During Week 8 to 10 of Term 1, Class 9 embarked on a dynamic and hands-on journey into the world of Conic Sections, in their Main Lesson block. Rather than beginning with abstract equations, students were invited to first engage with the physical and spatial reality of the topic—through direct, playful, and artistic experiences that brought mathematical concepts vividly to life. 

The Main Lesson opened with a series of explorations designed to build an experiential foundation. Students began by constructing cones from paper and straws. A highlight was cutting through party hats and play dough cones—an engaging and tactile way to experience how these familiar forms arise naturally from simple spatial transformations. By slicing through them at different angles they revealed the four distinct conic sections: the circle, ellipse, parabola, and hyperbola.  

From this experiential base, the class moved into more formal construction methods. Using compass and ruler, students constructed conic sections from intersecting circles and later through the elegant technique of envelope constructions. These artistic processes revealed the deep geometric harmony that underpins these shapes and showed clearly how each form is a metamorphosis of the circle—transformed through movement and perspective. 

This exploration wasn’t limited to the visual or tactile. Students also learned to describe conic sections algebraically using Cartesian equations, and then through the lens of locus definitions - bridging the gap between concrete experience and abstract reasoning. They observed how the shifting of foci transforms one conic section into another, deepening their understanding of form as dynamic and fluid. 

This Main lesson not only sharpened students’ spatial visualisation skills but also offered profound insights into the forces and forms shaping both the natural and built environment. From the orbit of planets to the design of bridges, the students discovered how conic sections appear all around us. 

Importantly, this topic laid essential groundwork for future study in Projective Geometry, where the idea of infinity and the interplay of space and form are explored further. Students gained an inner sense of the polar forces - radial and peripheral - that shape space, and learned to see geometry not just as a fixed system, but as a living, evolving language of form. 

Through the conic sections block, students experienced a truly integrative approach to mathematics—blending movement, drawing, construction, and algebra to build a rich and lasting understanding. It was a joy to witness the energy and creativity they brought to this topic, and the clarity they gained in return.