SPS Mathematics Blog

This June, we welcomed students for our annual Maths Partnership Day, running across Thursday 18 and Friday 19 June. Spread across two cohorts and two days of activities, the event brought together a rich mix of hands-on challenges, deep mathematical thinking, and collaborative problem-solving. Both days kicked off with Puzzles and Problems during the arrival slot, setting the tone nicely for what was to follow. From there, students moved into four structured sessions across the day, covering a diverse range of topics. Thursday's highlights included an exploration of lattice methods and area, a perennial favourite in the form of Sticky Tape and Spaghetti (always a reliable test of structural intuition), and a session on Chomp and Other Games, which gave students the chance to think about combinatorial strategy. A Cypher Challenge in the Physics Corridor added a codebreaking flavour to the early afternoon. Friday offered a different mathematical menu. Students tackled Modular Ari...

Students at St Paul's first learned about the OCR Large Dataset in L8th. Today, however, Ms Fickling led a lecture for the U8th to refresh this knowledge with its applications for the A level statistics exam. The session started by defining the key differences between categories of the dataset such as Unitary and Metropolitan Authorities. Then exam questions were given and strategies for approaching them were discussed. An excellent session just in time for the A level exam (fancy dress was optional!)

Déjà vu was a feature of the last Hans Woyda match report, and fittingly enough it reared its head again in Tuesday’s Semi Final against Haberdashers’ Boys’ School. This time, we have to go back to the 2023-24 Semi Final, when we welcomed Habs into St Paul’s for an exceedingly close game. In that match, St Paul’s were either tied or in the lead throughout, until Habs edged in front for the first time in the penultimate question and held off our U8th on the last question to extend their lead even further, knocking us out of the competition with a final score of 53 – 49. Two significant changes gave me hope that history wasn’t about to repeat itself. First, we were the ones making the long journey to the outskirts of Watford this time, as hosting duties had fallen to Habs for this match. Second, none of the current SPS team of Haoming (4 th ), Rafael (6 th ), Lucas (L8 th ) and Adavya (U8 th ) had been involved in that tragic loss. As the voyage northwards came to an end and we made our ...

I found myself experiencing the strangest sense of déjà vu in the run-up to the second knockout round of the Hans Woyda competition this year. Once again, we were due to host Queen Elizabeth’s School for the quarter final, and once again, when finding a suitable date for the match I had to navigate Olympiads, Chess tournaments and Adavya’s return to the Romanian Master of Mathematics competition after remedy. With few options left before the 24 th  February deadline, we ended up being forced to schedule the match for the last day of half term, and to avoid keeping everyone from their holiday we came to the unorthodox conclusion that the best time to host the match would be during lunch break. So it was that the SPS team of Haoming (4 th ), Rafael (6 th ), Lucas (L8 th ) and Adavya (U8 th ) took their seats straight after period 4 to kick off the match. Last year we ended up winning against Queen Elizabeth’s, gaining an early lead and maintaining it until the end of the match, ...

This talk took us through one of the most counterintuitive ideas: that not every polynomial can be factorised in terms of its solutions and that the barrier for that is so low as to be the cubic. Starting with the quadratic, a base of knowledge we all know, Toller's exceptional talk then brought us to the cubic, explaining its quirks and how to reduce it to a form we all know, with a neat trick to turn it into a depressed cubic. He then used a clever method to split x into u+v and then made everything a quadratic. After following through the algebra, we transitioned into the quartic, having solved a few examples with both real and complex roots. For the quartic, the method was more complicated but doable all the same. Yet he posed the idea that the quintic cannot be solved with a formula. This took us into a tour of group theory, starting with what a group is and its symmetries, then moving to the symmetric group of n things. Then he posed a clever game where, knowing the roots of ...

The start of the spring term is always a bittersweet moment in the Hans Woyda calendar. The excitement of moving through to the knockout rounds is tempered by the knowledge that I will soon have to pick the final team of 4 from the superb squad of 12 pupils who took part in last term’s group stage matches. As ever, the selection trials were fiercely contested, and any of the 81 different possible teams would have stood us in good stead for the remainder of the competition, but eventually Haoming (4 th ), Rafael (6 th ), Lucas (L8 th ) and Adavya (U8 th ) emerged victorious. I had provided each of the team members with a set of practice questions for the journey which they eagerly worked through, swapping sheets with each other and comparing methods for the hardest questions, and at one point Adavya started loudly listing all of the squares from  16 2 to  29 2 to ensure he had them to hand in case he needed them later. The west London traffic and soporific drizzle had dampene...