How to take the perfect penalty

In this summer of the European Championships and the Olympics, we thought this would be the perfect opportunity to explore sport from an angle you might not have thought much about before: the Mathematics of Sport! In these talks, Dr Tom Crawford (a lecturer in Maths at the University of Oxford, and founder of the Tom Rocks Maths website) looks how maths can be used to model various features of two of the world’s most popular sports: football and athletics.

In this first talk, Tom looks at the maths of penalties in a game of football, using Pythagoras’ Theorem, quadratic equations and other mathematical techniques to try to work out how to take the perfect penalty kick.

Extension activity

After watching Dr Tom Crawford’s video, take a look at the diagram below, which shows the placement of the 5 penalty kicks for two teams in a penalty shootout.

  1. Based on the content discussed in the lecture, which team would you expect to win?
  2. Can you calculate the ‘expected number of penalties’ that each team will score based on the placements shown?

Share with us!

We would love to see any examples of work that you do during your Inspire Summer School. This can be a photo of something you have made, a picture you have drawn, some written work (e.g. the start of a speech, or the answer to a question we asked), or some thoughts you have about what you have learnt! Submit your work to us through this form.

All pupils who share their work with us by August 31 2021 will receive a certificate of participation in the summer school and will be entered into a prize draw! A £10 Amazon voucher will be awarded to each winning entry, selected randomly from all submissions. If you give us permission, your entry may be shared on Inspire Digital and our social media alongside your first name.