7833
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<mdoxml version="1.0"><p>I've noticed that the cans that were stacked by Zizi in a triangle were $4$ high. Not only that but I counted and found that she used $10$ cans.</p>
<p style="text-align: center;"><mdo:image src="ten%20cans.jpg" style="text-align: -webkit-auto;"></mdo:image> <mdo:image src="March%202012%20cans.jpg"></mdo:image></p>
<p>Pete had made a triangle just $3$ high and I noticed that he used just $6$. </p>
<p>"Both even numbers!"</p>
<p>On another table Cas made a triangle $5$ high and used an odd number this time, $15$! and Sophie made an even bigger one of $21$ this was $6$ high.</p>
<p>"These were odd numbers!"</p>
<p> </p>
<p>What can you can about these pairs of even and then a pair of odds - will it often happen?</p>
<p>What do you think?</p>
<p>Can you prove that your ideas are right to others?</p>
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<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/7833">activity</a> provides an opportunity for pupils to both explore a mathematical pattern that is easily generated and find ways of proving what they can from their observations and beliefs.</div>
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<h3>Possible approach</h3>
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<h3>Key questions</h3>
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<h3>Possible extension</h3>
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<h3>Possible support</h3>
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I've noticed that . . . .