7237 /www/nrich/html/content/id/7237/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p><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></p> <p><span style="font-style: italic;">The activity is intended to extend</span> <a href="http://nrich.maths.org/72&amp;part="><span style="font-style: italic;">G</span>rrrreat Squares</a> <span style="font-style: italic;">for those who need/want something much more challenging.</span></p> <br></br> <p> <br></br> Choose one or more of the following five sets of pictures and explore them further for number patterns, area implications, trigonometrical facts and predictions.<br></br>  </p> <div style="text-align: center;">$1$</div> <div style="text-align: center;"> <mdo:image alt="2" height="272" src="Picture%202.jpg" width="254"></mdo:image></div> <div style="text-align: center;">------------------------------</div> <div style="text-align: center;">$2$</div> <div style="text-align: center;"> <mdo:image alt="3" height="249" src="Picture%203.jpg" width="575"></mdo:image></div> <div style="text-align: center;">------------------------------</div> <div style="text-align: center;">$3$</div> <br></br> <div style="text-align: center;"> <mdo:image alt="4" height="149" src="Picture%204.jpg" width="281"></mdo:image></div> <div style="text-align: center;">------------------------------</div> <div style="text-align: center;">$4$</div> <br></br> <div style="text-align: center;"> <mdo:image alt="5" height="193" src="Picture%205.jpg" width="396"></mdo:image></div> <div style="text-align: center;">------------------------------</div> <div style="text-align: center;">$5$</div> <br></br> <div style="text-align: center;"> <mdo:image alt="6" height="313" src="Picture%206.jpg" width="307"></mdo:image></div> <div style="text-align: center;"> </div> <br></br> <p> </p> <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/7237&amp;part=">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/72&amp;part=">Grrrrreat Squares</a>. It's an activity that is intended to give opportunities for those pupils to explore deeply using their intuition, flair and risk-taking skills.</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.  It may well be that choosing just one of the five pictures and staying with that for a considerable investigational time is the best way to use the activity. </div> <br></br> <h3>Key questions</h3> <div>Tell me about this/your thinking.</div> <br></br></mdoxml> 5 5 0 1 1 0 0 Explore one of these five pictures. Using, Applying and Reasoning about Mathematics Investigations Sequences, Functions and Graphs Sequences Measures and Mensuration Area