7509
/www/nrich/html/content/id/7509/
1
2011-09-20T12:11:21
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><comment> &lt;p&gt;
&lt;img alt="the4houses" height="105" src="/content/id/7509/the4houses.jpg" width="660" /&gt;&lt;/p&gt; </comment>
<p><mdo:image alt="tower" src="tower1.jpg" style="width: 160px; height: 95px; margin: 10px 2px; float: left;"></mdo:image><mdo:image alt="tower2" src="tower2.jpg" style="width: 160px; height: 95px; margin: 10px 2px; float: left;"></mdo:image><mdo:image alt="" src="tower3.jpg" style="clear:left;width: 160px; height: 95px; margin: 10px 2px; float: left;"></mdo:image><mdo:image alt="" src="tower4.jpg" style="width: 160px; height: 95px; margin: 10px 2px; float: left;"></mdo:image></p>
<p style="clear:left">These pictures show a tower with a pointed roof in the garden of a cottage.</p>
<p>The tower looks a different size in each of the pictures.<span style=""> </span> I wonder why?</p>
<p>Discuss your thoughts and ideas with others.</p>
<p>What would you like to find out about these four pictures?</p>
<p><br></br>
<br></br>
</p>
<p><br></br>
<br></br>
</p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><p><span class="editorial">We had nearly $50$ solutions sent in as well as several contributions to the <a class="blogbutton" href="http://www.nrich.maths.org/z/infinities">blog</a>. Overall there were many different ideas as to how the pictures came about.</span></p>
<p><span class="editorial">Here are some of them;</span></p>
<p><span class="editorial">Lisa from Le Rosey School in Switzerland wrote;</span></p>
<p>You can see the Pointed towers bigger than the other one because it's looked closer. The ones that look smaller is the ones that your seeing further. So the more you see closer the bigger you can see, same as if you look further then you can see smaller.</p>
<p><span class="editorial">Oscar from St. John the Baptist School in England had a look at the other challenge that was in the <a href="http://nrich.maths.org/7509/clue">hint</a>. He sent in;</span></p>
<p>The tower of $6$ blocks looks the same size as the one with three because of the distance between them, if the two towers were together the tower of six would be taller.</p>
<p><span class="editorial">Fabio from St. Pauls in Brazil sent in his idea about the importance of the angle;</span></p>
<p>At the first picture the photo was taken close to the tower and the picture was focusing into the tower so it seems as the tower taller than the house. At the second picture the photo was taken a little bit further so it seem that the house is a little bit smaller the tower. At the third picture the photo was taken a little bit further so it seem that the house is the same size as the
tower. At the fourth picture the photo was taken a little bit further so it seem that the house is bigger than the tower.</p>
<p><span class="editorial">Noor-Ul-Ain from Westfield Middle School sent is an alternative idea;</span></p>
<p>I think the solution to the problem eye view is:<br></br>
- In every picture someone puts the pointed tower closer or in front of the house each time.<br></br>
- Or they put the house further back or behind the house but on the side of the house.<br></br>
- This affect makes a great illusion and tricks the mind of the person looking at the photograph.</p>
<p><span class="editorial">The Maths Challenge group from St. Ainden's VC school in the UK sent in these ideas;</span></p>
<p>This made us think hard and we all had lots of different ideas! Zac and Izzy thought that the tower could be a different one i.e. different sizes in each picture OR the cottage could be different and the tower the same.</p>
<p>Louisa thinks the images of the tower have been taken from different positions. She thinks the cottage isn't real but is painted onto the lens of the camera so that it looks the same. Esme thinks that they are models put in different positions and photographed from different angles.</p>
<p>Marlo thinks the bricks used to build the tower are bigger than the bricks used to build the cottage. Luca thinks they used the same models but photographed them from different positions.</p>
<p><span class="editorial">From New City School in London the following pupils sent in a variety of different ideas as to how the pictures came about,</span><span class="editorial">Naziat ,Jacqueline and Akhlak, Suffyan,William & Anika, Aqsa, Zainab & Oscar, Rizwan, Arif & Joe, Hilin , Jamian & Hamza, Patrick, Sascha & Eldon, Chloe, Bakhtavar & Gokul.</span></p>
<p><span class="editorial">Thank you all of you for sharing your creative ideas with us.</span></p>
<p> </p></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Eye View</h2>
<comment> &lt;p&gt;
&lt;img alt="the4houses" height="105" src="/content/id/7509/the4houses.jpg" width="660" /&gt;&lt;/p&gt; </comment>
<p><mdo:image alt="tower" src="tower1.jpg" style="margin: 10px 2px; width: 160px; height: 95px; float: left;"></mdo:image><mdo:image alt="tower2" src="tower2.jpg" style="margin: 10px 2px; width: 160px; height: 95px; float: left;"></mdo:image><mdo:image alt="" src="tower3.jpg" style="margin: 10px 2px; width: 160px; height: 95px; clear: left; float: left;"></mdo:image><mdo:image alt="" src="tower4.jpg" style="margin: 10px 2px; width: 160px; height: 95px; float: left;"></mdo:image></p>
<p style="clear: left;">These pictures show a tower with a pointed roof in the garden of a cottage.</p>
<p>The tower looks a different size in each of the pictures.<span> </span> I wonder why?</p>
<p>Discuss your thoughts and ideas with others.</p>
<p>What would you like to find out about these four pictures?</p>
<p><br></br>
<br></br>
</p>
<p><br></br>
<br></br>
</p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/7509">activity</a> is designed to create a challenge that is completely new to pupils so they will not have practised particular ways to approach situations like it. They will therefore have to use their initiative and draw on potentially useful problem-solving skills. This task also provides an excellent opportunity for a discussion about different
approaches that have been used once children have had chance to tackle it in their own way.</div>
<br></br>
<h3>Possible approach</h3>
<div>Show the group the four pictures of the cottage and the tower, and invite them to talk to a partner about anything they notice. Share some ideas amongst the whole class. It is likely that they will notice the different size of the tower in each picture so you can explain that in fact these pictures show the same cottage and tower. (If you prefer, you could use the pictures
in the <a href="/7509&part=clue">Hint</a> as an initial stimulus.)
<p>Encourage them to make suggestions as to what has happened to create these pictures. Explain that you're not expecting them to know necessarily straight away how to do it so give them plenty of time to work on ideas in pairs or small groups. Pupils may also be encouraged to validate their suggestions, for example by using two items of their choice to position and compare.</p>
<p>Just as valuable as having a go at this activity is the discussion which should then follow. Bring everyone together and invite pairs/groups to explain how they went about the problem. You may like to jot a few notes on the board so by the time everyone has contributed, there is a record of the different approaches to which subsequent discussion can refer. What
are the advantages and disadvantages of each? Which approach might individuals use if they were having a go at a similar task? Why?</p>
</div>
<div> </div>
<h3>Key questions</h3>
<div>How do you think the pictures were created?<br></br>
Could you make something similar?<br></br>
What do you think about others' ideas?</div>
<div> </div>
<h3>Possible extension</h3>
<div>Pupils could create a similar set of pictures for others to understand. They could then progress to using more than two objects in the picture.</div>
<div> </div>
<h3>Possible support</h3>
<div>Some pupils may need to have this presented in 'real time' with the teacher using a camera and projecting the image directly onto a screen. It may also be useful to use the images which appear in the <a href="/7509&part=clue">Hint</a> and to have the two towers made.</div>
<p><br></br>
</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">
<p style="margin: 0.1pt 0cm;">The left picture below shows a tower of three red cubes and a tower of five blue cubes.<span style=""> </span></p>
<p style="margin: 0.1pt 0cm;">The right picture shows a tower of three red cubes and a tower of six blue cubes.<span style=""> </span></p>
<p style="margin: 0.1pt 0cm;">All the cubes are exactly the same size so why do the towers look the same height in both pictures?<span style=""> </span></p>
<p><mdo:image src="sm%203%265%20cubes.jpg"></mdo:image> <mdo:image src="sm%203%266%20cubes.jpg"></mdo:image></p>
<p> </p>
</mdoxml>
5
3
0
1
0
0
0
Eye View
Why does the tower look a different size in each of these pictures?
Using, Applying and Reasoning about Mathematics
Questioning
Using, Applying and Reasoning about Mathematics
Investigations
Admin
Upper primary mapping document