Grade 7: Celebrating Möbius’s Birthday in Math
When seventh graders walked into math class, streamers hung from the ceiling, signaling that Grade 7 math teacher Mr. Gregory Montoya had something special planned. To mark the birthday of August Ferdinand Möbius, the 19th-century mathematician known for studying unusual shapes and surfaces, students spent part of class exploring one of his most famous ideas: the Möbius strip.
To begin, students created their own strips by giving a narrow band of paper a half-twist before taping the ends together. This simple step forms a shape with only one continuous side. Students tested this by drawing a pencil line down the middle of the strip. As their lines looped all the way around and returned to the starting point, they discovered firsthand how the Möbius strip behaves.
With this understanding in place, Mr. Montoya brought the class together for a demonstration to show what happens when the strip is cut. When he followed the same line with scissors, the strip didn’t separate into two pieces as many expected. Instead, it widened into a larger loop with two twists. The unexpected result sparked excitement across the room as students wondered how that was possible.
To connect the activity to the real world, Mr. Montoya explained that certain machine belts use a twist inspired by the Möbius strip to help them wear more evenly. Throughout the lesson, students practiced skills central to Grade 7 math, including spatial reasoning, recognizing patterns, and observing how small changes can affect the properties of a shape.
By celebrating Möbius’s birthday in this hands-on way, students experienced how mathematical ideas can be both surprising and fun, and how a simple twist of paper can reveal something entirely new.
Graland Country Day School
Graland Country Day School is a private school in Denver, Colorado, serving students in preschool, kindergarten, elementary, and middle school. Founded in Denver in 1927, Graland incorporates a rich, experiential learning approach in a traditional classroom setting, emphasizing the development of globally and socially conscious leaders who excel academically.
