Mathematical Methods Unit 4

Further Mathematics Unit 4

Geometry and measurement module sample learning activity – championship competitions The modelling or problem-solving task is to be of 2 - 3 hours duration over a period of 1 week.

Introduction This task considers dimensions and measurements associated with various championship sports and international travel associated with corresponding events. Relevant context information can be obtained from various web sources. Every year, championships are held for a variety of sports at major cities in many different parts of the world. In addition, at regular intervals, there are major events such the IAAF World Championships (Indoor in Portland in 2016, Outdoor in London in 2017), Olympic Games (Rio de Janeiro in 2016), the European Cup for football (Paris in 2016) or the World Cup for football (Russia in 2018). Travel information can be obtained from websites such as: http://www.timeanddate.com/worldclock/converter.html; http://www.worldatlas.com/aatlas/infopage/distance_between_cities.htm and http://www.webjet.com.au/ . Many sports, particularly in track and field athletics events, have specific requirements for field design in terms of shape, measurement and line marking which can be accessed from websites such as: http://www.pntf.org/officials/ivars/Throwing_Event_Sector_Angles_Rev_F1.pdf; http://track.isport.com/track-guides/track-field-dimensions and www.fifa.com.

Part 1 Consider the set up for the field or area of competition for selected sports. a. Use relevant information to determine the amount of paint required to mark the lines required to delineate or mark lanes or other guides and boundaries for fields of play or areas of competition, given that the paint to be used has a specified rate of coverage in terms of square metres per litre. b. Determine the area of the competition field, as well as any safety allowances (to allow for errant javelin, discus or hammer throws for example) to a required of accuracy. c. Determine a suitable seating plan so that there is sufficient seating for the expected number of spectators, and that each spectator has a good view of the competition.

© VCAA Page 1 Part 2 Consider aspects of the competition and athletic performance. a. For throwing events, determine distances of or between, and bearings, of attempts, and explain whether a particular attempt of a particular distance and bearing is a fair or foul attempt. b. Determine how much further a distance runner will travel if they are forced to run at least a metre outside the ideal line for a specified number of laps. c. For sailing events, the race officer will need to set a particular course depending on the direction of the wind. Draw an accurate scale diagram of a sailing course for a particular event according to specified dimensions and conditions.

Part 3 Consider travel to international competition events. a. Select an international competition, and specify its location. Find another town/city in a different country on the same meridian of longitude and also another town/city in yet another country on the same parallel of latitude b. Calculate the distances between each of the three towns and an estimate of the area bounded by arcs that connect them. c. Calculate the time difference between this competition location and a range of capital cities from around the globe. A reporter from one of these has to present live reports to their home country to be received at a specific local time. Determine the local time at the venue for these reports to be made. e. Determine the travel time for an athlete departing a specified location at a particular local time and arriving at the venue at a particular local time.

Areas of study The following content from the areas of study is addressed through this task.

Area of study Content dot points Module – Geometry & measurement : Measurement & 1, 2, 3, 4 trigonometry 1, 2, 3, 4, 5, 6, 7 Module – Geometry & measurement : Spherical geometry Further Mathematics Unit 4

Outcomes The following outcomes, key knowledge and key skills are addressed through this task.

Outcome Key knowledge dot point Key skill dot point

1 1, 2, 3, 4, 5 1, 2, 3, 4, 5, 6

2 1, 2, 3, 4 1, 2, 3

3 1, 2, 3, 4, 5 1, 2, 3, 4, 8, 9, 10, 11