7128
/www/nrich/html/content/id/7128/
1
2011-02-01T00:00:01
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<div style="text-align: center;"><mdo:image width="364" height="209" alt="cubes pic" src="cubes%20pic.jpg"></mdo:image></div>
<div>Well, here I've placed a
group of cubes. They are in threes and coloured differently.</div>
<div> </div>
<div>What do you notice about
them?</div>
<div> </div>
<div>You could get $8$ triple
cubes like these, each triple a different colour. Don't separate
the triple but use them as building blocks to see what you can
make.</div>
<div> </div>
<div>For some of you it
would be good to keep the eight triple cubes facing their own ways
and not turn them around. In this way we keep eight arrangements
that are different.</div>
<div> </div>
<div>We can now use these as
building blocks to make interesting arrangements and shapes. Here
is one to start us off.</div>
<div style="text-align: center;"> <mdo:image width="367" height="211" alt="eg3" src="eg3%20pic.jpg"></mdo:image></div>
<div>Notice how I've joined
them together with square faces touching. This might be the
way that you decide to build.</div>
<div> </div>
<div>Or, you may include some
"edge" joining as in this one.</div>
<div style="text-align: center;"> <mdo:image width="296" height="208" alt="eg4" src="eg4%20pic.jpg"></mdo:image></div>
<div> </div>
<div>So now it's your turn to
see what you can make from these eight triple cubes.</div>
<br></br>
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<p class="editorial">Jimmy from Freshwater State School
managed to produce a rectangle that was $4$ by $8$. Well done
Jimmy. I am guessing that many may have explored various shapes
that they produced but did not feel they could send in their
findings.</p>
<p class="editorial">I would like to remind everyone that we are
interested in what happens from the starting point - it does not
have to be a final concluding result - but feel free to send them
in.</p>
<p class="editorial"> </p>
<br></br>
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<h2>Triple Cubes</h2>
<br></br>
<div style="text-align: center;"><mdo:image alt="cubes pic" height="209" src="cubes%20pic.jpg" width="364"></mdo:image></div>
<div>Well, here I've placed a group of cubes. They are in threes and coloured differently.</div>
<div> </div>
<div>What do you notice about them?</div>
<div> </div>
<div>You could get $8$ triple cubes like these, each triple a different colour. Don't separate the triple but use them as building blocks to see what you can make.</div>
<div> </div>
<div>For some of you it would be good to keep the eight triple cubes facing their own ways and not turn them around. In this way we keep eight arrangements that are different.</div>
<div> </div>
<div>We can now use these as building blocks to make interesting arrangements and shapes. Here is one to start us off.</div>
<div style="text-align: center;"> <mdo:image alt="eg3" height="211" src="eg3%20pic.jpg" width="367"></mdo:image></div>
<div>Notice how I've joined them together with square faces touching. This might be the way that you decide to build.</div>
<div> </div>
<div>Or, you may include some "edge" joining as in this one.</div>
<div style="text-align: center;"> <mdo:image alt="eg4" height="208" src="eg4%20pic.jpg" width="296"></mdo:image></div>
<div> </div>
<div>So now it's your turn to see what you can make from these eight triple cubes.</div>
<br></br>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://nrich.maths.org/7128&part=">activity</a> is an engaging one which may give opportunities for pupils to expand their spatial capabilities. It uses non-standard shapes to be put together and so stretches the imagination. Pupils will probably have had some experience of various construction materials and this offers something just a bit different.</div>
<br></br>
<h3>Possible approach</h3>
<div>Having prepared interlocking cubes in eight different colours, invite one pupil in the group to select one, then another child to choose another and connect it in some way to the first. Then invite a third child to choose another and connect it, etc. When all eight pieces are assembled together, pose questions and prompts such as: "Tell me about this."; "What do you see?"; "Any ideas as
to what this could be?" ...etc. Try to use open questions which will not stifle creativity or be too directive. </div>
<div> </div>
<div>Give children the chance to have a go on their own or in pairs. Plenty of interlocking cubes will be needed! Listen out for the way they describe their models and how they communicate with each other. Are they using appropriate vocabulary? Are they able to articulate where they are going to put the next shape? How are they going about the task? </div>
<div> </div>
Digital photos may be a good way of recording the children's constructions. You could then use the photos as a stimulus to conversations in small groups or with individuals at a later date.<br></br>
<h3>Key questions</h3>
<div>When they are making their own:</div>
<div>Tell me about this.</div>
<div>What are you making?</div>
<div>Do you have a name for this?</div>
<div>(Looking at theirs next to yours) Tell me about them.</div>
<br></br>
<h3>Possible extension</h3>
<div>You could challenge some children to make:</div>
<div>the longest one;</div>
<div>the one with most/least area touching the ground;</div>
<div>a mirror image of someone else's (including the colours);</div>
<div>the longest shape that can be picked up by holding just one cube.</div>
<br></br>
<h3>Possible support</h3>
<div>Some pupils may want to start with just four triple cubes and explore those first.</div>
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<mdoxml version="1.0">You'll need lots of interlocking cubes for this challenge! It
would be good to make the eight shapes in eight different colours
if you can.<br></br>
How will you put the shapes together?<br></br>
Perhaps you could compare your construction with some else's?
Or you could make another one and then look at what is the same and
what is different about the two.<br></br></mdoxml>
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Triple Cubes
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
3D Geometry, Shape and Space
Cubes
Using, Applying and Reasoning about Mathematics
Visualising
Using, Applying and Reasoning about Mathematics
Investigations
Mathematics Tools
Interlocking cubes
Admin
Lower primary mapping document
Admin
Upper primary mapping document