The MYP 4 Extended Mathematics classroom recently undertook a rigorous investigative project bridging the gap between abstract geometry and planetary physics. The task required students to treat the Earth and a physical classroom globe as mathematically similar spheres, exploring how properties such as distance, surface area, and volume behave when scaled across vast dimensions.

Rather than simply solving for a mathematical constant, students navigated a multi-stage inquiry that tested their ability to apply geometric principles to real-world geography. At its core, the investigation focused on the relationship between two spheres of vastly different scales.

The resulting presentations were not merely a display of correct answers, but a testament to the growth of our students as holistic learners. Several IB Learner Profile attributes were prominently on display:

• Thinkers: Students demonstrated critical thinking by recognizing that scaling is not "one size fits all." They had to distinguish when to use the linear scale factor, the area scale factor, and the volume scale factor. Applying these different dimensions to calculate the cost of paint versus the volume of nitrogen required complex problem-solving and a deep understanding of geometric relationships.
• Inquirers: The project began with a "how" and a "why." Students showed great curiosity in researching the Earth’s physical properties. Rather than simply accepting provided figures, they questioned how environmental factors—such as density and atmospheric pressure—might affect their mathematical models, demonstrating a drive for independent research.
• Communicators: Groups used visual aids, clear diagrams, and precise mathematical language to communicate their rationale. They explained how a string measured in centimeters on a desk could represent thousands of kilometers across the globe.
• Knowledgeable: By integrating concepts from geography (coordinate systems), physics (mass and volume), and economics (unit pricing), students showcased a broad range of understanding. They applied 3D geometry to solve tasks that mirrored the real-world challenges faced by cartographers and engineers.

Through this task, MYP 4 extended maths students moved beyond the textbook. They realized that mathematics is the language we use to describe our place in the universe. By shrinking the Earth to the size of a globe, they expanded their own understanding of how proportional reasoning shapes the world around us.