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The Illinois Mathematics Teacher THE ILLINOIS MATHEMATICS TEACHER EDITORS Marilyn Hasty and Tammy Voepel Southern Illinois University Edwardsville Edwardsville, IL 62026 REVIEWERS Kris Adams Chip Day Karen Meyer Jean Smith Edna Bazik Lesley Ebel Jackie Murawska Clare Staudacher Susan Beal Dianna Galante Carol Nenne Joe Stickles, Jr. William Beggs Linda Gilmore Jacqueline Palmquist Mary Thomas Carol Benson Linda Hankey James Pelech Bob Urbain Patty Bruzek Pat Herrington Randy Pippen Darlene Whitkanack Dane Camp Alan Holverson Sue Pippen Sue Younker Bill Carroll John Johnson Anne Marie Sherry Mike Carton Robin Levine-Wissing Aurelia Skiba ICTM GOVERNING BOARD 2012 Don Porzio, President Rich Wyllie, Treasurer Fern Tribbey, Past President Natalie Jakucyn, Board Chair Lannette Jennings, Secretary Ann Hanson, Executive Director Directors: Mary Modene, Catherine Moushon, Early Childhood (2009-2012) Com. College/Univ. (2010-2013) Polly Hill, Marshall Lassak, Early Childhood (2011-2014) Com. College/Univ. (2011-2014) Cathy Kaduk, George Reese, 5-8 (2010-2013) Director-At-Large (2009-2012) Anita Reid, Natalie Jakucyn, 5-8 (2011-2014) Director-At-Large (2010-2013) John Benson, Gwen Zimmermann, 9-12 (2009-2012) Director-At-Large (2011-2014) Jerrine Roderique, 9-12 (2010-2013) The Illinois Mathematics Teacher is devoted to teachers of mathematics at ALL levels. The contents of The Illinois Mathematics Teacher may be quoted or reprinted with formal acknowledgement of the source and a letter to the editor that a quote has been used. The activity pages in this issue may be reprinted for classroom use without written permission from The Illinois Mathematics Teacher. (Note: Occasionally copyrighted material is used with permission. Such material is clearly marked and may not be reprinted.) THE ILLINOIS MATHEMATICS TEACHER Volume 61, No. 1 Fall 2012 Table of Contents Guidelines for Submitting Manuscripts............................................................................. 35 Using Literature to Get to Pi ................................................................................................ 3 Deborah A. Crocker & Betty B. Long – General Interest Using the SmartArtTM Organization Chart to Create a Graphic Organizer ................................................................................................. 6 Dianna Galante – Technology Mind Mapping Fractions, Decimals and Percents ........................................................... 11 Geoffrey Lewis, Robert Hayes, & Marianne Wysocki – Elementary & Middle School Playground Equipment ....................................................................................................... 15 Ann Hanson & Peter Insley – High School Variations on the Witch of Agnesi ...................................................................................... 20 John Boncek & Sig Harden – High School Confetti – It’s Not Just for a Party Anymore! .................................................................. 25 Rena Pate – Elementary Problem Solving in the Primary Classroom ...................................................................... 28 Rena Pate – Elementary 101 102 uses for a paperclip ................................................................................................ 32 Charlotte Schulze-Hewett & Hana Sallouh – High School Quadrilaterals: Transformations for Developing Student Thinking ............................. 36 Colleen Eddy, Kevin Hughes, Vincent Kieftenbeld, & Carole Hayata – High School Illinois Mathematics Teacher – Fall 2012 .......................................................................................1 From the Editors… Welcome to the Fall 2012 issue of the Illinois Mathematics Teacher. It has been awhile, but we now have a great selection of articles to share with the members of ICTM. This issue of the IMT contains general interest articles as well as articles specific to a variety of levels of student learning. Deborah A. Crocker and Betty B. Long have written an article about using literature and technology to have students discover pi. Dianna Galante also addresses technology in her article about graphic organizers. Fractions are the topic of focus in an article by Geoffrey Lewis, Robert Hayes, and Marianne Wysocki. Two articles that may be of interest to high school teachers involve the mathematics associated with a playground swing and the mathematics of two famous curves. Rena Pate provides two articles in this issue that will be of interest to elementary level math teachers which discuss a readily available manipulative and problem solving. Charlotte Schulze-Hewett and Hana Sallouh discuss a manipulative that is readily available and how to implement it in your middle school or high school classroom. Finally, there is an article about using transformations in the high school geometry classroom. We want to thank all the readers of the IMT. We have enjoyed being the editors of this journal for the past eleven years. As Marilyn retires, we are passing the job of editor to two other members of ICTM. We wish them the best of luck and hope you continue to enjoy the IMT under their direction. Typically included at the end of each issue is a form for becoming a reviewer for the IMT. This form has not been included in this issue due to page considerations. If you are interested in becoming a reviewer, please email [email protected] and list the subject(s) or grade level(s) you would be interested in reviewing. In order to ensure that the articles are of interest to our readers, we send them to reviewers to get their approval. We would love to have reviewers willing to review in only one area or multiple areas. As postage prices continue to rise, we are trying to conduct most of our communications by email, so please update your information and your email address if you have not reviewed in the past year. Please consider submitting an article or classroom activity to the IMT. Consider writing about an activity that you use in your classroom and you would like to share with others. Your articles are needed to continue the sharing of ideas and the publishing of this journal on a regular basis. Thank you for sharing. Marilyn and Tammy editors Illinois Mathematics Teacher – Fall 2012 .......................................................................................2 Using Literature to Get to Pi Deborah A. Crocker – Appalachian State University, [email protected] Betty B. Long – Appalachian State University, [email protected] Literature is often used as a man. At this point, Radius goes to the springboard into mathematics at the carpenters, Geo of Metry and his brother elementary and middle school levels. Sym. While there, Radius has an idea about Stories can help motivate students to explore “across the middle” and “around the circle” and discover mathematical concepts. Even (p. 15). For the next several pages, in the if the reading level of the book is below story, Radius measures various circular grade level, the story can help students recall items. In table 1 is a list of the items that mathematical concepts and ideas. Sir Radius finds and their measures. Cumference and the Dragon of Pi: A Math Table 1 Adventure is an example of this type of Items measured by Radius in the story book. This activity incorporates literature in this manner and makes use of a handheld Across the Around the graphing device to discover pi using Item Middle Outside Edge multiple representations. Some prior (inches) (inches) knowledge of a handheld graphing device is Wheel 49 154 assumed. Onion Slice 3.5 11 As you read the story to your class, Basket 7 22 they will be introduced to the characters Sir Bowl 14 44 Cumference, his son Radius, and his wife Round of 17.5 55 Lady Di of Ameter. During lunch one day, Cheese Sir Cumference is accidentally turned into a dragon when Radius brings him a bottle Students should measure other circular labeled “Fire Belly” from the doctor’s objects such as tops of soda cans, hula- workroom to cure his stomachache. In the hoops, cookies, or plastic lids and add their doctor’s workroom, Radius looks for a cure measurements to table 1. The data can be to change his father back. He finds a entered on any handheld graphing device container with a poem written on the outside with the capability for scatterplots and linear that says: regression models. In this article, we will Measure the middle and circle show screens captured from the TI-73. The around, final table will be entered into the list editor Divide so a number can be found. on the TI-73. The “Across the Middle” Every circle, great and small – measurements are in L1 and the “Around the The number is the same for all. Outside Edge” measurements from the It’s also the dose, so be clever, literature book are in L2 (see fig. 1). Or a dragon he will stay . forever. (p. 13) Radius realizes he must solve the riddle in the poem involving a circle in order to change his dad back from a dragon into a Fig. 1 Screen shot of L1 and L2 Illinois Mathematics Teacher – Fall 2012 .......................................................................................3 The data in the list editor can be analyzed both graphically and numerically. Numerically, you can have the students create lists L3, L4, L5, and L6 containing L2/L1, L2 + L1, L2 - L1, and L2*L1, respectively. By analyzing the sum, Fig. 4 Screen shots showing how to set up a difference, product and quotient, students stat plot should observe that only the quotient appears to be approximately constant. (see The data in the scatter plot should
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