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2011-02-01T00:00:01
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<p>Well it's nice to move into
a new house sometimes. For some people it's great fun to design and
make a new house. I've been thinking of an idea where the house is
built out of blocks which are the rooms. I don't know whether
you've seen some builders' sheds set up this way on big building
sites when the sheds or offices are linked together with big steel
girders? Well I'm thinking that it could be good fun to design
houses with that sort of idea in mind.</p>
<p>Well we have to buy some
land first and suppose that we buy four big squares.</p>
<mdo:image alt="" src="sq.gif"></mdo:image><br></br>
<p>I reckon that a good house
may have about 7 rooms. So let's use some interlocking cubes to
stand for the rooms and arrange each of them so that they are
connected and NOT spilling over the 4 square base size.</p>
<p>Perhaps like this - I've
used 7 differently coloured cubes so as to follow things more
easily:-</p>
<div style="text-align: center;"><mdo:image width="112" height="170" src="newhouse1.jpg" alt="new1"></mdo:image></div>
<br></br>
<p>There are of course lots of
different designs.<br></br>
Take some interlocking cubes such as "multilink" and have a go at
making some now!</p>
Make sure that they stand up! You may be able to do one like:-
<div style="text-align: center;"><mdo:image width="114" height="159" src="newhouse2.jpg" alt="new2"></mdo:image></div>
<br></br>
<p>But according to what your
interlocking cubes are like you may or may not be able to do that
one.</p>
<p>But maybe you could
do:-</p>
<div style="text-align: center;"><mdo:image width="116" height="244" src="newhouse3.jpg" alt="new3"></mdo:image></div>
<br></br>
<p>The whole idea of this
investigation is to try to find all the different designs that you
can. You can decide for yourselves whether shapes that are just
turned around $90^\circ$ are the same or different. The same goes
for the designs that are reflections of another design.</p>
<p>YOU DECIDE.</p>
<p>It would probably be good
to see if you can find some kind of system/method/pattern for doing
these and try to write down those ideas that you have.</p>
Of course we have to ask "I wonder what would happen if ...":
<p>a/ the base was 5, 6, 7, 8,
or 9 squares?</p>
<p>b/ the base was bigger,
would it matter what shape the squares are arranged in?</p>
<p>c/ you had 8 or 9 or 10
rooms?</p>
<p>d/ etc.</p>
<p><a href="/content/99/02/bbprob2/Dotty%20paper.pdf">Here is some dotty
isometric paper</a> which might help for drawing the cubes.</p>
<p>If you're not sure about
drawing them on these dots it really does not matter. But if you
fancy that idea and you have not used these triangular arranged
dots before then this is what you do:</p>
<p>1/ Take 7 dots arranged
like a hexagon with one dot in the middle:-</p>
<div> <mdo:image width="79" height="78" src="7%20new%20dots.jpg" alt="7 new dots"></mdo:image></div>
<div> </div>
<br></br>
<p>2/ Draw a capital Y by
using every other dot:-</p>
<mdo:image alt="" src="selection2.gif"></mdo:image><br></br>
<p>3/ Draw in the six sides of
the hexagon:-</p>
<mdo:image alt="" src="selection3.gif"></mdo:image><br></br>
<p>Good luck</p>
<p>Remember to send in your
results.</p>
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<p><span class="editorial">From the same pupils at West Flegg came
some</span> <em class="editorial">Houses</em> <span class="editorial">ideas.</span></p>
<div style="text-align: center;"><mdo:image alt="" src="rachel.gif"></mdo:image></div>
<br></br>
<p class="editorial">These came from Rachel. Some others came but I
was unable to get them put onto the computer in a good way.</p>
<p class="editorial">I liked these ideas Rachel, and as you say
they are just a few of many ideas. If you have more, then do get in
touch. Please don't worry that your solution is not "complete" -
we'd like to hear about anything you have tried.</p>
<p class="editorial">Teachers - you might like to send in a summary
of your children's work.</p>
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<h2>New House</h2>
<br></br>
<p>Well it's nice to move into a new house sometimes. For some people it's great fun to design and make a new house. I've been thinking of an idea where the house is built out of blocks which are the rooms. I don't know whether you've seen some builders' sheds set up this way on big building sites when the sheds or offices are linked together with big steel girders? Well I'm thinking that it
could be good fun to design houses with that sort of idea in mind.</p>
<p>Well we have to buy some land first and suppose that we buy four big squares.</p>
<mdo:image alt="" src="sq.gif"></mdo:image><br></br>
<p>I reckon that a good house may have about 7 rooms. So let's use some interlocking cubes to stand for the rooms and arrange each of them so that they are connected and NOT spilling over the 4 square base size.</p>
<p>Perhaps like this - I've used 7 differently coloured cubes so as to follow things more easily:-</p>
<div style="text-align: center;"><mdo:image alt="new1" height="170" src="newhouse1.jpg" width="112"></mdo:image></div>
<br></br>
<p>There are of course lots of different designs.<br></br>
Take some interlocking cubes such as "multilink" and have a go at making some now!</p>
Make sure that they stand up! You may be able to do one like:-
<div style="text-align: center;"><mdo:image alt="new2" height="159" src="newhouse2.jpg" width="114"></mdo:image></div>
<br></br>
<p>But according to what your interlocking cubes are like you may or may not be able to do that one.</p>
<p>But maybe you could do:-</p>
<div style="text-align: center;"><mdo:image alt="new3" height="244" src="newhouse3.jpg" width="116"></mdo:image></div>
<br></br>
<p>The whole idea of this investigation is to try to find all the different designs that you can. You can decide for yourselves whether shapes that are just turned around $90^\circ$ are the same or different. The same goes for the designs that are reflections of another design.</p>
<p>YOU DECIDE.</p>
<p>It would probably be good to see if you can find some kind of system/method/pattern for doing these and try to write down those ideas that you have.</p>
Of course we have to ask "I wonder what would happen if ...":
<p>a/ the base was 5, 6, 7, 8, or 9 squares?</p>
<p>b/ the base was bigger, would it matter what shape the squares are arranged in?</p>
<p>c/ you had 8 or 9 or 10 rooms?</p>
<p>d/ etc.</p>
<p><a href="/content/99/02/bbprob2/Dotty%20paper.pdf">Here is some dotty isometric paper</a> which might help for drawing the cubes.</p>
<p>If you're not sure about drawing them on these dots it really does not matter. But if you fancy that idea and you have not used these triangular arranged dots before then this is what you do:</p>
<p>1/ Take 7 dots arranged like a hexagon with one dot in the middle:-</p>
<div> <mdo:image alt="7 new dots" height="78" src="7%20new%20dots.jpg" width="79"></mdo:image></div>
<div> </div>
<br></br>
<p>2/ Draw a capital Y by using every other dot:-</p>
<mdo:image alt="" src="selection2.gif"></mdo:image><br></br>
<p>3/ Draw in the six sides of the hexagon:-</p>
<mdo:image alt="" src="selection3.gif"></mdo:image><br></br>
<p>Good luck</p>
<p>Remember to send in your results.</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=61&part=">activity</a> can be a fun way of introducing pupils to the idea of considering a system/method/pattern when tackling some investigations.</div>
<br></br>
<h3>Possible approach</h3>
<div>If you are happy with a computer presentation package then a captivating way of introducing the problem would be for them to see a house gradually taking place.</div>
<div>I would suggest that recording is not made an issue here as it can be rather hard, although I have found that 9-10 year olds can usually invent quite good ways of recording each design. A simple example I've come across has been:-</div>
<div style="text-align: center;"><mdo:image alt="recording" height="189" src="houses%20record.jpg" width="238"></mdo:image></div>
<br></br>
and then various ways have been found for tackling the overhanging, balcony rooms.<br></br>
<br></br>
<h3>Key questions</h3>
<div>Tell me about the ways that you are finding more and more house shapes.</div>
<br></br>
<h3>Possible extension</h3>
<div>Using extension activities such as asking how much paint would be used to paint the outside of the designs is a good activity to link with surface area work. If children are challenged to find designs which use less paint and try to explain why that is so, really good-quality maths talk happens.</div>
<br></br>
<h3>Possible support</h3>
<div>As mentioned in the problem some <a href="/content/99/02/bbprob2/Dotty%20paper.pdf">isometric paper</a> can be a help for those who want to record in that way, however using a digital camera can make it easier for the pupils.</div>
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New House
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
3D Geometry, Shape and Space
2D representations of 3D shapes
Decision Mathematics and Combinatorics
Combinations
Using, Applying and Reasoning about Mathematics
Working systematically
Mathematics Tools
Interlocking cubes
Using, Applying and Reasoning about Mathematics
Investigations