7764 /www/nrich/html/content/id/7764/ 1 2011-12-10T10:39:12 <mdoxml version="1.0"><br></br> <p style="text-align: center;"> </p> <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 style="text-align: center;"><mdo:image src="diag%20cuts%20example.jpg"></mdo:image></p> <p style="text-align: center;"> </p> <p>Imagine the central square in a big city and its paved with large square tiles. It may be rectangular rather than square! You are going to go straight from one corner, diagonally across to the other corner. You may be walking, cycling, skate boarding or using roller blades. Which ever way you travel you will need to go absolutely straight from corner to corner.</p> <p>You see in the picture above showing a very, very small example (a $4$ by $3$ rectangle). The blue line of travel goes through six of the square tiles. Maybe there are other small rectangles other than this one that crosses $6$ tiles.</p> <p>Your challenge is to find what different sizes of rectangles would mean you travelled across $10$ tiles. </p> <p>Your extra challenge is to find a set of answers for $12$ tiles being crossed.</p> <p>Can you find a generalization/pattern/system from the ones you've done that would enable you to find solutions more easy to other numbers of tiles being crossed.</p> <p> </p> <p> </p> <p> </p> <br></br></mdoxml> <mdoxml version="1.0"><h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://nrich.maths.org.uk/7764">activity</a> challenges the most pupils in their abilities to link the numerical with the spatial.</div> <br></br> <h3>Possible approach</h3> <p>As this is intended for able pupils I would suggest printing out the activity and discussing together first of all, then let them produce their creations.</p> <p> </p> <h3>Key questions</h3> <div>Tell me about how you arrive at these solutions.</div> <div>So what relationships do you think are involved here?</div> <div>What further questions can you ask?</div> <p><br></br>  </p></mdoxml> <mdoxml version="1.0"> <p style="text-align: center;"> </p> <p>What would be the situation if it were like a standard chess-board?</p> <p> </p> </mdoxml> <mdoxml version="1.0"> <p>To go across 10 tiles, 2, 9   2, 10   3, 8   4, 7   5, 6   5,10   10,10</p> <p>To go across 12 tiles, 2,11   2,12   3,10   3,12   4,9   4,10   4,12   5,8   6,7   6,8   6,9   6,12,   12,12</p> <p> </p> <p> </p> </mdoxml> 2 5 0 1 1 0 0 Using, Applying and Reasoning about Mathematics Investigations Using, Applying and Reasoning about Mathematics Working systematically