4789
/www/nrich/html/content/id/4789/
1
2011-02-01T00:00:01
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<mdoxml version="1.0">This problem has been inspired by "The Man", a story by Raymond Briggs, which you might like to read.<br></br>
<br></br>
The Man is much smaller than you and me. <br></br>
Here is a picture of him standing next to a mug.<br></br><br></br><mdo:image width="320" height="240" src="littleMan.jpg" alt="A little man next to a big mug"></mdo:image><br></br><br></br>
Can you estimate how tall he is?<br></br>
Can you think of something that you have at school or home that is approximately twice as tall as the Man?<br></br>
What about something that is about half as tall?<br></br>
<br></br>
How tall do you think the Man's mug might be?<br></br>
Can you estimate how many "Man mugs" of tea might fill one of our mugs?<br></br>
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<p class="editorial">Alara from FMV Erenkoy Primary School sent us
a very full solution to this problem:</p>
Estimation of how tall he is : - It is not possible to say an exact
number or measurement for his height. There could only be some
estimations. However, I can make an estimation using the ratio of
the man's height to the mug's height.<br></br>
<br></br>
<p class="editorial">(Read on for Alara's estimation!)</p>
Something at school or at home which is approximately twice as tall
as the Man : - It depends on the mug's height; for example
according to my milk mug's height when I checked, my big dictionary
and my cd box is approximately twice as tall as the Man.<br></br>
<br></br>
Something which is about half as tall? And again, as I have written
above, according to my milk mug's height, my post-it papers and
small address note book are about half as tall as the Man.<br></br>
<br></br>
How tall the Man's mug might be? My mug's height is 10 cm and I am
150 cm tall. The ratio between me and my mug is 10/150, that is to
say 1/15. The Man's mug might be 15 times smaller than his height.
<br></br>
<br></br>
How many "Man Mugs" of tea might fill one of my mug? There is a way
to answer this question, if we take into considerationthe "ratio
principles". Above, I identified that I'm 15 times as tall as my
mug. So, let's assume the Little Man is as tall as my mug, so he is
10 cm tall. If we consider the same ratio between the Little Man
and his mug, the Man Mug is 15 times smaller than him. 15 "Man
Mugs" of tea might fill my mug.<br></br>
<br></br>
<p class="editorial">Sam from Farndon Primary School and Harri from
Pilgrim's School also estimated similar heights for the Man,
although Sam thought that 79 "Man Mugs" of tea would fill one of
our mugs. Do you agree with Alara or Sam? Can you explain why?</p>
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<h2>Little Man</h2>
This problem has been inspired by "The Man", a story by Raymond Briggs, which you might like to read.<br></br>
<br></br>
The Man is much smaller than you and me.<br></br>
Here is a picture of him standing next to a mug.<br></br>
<br></br>
<mdo:image alt="A little man next to a big mug" height="240" src="littleMan.jpg" width="320"></mdo:image><br></br>
<br></br>
Can you estimate how tall he is?<br></br>
Can you think of something that you have at school or home that is approximately twice as tall as the Man?<br></br>
What about something that is about half as tall?<br></br>
<br></br>
How tall do you think the Man's mug might be?<br></br>
Can you estimate how many "Man mugs" of tea might fill one of our mugs?<br></br>
</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=4789&part=index">This problem</a> offers a context in which to think about relative size and gives children chances to estimate quantities.</div>
<br></br>
<h3>Possible approach</h3>
<div>It might be appropriate to read the book "The Man" (by Raymond Briggs) with the class prior to working on this task.</div>
<br></br>
<div>Before looking at the problem specifically, it would be worth investigating how much liquid different everyday items hold, for example spoons, bowls, bottles and jugs. This practical exploration could be done in a water tray or simply a large bucket or bowl with small groups of learners.</div>
<br></br>
<div>Once the class comes onto looking at the questions, it is important that you encourage them to make estimations and explain how they arrived at their answer. It may be appropriate for you to share your own methods of estimating, particularly when it comes to the capacity of the man's mug. It would also be helpful to have a mug, ruler and measuring cylinder to hand so that everyone can check
whether their estimates are realistic.</div>
<br></br>
<h3>Key questions</h3>
<div>How long is one centimetre? Ten centimetres? So how high do you think a mug might be?</div>
<div>How did you come up with your answer?</div>
<div>Can you think of anything that you know holds about a litre of liquid?</div>
<div>How much do you think a mug might hold?</div>
<br></br>
<h3>Possible extension</h3>
<div>You could challenge children to articulate the relationship between the relative size of the man and one of them. Is the man about twice as small as us? Five times smaller? Ten times smaller? Will this relationship hold for everything?</div>
<br></br>
<h3>Possible support</h3>
<div>Some learners might find it helpful to have a series of tasks which requires them to estimate and then measure concrete items in the classroom before going on to estimate measurements of items they are visualising.</div>
<br></br>
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<mdoxml version="1.0"><div>Perhaps it would help to find a mug that you can look at.</div>
<div>Can you think of anything you have which might be about the same size as the Man's mug? Can you estimate how much tea that might hold?</div>
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Little Man
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
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