7517
/www/nrich/html/content/id/7517/
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2011-12-12T09:00:25
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<p style="text-align: center;"><em>This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)</em></p>
<p> </p>
<p>On the table in front of you is a grid like this:-</p>
<p> </p>
<div style="text-align: center;"> <mdo:image alt="" height="340" src="6x6%20grid.jpg" width="339"></mdo:image></div>
<div><br></br>
Now imagine that you have another grid, just the same but made of plastic that you can see through.</div>
<div>You place the plastic one over the one on the table so that it covers it completely.</div>
<div>You could have flipped it over and/or turned it around as you put the plastic one down.</div>
<div>Then the numbers that are paired, one above the other, are multiplied together.</div>
<div>Finally, all the results of multiplying together will be added together.</div>
<div> </div>
<div>Without doing the $36$ multiplications and then adding them together YOUR challenge is to say which way of flipping over and/or turning the plastic grid will give you the highest total and which way will give the lowest total.</div>
<div> </div>
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<h2>So It's Times!</h2>
<br></br>
<p style="text-align: center;"><em>This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)</em></p>
<p> </p>
<p>On the table in front of you is a grid like this:-</p>
<p> </p>
<div style="text-align: center;"> <mdo:image alt="" height="340" src="6x6%20grid.jpg" width="339"></mdo:image></div>
<div>Now imagine that you have another grid, just the same but made of plastic that you can see through.</div>
<div>You place the plastic one over the one on the table so that it covers it completely.</div>
<div>You could have flipped it over and/or turned it around as you put the plastic one down.</div>
<div>Then the numbers that are paired, one above the other are multiplied together.</div>
<div>Finally, all the results of multiplying together will be added together.</div>
<div> </div>
<div>Without doing the $36$ multiplications and then adding them together YOUR challenge is to say which way of flipping over and/or turning the plastic grid will give you the highest total and which way will give the lowest total.</div>
<div> </div>
<div> </div>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/7517&part=">problem</a> is presented for the more able pupils and can challenge them both in number and spatial skills.</div>
<br></br>
<h3>Possible approach</h3>
<div>If necessary before approaching the $6$ by $6$ array, present two sheets with a $4$ by $4$ array. Try not to go through it completely, but just try a couple of multiplications and then turn the top sheet over (or around, or both) and see what a few of the multiplications would be then.<br></br>
<br></br>
The six by six grid can be printed from here (<a href="/content/id/7517/Grid.doc">doc</a>, <a href="/content/id/7517/Grid.pdf">pdf</a>), and then presented to the pupil(s). The challenge may need to be explained very clearly so as to prevent a lot of unnecessary calculations being made.</div>
<br></br>
<h3>Key questions</h3>
<div>How did you arrive at this?</div>
<div>Explain to me the solutions that you have come to.<br></br>
What else could you explore?</div>
<br></br>
<h3>Possible extension</h3>
<div>Children could have a go at <a href="http://www.nrich.maths.org/7950">It's Times Again</a>.</div>
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<mdoxml version="1.0">You could print off the grid as a <a href="/content/id/7517/Grid.doc">Word document</a> or as a <a href="/content/id/7517/Grid.pdf">pdf</a>.</mdoxml>
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So it's times!
Transformations and their Properties
Translations
Transformations and their Properties
Reflections
Using, Applying and Reasoning about Mathematics
Investigations