4 /www/nrich/html/content/03/01/cupboardlove4/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <table width="100%" cellspacing="0" cellpadding="0" border="0" id="tableedit1"> <tbody> <tr valign="top" align="left"> <td width="18%"><mdo:image width="159" height="149" alt="" src="Polydron.gif"></mdo:image></td> <td width="82%"> <div>Squares can be made in two distinct ways using Polydron, as the picture shows.</div> <p>How much bigger is the one made from $4$ right angled isosceles triangles?</p> <br></br> <br></br></td> </tr> <tr> <td colspan="2">The chief characteristics of Polydron are its connectivity and fold-a-bility.<br></br> Squares can easily be clicked together to make other shapes.<br></br> A pentomino is a shape made from $5$ squares joined together along a common edge. Can you find all $12$ distinct pentominoes? Do all your pentominoes have the same perimeter length?<br></br> <br></br> How many pentominoes have line symmetry? Rotational symmetry?<br></br> <br></br> How many of the pentominoes will fold up and clip together to make 'lid-less' boxes? Why not discuss first which will fold up and which won't, before trying to fold them?</td> </tr> </tbody> </table> <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/public/viewer.php?obj_id=4&amp;part=">activity</a> can be a good start for exploring the special properties of polydrons</div> <br></br> <h3>Possible approach</h3> <div>Plenty of play with polydrons first and then challenges like the one focussed on in this activity.</div> <br></br> <h3>Key questions</h3> <div>What can you tell me about the square polydrons and the triangular polydrons?</div> <br></br> <h3>Possible extension</h3> <div>Pupils to produce their own questions using the polydrons.</div> <br></br> <h3>Possible support</h3> <div>text</div> <br></br> <br></br></mdoxml> 2 3 0 1 0 0 0 This activity investigates how you might make squares and pentominoes from Polydron. Decision Mathematics and Combinatorics Combinations Using, Applying and Reasoning about Mathematics Working systematically Mathematics Tools Polydron Using, Applying and Reasoning about Mathematics Practical Activity Transformations and their Properties Symmetry 2D Geometry, Shape and Space Squares Measures and Mensuration Perimeters