41. Connect-ME - Weblinks 3288 url=3288/ Junior/Intermediate fractals are chaos and order the user can explore the fractal results of is a collection of tangram activities that focuses http://educ.queensu.ca/connectme/weblinks/strands.htm

Classroom Resources for Teachers Curriculum Strands Measurement Magic Squares - Math Forum http://mathforum.org/alejandre/magic.square.html Late Primary - Intermediate The Math Page - Skill In Arithmetic http://www.themathpage.com/ARITH/arithmetic.htm Multiplication: An Adventure in Number Sense http://naturalmath.com/mult/index.html This site illustrates patterns in multiplying 2 numbers up to 10 x 10. By using patterns and and 'twin facts' a 10 by 10 multiplication table is reduced to only 13 facts to be memorized. Numbers: Facts, Figures and Fiction http://richardphillips.org.uk/number/ Primary/Junior Numbers: Facts, Figures and Fiction Place Value http://www.sedl.org/scimath/compass/v03n02/place.html Primary The activities described in this lesson reinforce students' understanding of place value by using rhythm, physical action, and introspection. Simply Number Sense http://library.thinkquest.org/17888/opening.shtml

42. WebLinks University; link to fractal and chaos applets; fractals Dimensions of fractal geometery; Sierpinski Triangle; extend the USDA; Grades K2 Prob/Stat activities; K-12 http://www.css.edu/users/aguckin/WebLinks.htm

Mathematics Web Sites The following links to web sites are provided to help you get started locating sites that will be helpful to you. The mathematics categories are similar to strands of the Minnesota K-12 Mathematics Frameworks. However, many of the sites are not restricted to one of these strands. It is difficult to keep any such lists current and accurate. Sometimes sites are inaccessible because they are busy, their location has changed or they have been eliminated. Start your own list of useful bookmarks and use names for your bookmarks that will be meaningful to you. Select a category: Discrete Mathematics Geometry Data Investigation Number Sense; Number Theory ... Technology Using Web sites carefully Just as everything we read in the newspaper is not necessarily accurate, everything we read on the Internet is not necessarily accurate. The following is an example of what can happen: Under the headline, "Whales in the Minnesota River? Only on the Web, Where Skepticism Is a Required Navigational Aid," the March 4 edition of the NewYork Times ran an interesting piece about how, on the Web, the "straight facts can be hard to find." Used as an example was a spoof site posted through Mankato State that highlighted Mankato as home to sunny beaches, an underwater city and whale watching as well as neighborhoods in which "the winter temperature has never dropped below a balmy 70 degrees." The following sites help with criteria for evaluating Web sites.

43. Venture Publishing Graphing Calculator Resource Materials AP Calculus Test Prepa Introduction to fractals and chaos. fractals and chaos is an exploration of discrete dynamical systems, using TI82 Graphing activities for Middle School. http://www.vent-pub.com/toc.html

graphing calculator resource books textbooks instructional videos software ... videos and software for middle school, high school and college mathematics, with a special focus on teaching materials for the graphing calculator - go directly to title list or price list Help your students prepare for the AP Calculus exams. Click here for sample questions Click here for related AP texts and resources Check out the 2 instructional videos by Sally Fischbeck for the TI-89 AP Calculus with the TI-89 Graphing Calculator Click here for additional Text Books Calculus, Concepts and Calculators The book should be a boon to teachers seeking a calculus text that supports the new AP course description. It emphasizes the concepts of calculus; however, unlike other reform texts, the exercise sections have a nice balance of routine and challenging problems. Click here for additional Videos Learning about the TI-89 Additional videos now available.

44. Math 8 - Frisbie Middle School is using the Glencoe instructional materials to teach mathematics Graphing and Functions, Linear and Exponential Functions, fractals and chaos Theory, Applied http://www.rialto.k12.ca.us/frisbie/math8.html

Math 8 As part of the Rialto Unified School District, Frisbie Middle School is using the Glencoe instructional materials to teach mathematics. Math 8 is a general mathematics course for eighth grade students not enrolled in Algebra I. Under the Curriculum Links the alignment of the course can be checked against the RUSD Math Matrix, California Framework Standards, and the NCTM Standards. Links are provided to support the Math 8 curriculum for students, teachers and parents. Some of the links are to Internet sites with information, others link to sites with interactive lessons which could be used at home as a supplement or during class and still others could be used as enrichment for students willing to work before or after school. A similar Math 7 page is available for the general mathematics course for all seventh grade students. As you use these pages, comments and/or suggestions would be appreciated. Please send them to Suzanne Alejandre Curriculum Links: Math Matrix - RUSD RUSD Course of Study CA Academic Standards Commission California Mathematics Framework Strands Unifying Ideas for the Middle Grades NCTM Standards Reference Links: Dr. Math FAQ - The Math Forum

45. AMATYC Phoenix - Workshops as well as introduce the phenomenon of chaos and fractals into calculus Participants in this workshop will discover contextual activities, created for an http://www.amatyc.org/Phoenix/Workshops.html

YOU'RE WANTED... FOR A PERFECT CONFERENCE 28th Annual AMATYC Conference November 14 - 17, 2002 Phoenix, Arizona Workshops The deadline for preconference registration has past. AMATYC 2002 Conference Page Local Conference Website Travel Information ... Phoenix Suns - AMATYC Night Miniprogram: Thursday Friday Saturday Sunday ... Special Events Information for Presenters: Presentation Policy and Fact Sheet Guidelines for Speakers Instructions on How to Do an Internet Presentation Without an Internet Connection A workshop includes active attendee participation, an in-depth treatment of a skill, and significant handouts. Assignments are made on a space available basis, as conference payments are received. Attendees may register for two workshops. The workshops listed as Off-site will be held in a computer lab at City Colleges Center Campus of Phoenix College. All participants should schedule at least 30 minutes each way for travel. The conference program will have a more detailed bus schedule. AMATYC is not responsible for the transportation of anyone who misses the bus. W1 Awesome Activities for Future Teachers Thursday Peter R. Wildman

46. Points And Angles will be used to illustrate the interplay between fractals and chaos, and their Extracurricular activities. http://www.mmcchicago.org/dinners00-01/P&AMar01.htm

Points and Angles Online March 2001 Table of Contents: Current Speaker Answers to last month's Mathacrostic Application For The MMC Scholarship Professional Development Units ... This month's puzzle that will Infuse You With Amazement Monica Neagoy Mathematics Consulting Services Rare is the student who is not fascinated by the beauty of fractals, or the teacher who is not captivated by the surprises of chaos. Multiple media will be used to illustrate the interplay between fractals and chaos, and their connection with mathematics and our world. Monica Neagoy was educated in France, Asia and the U.S. with her Ph.D. in mathematics from the University of Maryland. Her exposure to many cultures, her mastery of several languages, and her professional involvement in both the arts and sciences give her a unique perspective on the learning and teaching of mathematics. She is a national mathematics consultant (ie., The Annenburg/CPB Channel, The American Association for the Advancement of Science, PBS) and the head judge for MATHCOUNTS organization. Since 1985, she has worked with in-service teachers independently and through Georgetown University. She is also a professional actor and is the artistic co-director of the professional LE NEON Theater in Washington, D.C. This will be an exciting evening with Monica Neagoy on March 9, 2001.

47. Points And Angles classroom allows teachers to bring topics, such as chaos and fractals, that generate images Bob has found that “chaos club” activities allow students http://www.mmcchicago.org/dinners01-02/P&ASep01.html

Points and Angles Online September 2001 Table of Contents: Current Speaker Developing Proportional Reasoning: So Important, So Widely Ignored 2001 NCTM Central Regional Conference Answers to Mathacrostic No. 143, May 2001 ... Points from the Interior Start Visualizing Mathematics in the Heart of the Chicago Loop Robert L. Devaney Although we all know that the Como Inn has made many changes over the past 20 years, nothing could have a much greater impact on MMC than their announcement that they were closing for remodeling. For MMC, it causes a moment of chaos! So, as we embark upon the 2001-2002 year, MMC is going to experience “Adventures in Chaos” at the famous Berghoff Restaurant, which is located in the heart of the Chicago Loop. Robert L. Devaney of Boston University will deliver a talk entitled “The Adventures in the Chaos Club: Online Activities Involving Chaos and Fractals.” Bob’s talk will take us on a journey that will demonstrate a number of different internet-based tools that can be used to introduce topics from contemporary mathematics in both the middle school and high school curricula. All who have heard Robert Devaney speak can tell you how dynamic he is. Bob has given over 1,000 invited lectures in 49 of the 50 United States. He has also lectured on 6 continents worldwide. Robert Devaney has taught mathematics at several universities and he has held the position of chairman of the Department of Mathematics at Boston University. Dr. Devaney has also authored or edited numerous research papers and books, and he has developed software packages designed to teach students at all educational levels about the mathematics underlying captivating images. In addition to all of these individual accolades, he is also the director of the National Science Foundation Institutes and Projects.

48. Jurassic Park with dinocurosity, here are some activities that will not only pique students Ask the students if they are familiar with fractals and the chaos Theory. http://www.challenge.state.la.us/k12act/data/jurassic_park.html

La. Challenge Activities for the K-12 Classroom Jurassic Park by Mary Lacour Subject Area(s): Science Grade Level(s): Topic(s): Dinosaurs, Fossils, Chaos Theory, Fractals, Searching the Internet. Purpose(s) of Lesson: To use the Internet as a tool for doing research To use the Internet as a resource for finding information on dinosaurs To learn how fossils are formed and how they can tell us a story of the earth's past Materials Needed: Internet access: A copy of the novel Jurassic Park by Michael Crichton Strips of construction paper cut 1" X 11" <enough for each student and teacher> Time Required: 2 - 3 class periods Introduction: What do Blockbuster movies, best selling novels, and a top-rated television series have in common? Intriguing plots, celebrities, and DINOSAURS! From a scientific perspective, the resurgence of interest in prehistoric creatures is both positive and negative. On one hand, children are eager to learn about dinosaurs; on the other hand, much of what they learn is inaccurate. Now that your students are abuzz with dino-curosity, here are some activities that will not only pique students' curiosity, but will also teach them scientifically accurate information about prehistoric life on earth. We would like to acknowledge Charlene M. Czernaik for giving us some thoughts and direction on this lesson through her article "The Jurassic Spark", found in the October (1993) issue of

49. SLU 2000 Inquiry Seminar class you will participate in group activities, class discussions, computer activities, and will chaos What is a fractal? How can you create fractal images? http://sylow.slu.edu/teach/125Brochure.html

SLU 2000 Inquiry Seminar MT A125 Mathematical Thinking in the Real World Infinity, the Fourth Dimension, Chaos and Prime Numbers Fall 2003 MWF 9-9:50 Instructor: Dr. Darrin Speegle Fall 2003 MWF 12-12:50 Instructor: Dr. Steven Harris Spring 2004 MWF 1:10-2 Instructor: Dr. Russell Blyth Who should take this course? Mathematical Thinking in the Real World is for students in the humanities and other disciplines that require one math course at or above a set level (usually College Algebra) to satisfy a core requirement. It is designed for students who already know the material of College Algebra and who are looking for a new and definitely more interesting way to satisfy the math requirement. What do you learn in this course? We study some of the great ideas of mathematics: infinity, the fourth dimension, prime numbers and chaos. We explore these topics in a variety of ways, sometimes using puzzles to motivate us, and sometimes solving puzzles using the mathematics we study. A variety of often surprising applications arise along the way. The course will develop critical thinking and problem-solving skills, and let you see some fun mathematics that is usually hidden from view in lower division courses.

50. Resources - Teacher org.uk/issue11/features/physics_world/index.html Information on fractals and chaos ..lots of school lessons designed to extend handson activities and to http://www.spotsylvania.k12.va.us/resources/teacher.htm

Search for: Quick Links Superintendent School Board Administration Human Resources ... SCS Home Page General Information Directory What's Hot! 2003-2004 Calendar 2004-2005 Calendar ... More General Info Educational Resources For Parents For Students For Teachers School Home Pages Elementary Schools Middle Schools High Schools Alternative Schools Employment Job Postings GroupWise Web Access Elementary Middle High Administration Resources - Teacher SOL Tracker SOL Tracker is updated regularly. Click Here to download the most current version of the software. When the next window opens click "Save". On the next page in the dropdown list next to "Save in" select "Desktop" and click "Save" again. Once the download is complete click on the "Open" button to install the update. When the update is complete click the "Finish" button and restart your system. ENGLISH / LANGUAGE ARTS http://www.teachervision.com

51. Nixon Library I 514 PEI fractals for the classroom strategic activities vol. II. 3rd ed. Thompson, Silvanus P. 519.2 RUE Chance and chaos. Ruelle, David. http://www.butlercc.edu/nixon_library/parts/special_collections/math_sci_tech.cf

imgTag='Take Me To... Accounting Accounts Payable Accts Receivable Addictions Admin. Justice Admissions Advising ABE/GED/ESL Agriculture Allied Health Alumni Art Art Gallery Athletic Training Automotive Baseball Basketball - Mens Basketball - Womens Behavorial/Math Science Division Behavioral Science Biology Bookstore Business Education Butler Online CAD/Engineering Tech Career/Employment Services Center For Independent Study Center For Teaching Excellence Cheerleading Chemistry Computer Information Technology Cooperative Education Course Catalog Course Outlines Dance Early Childhood Development EC Apprenticeship Economics Educare Emergency Med Tech Engineering English Facilities Mgmt Faculty/Staff Dev. Financial Aid Finance Division Fire Science Football Foreign Language Foundation Grizzly Adventures Grizzly Ambassadors Grizzly Magazine Health Services History Housing Hospitality Mgmt Human Resources Humanities/FA Dept.

52. Additional Resources Both of these sites relate to the activities of the Number Sense Research Group at the to resources from the history of mathematics to fractals and chaos. http://www.mpt.org/learningworks/teachers/numbers_alive/resources.html

Additional Resources SURFING THE 'NET There are an incredible wealth of web sites related to mathematics on all levels. Here are some to get you started. For the most recent data, use your favorite search engine and enter terms like "mathematics education," "numbers sense," "kid's math," etc. to find the most recent entries. For Teachers http://www.pbs.org/mathline This is the site of PBS's innovative professional development site for mathematics teachers in elementary and middle grades, with an abundance of classroom resources and feedback from other teachers throughout the country. http://enc.org This is the homepage for the Eisenhower National Clearinghouse, a wealth of mathematics and science information, with extensive links to other Internet resources. Each month, 13 outstanding math and science sites are singled out for the spotlight in "The Digital Dozen." http://www.doe.mass.edu/frameworks/archive/math96/Mathnumsense.html A great nugget of individualized information from teachers using exemplary practices to teach number sense. Although all related to Massachusetts math curricula, the ideas and activities can probably spark some ideas that relate to your work. http://tiger.coe.missouri.edu/~barb/number.html

53. Math Simulations The sound of chaos (512) This site, part with its interactive introduction to two fractals, the Mandelbrot 8-12) This site contains activities for = students http://www.techtrekers.com/sim.htm

Educational Simulations English Studies Simulations The Alphabet superhighway (K-12) This World Wide Web (WWW) site, sponsored by the U.S. Department of Education's READ*WRITE*NOW! Initiative, helps students in grades 1 to 12 to create, locate, and communicate information through active learning, guided discovery, mentoring, competitions. Math Simulations The Stock Market Game SMG2000, the stock market game (4-12) This World Wide Web (WWW) site is designed to help students in grades 4 to 12 understand the stock market, the costs and benefits involved in decision making, and the sources and uses of capital and other related economic concepts Online Stock Market Trading Simulation The Investment Stock Game Invest smart This site contains an interactive stock market simulation in which high school classes can use a $100,000 fantasy money account to invest in the stock market or mutual funds. This market simulation is a hands-on tool. A Web-based Interactive Stock Market Learning Project for K-12 www.ncsa.uiuc.edu/edu/RSE/RSEyellow/gnb.html

54. Calculator Workbooks - TI-83 theorem of algebra, complex numbers, fractals and mathematics of chaos, combinatorics, probability and others are new activities made possible by http://www.eaiusa.com/mo__calculator__workbooks__ti83.htm

Casio Calculators TI Calculators Sharp Calculators More TI-83 Workbooks: New Releases Calculator Activities and Lessons General Graphing Calculators ... A-Z List Calculator Workbooks - TI- 83 New! Graphing Calculator Activities for Enriching Middle School Mathematics by Christine Browning and Dwayne Channell This workbook provides teachers with useful integrated math and science activities to use the TI-80/82/83 graphing calculators. The activities cover topics in number sense probability and statistics, measurement, and algebraic thinking. Teacher Notes including useful activity hints and problems solutions, are also provided. (Paperbound, 142 pages). W-7720-TI New! Graphing Calculator Activities by Charles Lund and Edwin Anderson This collection of 50 activities guides students to generate graphs quickly, as they study the functions encountered in Algebra I and II. For use with any graphing calculator, Graphing Calculator Activities offers explorations in graphing lines, inequalities, simultaneous equations, special functions, parabolas, circles, hyperbolas, matrices, and the exponential, logarithmic, and sine functions. Worksheets guide students through experiences by offering suggestions and asking questions. Also contains quick reference tips for the popular Texas Instruments TI-82 and TI-83, the Casio CFX-9850G, and the Sharp EL-9300 graphing calculator. (Paperbound, 240 pages).

55. Mathematics Web Sites University; link to fractal and chaos applets; fractals Dimensions of fractal geometry; Sierpinski Triangle; extend the USDA; Grades K2 Prob/Stat activities; K-12 http://frontpage.uwsuper.edu/aguckin/mathsites.htm

Mathematics Web Sites The following links to web sites are provided to help you get started locating sites that will be helpful to you. It is difficult to keep any such lists current and accurate. Sometimes sites are inaccessible because they are busy, their location has changed or they have been eliminated. Start your own list of useful bookmarks and use names for your bookmarks that will be meaningful to you. Select a category: Discrete Mathematics Geometry Data Investigation Number, Number Sense and Elementary Number Theory ... Parents More Teaching Resources and Policy Reports Using Web sites carefully Just as everything we read in the newspaper is not necessarily accurate, everything we read on the Internet is not necessarily accurate. The following is an example of what can happen: Under the headline, "Whales in the Minnesota River? Only on the Web, Where Skepticism Is a Required Navigational Aid," the March 4 edition of the New York Times ran an interesting piece about how, on the Web, the "straight facts can be hard to find." Used as an example was a spoof site posted through Mankato State that highlighted Mankato as home to sunny beaches, an underwater city and whale watching as well as neighborhoods in which "the winter temperature has never dropped below a balmy 70 degrees." Evaluating Web sites Thinking critically about world wide web resources: Checking quality of Web sites Referencing Web sites

56. Mathematics Links On The Web of algebra and geometry to new innovations in chaos theory and fractals. pguide/pguide.html An electronic booklet that includes activities for parents http://www.msu.edu/course/cep/816/wallacespring02/math.htm

Syllabus CEP816 Spring 2002 Technology, Teaching, and Learning Across the Curriculum Raven Wallace 342 Erickson Hall ravenmw@msu.edu Class meets: Thursdays, 6-9 pm Office hours: Thursdays, 2-4 pm Tuesdays, 5-6 pm Course Schedule Java Applets for Math tools . Cuisenaire Rods, Fraction Blocks, Pattern Blocks, INteger Bars National Council of Teachers of Mathematics NCTM is the professional organization for math teachers, and the source of the standards for math teaching and learning. On this page, you can find electronic links to the standards, sample lessons, and more. NCTM is a great resource for teachers - if you don't already belong, and you teach mathematics, you should consider joining. The journals they publish are full of great ideas, Web links, and announcements of meetings and conferences. Michigan Council of Teachers of Mathematics - The Michigan chapter of NCTM. CLIMB Michigan Math Standards and Benchmarks NCTM E-Standards Home Page This is a link from the NCTM homepage taking you directly to the new national standards. This is a full-text, electronic copy. You can also order the book from this Web site.

57. NECC '98 Paper ComputationallyRich activities for the Construction of and parallelism of MicroWorlds brings chaos theory within fractals are self-similar shapes with finite http://www.stager.org/articles/NECCmath98.html

articles/NECCmath98.html Computationally-Rich Activities for the Construction of Mathematical Knowledge - No Squares Allowed This paper was published in the proceedings of the 1998 National Educational Computing Conference in San Diego gstager@pepperdine.edu with cannings@pepperdine.edu Abstract The NCTM Standards state that fifty percent of all mathematics has been invented since World War II . (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found their way into the K-12 curriculum. This is most unfortunate since topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new mathematical topics tend to be more contextual, visual, playful and fascinating than adding columns of numbers or factoring quadratic equations. Logo provides a powerful medium for rich mathematical explorations and problem solving while providing a context in which students may fall in love with the beauty of mathematics. The examples in this paper are intended to spark the imaginations of teachers and explore several mathematical areas ripe for Logo-based investigations. Introduction Many educators equate Logo with old-fashioned turtle graphics or suggest that Logo is for the youngest of children. Neither of these beliefs is true. Although traditional turtle graphics continues to be a rich laboratory in which students construct geometric knowledge, Logo is flexible enough to explore the entire mathematical spectrum. Logo continues to satisfy the claim that it has no threshold and no ceiling. (Harvey, 1982) Best of all, Logo provides a context in which children are motivated to solve problems and express themselves.

58. Geology Books + Earth Science Books : Current Bestsellers List fractals and chaos in Geology and Soil Science Simplified; A Field Manual for the Amateur Geologist Tools and activities for Exploring Our Planet; http://www.crimsonbird.com/science/geologybooks.htm

Geology Books + Earth Science Books : Current Bestsellers List Link to the site main index Link to the science book reviews index page Please click on any book title to display the price, full description, estimated shipping time, and option to buy Books are listed in order of sales #1 is the bestseller This is a previous version of the geology books page. Clicking ... Link to the science books reviews index page

59. On Growth And Form Handson activities encourage students to predict the outcome In the chaos Game, students begin by placing Back to fractals in Science Simulations Back to CPS http://polymer.bu.edu/ogaf.html

On Growth and Form As part of the National Science Foundation Applications of Advanced Technologies funded project On Growth and Form: Learning Concepts of Probability and Fractals by ``Doing Science'' , a number of hands-on activities, laboratory experiments, and interactive visualization programs for the Macintosh platform have been developed to demonstrate how fundamentally random microscopic events can give rise to fractal macroscopic patterns. Click to download Macintosh and Windows software to your host computer. For further information on the following simulations, please contact us. Feedback would be most appreciated. Jump to: Random Walks Anthill Deer Many Walkers ... DNA Walk , or Chill Out Random Walks Hands-on activities encourage students to predict the outcome of flipping a set of ten coins 1000 times. How many times would all ten coins come up heads? How many times would nine coins come up heads? etc. Then students flip coins for themselves and average results over the entire class. Students then are given a number line and a walker. Students place the walker in the center of the number line and move it left or right depending on the outcome of a coin flip. The Random Walk program allows allows the student to flip a set of ten coins a large number of times quickly and summarizes in the form of a histogram the number of heads resulting from each trial. Another part of the program models the direction of a one dimensional random walker by the flip of a coin. Where the walker lands at the end of ten steps is compiled in a histogram at the bottom of the screen.

60. TRENTON STATE COLLEGE fractals for the Classroom, Part One Introduction to fractals and chaos, NCTM, 1992 Peitgen, et.al, fractals for the Classroom Strategic activities, Vol.1 http://www.tcnj.edu/~mathstat/outlines/300Syllabi/390Syllabi.htm

THE COLLEGE OF NEW JERSEY MATHEMATICS AND STATISTICS DEPARTMENT Professionalized subject matter. Teaching techniques and lesson planning including a variety of classroom formats. Cooperative group work, writing in the mathematics classroom, technology and manipulatives. Curriculum trends, professional obligations and responsibilities, student assessment. Content will include discrete mathematics, problem solving concept of proof, and mathematical modeling. Be able to present the mathematics of the secondary school with emphasis on reasoning as well as techniques of operation. Be able to use instructional strategies based on current research as well as national, state and local standards relating to mathematics instruction. Be adept in using manipulatives for meaningful student learning. Student reactions and evaluations. Revised 2/9/01 bc

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