7340
/www/nrich/html/content/id/7340/
1
2011-03-18T16:14:24
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<mdoxml version="1.0"><br></br>
Have a look at the sets of four quantities below. Can you rank them
in order from smallest to largest?<br></br>
<br></br>
To help you decide, you may need to find extra information or carry
out some experiments.<br></br>
<br></br>
Can you convince us that your order is right?<br></br>
<br></br>
<table border="0">
<tbody>
<tr>
<td> <mdo:image width="100" height="100" src="clock.gif" alt=""></mdo:image></td>
<td>
<div style="font-weight: bold;">Time</div>
<div>Taken to travel to school</div>
<div>For mustard and cress to grow from seeds</div>
<div>Taken to eat a biscuit</div>
<div>Between your 6th and 7th birthdays </div>
</td>
</tr>
<tr>
<td> <mdo:image width="100" height="100" src="ruler.jpg" alt=""></mdo:image></td>
<td>
<div style="font-weight: bold;">Distance</div>
<div>You could jump up in the air</div>
<div>You can kick a football</div>
<div>You can run in half a minute</div>
<div>Length of a ladybird </div>
</td>
</tr>
<tr>
<td> <mdo:image width="100" height="100" src="scales.jpg" alt=""></mdo:image></td>
<td>
<div style="font-weight: bold;">Mass</div>
<div>Of a blown-up balloon</div>
<div>Of a bar of chocolate</div>
<div>Of a loaf of bread</div>
<div>Of your teacher </div>
</td>
</tr>
</tbody>
</table>
<br></br>
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<p class="editorial">Daisy from Ricards Lodge has given us lots of
details to explain how she ordered the quantities. Are you
convinced by what Daisy says?</p>
<br></br>
Time: (shortest to longest)<br></br>
Eat a biscuit - I think that to eat a normal sized circular biscuit
takes roughly $30$ seconds to eat at a usual pace!<br></br>
Taken to travel to school - The journey from my house to school
takes $40$ minutes and this is quite a common length of time for
the journey amongst my classmates.<br></br>
Taken for mustard and cress to grow from seeds - in a suitable
climate this process should take no longer than three days.<br></br>
The period between your 6th and 7th birthday - this is $365$ days,
(unless your birthday is on a leap year) a whole year, clearly the
longest amount of time on this list.<br></br>
<br></br>
Distance: (shortest to longest)<br></br>
Length of a ladybird - they grow up to approximately $4$mm.<br></br>
How high you can jump in the air - This really depends on your
height but it is very likely to still be measured in cm; which is
why I put it second on the list.<br></br>
How far you can kick a football - Amateur footballers can kick a
ball up to $50$m, definitely a longer distance than the last
measurement.<br></br>
How far can you run in $30$ seconds - In my age group, it is
possible to run $200$m in under half a minute, considerably longer
than the length you can kick a ball.<br></br>
<br></br>
Mass: (lightest to heaviest)<br></br>
A balloon - I estimate that the mass of a balloon is about a gram
as it is practically all gas which has a very minimal mass.<br></br>
Bar of chocolate - A usual bar of chocolate (measuring roughly
$20$cm) weighs between $50$g and $60$g.<br></br>
Loaf of bread - A loaf of shop-bought pre-sliced bread weighs
$800$g.<br></br>
Teacher - The average weight of a woman in the UK is $65$kg and for
men, $72$kg. This makes it the heaviest measurement in the list.
<br></br>
<br></br>
<p class="editorial">Let us know if you have any comments about
Daisy's estimations.</p>
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<mdoxml version="1.0"><div class="embed">
<h2>Order, Order!</h2>
<br></br>
Have a look at the sets of four quantities below. Can you rank them in order from smallest to largest?<br></br>
<br></br>
To help you decide, you may need to find extra information or carry out some experiments.<br></br>
<br></br>
Can you convince us that your order is right?<br></br>
<br></br>
<table style="" border="">
<tbody>
<tr>
<td> <mdo:image alt="" height="100" src="clock.gif" width="100"></mdo:image></td>
<td>
<div style="font-weight: bold;">Time</div>
<div>Taken to travel to school</div>
<div>For mustard and cress to grow from seeds</div>
<div>Taken to eat a biscuit</div>
<div>Between your 6th and 7th birthdays </div>
</td>
</tr>
<tr>
<td> <mdo:image alt="" height="100" src="ruler.jpg" width="100"></mdo:image></td>
<td>
<div style="font-weight: bold;">Distance</div>
<div>You could jump up in the air</div>
<div>You can kick a football</div>
<div>You can run in half a minute</div>
<div>Length of a ladybird </div>
</td>
</tr>
<tr>
<td> <mdo:image alt="" height="100" src="scales.jpg" width="100"></mdo:image></td>
<td>
<div style="font-weight: bold;">Mass</div>
<div>Of a blown-up balloon</div>
<div>Of a bar of chocolate</div>
<div>Of a loaf of bread</div>
<div>Of your teacher </div>
</td>
</tr>
</tbody>
</table>
<br></br>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/7340&part=">This activity</a> offers an opportunity to combine skills from mathematics and science. Learners are required to make estimates, understand and use appropriate units, and find information to draw conclusions.</div>
<div> </div>
<div>This problem highlights the fact that in science it is rather hard to calculate anything without making some sort of assumptions. Good science will clearly state and be aware of these assumptions; bad science will ignore them. This idea is likely to come up informally as the children talk to each other and so you can draw attention to examples that they themselves bring up.</div>
<br></br>
<h3>Possible approach</h3>
<div>Give each pair or group of children a copy of <a href="/content/id/7340/OrderOrder.pdf">these cards</a>. Each card has one of the statements on it along with a picture. The picture will help those who cannot read so well remember the content. Invite the pupils to put the four time cards in front of them to start with and ask them to order the cards in their pairs/groups.
At this stage, make it clear that it doesn't matter if they are unsure. Have a brief discussion about their thoughts and then have a go at the distance and mass statements in a similar way.</div>
<div> </div>
<div>Then, allocate one of the sets of cards (i.e. time, distance or mass) to each pair or group. The aim now is for each pair/group to come up with an order for the quantities they have been given, together with a convincing presentation of evidence to justify their order. Allow pupils access to reference materials, measuring equipment, and anything else that might be useful, and give them
plenty of time for research and experiment.</div>
<div> </div>
<div>Once they have finished, take each set of quantities and invite the different groups to present their rankings and reasoning. Ask the rest of the class to judge the different presentations on the strength of the evidence they have offered. </div>
<br></br>
<h3>Key questions</h3>
<div>Do you have an idea of what order they might go in?</div>
<div>What could you do to find out how long/how far/how heavy that is?</div>
<br></br>
<h3>Possible extension</h3>
Some children might like to have a go at a similar problem <a href="http://nrich.maths.org/7341&part=">In Order</a>, which demands more clarity about the assumptions they are making.<br></br>
<h3>Possible support</h3>
Reassure learners that there are often no exact values (so no "wrong" answers), and their task is simply to find some evidence to convince others of the order. Encourage them to experiment, and offer some guidance on how to search for suitable data.<br></br>
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<mdoxml version="1.0">How could you estimate each of the quantities? <br></br>
What extra information might you need to find out? <br></br></mdoxml>
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Order, Order!
Can you place these quantities in order from smallest to largest?
Applications
STEM - General
Measures and Mensuration
Time
Measures and Mensuration
Mass and weight
Measures and Mensuration
Length/distance
Using, Applying and Reasoning about Mathematics
Selecting and using information
Admin
Lower primary mapping document