Mathematics in School

16 Mathematics in School, November 2021 The MA website www.m-a.org.uk Extracurricular Maths Sports Elsewhere in this special edition, we read about the diverse ways in which mathematics is used by archaeologists, journalists, musicians and opticians and how it is, in Sue Greaney’s words, ‘connected to everything’ (page 3). As a historian turned mathematician with a knitting obsession, I am always excited by the opportunity to go “off curriculum”, and at one time ran a club for able and keen year 5 and 6 students called ‘Awesome Maths’. Each half term had a theme which allowed broad and varied exploration of mathematics (for example, mazes, art, time, optical illusions and maps). One half term was dedicated to exploring the many different ways in which maths is connected to sport. Here are some of the sport activities that went down particularly well with both me and the young mathematicians. Balls Why is a football a truncated icosahedron? Starting from regular tilings, we used the patterns and generalisations we had noticed about angles in the plane to prove that there are only five regular solids. We built them and had some fun establishing that none of them was suitable for use as a football, which led us to see how the icosahedron can be adapted through truncation to a better approximation of a sphere. We discussedwhywe couldn’t just have a sphere (because we needed a net constructed from2-dimensional shapes) which led intoa further session trying to construct nets for other sports balls (tennis balls, rugby balls, basketballs) and researching design and construction techniques for others. While we didn’t go into the mechanics behind the dimples on a golf ball, there was no little excitement that it was mathematics which determined their existence and design. Scoring What final scores are impossible in rugby union? What final scores can be achieved in more than one way, and is there a pattern to this? Only two of the children knew anything about rugby before we started – another insisted that he had no interest in sport because he was a maths geek. Needless to say, by the time we had indulged in a little number theory exploring the different combinations of scores, he was a convert! Subjective scoring created even more excitement. We started with the Salt Lake City skating scandal of 2002 and the consequent revamped scoring system which we agreed was still not perfect and so set about designing and then testing our own scoring system against a range of scenarios. Yes, not only were we doing maths in the context of sport, but we got real and passionate debate raging too! Tournaments In a knock-out tournament with 120 entrants, how many matches are played? The simplicity of the solution (always n – 1, because everyone loses exactly one match except the winner) wowed the pupils, as much as the complexity of tournament design that we moved onto next. We modelled tournaments based on a knock- out, round robin or hybrid (round robin followed by knock-out, as the football world cup) structures before discussing the relative pros and cons. Again, there was excellent debate exploring how mathematical models influence ideas of fairness and entertainment value. We also explored league tables, including having a beetle drive to critique ladder leagues and the history of how the football league tables have been decided and why we have our current system. by Fiona Yardley Keywords:  Extracurricular; Sport Author Fiona Yardley, Senior Lecturer, Faculty of Education, Canterbury Christ Church University, North Holmes Road, Canterbury CT1 1QU e-mail: fiona.yardley@canterbury.ac.uk Icosahedron and truncated icosahedron (football) Images created by Ben Sparks