Year 9 Investigate Euler’s Theorem with Jelly Beans and Cocktail Sticks
Year 9 took a hands-on approach to exploring one of the most beautiful relationships in mathematics: Euler’s Theorem. Armed with nothing more than jelly beans, cocktail sticks and a lot of curiosity, students built their own 3D shapes to uncover a powerful rule connecting faces, edges, and vertices.
Rather than being told the formula, students were challenged to discover it.
They began by constructing different 3D shapes using jelly beans as vertices and cocktail sticks as edges. From cubes to pyramids to triangular prisms, the classroom quickly filled with colourful geometric models. As each shape was completed, students carefully counted:
- Faces
- Edges
- Vertices
They recorded their results in a table and searched for a pattern.
Soon, the excitement grew as pupils began to notice something surprising…no matter the shape, the same relationship kept appearing.
Faces + Vertices − Edges = 2
They had independently arrived at Euler’s Theorem.
Learning in Action
The practical element made a big difference. Handling the models allowed students to see the structure of each solid clearly. Counting edges on a drawing can be tricky; counting cocktail sticks is not!
Students then used an online activity to test their understanding further by identifying faces, edges and vertices on a range of digital 3D models, applying the rule they had just discovered physically.
The combination of concrete modelling and digital practice helped to secure both understanding and confidence.
The Mathematician Behind the Theorem – Leonhard Euler
Leonhard Euler was born on 15 April 1707 and died on 18 September 1783. He lived for 76 years and in that time produced more mathematics than most people could read in a lifetime.
His work laid foundations for much of modern mathematics and Euler’s Theorem is still a key idea in geometry and topology today.
What made this lesson special is that Year 9 didn’t just learn Euler’s rule, they recreated the discovery process themselves.
Students’ Models and Investigations
Below are some moments captured during the investigation as students built, tested, counted and generalised their findings:
Why this mattered:
This lesson wasn’t just about counting edges. It developed:
- Problem solving
- Pattern spotting
- Mathematical reasoning
- Collaborative discussion
- Confidence in forming generalisations.
Most importantly, students experienced the joy of discovering a mathematical rule for themselves, the same way mathematicians do.
A table full of jelly beans and cocktail sticks turned into a genuine mathematical investigation, proving that sometimes the simplest resources create the richest learning.
Mrs Bennett
Maths Department
