7489 /www/nrich/html/content/id/7489/ 1 2011-06-28T10:40:59 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>Here are ten graphs showing how Olympic records have changed over time in ten athletic events. You can click on the links to view each graph, or download <a href="http://nrich.maths.org/content/id/7489/Olympic%20Record%20Graphs.pdf" target="_blank">this PDF</a> with all the graphs.</p> <div> <ul id="olympicgraphs"> <li><a href="http://nrich.maths.org/content/id/7489/Graph1.jpg" target="_blank">Graph 1</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph2.jpg" target="_blank">Graph 2</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph3.jpg" target="_blank">Graph 3</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph4.jpg" target="_blank">Graph 4</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph5.jpg" target="_blank">Graph 5</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph6.jpg" target="_blank">Graph 6</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph7.jpg" target="_blank">Graph 7</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph8.jpg" target="_blank">Graph 8</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph9.jpg" target="_blank">Graph 9</a></li> <li><a href="http://nrich.maths.org/content/id/7489/Graph10.jpg" target="_blank">Graph 10</a></li> </ul> <div id="olympicaftergraphs"><comment> This has CSS clear:left, because I can&#39;t work out the &quot;proper&quot; way to stack the above horizontally but make the rest of the content go underneath. </comment></div> </div> <p><strong>Can you deduce which event each graph represents?</strong></p> <p>Here are some questions to consider, which may help you to make sense of the graphs:</p> <ul> <li>Can you determine what the units might be on the vertical axis for each graph?</li> <li>Why do some graphs show a decreasing trend and some an increasing trend?</li> <li>Are there any unusual features on any of the graphs? Can you think of a plausible explanation for them?</li> </ul> <p><em>Thanks to Alan Parr for suggesting this problem.</em></p> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <br></br> <span class="editorial">Thank you to everyone who submitted solutions to this problem. You all did very well. Here are the answers:</span><br></br>  <br></br> <table border="1"> <tbody> <tr> <td style="text-align: center;">Graph</td> <td style="text-align: center;">Event</td> <td style="text-align: center;">Units</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">Men's 100 metres</td> <td style="text-align: center;">seconds</td> </tr> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">Men's Long Jump</td> <td style="text-align: center;">metres</td> </tr> <tr> <td style="text-align: center;">3</td> <td style="text-align: center;">Women's 1500 metres</td> <td style="text-align: center;">minutes</td> </tr> <tr> <td style="text-align: center;">4</td> <td style="text-align: center;">Men's High Jump</td> <td style="text-align: center;">metres</td> </tr> <tr> <td style="text-align: center;">5</td> <td style="text-align: center;">Men's Javelin</td> <td style="text-align: center;">metres</td> </tr> <tr> <td style="text-align: center;">6</td> <td style="text-align: center;">Women's High Jump</td> <td style="text-align: center;">metres</td> </tr> <tr> <td style="text-align: center;">7</td> <td style="text-align: center;">Men's Decathlon</td> <td style="text-align: center;">points</td> </tr> <tr> <td style="text-align: center;">8</td> <td style="text-align: center;">Women's 10000 metres</td> <td style="text-align: center;">minutes</td> </tr> <tr> <td style="text-align: center;">9</td> <td style="text-align: center;">Men's 4 x 100 metres relay</td> <td style="text-align: center;">seconds</td> </tr> <tr> <td style="text-align: center;">10</td> <td style="text-align: center;">Women's 100 metres</td> <td style="text-align: center;">seconds</td> </tr> </tbody> </table> <div> </div> <div><span class="editorial">Well done to students from Wilson's School, Jess Jemiera in Dubai, Broomhill in Aberdeen, St Helen's C of E Primary School, Allenbourn Middle School, Tenby Junior School, Lady Elizabeth Hastings School, Baston C of E Primary School, Leicester High School for Girls, Colonel Frank Seely School, Garden International School in Malaysia, All Saints School and Chatham Grammar School for Boys for getting them right.</span></div> <div> </div> <div><span class="editorial">Here are just some of the ways you justified your answers:</span></div> <div> </div> <div>The improvement of the results in the Olympics over time is expected due to the growing knowledge of the human body. We know all of the essentials, and added bonuses that help us to train the body and mind for the Olympic Games to get closer to our full potential.</div> <div><span class="editorial">(Joe, Chatham Grammar School for Boys)</span></div> <div> </div> <div>Looking at the graphs, we were straight away able to tell that decreasing records have to do with track events and increasing have to do with field events.</div> <div><span class="editorial">(Adriel, Garden International School )</span></div> <div> </div> <div>This is because in all of the running events, the person with the quickest, i.e. the smallest time wins. Therefore the records will be getting quicker and quicker, so the graph is decreasing. In throwing and jumping events, the person who gets the greatest distance or height wins i.e. the biggest so the records will get bigger and the graph will increase.</div> <div><span class="editorial">(Kartik from Wilson's School)</span></div> <div> </div> <div>We think that graph 1 is the Men's 100m race because we can see that the records start from the first ever Olympic games, which means it can't have been women as they weren't treated as equal to men and therefore would not have participated in the games.</div> <div><span class="editorial">(Pythagoreans, All Saints School)</span></div> <div> </div> <div><span class="editorial">Some of you were also able to explain unusual features on the graphs:</span></div> <div> </div> <div>With the Javelin they were throwing too far and there was danger of hitting the runners so they made the Javelins heavier in 1986.</div> <div><span class="editorial">(Sophie, Rae and Chloe - Jess Jumeirah, Dubai)</span></div> <div> </div> <div>For the Decathlon event, athletes were scored by the relative quality of their performance, not against each other, and we think the scoring system changed several times.</div> <div><span class="editorial">(Adriel, Garden International School)</span></div> <div> </div> <div>We think the men's javelin distance suddenly increased in 1956 because Frank Held invented the hollow javelin that gave it 27% more surface area therefore it made the javelin flight much longer.</div> <div><span class="editorial">(The group from Lady Elizabeth Hastings)</span></div> <div> </div> <div>The reason graph 2 rose up so drastically in 1968 may be because there was no drug-testing then and the person who set the record could've taken performance enhancing drugs.</div> <div><span class="editorial">(Emily, Garden International School)</span></div> <div> </div> <div><span style="font-style: italic;" class="editorial">Editor's note: In making his record jump in 1968, Beamon enjoyed a number of advantageous environmental factors. At an altitude of 2240 m (7349 ft), Mexico City's air had less resistance than air would have at sea level. This allows runners to run faster and jumpers to jump farther. In addition to Beamon's record, world records were broken in most of the sprinting and jumping events at the 1968 Olympic Games. Beamon also benefited from a trailing wind of 2 meters per second on his jump, the maximum allowable for record purposes.</span></div> <div> </div> <div> </div> <div><span class="editorial">Lots of you also noticed that there were no records made in 1940 or 1944 because the games were cancelled due to the Second World War. Well done everyone!</span></div> <br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3>Why do this problem?</h3> This problem gives students the opportunity to make sense of graphical data and challenges them to apply their own knowledge about athletics to explain and interpret key features of the graphs.<br></br> <h3>Possible approach</h3> <div>Arrange the class in groups of three or four, and give each group the <a href="/content/id/7489/Olympic%20Record%20Graphs.pdf">ten graphs</a>.</div> <div>(Alternatively, you could show the graphs using this <a href="/content/id/7489/Olympic%20Records.ppt">PowerPoint presentation</a>.)</div> <div> </div> <div>"You need to look at the graphs and work out which Olympic athletics event each graph represents. The graphs all show how the Olympic records have changed since the modern Olympics began."</div> <div> </div> <div>Give the groups plenty of time to look at all the graphs, discuss them and start to make sense of which events they could be. Towards the end, ask them to write down a list of the events.</div> <div> </div> <div>Collect the lists from each group. </div> <div> </div> <div>"Most of you thought graph 1 was ... and a few groups thought it was ... or ...</div> <div>Does anyone have any convincing reason why it might be ...? Or why it might NOT be ...?"</div> <div> </div> <div>Go through the graphs in this way to draw out the key points of the graphs and the convincing reasoning each group came up with. <a href="/content/id/7489/Olympic%20Athletics%20events.pdf">This list</a> has the ten events that actually generated the graphs (although not in order!)</div> <div> </div> <div>If a computer room is available, groups may wish to look up <a href="http://www.olympic.org/athletics">Olympic record data</a> online to check which event gave rise to each graph.</div> <div> </div> <h3>Key questions</h3> What can you deduce about the event if the record increases/decreases over time?<br></br> <br></br> <h3>Possible extension</h3> <div>Ask students to carry out some extra research in order to explain unusual features in the graphs, such as:</div> <ul> <li>Drastic changes</li> <li>Long gaps</li> <li>Absence of data in the early twentieth century</li> <li>Records that go both up and down</li> </ul> <h3>Possible support</h3> Hand out <a href="/content/id/7489/Olympic%20Athletics%20events.pdf">this list of events</a> and ask students to match them to the ten graphs.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">This <a href="/content/id/7489/Olympic%20Athletics%20events.pdf">PDF</a> contains a list of the ten events.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><table border="1"> <tr> <td style="text-align: center;">Event</td> <td style="text-align: center;"> </td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">Men's 100 metres</td> </tr> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">Men's Long Jump</td> </tr> <tr> <td style="text-align: center;">3</td> <td style="text-align: center;">Women's 1500 metres</td> </tr> <tr> <td style="text-align: center;">4</td> <td style="text-align: center;">Men's High Jump</td> </tr> <tr> <td style="text-align: center;">5</td> <td style="text-align: center;">Men's Javelin</td> </tr> <tr> <td style="text-align: center;">6</td> <td style="text-align: center;">Women's High Jump</td> </tr> <tr> <td style="text-align: center;">7</td> <td style="text-align: center;">Men's Decathlon</td> </tr> <tr> <td style="text-align: center;">8</td> <td style="text-align: center;">Women's 10000 metres</td> </tr> <tr> <td style="text-align: center;">9</td> <td style="text-align: center;">Men's 4 x 100 metres relay</td> </tr> <tr> <td style="text-align: center;">10</td> <td style="text-align: center;">Women's 100 metres</td> </tr> </table> <br></br></mdoxml> 2 3 0 0 1 0 0 Can you deduce which Olympic athletics events are represented by the graphs? 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