8328
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<mdoxml version="1.0"><p><mdo:image src="ba%3B%3B%20throws.jpg"></mdo:image> <mdo:image alt="" src="hop.jpg" style="width: 248px; height: 248px;"></mdo:image></p>
<p>Sean threw his beanbag $20$ paces. Henry threw his beanbag $18$ paces. Janine threw her beanbag $21$ paces.</p>
<p>Who was the winner?</p>
<p>James hopped on one leg for $25$ hops. Anna hopped on one leg for $32$ hops. Gina hopped on one leg for $29$ hops.</p>
<p>Who was the winner?</p>
<p>Amit ran across the playground in $20$ seconds. Sara took $18$ seconds. Marek took $17$ seconds.</p>
<p>Who was the winner?<br></br>
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</p>
<pre>
Photograph acknowledgements
http://www.kidzin2sport.co.uk/about-us.php
http://photographicdictionary.com/h/hop
</pre>
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<mdoxml version="1.0"><span class="editorial">Among the solutions sent in we had these three good answers. First from Elena at Estes Hills Elementary School NC USA</span><br></br>
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Janine is the winner of the beanbag tose because she threw the farthest.<br></br>
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Anna is the winner of the hopping contest because she hopped the most.<br></br>
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Marek is the winner of the race because he ran the quickest.<br></br>
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<span class="editorial">From St. Anselm's Prep School in England first Tom's and then Toby's solutions;</span><br></br>
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For the first question the winner was Janine.<br></br>
For the second question the winner was Anna.<br></br>
For the third question the winner was Marek.<br></br>
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So first Janine won by one pace then Anna won by three hops and finally Marit won by one second. I worked this problem out by carefully looking at the scores and selecting the largest one although on the last one you had to select the lowest amount of seconds because you select the person who took the least time to run across the playground.<br></br>
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<span class="editorial">On the last day for submissions we had this lengthy response which I had to shorten to fit into this page, from</span> <span class="editorial">Swaathi at the Garden International School in Malaysia. She wrote:</span><br></br>
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The winner for this is Janine because it is 21 paces.<br></br>
Next I continued with the second problem<br></br>
The winner is Anna with 32 paces.<br></br>
Finally, it is clear that Marek won because he took the shortest time among the three.<br></br>
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<span class="editorial">Thank you for these and the others that came in. It caused you to think now that it is not always the highest number that is the winner.</span></mdoxml>
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<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This problem gives the children experiences of different ways of winning. Usually children expect a larger score to be the winning one. This holds in many sports (high jump, javelin throwing) but in timed events the smaller the number, the better. Confronting and discussing this contradiction may help them to understand some of the conversations about Olympic scores they may hear as
well as supporting their longer term understanding of measure.</div>
<div> </div>
<h3>Possible approach</h3>
<div>As with many activities, this one becomes all the richer when the children actually do the activity. You could try all three competitions with your class as an introduction to the topic or use work they have already done in tackling <a href="http://nrich.maths.org/8327">Can you do it too?</a></div>
<div>If it's not possible to do a whole class activity, you could demonstrate one of the questions using three children. One is the winner. The children will need to share their understandings of what winning means, identify who is the winner and to say how they know.</div>
<div>The paces activity activity is an ideal one to introduce the idea of using a standard measure for comparison. Does it matter that the paces are all different lengths? Why?</div>
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<h3>Key questions</h3>
<div>Who do you think will win? Why? how do you know?</div>
<div>Is it the highest number of .... or the lowest number? </div>
<div>Why?</div>
<div>Can you put the results in order to see who came first, second and third?</div>
<div>Was it a fair competition? Why?</div>
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<h3>Possible extension</h3>
<div>The children could try the competitions for themselves and order the results for the whole group. They could then identify who the gold, silver and bronze medal winners would be.</div>
<div>They could also look at some real results from Olympic competitions to find the gold, silver and bronze medal winners. This could contribute to your Olympic display.</div>
<h3> </h3>
<h3>Possible support</h3>
<div>Some children may need lots of support to make sense of the numbers and what they mean. Focus on a small group of activities where the higher number wins, then change to another where the shorter time wins. Understanding that the lower numbers are better results for some competitions but worse for others is tricky and will need a lot of work on the sense making aspects of the
situation.</div>
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<mdoxml version="1.0"><p>Is the highest number the best score?</p></mdoxml>
2
4
1
0
0
0
0
Who can be the winner?
Some children have been doing different tasks. Can you see who was the winner?
Using, Applying and Reasoning about Mathematics
Selecting and using information
Numbers and the Number System
Comparing and Ordering numbers
Applications
sport