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<mdoxml version="1.0"><div>Let's explore making spirals from the middle outwards.</div>
<div>We'll use a short list of numbers repeated over and over again.<br></br>
Here we see one I've explored a bit. I used the numbers $1$ to $6$ and went anticlockwise.<br></br>
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<mdo:image src="new%20spiral%20of%206%20pic.jpg"></mdo:image></div>
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I noticed that often when I got to the number $6$ I had completed a rectangle.<br></br>
I coloured these $6$'s yellow and drew a rectangles out of dashes.<br></br>
You could explore that idea further. There are many other things you can explore.<br></br>
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We could also look at starting it in a different way.</div>
<div style="text-align: center;"><mdo:image src="diff%206%20spiral.jpg"></mdo:image></div>
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Perhaps you could try a new one using the numbers $1$ to $4$.<br></br>
Try any other sets of numbers and explore what happens when you use them to form a spiral.</div></mdoxml>
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<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org.uk/8498">activity</a> is to extend the making of cuisenaire. It provides a good environment for discovery and surprise. There are lots of different ways of exploring the ideas once the main ideas have been grasped. It can help develop skill in numerical pattern spotting.</div>
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<h3>Possible approach</h3>
<div>It would be expected that the pupils will have achieved well in Cuisenaire Spirals found <a href="http://nrich.maths.org.uk/8293">here</a>. This is an extension of that activity and there should be little need of an introduction beyond what is written on the main activity page.</div>
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<h3>Key questions</h3>
<div>What do you notice?<br></br>
Is there some reason why that happens?<br></br>
What other sets of numbers could you use?<br></br>
Can you predict the pattern that using sets of numbers produce?</div>
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Number Spirals