5880
/www/nrich/html/content/id/5880/
1
2011-02-01T00:00:01
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<mdoxml version="1.0"><br></br>
<mdo:image width="436" height="139" src="Knots1.gif" alt="two knots"></mdo:image><br></br>
<br></br>
You can see how many loops of string were used to make these string
patterns because the strings are different colours. <br></br>
<br></br>
In the next pictures can you work out how many loops were used?
<br></br>
<br></br>
<mdo:image width="411" height="215" src="Knots2.gif" alt="three more knots"></mdo:image><br></br>
<br></br>
How many pieces of string do you need to make this string
pattern?<br></br>
<br></br>
<mdo:image width="188" height="187" src="Knots3.gif" alt="tangle of string"></mdo:image><br></br>
<br></br>
Can you explain how you decided?<br></br>
Here is a <a href="/content/id/5880/Knots1.pdf">pdf</a> of the
string images which you could print off if you find it easier to
work on paper.<br></br>
<br></br>
<p><span style="font-style: italic;">If you enjoyed this problem,
you might like to have a go at</span> <a href="http://nrich.maths.org/public/viewer.php?obj_id=5881&part=index" style="font-style: italic;">How Many Pieces This Time?</a></p>
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<mdoxml version="1.0"><p><span class="editorial">Thank you to everyone who sent in a
solution to this problem. Most of you agreed that there
was just one piece of string in the first picture, two in the
second, one in the third and two in the fourth.</span></p>
<p class="editorial">Thomas from St Luke's School in Frodsham
explained how he worked out the number of pieces of string in the
last picture:</p>
I started at one point, followed the string round in one direction
and found that I came back to where I started. I realised that I
hadn't been everywhere, so I started from a place that I hadn't
been and went around again. When I got back to the start again, I
had been everywhere, so there are two loops.<br></br>
<br></br>
<p class="editorial">This is very clear - thank you Luke.</p>
<p class="editorial">Well done also to Diana, Kate and Georgia from
Danebank School who also wrote clear explanations of how they
counted the pieces of string.</p>
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<mdoxml version="1.0"><div class="embed">
<h2>How Many Pieces?</h2>
<br></br>
<mdo:image alt="two knots" height="139" src="Knots1.gif" width="436"></mdo:image><br></br>
<br></br>
You can see how many loops of string were used to make these string patterns because the strings are different colours.<br></br>
<br></br>
In the next pictures can you work out how many loops were used?<br></br>
<br></br>
<mdo:image alt="three more knots" height="215" src="Knots2.gif" width="411"></mdo:image><br></br>
<br></br>
How many pieces of string do you need to make this string pattern?<br></br>
<br></br>
<mdo:image alt="tangle of string" height="187" src="Knots3.gif" width="188"></mdo:image><br></br>
<br></br>
Can you explain how you decided?<br></br>
Here is a <a href="/content/id/5880/Knots1.pdf">pdf</a> of the string images which you could print off if you find it easier to work on paper.<br></br>
<br></br>
<p><span style="font-style: italic;">If you enjoyed this problem, you might like to have a go at</span> <a href="http://nrich.maths.org/public/viewer.php?obj_id=5881&part=index" style="font-style: italic;">How Many Pieces This Time?</a></p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/5880&part=">This problem</a> has potential in several different ways. You could focus on visualisation - asking the children to try and decide whether the patterns are made from more than one piece of string simply by looking.</div>
<br></br>
<div>Alternatively, you could make this a more practical task and encourage your class to recreate the patterns using prepared loops (large elastic bands could be useful perhaps, or bits of ribbon/string/thread tied into loops).</div>
<br></br>
<div>Here is a <a href="/content/id/5880/Knots1.pdf">pdf</a> of the string images which you could print off for the children to use.</div>
<br></br>
<h3>Key questions</h3>
<div>Can you explain how you decided on the number of loops there are?</div>
<div>What happens when you choose a starting point and follow the string from there?</div>
<div>Would it help to use a coloured pencil?</div>
<h3>Possible extension</h3>
Learners could go on to <a href="http://nrich.maths.org/5881&part=">How Many Pieces This Time</a>?<br></br>
<h3>Possible support</h3>
Suggest using <a href="/content/id/5880/Knots1.pdf">this sheet</a> to follow round the pieces of string with a coloured pencil.<br></br>
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<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">What happens when you choose a starting point and follow the string
from there?<br></br>
You could print off <a href="/content/id/5880/Knots1.pdf">this
picture</a> of the patterns and use a pencil to follow a
loop.<br></br></mdoxml>
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How Many Pieces?
How many loops of string have been used to make these patterns?
Decision Mathematics and Combinatorics
Route inspection problems
Using, Applying and Reasoning about Mathematics
Visualising