50
/www/nrich/html/content/98/09/bbprob1/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<div style="text-align: center;"><mdo:image src="dalis_small.gif" alt=""></mdo:image></div>
<br></br>
<br clear="all"></br>
<p>I've been wandering around the shops where I live in Cambridge -
there are a lot of shops that seem to be selling interesting
looking watches and clocks. Some challenges on NRICH are about
digital numbers but lots of people like to use an analogue clock or
watch instead. ('Analogue' for our use, means that it is not
digital and has a round face with two hands and twelve
numbers!)</p>
<p>Well, there are some fascinating ideas. I have a clock in which
the hands go around anticlockwise and so do the numbers! There are
so many designs, perhaps you've seen some and have been fascinated
by them.</p>
<p>I was wondering about different shaped hands. How about a pair
of square hands, but we will tilt each hand 45 degrees so that the
corner points and the opposite corner is in the centre. I've tried
drawing some of these ideas. (However I have not allowed the hour
hand to move and the hour is 12, it's only the minute hand that's
moving at the moment!). To help to understand the pictures I placed
a little dot where the hands are pointing.</p>
<p>So at 12 o'clock it would look like this:-</p>
<p style="text-align: center;"><mdo:image height="106" width="106" alt="pic1" src="Picture%201.jpg"></mdo:image></p>
<p style="text-align: center;"> </p>
<br></br>
<p>Every ten minutes later (Remember that I'm not allowing the hour
hand to move) we'll have:-</p>
<p style="text-align: center;"><mdo:image height="405" width="638" alt="pic2" src="Picture%202.jpg"></mdo:image></p>
<p style="text-align: center;"> </p>
<br></br>
<p>I like the overlap shapes that have been formed.</p>
<br></br>
<table cellpadding="5">
<tbody>
<tr>
<th></th>
<th></th>
<th></th>
</tr>
<tr>
<td align="center"></td>
<td align="center"></td>
<td align="center"></td>
</tr>
</tbody>
</table>
<br></br>
<p>You could try this with paper squares and a pin stuck very, very
close to the corner that's pretending to be the middle of the clock
face. I do not have any coloured see-through sheets but I guess
that would be great, and even better if you can borrow the OHP in
the classroom.</p>
<p>Have a go and see what things occur as the minute hand moves and
you hold the hour hand still, look at shapes of overlap and a sort
of "Jaw" shape that opens and closes.</p>
<br></br>
<p>We should be used to asking "I wonder what would happen if
...?''</p>
<p>As you can guess I do this frequently and so I used my computer
to help me with an equilateral triangular one. Here they are:-</p>
<p><mdo:image height="406" width="639" alt="pic3" src="Picture%203.jpg"></mdo:image></p>
<br></br>
<p>Of course why should we stop there? Circles!:-</p>
<p><mdo:image height="409" width="648" src="Picture%204.jpg" alt="pic 4"></mdo:image></p>
<br></br>
<p>You can try and explore all different designs. You don't have to
just look at the position every ten minutes like I have done; you
could try any minutes past/to that you liked.</p>
<p>If you are the sort of person who prefers to work with a clock
that the hour hand moves properly with the minutes hand then you
might like to look at these:-</p>
<p><mdo:image height="392" width="651" alt="pic 6" src="Picture%206.jpg"></mdo:image></p>
<p>Good luck.</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p><span class="editorial">It seems that everyone found this a bit
tough! It certainly is very hard to picture the shapes moving
around. You really need to find some clear plastic to draw the
shapes on, so you can turn them around and see what happens. Or,
you could just cut some out of cardboard. You might try drawing
them on thin paper and holding them up on a window to let the light
shine through.</span></p>
<br></br>
<p><span class="editorial">Try one of these ways of making the
clock hands and have another go at the investigation. We would be
thrilled to get some solutions on this one.</span></p>
<br></br>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Clock Hands</h2>
<br></br>
<div style="text-align: center;"><mdo:image alt="" src="dalis_small.gif"></mdo:image></div>
<br></br>
<br clear="all"></br>
<br></br>
<p>I've been wandering around the shops where I live in Cambridge - there are a lot of shops that seem to be selling interesting looking watches and clocks. Some challenges on NRICH are about digital numbers but lots of people like to use an analogue clock or watch instead. ('Analogue' for our use, means that it is not digital and has a round face with two hands and twelve numbers!)</p>
<p>Well, there are some fascinating ideas. I have a clock in which the hands go around anticlockwise and so do the numbers! There are so many designs, perhaps you've seen some and have been fascinated by them.</p>
<p>I was wondering about different shaped hands. How about a pair of square hands, but we will tilt each hand 45 degrees so that the corner points and the opposite corner is in the centre. I've tried drawing some of these ideas. (However I have not allowed the hour hand to move and the hour is 12, it's only the minute hand that's moving at the moment!). To help to understand the pictures I placed
a little dot where the hands are pointing.</p>
<p>So at 12 o'clock it would look like this:-</p>
<p style="text-align: center;"><mdo:image alt="pic1" height="106" src="Picture%201.jpg" width="106"></mdo:image></p>
<p style="text-align: center;"> </p>
<br></br>
<p>Every ten minutes later (Remember that I'm not allowing the hour hand to move) we'll have:-</p>
<p style="text-align: center;"><mdo:image alt="pic2" height="405" src="Picture%202.jpg" width="638"></mdo:image></p>
<p style="text-align: center;"> </p>
<br></br>
<p>I like the overlap shapes that have been formed.</p>
<br></br>
<table >
<tbody>
<tr>
<th> </th>
<th> </th>
<th> </th>
</tr>
<tr>
<td align="center" style="padding:5px;"> </td>
<td align="center" style="padding:5px;"> </td>
<td align="center" style="padding:5px;"> </td>
</tr>
</tbody>
</table>
<br></br>
<p>You could try this with paper squares and a pin stuck very, very close to the corner that's pretending to be the middle of the clock face. I do not have any coloured see-through sheets but I guess that would be great, and even better if you can borrow the OHP in the classroom.</p>
<p>Have a go and see what things occur as the minute hand moves and you hold the hour hand still, look at shapes of overlap and a sort of "Jaw" shape that opens and closes.</p>
<br></br>
<p>We should be used to asking "I wonder what would happen if ...?''</p>
<p>As you can guess I do this frequently and so I used my computer to help me with an equilateral triangular one. Here they are:-</p>
<p><mdo:image alt="pic3" height="406" src="Picture%203.jpg" width="639"></mdo:image></p>
<br></br>
<p>Of course why should we stop there? Circles!:-</p>
<p><mdo:image alt="pic 4" height="409" src="Picture%204.jpg" width="648"></mdo:image></p>
<br></br>
<p>You can try and explore all different designs. You don't have to just look at the position every ten minutes like I have done; you could try any minutes past/to that you liked.</p>
<p>If you are the sort of person who prefers to work with a clock that the hour hand moves properly with the minutes hand then you might like to look at these:-</p>
<p><mdo:image alt="pic 6" height="392" src="Picture%206.jpg" width="651"></mdo:image></p>
<p>Good luck.</p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=50&part=">problem</a> is one that explores spatial awareness more than exploring the pupils' ability to read clock faces.</div>
<br></br>
<h3>Possible approach</h3>
<div>It would probably be good to have something visual to help children to enter more confidently into this problem. Some cardboard cut-outs that enable the rotation would help.</div>
<div style="text-align: center;"><mdo:image alt="cutout2" height="165" src="cutout2.jpg" width="549"></mdo:image></div>
<br></br>
<br></br>
<h3>Key questions</h3>
<div>How are you working out where the shapes should go?</div>
<div>Tell me about the overlap you've got here?</div>
<br></br>
<h3>Possible extension</h3>
<div>As suggested in the problem, exploring different shapes and looking at angles when both hands have moved might be a good next step.</div>
<br></br>
<h3>Possible support</h3>
<div>Some pupils who find it hard to get into this problem might benefit from observing a more usual clock face with geared hands.</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">You could cut out hands from coloured tissue paper or coloured
overhead transparencies so you can see the overlap better.<br></br></mdoxml>
2
5
0
1
0
0
0
Clock Hands
This investigation explores using different shapes as the hands of
the clock. What things occur as the the hands move.
Measures and Mensuration
Time
Transformations and their Properties
Rotations
2D Geometry, Shape and Space
Regular polygons
2D Geometry, Shape and Space
Angles
Mathematics Tools
Sets of shapes
Mathematics Tools
Clock