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/www/nrich/html/content/99/04/bbprob1/
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2011-02-01T00:00:01
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<mdoxml version="1.0"><br></br>
<p>Some of you reading this live in different continents and know
about other animals but I've chosen sheep since they are pretty
common across many parts of the world. The young lamb</p>
<div style="text-align: center;"><mdo:image alt="" src="lamb.gif"></mdo:image></div>
<p>has a piece of land which it likes but the shepherd is concerned
at night time that wild animals may come and attack, and the sheep
also needs protection at those times from cold weather. So the
thoughtful shepherd used bales of straw:</p>
<div style="text-align: center;"><mdo:image alt="" src="bale.gif"></mdo:image></div>
<p>He arranges these bales of straw around lambs, sometimes one,
sometimes two ... sometimes 10 lambs together.</p>
<p>You can see by the area of dark green just how much space each
lamb needs. You can also see how the bales are arranged so that the
corners are strong and deep around the lamb.</p>
<div style="text-align: center;"><mdo:image alt="" src="two_bales_ok.gif"></mdo:image></div>
<p>It would not be so good to have them like this</p>
<div style="text-align: center;"><mdo:image alt="" src="two_bales_not_ok.gif"></mdo:image></div>
<p>Here are some examples of how it could be done for 1, 2 and 3
lambs.</p>
<div style="text-align: center;"><mdo:image alt="" src="one_lamb.gif"></mdo:image> <mdo:image alt="" src="two_lambs.gif"></mdo:image> <mdo:image alt="" src="three_lambs.gif"></mdo:image></div>
<p>If you are doing this in school you may find that a teacher has
some useful blocks to help. Ask about Cuisenaire blocks that are
differently coloured according to how long they are and you could
use a white block to stand for a lamb and a RED [2] for a bale of
straw. You could also use multilink blocks as a help.</p>
<p>There are also some graphical computer programs that may help,
isometric grids are probably better than square ones on this
occasion.</p>
<p>Remember these particular rules:-</p>
<ol>
<li>Each lamb must have an area of ground the same as shown
above.</li>
<li>When you have quite a few lambs they should be next to each
other, because they like the company!</li>
<li>You should use as few bales as possible each time and these
bales are 2 by 1 by 1 in lengths.</li>
</ol>
<p>Any other rules that you might wonder about are up to you to
decide about.</p>
<p>When you send in your results make sure that you tell us what
the rules are that you have made extra to my rules.</p>
<p>It will be interesting to see how you put your results together
for 1, 2, 3, 4, 5, 6, 7, 8, 9 and10 lambs.</p>
<p>Well Good luck!</p>
<hr></hr>
<p>Once you've done a set of solutions for 1 ... 10 lambs then have
a go at altering the rules, saying "I wonder what would happen if .
. . ?"</p>
<p>Here are some possible questions:-</p>
<ul>
<li>"I wonder what would happen if the lambs had an illness and had
to be separate from each other, how would this affect the number of
bales used?"</li>
<li>"I wonder what would happen if the bales were 3 by 1 by
1?"</li>
<li>"What happens if I just investigate using 5 lambs but arrange
their areas differently?"</li>
</ul>
<mdo:image alt="" src="five_lambs_1.gif"></mdo:image>
<mdo:image alt="" src="five_lambs_2.gif"></mdo:image>
<mdo:image alt="" src="five_lambs_3.gif"></mdo:image><br></br></mdoxml>
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<mdoxml version="1.0"><br></br>
There are lots of answers to this problem, depending on what
questions you choose to ask. <br></br>
<br></br>
Have a go yourself, and if you discover anything interesting,
<a href="mailto:%20nrich@damtp.cam.ac.uk">e-mail</a> us to tell us
what you've done! Please don't worry that your solution is not
"complete" - we'd like to hear about anything you have tried.
Teachers - you might like to send in a summary of your
children's work. <br></br></mdoxml>
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<mdoxml version="1.0"><div class="embed">
<h2>Fencing Lambs</h2>
<br></br>
<p>Some of you reading this live in different continents and know about other animals but I've chosen sheep since they are pretty common across many parts of the world. The young lamb</p>
<div style="text-align: center;"><mdo:image alt="" src="lamb.gif"></mdo:image></div>
<p>has a piece of land which it likes but the shepherd is concerned at night time that wild animals may come and attack, and the sheep also needs protection at those times from cold weather. So the thoughtful shepherd used bales of straw:</p>
<div style="text-align: center;"><mdo:image alt="" src="bale.gif"></mdo:image></div>
<p>He arranges these bales of straw around lambs, sometimes one, sometimes two ... sometimes 10 lambs together.</p>
<p>You can see by the area of dark green just how much space each lamb needs. You can also see how the bales are arranged so that the corners are strong and deep around the lamb.</p>
<div style="text-align: center;"><mdo:image alt="" src="two_bales_ok.gif"></mdo:image></div>
<p>It would not be so good to have them like this</p>
<div style="text-align: center;"><mdo:image alt="" src="two_bales_not_ok.gif"></mdo:image></div>
<p>Here are some examples of how it could be done for 1, 2 and 3 lambs.</p>
<div style="text-align: center;"><mdo:image alt="" src="one_lamb.gif"></mdo:image> <mdo:image alt="" src="two_lambs.gif"></mdo:image> <mdo:image alt="" src="three_lambs.gif"></mdo:image></div>
<p>If you are doing this in school you may find that a teacher has some useful blocks to help. Ask about Cuisenaire blocks that are differently coloured according to how long they are and you could use a white block to stand for a lamb and a RED [2] for a bale of straw. You could also use multilink blocks as a help.</p>
<p>There are also some graphical computer programs that may help, isometric grids are probably better than square ones on this occasion.</p>
<p>Remember these particular rules:-</p>
<ol>
<li>Each lamb must have an area of ground the same as shown above.</li>
<li>When you have quite a few lambs they should be next to each other, because they like the company!</li>
<li>You should use as few bales as possible each time and these bales are 2 by 1 by 1 in lengths.</li>
</ol>
<p>Any other rules that you might wonder about are up to you to decide about.</p>
<p>When you send in your results make sure that you tell us what the rules are that you have made extra to my rules.</p>
<p>It will be interesting to see how you put your results together for 1, 2, 3, 4, 5, 6, 7, 8, 9 and10 lambs.</p>
<p>Well Good luck!</p>
<hr></hr>
<p>Once you've done a set of solutions for 1 ... 10 lambs then have a go at altering the rules, saying "I wonder what would happen if . . . ?"</p>
<p>Here are some possible questions:-</p>
<ul>
<li>"I wonder what would happen if the lambs had an illness and had to be separate from each other, how would this affect the number of bales used?"</li>
<li>"I wonder what would happen if the bales were 3 by 1 by 1?"</li>
<li>"What happens if I just investigate using 5 lambs but arrange their areas differently?"</li>
</ul>
<mdo:image alt="" src="five_lambs_1.gif"></mdo:image> <mdo:image alt="" src="five_lambs_2.gif"></mdo:image> <mdo:image alt="" src="five_lambs_3.gif"></mdo:image></div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This particular <a href="http://nrich.maths.org/public/viewer.php?obj_id=64&part=">activity</a> is a good one to start with if you are not used to carrying out open activities. The children usually enjoy it providing that the introduction is carried out in a way that captivates them! It also provides an easy situation for pupils to start altering the rules for further
investigations.</div>
<br></br>
<br></br>
<h3>Possible approach</h3>
<div>Show the cuboids and the spaces for the lambs with some suitable resources rather than relying on the pictures, for example Cuisenaire rods or mutlilink cubes joined together.</div>
<br></br>
<h3>Key questions</h3>
<div>How are you checking that you've got the young lamb safely protected?</div>
<br></br>
<h3>Possible extension</h3>
<div>Encourage pupils to ask and pursue their own questions.</div>
<br></br>
<h3>Possible support</h3>
<div>Some children may need help with recording their work, for example using a drawing program on the computer.</div>
<br></br>
<br></br></mdoxml>
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<mdoxml version="1.0"><br></br>
<div>This particular activity is a good one to start with if you
are not used to carrying out open activities.</div>
<div>The children usually enjoy it providing that the introduction
is carried out in a way that captivates them! Using Cuisenaire Rods
or Colour Factor that are often forgotten pieces of equipment that
can help pupils literally get to grips with problems, will be of
great help.</div>
<div>It has a great benefit also for helping pupils to learn about
communicating their results. They often need an easy task like this
if it is the first time that they are having freedom to record
their results in any way.</div>
<div>I have used this activity successfully with years 3, 4,
5,& 6.</div>
<br></br>
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Fencing Lambs
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Measures and Mensuration
Perimeters
Measures and Mensuration
Area
Using, Applying and Reasoning about Mathematics
Investigations
Mathematics Tools
Interlocking cubes
Mathematics Tools
Cuisenaire rods
Using, Applying and Reasoning about Mathematics
Working systematically