During weeks four through to six, Class 8 stepped through an invisible threshold—into the realm of Plato’s Academy. Inspired by Plato’s Theory of Forms, we explored the idea that perfect shapes already exist in an invisible realm of truth. What we see or draw are mere reflections of these perfect ideals. Through this lens, geometry became more than a technical skill—it became a way of seeing and connecting with the harmony beneath the surface of things. 

We began with the foundations: learning to construct regular polygons using only a straight edge and compass, just as the ancients did. With these tools, students stepped into the historical and artistic tradition of geometry—experiencing firsthand the precision and patience it requires. 

From this base, we explored the art of tessellation, first through guided practice and then through a creative project using the Seed of Life as inspiration. Students designed intricate tessellation posters that expressed both symmetry and imagination—revealing how geometry lives in the natural world and in the human hand. 

With growing confidence, we entered the heart of the lesson: the five Platonic Solids—the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Each was constructed, studied, and admired for its unique properties. Through careful observation, students uncovered hidden relationships within and among the solids—how the faces meet, how the angles relate, and how one solid can be nested within another. 

To deepen this exploration, students drew and crafted nets and perspective views of each solid, again using only traditional geometric tools. This not only developed their mathematical thinking but also cultivated an appreciation for how geometry evolved historically—emerging from the minds and hands of early thinkers seeking order in the cosmos. 

Throughout this Main Lesson, the students were invited not just to do geometry, but to experience it as a bridge between thought and form, spirit and matter. The block wove together logic and beauty, precision and creativity—a reflection of the greater whole that geometry reveals. 

Tamsin Formaggio & Juliana Sao Pedro Gusmao

Mathematics and Science Teachers