Maths and Sport

Summary

When this resource was first used, it was around the time of the Commonwealth Games and World Cup held in 2002. This material focuses on the maths of various sports, giving students an opportunity to model what is happening on the sports field in terms of mathematics.

This material could be used to supplement GCSE or A level courses in maths or physics. Students will encounter the concepts of mass, weight, gravity, work, energy, and power. Alternatively, they could work on the probabilities involved in ranking tables and league tables. Simple projectiles are also covered.

You can find information about a variety of sports at http://news.bbc.co.uk/sportacademy/default.stm

This website was used with videoconferences led by Professor John Barrow of the Millennium Mathematics Project, University of Cambridge, and a very well-known author of many popular books on mathematics. Schools involved in these videoconferences came from Fareham, India, London, and Singapore.

Any student or teacher is now welcome to use it. Comments or requests for help should be sent to Jenny Gage (jag55@cam.ac.uk).

Talk

• Introduction to the Videoconference. An introduction to the maths of sport, and to the content which John will introduce during his first videoconference, which students will work on further as they do their projects.
• Introduction to John's talk. All these sections contain the prepared slides John used at the conference at the moment, as a reminder for those involved of the content. As soon as possible, we will add a fuller text for those who were not present.
• Weight and strength.
• Effects of gravity and wind.
• May the best team win.

Project work

• Preliminary Material. This page contains material students need to have considered before the first videoconference if they are to understand it fully.
• Project 1: Track and Field Athletics. Maths of high jump, sprinting, distance running, long jump plus effects of variation in the value of g and wind assistance
  Schools involved:John Kelly Girls Technology College, London; Seven Kings School, London; Pickering High School, Hull; Lady Ankal Vankata Subba Rao Matriculation School, India
• Project 2: Strength and size - the effects of scaling. This is about how strength events are affected by the size of the person competing. It includes weight lifting, jumping and rowing.
  Schools involved Northolt School, London; Queens Park School, London; Chettinad Vidyasharam School, India; Bedok Town Secondary School, Singapore
• Project work 3: Team games. This is about using mathematical modelling to make predictions about winners and losers in team games. It involves simulating a league, and seeing if the best team actually wins.
  Schools involved: Quintin Kynaston School, London; Henry Cort Community School, Fareham; Padma Seshadri Bal Bhavan Senior Secondary School, India
• Extension material for all three project areas. Rather than trying to cover everything in your project area, it might be better to concentrate on one or two areas, then look here to see if you can extend what you have done so far.

Additional material

• Additional Notes. Background notes for the projects for students and teachers. These notes give you the derivation of the wind assistance formula in Project 1, and some background notes on log-log graphs for Project 2, and generating random numbers with a graphic calculator or Excel for Project 3. If anyone doing these projects thinks of something else that would be useful here, let me know (jag55@cam.ac.uk) as soon as you can, and I'll do something about it. You can get further information from the following article: "Physics of Sport" American Journal of Physics, July 1986, volume 54, issue 7, pp Resource letter PS-1. This Resource Letter provides a guide to the literature on the physics of sports. The letter E after an item indicates elementary level or maths of general interest to persons becoming informed in the field. If you would like a copy of this article, let us know (jag55@cam.ac.uk) and we will send it to you.