# Training schedule

## Problem

- 200m sprint
- 800m run
- 100m hurdles
- high jump
- long jump
- shot put
- javelin

The values for a, b, and c in each event are given below:

Event | a | b | c |

200 meters | 4.99087 | 42.5 | 1.81 |

800 meters | 0.11193 | 254 | 1.88 |

100 metres hurdles | 9.23076 | 26.7 | 1.835 |

High Jump | 1.84523 | 75 | 1.348 |

Long Jump | 0.188807 | 210 | 1.41 |

Shot Put | 56.0211 | 1.5 | 1.05 |

Javelin Throw | 15.9803 | 3.8 | 1.04 |

In the table below are the best times and distances of an Olympic hopeful in training, as well as the World Records for each heptathlon event (as of April 2011).

Event | Olympic hopeful | World records |

200m | 25.34s | 21.34s |

800m | 2min 13.00s | 1min 53.28s |

100m hurdles | 13.65s | 12.21s |

High jump | 1.43m | 2.09m |

Long jump | 5.67m | 7.52m |

Shot put | 12.45m | 22.63m |

Javelin | 45.05m | 72.28m |

## Getting Started

Why not use a spreadsheet to calculate quickly the score for each event given the athlete's times or distances?

Then try tweaking her times and distances to see how her scores can be affected by different training schedules.

## Student Solutions

Joseph from Park View Community School sent us the following solution:

Find the percentage away from the world record for each event. Increase the 3 lowest events by 20% and accordingly maintain current levels for the 3 greatest events. increase performance by 10% on the remaining event. I calculated all points including all percentage increases as well using excel.

You can download Joseph's spreadsheet to see how he calculated this solution here.

## Teachers' Resources

### Why do this problem?

When we watch sports coverage of the multi-discipline events such as the heptathlon, the scoring mechanism is not usually made explicit. This problem explores some of the maths behind the scoring system and invites students to optimise an athlete's performance by choosing a suitable training schedule. Along the way, students can practise substituting into formulas, make sense of functions, and use spreadsheets to repeat routine calculations quickly.

### Possible approach

Set the scene by introducing the seven heptathlon events (perhaps asking students if they can name the events). Then display the two equations:

### Key questions

### Possible support

Students may opt to use a calculator to solve this problem, but it is much more efficient to use a spreadsheet. In order to make the most of the task, it may be worthwhile spending some time with the whole class talking about how to set up formulas in a spreadsheet and how to make changes to investigate different training schedules.### Possible extension