Math on the Street: Using Origami to Teach Math Links

<div id="SideBar"> <p align="center"> <a href="http://math.serenevy.net/?page=Home" target="_top"><img src="http://math.serenevy.net/Images/SmallLogo.gif" alt="Math on the Street" border=0 width=166 height=70></a> </p> <p><img src="http://math.serenevy.net/Images/RedDot.gif" alt="" height=8 width=8> <a href="http://math.serenevy.net/?page=About" target="_top">About the Project</a></p> <p><img src="http://math.serenevy.net/Images/RedDot.gif" alt="" height=8 width=8> <a href="http://math.serenevy.net/?page=Acknowledgments" target="_top">Acknowledgments</a></p> <p><img src="http://math.serenevy.net/Images/RedDot.gif" alt="" height=8 width=8> <a href="http://math.serenevy.net/?page=FunMath" target="_top">Fun Math Activities</a> <ul> <li><a href="http://math.serenevy.net/?page=OrigamiHome" target="_top">Origami</a></li> </ul> </p> </div>      <div id="Content"> <h1>Origami</h1> <center><table width="85%"><tr><td width="33%" align="center"><a href="http://math.serenevy.net/?page=OrigamiHome" class="button" target="_top">Polyhedra</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Figures" class="button" target="_top">Magic Pinwheel</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-WhereMath" class="button" target="_top">Where's The Math?</a></td></tr></table><table width="85%"><tr><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Challenge" class="button" target="_top">Challenge Problems</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Handouts" class="button" target="_top">Handouts</a></td><td width="33%" align="center"><a href="http://math.serenevy.net/?page=Origami-Links" class="button" target="_top">Links</a></td></tr></table></center><center><hr width=80% /></center> <br> <h2>Links</h2> <ul> <a href="http://math.serenevy.net/?page=Origami-PolyhedraLinks" target="_top">Instructions for Making Origami Polyhedra</a><br> <a href="http://math.serenevy.net/?page=Origami-OtherFigureLinks" target="_top">Instructions for Making Other Origami Figures</a><br> <a href="http://math.serenevy.net/?page=Origami-ArtLinks" target="_top">Mathematics in Origami</a><br> <a href="http://math.serenevy.net/?page=Origami-TeachingLinks" target="_top">Using Origami to Teach Standard Mathematics Topics</a><br> <a href="http://math.serenevy.net/?page=Origami-MathLinks" target="_top">Origami as a Field of Mathematics</a><br> <a href="http://math.serenevy.net/?page=Origami-ApplicationLinks" target="_top">Applications of Mathematical Origami</a><br> <a href="http://math.serenevy.net/?page=Origami-SonobeHistoryLinks" target="_top">History of the Sonobe Module</a><br> </ul> <br><br><hr width="50%"><br><br> <h3>Using Origami to Teach Standard Mathematics Topics</h3> <ul> <a href="#Lessons">On-Line Lesson Plans</a><br> <a href="#Ideas">Ideas for Using Origami to Teach Mathematics</a><br> <a href="#Benefits">Benefits of Origami in the Classroom</a><br> <a href="#Resources">Books and Other Resources for Teachers</a><br> </ul> <br><br><hr width="50%"><br><br> <a name="Lessons"><h4>On-Line Lesson Plans</h4></a> <ul> <li>Daniel Meyer and Jeanine Meyer have a beautiful and extensive web page on <a href="http://rachel.ns.purchase.edu/~Jeanine/origami/" target="_top">using origami to teach mathematics</a>. They include theoretical discussion of educational uses of origami, general strategies for teaching origami and tying it to mathematics, and many origami folding instructions and lesson plans.<br><br></li> <li>The Finger Lakes Paperfolders held an <a href="http://www.geocities.com/fingerlakespaperfolders/" target="_top">Exapanding Your Horizons (EYH) workshop on applied origami</a> for girls in junior high. Their site includes a number of their handouts, resources, and lots of photos of the event.<br><br></li> <li>Bill Wagner has a lesson plan that uses simple paper folding to develop concepts relating to <a href="http://www.iit.edu/~smile/ma9320.html" target="_top">fractions</a>.<br><br></li> <li> <a href="http://geoinfo.nmt.edu/staff/love-d/abstracts/absnmgs299.html" target="_top">Dave Love</a> and Bill Haneberg give a lesson plan, currently hosted on <a href="http://britton.disted.camosun.bc.ca/home.htm" target="_top">Jill Bretton's math page</a> that brings <a href="http://britton.disted.camosun.bc.ca/tremors/origami.html" target="_top">geometry, origami, and geology</a> together. They give instructions for creating paper tetrahedra from envelopes, geology themed templates, and assembly instructions for making a neat kaleidocycle. If you don't want to use a geology theme, you might let the students color their own kaleidocycle designs using the template shape.<br><br></li> <li>Barbara Pearl gives a simple <a href="http://www.mathinmotion.com/whalefld.html" target="_top">origami whale lesson</a> that involves basic mathematical vocabulary and some geometric thinking. This page also includes an address where you can write to receive a free copy of <em>101 Ways to Use Origami in the Classroom</em>.<br><br></li> <li> Japan Overseas Cooperation Volunteers gives several lessons that use origami to teach or reinforce <a href="http://www.addu.edu.ph/college/rstc/handouts/handouts_math.html" target="_top">high school geometry</a> concepts.<br><br></li> </ul> <a name="Ideas"><h4>Ideas for Using Origami to Teach Mathematics</h4></a> <ul> <li><a href="http://www.mathematische-basteleien.de" target="_top">Juergen Koeller</a> has a web page with lots of fun math activities. One of these shows how to make an <a href="http://www.mathematische-basteleien.de/oricube.htm" target="_top">origami cube</a> and then gives a mathematical discussion about the ratio of the side of the final cube to the length of the side of the original square. This is then compared with another way of getting a cube out of a square and with a theoretical limit. Developing this line of thinking could result in a nice math lesson.<br><br></li> <li>Eric M. Anderson has an extensive origami web page that includes a discussion on <a href="http://www.paperfolding.com/math" target="_top">using origami to teach math</a>. This page mentions many specific math concepts that come up in origami, and gives lots of leads for designing your own lesson plan or class project. He gives examples of mathematical origami questions in geometry, topology, and combinatorics. These questions do not require mathematical background, but they do require students who are tenacious problem solvers.<br><br></li> <li><a href="http://www.origami-usa.org/" target="_top">Origami USA</a> has some helpful <a href="http://www.origami-usa.org/teaching_tips.htm" target="_top">tips for teaching origami</a>.</li> </ul> <a name="Benefits"><h4>Benefits of Origami in the Classroom</h4></a> <ul> <li>Karen Bass writes about her experiences using origami to teach <a href="http://math.serenevy.net/?page=Origami-KarenArticle" target="_top">sixth grade math.</a><br><br></li> <li>Emma Craib, an elementary art teacher, talks about <a href="http://www.geocities.com/CapeCanaveral/Lab/5466/ori_good.html" target="_top">intrinsic benefits of learning origami</a> outside the context of a formal math lesson. She also includes some folding instructions.<br><br></li> </ul> <a name="Resources"><h4>Books and Other Resources for Teachers</h4></a> <ul> <li><a href="http://www.mizushobai.freeserve.co.uk/" target="_top">David Mitchell</a> has <a href="http://www.mizushobai.freeserve.co.uk/publications.htm" target="_top">several books on using origami to teach math</a>. <em>Exploring Mathematical Ideas with Origami</em> makes an excellent reference for teaching problem solving, ratios, and geometry. It includes instructions for making beautiful origami tesselations and explores mathematical ideas in great depth. <em>Paperfolding Puzzles</em> features lots of neat hands-on brain teasers. <em>Mathematical Origami</em> shows how to construct a variety of origami polyhedra. This site also includes some free sample articles on mathematical origami that you can download.<br><br></li> <li> Betsy Franco's <a href="http://www.keypress.com/catalog/products/supplementals/Prod_UnfoldOrig.html" target="_top">Unfolding Mathematics with Unit Origami</a> is a book of lesson plans for algebra and geometry students in grades 7-11. This book includes discussions of algebraic and angle relationships, symmetry in 2 and 3 dimensions, and other concepts. It includes teaching strategies, suggestions for assessing student work, and possible extensions of the activities.<br><br></li> <li>Barbara Perl's program, <a href="http://www.mathinmotion.com/" target="_top">Math in Motion: Origami in the Classroom K-8</a>, offers workshops and books that use origami to make learning come to life. This program includes educational objectives in subject areas across the curriculum. Among the mathematical objectives are developing fundamental geometric ideas and spatial intuition; teaching mathematical vocabulary; learning about symmetry, congruence, and angles; practicing fractions, ratios, proportions, and measurement; and developing problem solving and critical thinking skills.<br><br></li> <li>The book <a href="http://www.allbookstores.com/book/0964872412/Paper_Folding.html" target="_top">Paper Folding: A Fun and Effective Method for Learning Math</a> includes a curriculum appropriate for a wide range of ages. Math topics covered include geometry, conic sections, isometries, fractions, tessellations, tangram puzzles, and symmetries.<br><br></li> <li>A great deal of work has been done on the use of origami in education and therapy. Tom Hull has posted <a href="http://www.merrimack.edu/~thull/omfiles/coet91.html" target="_top">proceedings</a> from a 1991 conference on this topic.<br><br></li> </ul> <div id="BottomBar"> <p /><hr> <img class="left" src="http://math.serenevy.net/Images/BWLogo.gif" alt="Math on the Street!" border=0 width="150" height="57"> <p class="about"> Last Updated: February 2003<br> <a href="http://math.serenevy.net/?page=Home" target="_top">http://math.serenevy.net/</a><br> Amanda Katharine Serenevy<br> <a href="mailto:viajera@bu.edu" target="_top">viajera@bu.edu</a><br> </p> </div> </div>