6921 /www/nrich/html/content/id/6921/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"><br></br> Take a long (at least 200cm) piece of narrow paper:<br></br> <div style="text-align: center;"><mdo:image width="330" height="220" alt="1 sheet" src="1%20sheet.jpg"></mdo:image></div> <br></br> Fold it in half by taking the right end over to the left (the pictures show it slightly opened just to make it clearer):<br></br> <div style="text-align: center;"><mdo:image width="330" height="220" src="1st%20fold.jpg" alt="1st fold"></mdo:image></div> <br></br> Fold it in half again, right over left:<br></br> <div style="text-align: center;"><mdo:image width="330" height="220" src="2nd%20fold.jpg" alt="2nd fold"></mdo:image></div> <br></br> and again:<br></br> <div style="text-align: center;"><mdo:image width="330" height="220" src="3rd%20fold.jpg" alt="3rd fold"></mdo:image></div> <div style="text-align: left;">(It may be that you always prefer to fold left over to the right - that's ok, as long as you are always doing the same!)</div> <br></br> <div style="text-align: center;">THEN</div> <br></br> <div>1. Keep on folding into halves as many times as you can.</div> <div>2. Press VERY hard onto the fold to make good creases.</div> <div>3. Open out the paper so that it stands up on edge like in the pictures and make each fold a right angle (re-creasing may be necessary, but do not reverse the fold).</div> <div>4. Stand a long way above and look down at what you can see!</div> <div>5. Discuss with others what you notice.</div> <br></br></mdoxml> <mdoxml version="1.0"><br></br> <p class="editorial">Spencer, Kaya, Miriam, Carolyn, Hannah and Aeena from the Learning Studio, USA, told us that their paper curves looked a bit like a dog, a bird head, a bear, a flower, a tree, a dragon and even a chicken playing a trombone! Here are some photos from the Learning Studio.</p> <p class="editorial"> </p> <p class="editorial"><mdo:image alt="" src="LearningStudio1.jpg" style="width: 320px; height: 213px;"></mdo:image><mdo:image alt="" src="LearningStudio2.jpg" style="width: 320px; height: 213px;"></mdo:image></p> <p class="editorial"><mdo:image alt="" src="LearningStudio3.jpg" style="width: 320px; height: 213px;"></mdo:image><mdo:image alt="" src="LearningStudio4.jpg" style="width: 320px; height: 213px;"></mdo:image><mdo:image alt="" src="LearningStudio5.jpg" style="width: 320px; height: 213px;"></mdo:image></p></mdoxml> <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/6921&amp;part=">problem</a> offers a novel way of exploring connections between Mathematics and Art. It is important for learners to have plenty of opportunity to discuss with others and to verify ideas.</div> <br></br> <h3>Possible approach</h3> <div>Some groups of children may need a demonstration by an adult, particularly to ensure good folding and creasing as you work through the instructions given. Encouraging them to work in pairs will mean they can help each other produce the folds and they also have someone with whom to talk.</div> <br></br> <div>(For checking purposes, <a href="/content/id/6921/3rd%20to%208th%20fold.jpg">this image</a> shows the progression in folds from the third to the eighth.)</div> <br></br> <div>In fact, this series of folds produces what is known as a 'dragon curve'. It will be interesting to see whether any children observe the dragon shape. They are likely to be fascinated and amused by the fact that it has been investigated by several mathematicians!</div> <br></br> <h3>Key questions</h3> <div>What do you see?</div> <div>Does it look like anything?</div> <div>What could you try now?</div> <br></br> <h3>Possible extension</h3> <div>Try slightly different alternatives like folding right over left and then left over right etc. Ask pupils to predict whether the result will be the same or different and why.</div> <div>Drawing on a computer may be enhanced by producing a curved turn rather a right angle. Five folds using right over left then left over right produced the following:</div> <br></br> <div><mdo:image width="462" height="307" alt="" src="drag1.jpg"></mdo:image></div> <br></br> <div>Some pupils may like to go further by looking at the successive mid-points:</div> <br></br> <div><mdo:image width="512" height="626" src="drag2.jpg" alt=""></mdo:image></div> <br></br> <h3>Possible support</h3> <div>Some pupils may require adult help with the manipulative skills of folding and creasing.</div> <br></br> <br></br></mdoxml> <mdoxml version="1.0"><br></br> It might help to have a partner who will help you fold the paper. Between the two of you, you can make sure you fold in the same way each time.<br></br> Try looking at your resulting folded paper strip from different orientations - you might notice different things.<br></br></mdoxml> 5 3 0 1 0 0 0 This is a simple paper-folding activity that gives an intriguing result which you can then investigate further. Using, Applying and Reasoning about Mathematics Practical Activity Applications Art Fractions, Decimals, Percentages, Ratio and Proportion Fractal