8171
/www/nrich/html/content/id/8171/
1
2012-06-01T00:00:00
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<mdoxml version="1.0"><p>In $1908$ the Olympic Games were held in London, that's just over $100$ years ago. Then, just after World War $2$ they were again in London in $1948$</p>
<p>Here are the results from some track events;</p>
<div class="col_layout">
<div class="grid_2" p="">$1908$
<p>$100$ metres $10.8$ secs</p>
<p>$200$ metres $22.6$ secs</p>
<p>$400$ metres $50.0$ secs</p>
<p>$800$ metres $112$ secs</p>
<p>$1500$ metres $240$ secs</p>
</div>
<div class="grid_2" p="">$1948$
<p>$100$ metres $10.3$ secs</p>
<p>$200$ metres $21.1$ secs</p>
<p>$400$ metres $46.2$ secs</p>
<p>$800$ metres $109$ secs</p>
<p>$1500$ metres $229$ secs</p>
</div>
<p><br></br>
The 2012 London Olympics were another 64 years later.<br></br>
How did the results differ?<br></br>
Could you have predicted the results?<br></br>
Perhaps more importantly, what's the reason for your answer?</p>
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<mdoxml version="1.0"><span class="editorial">We had some really good ideas sent in for the times that may be expected in the $2012$ games<br></br>
There was a range of ideas as follows;</span><br></br>
<span class="editorial">$100$ metres $9.50$ to $10.00$ secs</span><br></br>
<span class="editorial">$200$ metres $18.56$ to $20.30$ secs</span><br></br>
<span class="editorial">$400$ metres $38.52$ to $ 43.92$ secs</span><br></br>
<span class="editorial">$800$ metres $99.00$ to $108.00$ secs<br></br>
$1500$ metres $211.00$ to $224.00$ secs</span><br></br>
<br></br>
<span class="editorial">So we will have to wait for the games to see if they are the correct figures! Most results came from Manorfield Primary School from these pupils: Natasha, Jennifer, Lauren, Isabelle, Emily, Ben, Heather, Becky, Olivia, Hannah, Kayla, Abbie-mai, Chloe, Jade, Stephanie and Nazra.</span><br></br>
<br></br>
<br></br>
<span class="editorial">Joe from St. Joseph's School wrote;</span><br></br>
<br></br>
It can not keep going on in the same pattern as the difference between the time and the improved results, because if it did, it would go into negative results and races can't be run in minus numbers. See these results up until year 2828.<br></br>
<div style="text-align: center;"><mdo:image src="Joe.jpg"></mdo:image></div>
<div><span class="editorial">Patrick from Manorcroft Primary school, Egham wrote the following thorough explanation of what they did at his school.</span></div>
<div><br></br>
1/ We first compare the rates and find how much they improved [a]. Then we divide [a] by the number of years ($40$) to find the $%/$year rate [b]. We × [b] by $64$ (the number of years later) to find the improvement rate [c],<br></br>
∴ × [c] by the time (e.g. $400$m is $50$ secs → $46.2$ secs<br></br>
∴ $46.2$ × improvement rate [c] = new time).<br></br>
2/ But people can’t go on competing in the Olympics for $40$ years.<br></br>
There are food changes, different exercise schedules & completely different people.<br></br>
3/ ∴ I think there is no pattern to predict the results.<br></br>
<br></br>
<span class="editorial">Well thank you all, it was a very worthwhile activity for you all to get involved in.</span><br></br>
<br></br>
</div></mdoxml>
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<mdoxml version="1.0"><div class="embed">
<h2>Now and Then</h2>
<p>In $1908$ the Olympic Games were held in London, that's just over $100$ years ago. Then, just after World War $2$ they were again in London in $1948$</p>
<p>Here are the results from some track events;</p>
<div class="col_layout">
<div class="grid_2" p="">$1908$
<p>$100$ metres $10.8$ secs</p>
<p>$200$ metres $22.6$ secs</p>
<p>$400$ metres $50.0$ secs</p>
<p>$800$ metres $112$ secs</p>
<p>$1500$ metres $240$ secs</p>
</div>
<div class="grid_2" p="">$1948$
<p>$100$ metres $10.3$ secs</p>
<p>$200$ metres $21.1$ secs</p>
<p>$400$ metres $46.2$ secs</p>
<p>$800$ metres $109$ secs</p>
<p>$1500$ metres $229$ secs</p>
</div>
<p><br></br>
The 2012 London Olympics were another 64 years later.<br></br>
How did the results differ?<br></br>
Could you have predicted the results?<br></br>
Perhaps more importantly, what's the reason for your answer?</p>
</div>
</div>
<h3 style="text-align: left;"><span style="font-weight: bold;">Why do this problem</span></h3>
<div>This <a href="http://www.nrich.maths.org.uk/8171">activity</a> gives an opportunity for pupils to examine data and then consider all different kinds of influencing factors in order to predict what will happen another $64$ years on. It can offer a good forum for debate and discussion while sharing views about things that will affect the results. It may help some children to understand that
any answer can be deemed 'correct' so long as it can be justified.</div>
<div> </div>
<h3>Possible approach</h3>
<div>For many classrooms it would be best to give the results of one event to each group of pupils. They will obviously need opportunities to work as a group and come up with an agreed result. When these results are shared towards the end of the session, there could be some further discussions about the results for one year. This could involve looking at the relationships between the timings for
different distances.</div>
<br></br>
<h3>Key questions</h3>
<div>What do you think is important about deciding the times for that race in $2012$?</div>
<div>Tell me about your ideas.</div>
<div>Do the whole group agree? If not, why?</div>
<br></br>
<h3>Possible extension</h3>
<div>Ask questions such as:<br></br>
What do you think about these results getting better and better as time goes on?<br></br>
What about the results in another $100$ years time?<br></br>
This should give the opportunity for some good creative thoughts to be shared.</div>
<div>Results from other years could also be examined to see whether results steadily improve or whether there are any sudden changes in the patterns. What might be the reasons for this? Children who are beginning to understand what graphs can mean may like to take a look at those in the activity <a href="http://nrich.maths.org/7489">Olympic Records</a>.</div>
<div> </div>
<h3>Possible support</h3>
<div>Some pupils may need help in making sense of the results. They could look at the distances on the sports field to get a real idea of what the distances are like.</div>
<div>It may also be helpful to see what they can do in periods of $10$ secs, $21$ secs, and $22$ secs so that they understand just how quickly these races are being run.<br></br>
</div>
<p> </p>
<pre>
Photograph acknowledgement for icon
www.olympic.org.nz/sites/olympic/files/styles/grid-9/public/games/paris-
</pre></mdoxml>
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<mdoxml version="1.0"><br></br>
<p>How far is 100m? 200m?...</p>
<p>Can you imagine or measure this distance?</p>
<p>How long would it take you to run this distance?<br></br>
<br></br>
How far could you run in 10 sec, 20 sec?</p>
<br></br></mdoxml>
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Now and Then
Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.
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