4806
/www/nrich/html/content/id/4806/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
This problem could be worked on in a group of about four. For more
details about how you might go about doing this, please read the <a href="http://nrich.maths.org/4806&part=note">Teachers'
Notes</a>.<br></br>
<br></br>
Sam and Julie are friends. Both of them have rather odd clocks at
home.<br></br>
In Sam's bedroom there is an old alarm clock which his Dad had
thrown out because it had lost its minute hand. Although it has
only its small hand, Sam can still tell the time using it. He can
tell the hour, such as midday. He can tell when it is time to get
up, time to go to school and time to turn his light out at
night.<br></br>
<br></br>
<mdo:image height="163" width="506" src="MarchCl1.gif" alt="four clock faces with only hour hands"></mdo:image><br></br>
<br></br>
Which clock is showing it is midday?<br></br>
At what time does Sam get up?<br></br>
At what time does Sam go to school?<br></br>
At what time is Sam supposed to turn out his light?<br></br>
<br></br>
In Julie's hall there is a very old clock which lost its hour hand
a long time ago.<br></br>
<br></br>
<div style="text-align: center;"><mdo:image height="384" width="102" src="MarchCl2.gif" alt="grandfather clock with minute hand at 25 past"></mdo:image></div>
<br></br>
<br></br>
<br></br>
School finishes at half past three and it takes Julie at least half
an hour to get home. Sometimes she goes to the shop on the way, and
sometimes she leaves school a bit later. When she first gets home
Julie always looks at the clock in the hall to see what time it
is.<br></br>
One week these were the times she saw:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image height="113" width="484" src="MarchCl3.gif" alt="clocks with just minute hands"></mdo:image></div>
<div>On which day was it raining so she hurried straight
home?</div>
<div>On which day did she go to the shop to buy some sweets on the
way home?</div>
<div>On which day did she stay at school to practise in the
band?</div>
<div>On which day did she play with Sam for about half an hour
before setting off for home?</div>
<div>On which day did her teacher keep the class in for five
minutes?</div>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p><span class="editorial">This problem needed a great deal of
logical thinking. Excellent solutions were sent in by Zartasha from
St Mary's C of E High School, Bryan from The British School of
Guangzhou, Aporva from Brackensdale Junior and James B, James H,
Jack W and Jack H from Tunbury Primary School. Remember that we
like to hear the reasons for your answers, not just the
answers.</span></p>
<p><span class="editorial">The group of boys from Tunbury
wrote:</span></p>
Clock B is showing midday because midday is $12$ o'clock and the
hand is pointing at $12$.<br></br>
Clock D is showing the time when Sam gets up. Sam gets up at $7.20$
am <span class="editorial">(or thereabouts, perhaps $7.15$
am)</span> because the other clocks would make him too late for
school.<br></br>
A shows when he goes to school because D is when you get up and get
ready and $8.30$ am is roughly the time that you go to school. The
other times are too early or too late.<br></br>
Clock C shows that Sam turns out his light at $9.40$ pm <span class="editorial">(again, some of you thought this might be $9.45$
pm which is fine)</span> .<br></br>
<br></br>
Julie ran home from school on Friday because it took her $30$
minutes .<br></br>
She stopped to buy some sweets on Monday because she got home at
$10$ past $4$.<br></br>
Julie stayed at school to practise with the band on Thursday
because she got home at $10$ to $5$.<br></br>
She stayed to play with Sam on Tuesday because she got home at $25$
to $5$.<br></br>
Her teacher held the class in on Wednesday because she got home at
$5$ past $4$.<br></br>
<p class="editorial">Bryan from The British School of Guangzhou
also sent in a clearly-reasoned solution for Julie's clock:</p>
<div>Monday the time is 4.10pm, buying sweets in the shop doesn't
take a long time and it only takes $5$-$10$ minutes so she reached
home at 4.10pm.</div>
<div>Tuesday the time is 4.35pm, she played with Sam for $30$
minutes and she might spend an extra 5 minutes getting home.</div>
<div>Wednesday the time is 4.05pm, her teacher kept the class for
$5$ mins and she reached home at 4.05pm, but if she hadn't stayed
she would have reached home at 4.00pm.</div>
<div>Thursday the time is 4.50pm, she practised with the band for
about $45$-$50$ minutes so she got home at 4.50pm.</div>
<div>Friday the time is 4.00pm, it was raining so she hurried
straight home and she did nothing in school so she might have got
home in $30$ minutes.</div>
<br></br>
<p class="editorial">Well done all of you!</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Two Clocks</h2>
<br></br>
This problem could be worked on in a group of about four. For more details about how you might go about doing this, please read the <a href="http://nrich.maths.org/4806&part=note">Teachers' Notes</a>.<br></br>
<br></br>
Sam and Julie are friends. Both of them have rather odd clocks at home.<br></br>
In Sam's bedroom there is an old alarm clock which his Dad had thrown out because it had lost its minute hand. Although it has only its small hand, Sam can still tell the time using it. He can tell the hour, such as midday. He can tell when it is time to get up, time to go to school and time to turn his light out at night.<br></br>
<br></br>
<mdo:image alt="four clock faces with only hour hands" height="163" src="MarchCl1.gif" width="506"></mdo:image><br></br>
<br></br>
Which clock is showing it is midday?<br></br>
At what time does Sam get up?<br></br>
At what time does Sam go to school?<br></br>
At what time is Sam supposed to turn out his light?<br></br>
<br></br>
In Julie's hall there is a very old clock which lost its hour hand a long time ago.<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="grandfather clock with minute hand at 25 past" height="384" src="MarchCl2.gif" width="102"></mdo:image></div>
<br></br>
<br></br>
<br></br>
School finishes at half past three and it takes Julie at least half an hour to get home. Sometimes she goes to the shop on the way, and sometimes she leaves school a bit later. When she first gets home Julie always looks at the clock in the hall to see what time it is.<br></br>
One week these were the times she saw:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="clocks with just minute hands" height="113" src="MarchCl3.gif" width="484"></mdo:image></div>
<div>On which day was it raining so she hurried straight home?</div>
<div>On which day did she go to the shop to buy some sweets on the way home?</div>
<div>On which day did she stay at school to practise in the band?</div>
<div>On which day did she play with Sam for about half an hour before setting off for home?</div>
<div>On which day did her teacher keep the class in for five minutes?</div>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=4806&part=index">This problem</a> can help children understand that the analogue clock is really two scales superimposed on each other. This is what makes it so difficult for children to read. Focusing on the hands separately will help children understand what each one indicates. The novel context of this problem could provide a
good assessment opportunity.</div>
<br></br>
<div>The problem lends itself to collaborative working, both for children who are inexperienced at working in a group and children who are used to working in this way. By working together on this problem, the task is shared and therefore becomes more manageable than if working alone.</div>
<br></br>
Many NRICH tasks have been designed with group work in mind. <a href="http://nrich.maths.org/7011&part=">Her</a>e we have gathered together a collection of short articles that outline the merits of collaborative work, together with examples of teachers' classroom practice.<br></br>
<h3>Possible approach</h3>
<div>Before tackling this problem, children will need experience of reading analogue clocks. It would be helpful to have a large demonstration clock available to use with them and of course referring to a 'real' clock on the wall of the classroom might also be useful. Alternatively (or as well), you could make use of an interactive version on your whiteboard, such as <a href="http://www.oswego.org/ocsd-web/games/ClassClock/clockres.html">this free one</a>.</div>
<br></br>
<div>Ask the children to work in pairs on the first part of the problem so that they are able to talk through their ideas with a partner. <a href="/content/id/4806/TwoClocksPart1.pdf">This sheet</a> contains two copies of the four clock faces. Once they have had chance to solve it, bring the group back together and allow them to explain how they reached their conclusions. You might expect quite
sophisticated reasoning from some children, which also indicates some understanding of why the hand is at the point it is between two digits. You can always demonstrate the movement of the hands using a real or virtual clock.</div>
<br></br>
<div>The combination of 'real-life' reasoning and telling the time makes the second part of the problem quite a challenge. So, ask two pairs to join together to make groups of four. Allocating these clear roles (<a href="/content/id/4806/Roles.doc">Word</a>, <a href="/content/id/4806/Roles.pdf">pdf</a>) can help the group to work in a purposeful way - success on this task could be measured by how
effectively the group members work together as well as by their final solution. <a href="/content/id/4806/SimplifiedRoles.doc">This version</a> of the roles has been adapted for primary children.</div>
<br></br>
<div>Introduce the four group roles to the class. It may be appropriate, if this is the first time the class has worked in this way, to allocate particular roles to particular children. If the class works in roles over a series of lessons, it is desirable to make sure everyone experiences each role over time.</div>
<br></br>
<div>For suggestions of team-building maths tasks for use with classes unfamiliar with group work, take a look at <a href="http://nrich.maths.org/6933&part=">this article</a> and the accompanying resources.</div>
<br></br>
<div>Give each group of four <a href="/content/id/4806/TwoClocksPart2.pdf">this sheet</a>, which summarises the second part of the problem. You could also give them <a href="/content/id/4806/TwoClocksPart2Cards.pdf">these twelve cards</a>, five of which have the clock faces on them and five of which give the information about each day of the week. Challenge them to work on the task in their
groups so that they can match the clock face with the day. Explain that you will expect them to report back at the end of the session and at that point you will be looking out for good explanations of how they went about the task. Give each group a large sheet of paper on which to record notes for feeding back, including any questions that they may have as a result of having had a go at the
task.</div>
<br></br>
<div>There are many ways that groups can report back. Here are just a few suggestions:</div>
<ul>
<li>Every group is given a couple of minutes to report back to the whole class. Learners can seek clarification and ask questions. After each presentation, children are invited to offer positive feedback. Finally, pupils can suggest how the group could have improved their work on the task.</li>
<li>Everyone's posters are put on display at the front of the room, but only a couple of groups are selected to report back to the whole class. Feedback and suggestions can be given in the same way as above. Additionally, children from the groups which don't present can be invited to share at the end anything they did differently.</li>
<li>Two children from each group move to join an adjacent group. The two "hosts" explain their findings to the two "visitors". The "visitors" act as critical friends, requiring clear mathematical explanations and justifications. The "visitors" then comment on anything they did differently in their own group.</li>
</ul>
You may find that there is not agreement on the 'final' solution. The important thing is that each group can justify its reasoning. This may lead to a consensus amongst the whole class, but it may not.<br></br>
<h3>Key questions</h3>
<div>If your focus is effective group work, this list of skills may be helpful (<a href="/content/id/4806/Skills.doc">Word</a>, <a href="/content/id/4806/Skills.pdf">pdf</a>). Ask learners to identify which skills they demonstrated, and which skills they need to develop further; or ask them to identify someone else in the group who demonstrated a particular skill.</div>
<br></br>
<div>If your focus is mathematical, these prompts might be useful:</div>
<div>What does that hand tell you?</div>
<div>What time could the clock be showing? How do you know?</div>
<div>Roughly, what could the time be on Monday/Tuesday etc?</div>
<div>Which three clocks show minute hands five minutes apart?</div>
<div>How might that help you to decide which days they were?</div>
<br></br>
<h3>Possible extension</h3>
Those who already tell the time efficiently could write the time when various activities take place at school on both one-handed clocks.<br></br>
<h3>Possible support</h3>
Some children find telling the time with analogue clocks extremely difficult. A (one-handed) model clock would be very useful at this point.<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
Approximately what time do you think each clock is showing?<br></br>
Can you order these times together to fit in with Sam's day? <br></br>
Thinking about Julie's week, where might the minute hand of the clock be if she hurries home from school and it takes about half an hour? <br></br>Which three clocks show minute hands five minutes apart? Might that help you to decide which days they were?<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Sam: <br></br>Midday ? clock B
<br></br>
<div style="clear: both;">Gets up - 7.15
<br></br>
<div style="clear: both;">To school - 8.30.
<br></br>
<div style="clear: both;">Light out - 9.45</div>
<div style="clear: both;"></div><div style="clear: both;">Julie: <br></br>
<div style="clear: both;">TV - 25 past
<br></br>
<div style="clear: both;">1. Friday
<br></br>
<div style="clear: both;">2. Monday<br></br>
<div style="clear: both;">
3. Thursday
<br></br>
<div style="clear: both;">4. Tuesday
<br></br>
<div style="clear: both;">5. Wednesday</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<br></br></mdoxml>
2
4
0
1
0
0
0
Two Clocks
These clocks have only one hand, but can you work out what time
they are showing from the information?
Mathematics Tools
Clock
Measures and Mensuration
Time
Using, Applying and Reasoning about Mathematics
Group worthy
Admin
Upper primary mapping document