sketches, or just point out to one another the patterns they see in a space at which they may have never looked closely.

To multiplicity, cheers!

Jen Munson and the multiplicity lab group