Thursday 11th January saw 12 Year 10 students head to the University of East Anglia for an ‘Explore Maths’ day hosted by the Advanced Maths Support Programme. An opportunity to listen to inspiring enrichment talks and attend hands-on workshops, all on a mathematical theme, our Year 10s approached the day with enthusiasm and open minds.
Before the event started, students were reminded of the different mathematical pathways and options they could take post 16. We look forward to a number of them choosing A-Level Maths and A-Level Further Maths with us a Dereham Sixth Form when the time comes.
The first speaker was Ben Sparks, a former Maths teacher, who now gives talks all over the country. He posed the question, ‘where do numbers come from?’ This immediately sparked all sorts of questions and debate and really got the audience thinking. He took us on a journey from the counting numbers, to fractions (rational numbers), irrational numbers, negative numbers, zero and then complex numbers. It was a really interesting look at how people have used numbers over history and got us thinking about whether numbers were created or discovered. We couldn’t come up with a definitive answer but it gave us all food for thought! This was the favourite session of a number of our group.
Our first hands-on workshop was based on the Bridges of Königsberg problem. According to folklore, the question arose of whether a citizen could take a walk through the town in such a way that each of the seven bridges would be crossed exactly once. Give it a try!
In 1735 the Swiss mathematician Leonhard Euler presented a solution to this problem, concluding that such a walk was impossible. This led to an introduction to graph theory, a branch of mathematics that is studied at university. Our group also looked at the envelope problem – deciding whether the open, double-open or closed envelope can be drawn completely without taking your pencil off the paper or travelling along an edge more than once. They could link the introduction to graph theory to this problem to see which of the possibilities worked and which didn’t.
The second workshop was all about McDonalds and Maths! Ever been to a McDonalds and order McNuggets? In the UK they come in boxes of 6, 9 and 20 (if you’re feeling particularly hungry). Have you ever thought which numbers of McNuggets can’t be ordered using combinations of boxes of 6, 9 and 20? Well, this was the challenge set to our students. They set about finding which numbers from 1 to 60 could and couldn’t be made and it resulted in them finding the McNugget number – the largest number of McNuggets that cannot be made. We won’t spoil it for you – have a go and see if you can work it out!
This activity lead onto the group being introduced to Frobenius numbers. (For those that are interested, for two coprime numbers, the Frobenius number is the greatest integer that cannot be expressed as a linear combination of the two numbers). For example, if you are looking at boxes of 5 and 7 McNuggets, the greatest number of McNuggets you can’t make is 23. After some investigation our students were able to come up with a general formula for this problem – amazing!
After lunch, we were treated to the final talk of the day by Alison Kiddle, a former Maths teacher, who also now gives talks. Her talk was titled ‘Noticing, Wondering and Mathematical beauty’ and was aimed at getting us all to take notice and think about the beauty in mathematics. Whether it’s noticing patterns or symmetry in nature with flowers or bee’s honeycomb, or noticing the maths in road signs or buildings, or even in abstract maths with Pascal’s triangle or Sierpinski’s triangle. It really got everyone thinking about the maths around them every day.
A big thank you to AMSP for putting on this inspiring day of maths and to the UEA for hosting the event – we all had a great time putting some maths already known into practice but also learning about new maths from our problem solving sessions.
