Starting off Term 4, Class 8 are journeying through one of mathematics’ most fascinating landscapes — the world of Pi and Pythagoras. Through story, exploration, and hands-on discovery, students have begun uncovering the deep connection between form, rhythm, and number that underpins both nature and geometry.

The Main Lesson began with a reflection on cycles in nature, noticing how circles appear all around us — in the sun and moon, the changing seasons, the growth rings of trees, and the life cycles of plants and animals. From there, students explored the parts of a circle to find relationships between diameter, radius, and circumference.

Their investigations led to the remarkable discovery that for every circle, the ratio between the circumference and the diameter is always the same. This mysterious and infinite number Pi (π)  became our focus. As the Main Lesson continues, students will meet Archimedes, who first approximated Pi using polygons, and consider how this simple ratio links the natural and mathematical worlds.

With rulers, compasses, and imagination, the class will apply Pi to calculate circumference and area, and explore the beauty of geometry through artistic constructions and “pizza-slice” circle dissections to visualise area formulas. Students will also connect their learning to the importance of circles in First Nations cultures, linking the area of a circle to the space taken up by dancing circles made up of different-sized groups.

The second part of the block will turn to Pythagoras, the ancient Greek philosopher who saw number and harmony as the foundation of the universe. Through practical investigations, students will build and compare right-angled triangles, physically fitting the squares of sides a and b into c, and witnessing the truth of the Pythagorean theorem unfold before their eyes.

They will then extend their explorations into irrational numbers, creating colourful Pythagorean Spirals to visualise square roots and the infinite growth of geometric relationships. To complete the block, students will delve into the age-old challenge of “squaring the circle,” an activity that invites reflection on the limits of measurement and the wonder of infinity.

This Main Lesson beautifully brings together mathematics, art, and history, reminding us that geometry is not just about numbers — it is a way of seeing the harmony within the world. Class 8’s work shows that the same principles that shape a circle or triangle are also at play in the turning of the planets and the patterns of life itself.

Juliana Sao Pedro Gusmao & Tamsin Formaggio

Maths / Science Teachers