Virginia Mathematics Teacher Volume 37, No. 2 Spring, 2011 The Five Platonic Solids A Resource Journal for Mathematics Teachers at all Levels. Virginia MatheMatics teacher Volume 37, No. 2 Spring, 2011 The VIRGINIA MATHEMATICS TABLE OF CONTENTS TEACHER (VMT) is published twice yearly by the Virginia Council of Teach- Grade Levels Titles and Authors ................................................................. Turn to Page ers of Mathematics. Non-profit organizations are granted permission to reprint articles appearing in the VMT provided that one copy of the General President’s Message ..........................................................................1 publication in which the material is reprinted is sent to the Editor and (Beth Williams) the VMT is cited as the original source. EDITORIAL STAFF General Statistical Outreach and the Census: A Summer David Albig, Editor, Learning Experience. ..........................................................................2 e-mail: [email protected] (Gail Englert) Radford University Editorial Panel General Teaching Time Savers: Reviewing Homework....................................3 Bobbye Hoffman Bartels, Christopher Newport University; (Jane M. Wilburne) David Fama, Germana Community College; Jackie Getgood, Spotsylvania County Mathematics Supervisor; Sherry Pugh, Southwest VA Governor’s School; General Enlivening School Mathematics Through the History Wendy Hageman-Smith, Longwood University; of Mathematics ...................................................................................4 Ray Spaulding, Radford University (Martin Bartelt and Stavroula K. Gailey) Jonathan Schulz, Montgomery County Mathematics Supervisor MANUSCRIPTS & CORRESPONDENCE General Affiliates’ Corner .................................................................................5 For manuscript, submit two copies, typed double spaced. We favor manuscripts on disk or presented electronically in Word. Drawings General The Five Platonic Solids .....................................................................6 should be large, black line, camera ready, on separate sheets, referenced in the text. Omit author names from the text. Include a cover (Theoni Pappas) letter identifying author(s) with address, and professional affiliation(s). General VCTM Awards Two Scholarships ........................................................7 Send correspondence to Dave Albig at: Box 6942 Radford University General Problem Corner ................................................................................10 Radford, VA 24142 (Ray Spaulding) Virginia Council of Teachers of Mathematics President: Beth Williams, Bedford County Schools General William C. Lowry Award Winners ......................................................34 Past-President: Carolyn Williamson, Retired from Hanover County Public Schools Secretary: Debbie Delozier, Stafford County Public Schools Grades K-5 Clearing the Confusion over Calculator Use in Grades K-5 .............18 NCTM Rep.: Margaret Coffey, Fairfax County Public Schools (Barbara J. Reyes and Fran Arbaugh) Math Specialist Rep.: Corinne Magee Elected Board Members: Elem. Rep: Sandy Overcash, Virginia Beach City Schools; Meghann Grades 2-6 Teaching Addition and Subtraction Facts: A Chinese Perspective ...22 Cope, Bedford County Schools (Wei Sun and Joanne Y. Zhang) Middle School Reps: Anita Lockett, Fairfax County Public Schools; Alfreda Jornegan, Norfolk Public Schools Secondary Reps: Ian Shank, Hanover Public Schools; Cathy Shelton, Grades 3-6 Dividing Fractions: Reconciling Self-Generated Solutions Fairfax County Public Schools. with Algorithmic Answers ..................................................................25 2 Yr. College Rep: Joseph Joyner, Tidewater Community College (Marcela Perlwitz) 4 Yr. College Rep: Joy Whitenack, Virginia Commonwealth; Maria Timmerman, Longwood University Grades 3-6 Developing Ratio Concepts: An Asian Perspective ..........................29 Membership: Ruth Harbin-Miles (Jane-Jane L, Tad Watanabe, and Jinga Cai) Publicity: Laura Rightnour, Hanover County Public Schools Treasurer: Diane Leighty, Powhatan County Public Schools Grades 7-10 Pick a Number ..................................................................................33 Webmaster: Jennifer Springer, Charlottesville City Schools (Margaret Kidd) Webpage: www.vctm.org Grades 7-12 Those Darn Exponents: Fifty Challenging True-False Questions .....35 Membership: Annual dues for individual membership in the Council (Tim Tilton) are $20.00 ($10.00 for students) and include a subscription to this journal. To become a member of the Council, send a check pay- Grades 13-16 Abstractmath.org: A Web Site for Post-Calculus Math .....................36 able to VCTM to: VCTM c/o Pat Gabriel; 3764A Madison Lane, Falls Church, VA 22041-3678 (Charles Wells) ABOUT THE COVER: From the book “The Joy of Mathematics” by Theoni Pappas. Reprinted by permission of Wide World Publishing (http:/www.wideworldpublishing.com) Printed by Wordsprint Christiansburg 225 Industrial Drive, Christiansburg, VA 24073 Please see the The Five Platonic Solids article on page 6. GENERAL INTEREST President’s Message Beth Williams This spring has been a busy one for our organization! Two Virginia finalists were also recognized as Presiden- If you didn’t get to attend our Annual Conference in Rich- tial Awardees for Excellence in Mathematics and Science mond, you missed an extraordinary event. Fabulous Teaching on Friday night. These colleagues have advanced speakers led every session. Our Department of Education to the state selection in this prestigious mathematics award. mathematics colleagues keynoted two sessions. Deborah We wish Pamela Bostwick and Victoria Hugate both well as Wickham and Michael Bolling shared upcoming events and the PAEMST selection process continues. happenings at the state level to keep us informed and en- Part of being a teacher is being a lifelong learner, studying, ergized to move forward in our work. Many thanks to our researching, and listening to find ways to improve our in- Conference Program Chair, Lisa Hall, the VCTM Executive struction and help more students succeed. To this end, my Board, and the Greater Richmond Council volunteers who goal will be to pose a new question to you in each Journal made the “Making Mathematics Monumental” conference edition. This month my question for you would be: What a wonderful affair! do you know about the Common Core Standards and their VCTM is an affiliate of the National Council of Teachers of implementation? Mathematics, and we support the work that they advocate. In January, NCTM released news of a joint task force In 2010, NCTM released a position paper recommending made up of the Association of Mathematics Teacher Edu- the use of mathematics specialists to enhance teaching, cators, The Association of State Supervisors of Mathemat- learning and assessing of mathematics to improve stu- ics, The National Council of Supervisors of Mathematics, dent achievement. In Virginia, we have been blessed with and the National Teachers of Mathematics. The work of many grants through the National Science foundation, the the task force is to develop actions and resources needed Virginia Department of Education Mathematics and Sci- to help teachers implement the Common Core State Stan- ence Partnership (MSP), NCLB Title II funds and through dards in Mathematics (CCSSM). This task force also con- the ExxonMobil Foundation that support developing math- sidered ways in which the organizations can collaborate ematics specialist programs. in supporting their members and other groups to advance In addition, a program to provide additional leadership their vision of school mathematics. The task force report opportunities for 25 specialists has been implemented identifies five priority actions to be taken as soon as pos- through Virginia Commonwealth University, University of sible. There are also PowerPoint presentations that can in- Virginia, and Norfolk State University with funds from the form all stakeholders. These information opportunities are National Science Foundation. available for you to read at www.nctm.org/news/highlights During the Annual Conference, a large group of mathe- NCTM is working with other groups like NCSM to write sup- matics specialists and coaches from across the state came porting tasks, videos and documents for implementing the together for the first time to begin to formulate ways to CCSSM. Dr. William G. Mccallum led the work to write the engage in professional growth and networking opportuni- standards using the NCTM Focal Points and High School ties. This social time allowed one group of specialists that Sense Making as their foundation. His group is working has been supported by the Leadership Program to identify on a new website, www.illustrativemathematics.org where and connect with other professionals who share similar job good tasks for formative assessments and videos of good responsibilities. Our annual conference banquet Friday teaching strategies will be shared. Dr. Mccallum also has night was a celebration of many accomplishments. Con- a blog at commoncoretools.wordpress.com tina Martin and Vickie Inge shared exciting work from this Even though Virginia has not adopted the Common Core Leadership Program. If you are interested in more informa- State Standards, The Virginia Board of Education has ad- tion about this networking fellowship, seek out the link to opted a supplement to the Curriculum Frameworks to bring mathematics