1140
/www/nrich/html/content/02/11/penta2/
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2011-02-01T00:00:01
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<mdoxml version="1.0"><br xmlns="http://www.w3.org/1999/xhtml"></br>
<p xmlns="http://www.w3.org/1999/xhtml">Here are the six faces of a
cube - in no particular order:</p>
<div xmlns="http://www.w3.org/1999/xhtml" style="text-align: center;"><mdo:image width="435" height="63" alt="Six faces of a cube showing a purple star, a blue cross, a red cross, a square, a red star and a circle" src="Cube6.gif"></mdo:image></div>
<p xmlns="http://www.w3.org/1999/xhtml">Here are three views of the
cube:</p>
<div xmlns="http://www.w3.org/1999/xhtml" style="text-align: center;"><mdo:image width="408" height="132" alt="1st cube - top face=square, left face=circle, right face =blue cross. 2nd cube - top face=square, left face=blue cross, right face=purple star. 3rd cube - top face=circle, left face=square, right face=red star" src="Cube3.gif"></mdo:image></div>
<p xmlns="http://www.w3.org/1999/xhtml">Can you deduce where the
faces are in relation to each other and record them on the net of
this cube?</p>
<div xmlns="http://www.w3.org/1999/xhtml" style="text-align: center;"><mdo:image width="230" height="174" alt="cube net" src="CubeNet.gif"></mdo:image></div>
<div xmlns="http://www.w3.org/1999/xhtml">You can use this
interactivity to try out your ideas. You will still have to
visualise the cube folded up!</div>
<br xmlns="http://www.w3.org/1999/xhtml"></br>
<div xmlns="http://www.w3.org/1999/xhtml"><a href="/content/02/11/penta2/PCube.swf">Full screen
version</a></div>
<mdo:flash height="400" width="550"><param value="/content/02/11/penta2/PCube.swf" name="movie" ></param><param value="8" name="flashplayerversion" ></param></mdo:flash> <br xmlns="http://www.w3.org/1999/xhtml"></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<table width="100%" cellspacing="0" cellpadding="5" border="0" id="tableedit1">
<tbody>
<tr>
<td colspan="2">This problem is a little more difficult than it
looks. However, we had many correct reponses. Although there is
only one cube, its net can be drawn in different ways. Bronya from
Tattingstone School describes how she went about solving the
puzzle:</td>
</tr>
<tr>
<td>
<div class="c1">First I drew the first three faces of the cube as a
net:</div>
</td>
<td><mdo:image width="107" height="103" alt="three squares in L shape - topleft = rectangle image, underneath that = circle, to right of circle is cross on yellow background" src="Bronya1.gif"></mdo:image></td>
</tr>
<tr>
<td>Then I looked at the next 3 faces. I saw that the 4 pointed
star was next to one of the shapes I had put down. I added it onto
the net:</td>
<td><mdo:image width="139" height="90" alt="star face added to right of cross on net " src="Bronya2.gif"></mdo:image></td>
</tr>
<tr>
<td>On the third picture of the cube the square was on the side and
the circle on the top. If the circle was on the side the other
symbol would be at the side. I put the shape down on my net:</td>
<td><mdo:image width="195" height="107" alt="red star added on net to left of circle" src="Bronya3.gif"></mdo:image></td>
</tr>
<tr>
<td>There was only one shape left so it had to go at the bottom. I
put this down on my net:</td>
<td><mdo:image width="176" height="136" alt="red flag cross added beneath red star" src="Bronya4.gif"></mdo:image></td>
</tr>
<tr>
<td>To check, I made one of my own to see if it would fit with all
the pictures. It did!</td>
<td><mdo:image width="299" height="230" alt="full net " src="Bronya5.gif"></mdo:image></td>
</tr>
<tr>
<td colspan="2">Kyle and Allyssa from Oakwood Junior School both
tried out their ideas on paper before drawing these nets:</td>
</tr>
<tr>
<td>
<div class="c2"><mdo:image width="297" height="203" alt="cube net" src="kyle.gif"></mdo:image></div>
</td>
<td>
<div class="c2"><mdo:image width="314" height="217" alt="cube net" src="allyssa.gif"></mdo:image></div>
</td>
</tr>
<tr>
<td colspan="2">Tom Neill sent in another net of the same cube
which was also sent by Angus from Maldon Court Preparatory
School:</td>
</tr>
<tr>
<td>
<div class="c2"><mdo:image width="205" height="152" alt="cube net" src="Tom.gif"></mdo:image></div>
</td>
<td>1 is the cross on the yellow background<br></br>
2 is the circle on the orange background<br></br>
3 is the flag cross on the blue background<br></br>
4 is the star on the red background<br></br>
5 is the rectangle on the purple background<br></br>
6 is the star on the green background</td>
</tr>
<tr>
<td colspan="2">Philip who goes to Arnold School in Lancashire
said, "I looked at it from different views to find the solution."
Here is Philip's net:</td>
</tr>
<tr>
<td colspan="2">
<div class="c2">
<p><mdo:image width="404" height="313" alt="cube net" src="philipcropped.gif"></mdo:image></p>
</div>
</td>
</tr>
<tr>
<td colspan="2">Martha, also from Tattingstone, made up a cube from
the net before deciding which face the shapes were on. Here is her
work:</td>
</tr>
<tr>
<td colspan="2">
<div class="c2"><mdo:image width="650" height="388" alt="cube net" src="cube-%20Martha%20Tattingstone.gif"></mdo:image></div>
</td>
</tr>
<tr>
<td colspan="2">Well done to all of you.</td>
</tr>
</tbody>
</table>
<br></br></mdoxml>
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<mdoxml version="1.0"><div class="embed">
<h2>A Puzzling Cube</h2>
<br xmlns="http://www.w3.org/1999/xhtml"></br>
<br></br>
<p xmlns="http://www.w3.org/1999/xhtml">Here are the six faces of a cube - in no particular order:</p>
<div style="text-align: center;" xmlns="http://www.w3.org/1999/xhtml"><mdo:image alt="Six faces of a cube showing a purple star, a blue cross, a red cross, a square, a red star and a circle" height="63" src="Cube6.gif" width="435"></mdo:image></div>
<p xmlns="http://www.w3.org/1999/xhtml">Here are three views of the cube:</p>
<div style="text-align: center;" xmlns="http://www.w3.org/1999/xhtml"><mdo:image alt="1st cube - top face=square, left face=circle, right face =blue cross. 2nd cube - top face=square, left face=blue cross, right face=purple star. 3rd cube - top face=circle, left face=square, right face=red star" height="132" src="Cube3.gif" width="408"></mdo:image></div>
<p xmlns="http://www.w3.org/1999/xhtml">Can you deduce where the faces are in relation to each other and record them on the net of this cube?</p>
<div style="text-align: center;" xmlns="http://www.w3.org/1999/xhtml"><mdo:image alt="cube net" height="174" src="CubeNet.gif" width="230"></mdo:image></div>
<div xmlns="http://www.w3.org/1999/xhtml">You can use this interactivity to try out your ideas. You will still have to visualise the cube folded up!</div>
<br xmlns="http://www.w3.org/1999/xhtml"></br>
<br></br>
<div xmlns="http://www.w3.org/1999/xhtml"><a href="/content/02/11/penta2/PCube.swf">Full screen version</a></div>
<mdo:flash height="400" id="/content/02/11/penta2/PCube.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/02/11/penta2/PCube.swf"></param>
<param name="flashplayerversion" value="8"></param>
</mdo:flash><br xmlns="http://www.w3.org/1999/xhtml"></br>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<a href="http://nrich.maths.org/public/viewer.php?obj_id=1140&part=index">This problem</a> is a little more difficult than it looks. It requires children to visualise the adjoining faces of the cube and transfer this to a net of the cube.<br></br>
<h3>Possible approach</h3>
<div>You could start by showing the group the problem on an interactive whiteboard or data projector. When you have discussed it and what needs to be done children could work in pairs so that they are able to talk through their ideas with a partner. They could use a print out of <a href="/content/02/11/penta2/1140A.pdf">this sheet</a> or draw the faces of the cube for themselves. Scissors and
sticky tape would be useful!</div>
<br></br>
<div>When they have built the cube they should then transfer it to a net. This can be any arrangement which can be folded into a cube not necessarily just the conventional cross given on the sheet. At the end of the lesson, the children could show the whole group both their cubes and the nets they have drawn. The class' work would make a great display, along with a copy of the challenge
itself.</div>
<br></br>
<div><a href="/content/02/11/penta2/1140B.pdf">This sheet</a> gives larger coloured faces of the cube which can be made from card or stuck onto six square "Polydron" pieces so the puzzle can be done again and again.</div>
<br></br>
<h3>Key questions</h3>
<div>Why do you think these two faces are next to each other on the cube?</div>
Look at these two faces. Which other one goes near them?<br></br>
<h3>Possible extension</h3>
Those who found this task straightforward could try to make the net of the octahedron from <a href="/content/02/11/penta2/1140C.pdf">this sheet</a> .<br></br>
<h3>Possible support</h3>
Suggest making a net from <a href="/content/02/11/penta2/1140A.pdf">this sheet</a> and leaving it so it can be folded and unfolded. Then draw or paste on the faces one by one. If "Polydron" squares are available the cube can be built up using the pieces from <a href="/content/02/11/penta2/1140B.pdf">this sheet</a> .<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>You could print out <a href="/content/02/11/penta2/1140A.pdf">this sheet</a> or draw the faces
of the cube to help you. Cut out each one separately and move them
around until they fit the views of the cube given. You
might need some sticky tape!</p>
<p>Try concentrating on two the faces which are next to each other
to start with. Which other face is near them?</p>
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A Puzzling Cube
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
Using, Applying and Reasoning about Mathematics
Visualising
3D Geometry, Shape and Space
Cubes
3D Geometry, Shape and Space
Nets
Admin
Upper primary mapping document