990 /www/nrich/html/content/00/03/penta2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Look at this shape. The dotted line shows how it can be cut in half to make two shapes that are the same shape and size.</p> <div style="text-align: center;"><mdo:image height="99" width="169" src="fig1.gif" alt="Shapes"></mdo:image></div> <br></br> <p>How can these shapes be cut in half to make two shapes the same shape and size?</p> <mdo:image height="209" width="460" src="fig2.gif" alt="Shapes"></mdo:image><br></br> <p>Can you find more than one way to do it?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <mdo:image height="291" width="527" alt="Shapes" src="fig3.gif"></mdo:image><br></br> <p><span class="editorial">A correct set of solutions was sent in by Christina</span> <span class="editorial">(Malborough Primary School, UK), Ceren, Idi, Ece, Eda and Ece O</span> <span class="editorial">(Private IRMAK Primary &amp; Secondary School, Istanbul, Turkey).</span></p> <p><span class="editorial">Some managed to find two different ways to halve the orange S shape, and Jason</span> <span class="editorial">(Priory School) found all four ways.</span></p> <p><span class="editorial">Evren and Christian</span> <span class="editorial">(Private IRMAK Primary &amp; Secondary School, Istanbul, Turkey) sent in one that no-one else found:</span></p> <div style="text-align: center;"><mdo:image height="81" width="148" alt="Shapes" src="fig4.gif"></mdo:image></div> <br></br> <p><span class="editorial">Thomas (Tattingstone School UK) says there are an infinite number of lines that can be drawn like the ones below.</span></p> <div style="text-align: center;"><mdo:image height="81" width="148" alt="Shapes" src="fig5.gif"></mdo:image></div> <br></br> <p><strong class="editorial">What do think? Are there more solutions for this shape?</strong></p> <p><strong class="editorial">Why are there so many for this one and not the other shapes?</strong></p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Same Shapes</h2> <br></br> <p>Look at this shape. The dotted line shows how it can be cut in half to make two shapes that are the same shape and size.</p> <div style="text-align: center;"><mdo:image alt="Shapes" height="99" src="fig1.gif" width="169"></mdo:image></div> <br></br> <p>How can these shapes be cut in half to make two shapes the same shape and size?</p> <mdo:image alt="Shapes" height="209" src="fig2.gif" width="460"></mdo:image><br></br> <p>Can you find more than one way to do it?</p> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This activity will be very useful when wishing to challenge and extend pupils&#39; spatial awareness with 2D shapes. It can also be an exercise in perseverence.</div> <br></br> <h3>Possible approach</h3> <div>The problem <a href="http://nrich.maths.org/public/viewer.php?obj_id=217&amp;part=index">Happy Halving</a> might be suitable to start with, before tackling the shapes in this problem. There are detailed suggestions of an approach in the <a href="http://nrich.maths.org/public/viewer.php?obj_id=217&amp;part=note">teachers&#39; notes</a> of Happy Halving.</div> <br></br> <div>If you would prefer to tackle this problem as it stands, it would be good to have a large image of one the shapes for all the pupils gathered around to see. This could give a good opportunity for a class discussion.</div> <br></br> <h3>Key questions</h3> <div>Are you able to show me that your two halves are the same shape and size?</div> <div>Are there other ways of halving this shape?</div> <br></br> <h3>Possible extension</h3> <div>Some learners will enjoy inventing some shapes of a similar nature - THAT WORK!</div> <br></br> <h3>Possible support</h3> <div>It would be good if pupils could work in pairs. We must remember that some children excel in spatial work while being much poorer in arithmetic, and visa versa.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Try drawing the shapes on squared paper.<br></br> You could cut the shape to check whether the two parts are identical.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> [fig 3]<br></br> A correct set of solutions was sent is by Christina (Malborough Primary School, UK), Ceren , Idi , Ece , Eda and Ece O (Private IRMAK Primary &amp; Secondary School, Istanbul, Turkey). <br></br> Some managed to find two different ways to halve the orange S shape, and Jason (Priory School) found all four ways. Evren and Christian (Private IRMAK Primary &amp; Secondary School, Istanbul, Turkey) sent in one that no-one else found.<br></br> [fig 4]<br></br> Thomas (Tattingstone School UK) says there are an infinite amount of lines that can be drawn like the ones below. <br></br> [fig 5] <br></br> <br></br> What do think? Are there more solutions for this shape? Why are there so many for this one and not the other shapes?<br></br></mdoxml> 2 5 1 0 0 0 0 How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it? Fractions, Decimals, Percentages, Ratio and Proportion Fractions Transformations and their Properties Rotations 2D Geometry, Shape and Space Other polygons