10 Dec 2024

Year 7–9 Academic Scholars had an engaging and challenging Maths session

A creative Maths session exploring Pick’s Theorem.

The Year 7–9 Academic Scholars had an engaging and challenging session led by Maths teacher Emma Arnold. Designed to stretch the minds of Seaford’s most able mathematicians, the session delved into Pick’s Theorem, a fascinating mathematical formula used to calculate the area of polygons with vertices on a lattice grid. 

Pick’s Theorem has broad applications in geometry and combinatorics, making it a great topic for exploration. Students worked with shapes such as squares, rectangles, triangles, octagons and rhombuses to uncover patterns and develop insights into this formula. 

Key Concepts Explored: 

P (Perimeter Dots): The number of dots that lie along the shape's boundary. 

I (Interior Dots): The number of dots fully enclosed within the shape. 

A (Area): The area of the shape itself. 

The class started by examining the area of a pentagon, discussing different strategies and identifying relationships between P, I, and A. Students hypothesised and tested various methods for finding connections between these values. 

Through hands-on exploration and pattern analysis, students noticed intriguing trends and gradually, they worked out a formula that fit every case they tested: 

P/2 add I and takeaway 1 = A 

Emma Arnold encouraged students to test this formula with various shapes, confirming its accuracy. 

One student said: “It feels like there’s something going on here” as patterns emerged from their calculations. This moment of discovery is exactly what these sessions aim to spark—a deeper understanding and a passion for mathematical exploration. 

The session was an inspiring example of how exploring new concepts through collaboration and curiosity can lead to valuable insights. Pick’s Theorem will surely remain a memorable topic for these budding mathematicians.  

Thank you Emma for a fantastic session!