4762
/www/nrich/html/content/id/4762/
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2011-02-01T00:00:01
<mdoxml version="1.0"><br></br>
<p>Here is a picture of a UK £2 coin with two pink circles drawn on it:<br></br>
</p>
<div style="text-align: center;"><mdo:image alt="two pound coin" height="455" src="2poundcoin.jpg" width="450"></mdo:image></div>
<br></br>
<p>If you look at the band between the two pink circles, you will see that it contains lots of cogwheels.<br></br>
<br></br>
Can you explain what is wrong with these cogs?<br></br>
<br></br>
To get an idea of how cogwheels move, you could look at the interactivity in this month's <a href="http://nrich.maths.org/public/viewer.php?obj_id=4771&part=index">Turning Cogs</a> problem.<br></br>
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<mdoxml version="1.0"><br></br><p><span class="editorial">
Congratulations to Miriam of Rosh Pinah Primary, Tom of Silverdale, Uwais from Kings Monkton and Esther.</span>
</p>
<p class="editorial">Miriam says:</p>
It won't turn because in a cog circle each cog turns a different way.
Because there is an odd number of cogs it would be impossible for each
one to turn in a different direction.<br></br></mdoxml>
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<mdoxml version="1.0"><div class="embed">
<h2>Coin Cogs</h2>
<br></br>
<p>Here is a picture of a UK £2 coin with two pink circles drawn on it:<br></br>
</p>
<div style="text-align: center;"><mdo:image alt="two pound coin" height="455" src="2poundcoin.jpg" width="450"></mdo:image></div>
<br></br>
<p>If you look at the band between the two pink circles, you will see that it contains lots of cogwheels.<br></br>
<br></br>
Can you explain what is wrong with these cogs?<br></br>
<br></br>
To get an idea of how cogwheels move, you could look at the interactivity in this month's <a href="http://nrich.maths.org/public/viewer.php?obj_id=4771&part=index">Turning Cogs</a> problem.<br></br>
</p>
</div>
<br></br>
This problem has deliberately been left open-ended, but if children have explored the interactivity in the <a href="http://nrich.maths.org/public/viewer.php?obj_id=4771&part=index">Turning Cogs</a> problem, then they will become familiar with the way that cogs work. Allowing them to experiment and talk about their discoveries with each other might be the best way to get them going on this
challenge.<br></br>
<br></br>
If the interactivity is not available,you may like to print off this <a href="/content/id/4762/cogs.doc">sheet of cogs</a> to cut out and give to the children, or use on an OHP.<br></br></mdoxml>
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<mdoxml version="1.0">Choose one of the cogs and imagine it turning in a particular direction. Which way would the cog/s next to it turn?<br></br></mdoxml>
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<mdoxml version="1.0">There are 19 cogs.<br></br>If one cog is moving clockwise, then if forces the cog on either side of it to turn anticlockwise. Therefore if a circle of cogs is going to move round, there cannot be an odd number because two next to each other would be turning in the same direction.<br></br></mdoxml>
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Coin Cogs
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Using, Applying and Reasoning about Mathematics
Visualising
Information and Communications Technology
Interactivities
Mechanics
Forces