7239 /www/nrich/html/content/id/7239/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="text-align: left; font-style: italic;"><em>This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)</em></div> <div style="text-align: left; font-style: italic;">It can be used as a follow-on from <a href="http://nrich.maths.org/1997&amp;part=">Two on Five</a>.</div> <div style="text-align: left;"> </div> <div>You have interlocking cubes of three different colours - $2$ of one colour, $3$ of another colour and $4$ of the third colour.</div> <div>It could look like this;</div> <div style="text-align: center;"><mdo:image alt="2,3,4" height="91" src="2%2C3%2C4.jpg" width="328"></mdo:image></div> <br></br> <p> This is slightly different from <a href="http://nrich.maths.org/1997&amp;part=">Two on Five</a> but is seen as an extension for the highest attaining. You might like to go there first!<br></br>  <br></br> The nine cubes are to be connected in the usual way with the following rules being applied.<br></br>  <br></br> THE TWO YELLOW CUBES ARE NOT ALLOWED TO TOUCH WALL OR FLOOR SURFACES.<br></br>  <br></br> THE THREE BLUE CUBES MUST TOUCH ONE SURFACE ONLY, NOT TWO.<br></br>  <br></br> THE FOUR RED CUBES MUST TOUCH BOTH SURFACES.<br></br>  <br></br> Here are two examples that obey the rules;<br></br>  </p> <div style="text-align: center;"> <mdo:image alt="new 2on3on4" height="268" src="New%202on3on4.jpg" width="529"></mdo:image></div> <div style="text-align: center;"> </div> <div style="text-align: left;">See what others you can find.</div> <div style="text-align: left;">How many will there be?</div> <div style="text-align: left;">At some point ask yourself "I wonder what would happen if I ...?"</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://nrich.maths.org/7239">activity</a> is specially designed for the highest-attaining pupils that you ever come across. It acts as a further extension to <a href="http://nrich.maths.org/1997&amp;part=">Two on Five</a>. It&#39;s an activity that is intended to give opportunities for those pupils to explore deeply using their intuition and flair in the area of spatial awareness, also with an opportunity to create a system for solving such problems.</div> <br></br> <h3>Possible approach</h3> <div>As this is designed for the highest attaining, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.</div> <br></br> <h3>Key questions</h3> <div>Tell me about what you have found.</div> <div>Can you describe the ways that you arrived at these shape arrangements?</div> <div>How did you construct these on the computer?</div> <br></br> </mdoxml> 5 5 0 1 0 0 0 How many models can you find which obey these rules? Using, Applying and Reasoning about Mathematics Practical Activity Using, Applying and Reasoning about Mathematics Working systematically Using, Applying and Reasoning about Mathematics Investigations 3D Geometry, Shape and Space Cubes Mathematics Tools Interlocking cubes