Importance of ZeroDate: 12/19/95 at 14:33:47 From: Anonymous Subject: Introducing importance of zero Dear Dr. Math, This is really a question for elementary school teachers: We all know that zero is very important in our number system. Has anyone developed an inquiry based activity for the classroom in which students in grade 5 can explore the importance of zero? I am thinking of having them invent their own number systems, but my idea is very half-baked and I could use some input. I'd like them to explore in such a way that they on their own could get to an "Ah Ha!" Claire Groden Elementary math specialist Watertown, MA Date: 6/24/96 at 20:5:18 From: Doctor Jodi Subject: Re: Introducing importance of zero Hi there! I think we've finally found some relevant material. Here are some reviews from the ENC resource collection, which you can search yourself from their web site at http://enc.org The first item is a literature collection. The number sense section has a few stories about zero (including a K-4 level story called "Zero: is it something, is it nothing?") After that review, you'll find a description of a 4-8 level series about the Mayans. To my knowledge, the Mayans were the first (among the first?) to have a symbol for zero. It looks like this series takes advantage of this, starting with Egyptian numbers (which don't have a symbol for zero) and including sections like "Where did the idea of zero come from?" It sounds like an exploration-based series with connections among math, science, and history. (Actually, it sounds like a lot of fun, too!) I hope you get a chance to take a look at it - I'd like to know if it is as good as it sounds. I hope that this helps. Please let us know if we can help again, and tell us how your project goes! ENC Number: ENC-002775 Record status: Complete record. 10/19/95 Title: Math through children's literature: making the NCTM standards come alive [Print Materials] Author: Kathryn L. Braddon, Nancy J. Hall, Dale Taylor Date: c1993 Publisher: Englewood, CO : Teacher Ideas Press Grade Level:Kindergarten,1,2,3,4,5,6 Audience: Administrators Elementary school teachers Middle school teachers Parents Secondary teachers Supervisors Teacher educators Teachers Resource Type: Activities Print materials Reference materials Trade books (Non-fiction) Language: English Standards: I. NCTM Standards (1989). I.A. Content Standards: Grades K-4 I.A.1.Mathematics as problem solving. I.A.2. Mathematics as communication. I.A.3. Mathematics as reasoning. I.A.4. Mathematical connections. I.A.7. Concepts of a whole number operations. I.A.9. Geometry and spatial sense. I.A.10.Measurement. I.A.11.Statistics and probability. I.A.12.Fractions and decimals. I.A.13.Patterns and relationships. Subjects: Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics. Children's literature. Decimals. Fractions. Geometry. Integrated / Interdisciplinary approaches. Literature. Mathematics education. Mathematics standards. Mathematics. Measurement. Number concepts. Numeration. Patterns (Mathematics). Probability. Statistics. Whole number operations. Abstract: This book is intended for use in grades K to 6 and is designed to recognize and apply the idea that children learn through active involvement, and uses familiar stories to address mathematical ideas. This book utilizes the National Council of Teachers of Mathematics (NCTM) Standards as a base for the mathematics activities and features children's literature that is widely available. The first part of this book gives an overview of mathematics education, and the second provides an overview of the first five NCTM mathematics standards for grades K to 4. The remainder of the book explores books and related math activities for grades K to 3 and 4 to 6 related to the remaining NCTM K to 4 standards. Related books and references are suggested for further exploration. (Author/DDD) Contents: Preface Acknowledgments How to use this book The mathematics curriculum An overview of mathematics education Historical perspective; The essentials of education; The role of reading; Change; Rote learning of mathematics basic facts; The breadth of mathematics; Why study mathematics? Integration; Calculators in the mathematics classroom; Notes The process components An overview of math standards 1 through 5 Standard 1, Mathematics as problem solving; Standard 2, Mathematics as Communication; Standard 3, Mathematics as reasoning; Standard 4, Mathematics as connections; Standard 5, Estimation The content components Standard 6, Number sense and numeration Books for grades K-3 {Mathematical content vocabulary; 10 bears in my bed; Harriet goes to the circus; The life of numbers; How many snails; One watermelon seed; One wide river to cross; Zero, Is it something? Is it nothing?}; Books for grades 4-6 {Mathematical content vocabulary; How did numbers begin?; Roman numerals; Harriet's Halloween candy; This is 4, the idea of a number; Less than nothing is really something; Number families; How to count like a Martian}; Related books and references {Counting; Large numbers and infinity; Number concepts; Numerals and art; Ordinals; Other base systems; Zeros and negative numbers; Miscellaneous; Adult references} Standard 7, Concepts of whole-number operations and Standard 8, Whole-number computation Books for grades K-3 {Mathematical content vocabulary; Counting wildflowers; So many cats; Annie's one to ten; The great take-away; Penelope gets wheels; Bunches and bunches of bunnies; The doorbell rang}; Books for grades 4-6 {Mathematical content vocabulary; Popcorn; Alexander, who used to be rich last Sunday; Anno's mysterious multiplying jar; How much is a million; The magic school bus lost in the Solar System; The toothpaste millionaire}; Related books and references {Addition and subtraction; Calculators; Multiplication and division; Miscellaneous; Adult references} Standard 9, Geometry and spatial sense Books for grades K-3 {Mathematical content vocabulary; The shape of me and other stuff; The shapes game; What is symmetry?; Flat Stanley; Anno's math games III; Grandfather Tang's story}; Books for grades 4-6 {Mathematical content vocabulary; Paper John; The boy with square eyes; Spirals; Shape, the purpose of forms; What can she be? An architect; Rubber bands, baseballs, and doughnuts}; Related books and references {Architecture; Dimensionality; Drawing and computer graphics; Geometric shapes and concepts; Miscellaneous; Non-geometric shapes; Paper-folding and paper-cutting geometry and symmetry; Proportionality; Quilting; Shadows and reflections; Topology; Adult references} Standard 10, Measurement Books for grades K-3 {Mathematical content vocabulary; The grouchy ladybug; How big is a foot; Pezzettino; Space, shapes, and sizes; Heavy is a hippopotamus; The day that Monday ran away}; Books for grades 4-6 {Mathematical content vocabulary; Diary of a church mouse; 8,000 stones; Time for Horatio; The magic school bus inside the Earth; The magic school bus inside the human body; Around the world in eighty days}; Related books and references {Area; Calendar; Days of the week; Linear measurement; Miscellaneous measurement; Temperature; Time; Volume and capacity; Weight and mass; Adult references} Standard 11, Statistics and probability Books for grades K-3 {Mathematical content vocabulary; Statistics; Fleet-footed Florence; Moira's birthday; Averages; Probability}; Books for grades 4-6 {Mathematical content vocabulary; What do you mean by average?; Miss Pickerell and the weather satellite; Do you wanna bet?; Million dollar jeans; Socrates and the three little pigs}; Related books and references {Probability and statistics; Weather; Adult references} Standard 12, Fractions and decimals Books for grades K-3 {Mathematical content vocabulary; Gator pie; Dollars and cents for Harriet; Fractions are parts of things; Henry's pennies; Arthur's funny money; Harold & Chester in hot fudge}; Books for grades 4-6 {Mathematical content vocabulary; Alice and the boa constrictor; What's cooking, Jenny Archer?; If you made a million; Jason and the money tree; The Turtle Street Trading Co.; The magic school bus at the waterworks}; Related books and references {Fractions, Cooking; Fractions, Music; Fractions, Pies and pizzas, food; Fractions, Miscellaneous; Decimals; Money, Miscellaneous; Money-making ideas for kids} Standard 13, Patterns and relationships Books for grades K-3 {Mathematical content vocabulary; Some things go together; A, my name is Alice; Number ideas through pictures; Sam Johnson and the blue ribbon quilt; The case of the stolen code book}; Books for grades 4-6 {Mathematical content vocabulary; Too hot to hoot; Sea witches; Solomon Grundy, born on oneday; Visual magic; A clue in code}; Related books and references {Pattern books; Poetry patterns; Secret codes; Visual patterns; Miscellaneous; Adult references} Appendix, Traditional patterns of teaching mathematics with changes suggested by the NCTM standards Incorporating the standards into the traditional mathematics scope and sequence; Content traditionally covered in grades K-6 and suggested changes Index About the authors. Specifications: xviii, 218 pages : illustrated ; 28 cm Availability: As of: 1995 Teacher Ideas Press/Libraries Unlimited, ATTN: Dept. NCTM (publisher) P. O. Box 6633 Englewood, CO 80155-6633 Toll-free no.: 800/237-6124 1 text: ; ISBN 0-87287-932-1 ; $23.50 Source Note: Gift of Teacher Ideas Press. Added Entries: Braddon, Kathryn L. Hall, Nancy J. Taylor, Dale. Teacher Idea Press. (Publisher) ----------------------------------------------------------- ENC Number: ENC-002553 Record status: Complete record. 3/31/96 Title: Maya math [Software] Series: The second voyage of the Mimi. Maya math module. Author: software designed by Ralph Smallberg, Shari Robinson, Margaret Honey, Samuel Y. Gibbon, Jr.; programming by Dennis Sullivan ; computer graphics by Joan Auclair ; written by Magdalene Lampert and Ralph Smallberg Date: c1990. Publisher: Scotts Valley, CA : WINGS for Learning, Inc. Grade Level: 4,5,6,7,8 Resource Type: Software Teaching units Language: English Subjects: Archaeology. Arithmetic. Calendars. Earth science. Integrated/Interdisciplinary approaches. Mathematics. Numbers. Place value. Science. Social studies. Abstract: This curriculum, developed for grades 4 to 8, is based on the story of the crew of the ketch Mimi and two archaeologists, who explore the mystery of Mayan ruins. The program combines laserdiscs, computer software, sensors, and print materials to present an integrated set of concepts in mathematics, science, social studies, and language arts. This component of the program explores the concept of place value with Mayan numbers and the Mayan calender. Through hands-on and computer activities, students learn arithmetic operations by means of graphic representations. This component includes a student's guide, a teacher's guide, and computer disks. The student's guide provides an introduction, procedures, and a worksheet for each activity. The teacher's guide includes introduction to the activities, teaching strategies, questions and answers for discussion, masters of student worksheets, and operation guides for software programs. (Author/KSR/CCC) Support items: Supporting materials include: The second voyage of the Mimi (ENC-002551); Scuba science (ENC-002552); Sun lab (ENC- 002554). Contents: Student guide: Introduction Who are the Maya?; The mystery of the Maya; Breaking the code; An archaeologist's question How did people count before they invented numbers? Counting without numbers; Grouping solves a problem; Symbols for groups; Symbols for groups of groups; Workpage 1 More on symbols for groups and groups of groups Egyptian numbers; Workpage 2; Roman numerals; Maya numbers; Order of symbols Counting in Maya Bars and dots; Trading in Maya numbers; Trading in our numbers; Counting fingers; Counting fingers and toes; Workpage 3; Calculator activity 1 Where did the idea of zero come from? Counting with counting boards; A problem; An important invention, zero; Workpage 4 The third place, what's it worth to you? Calculator activity 2; The third place in Maya numbers; Workpage 5; Stirling's stela; Workpage 6 The fourth and fifth places in Maya numbers How much can the third place hold?; Calculator activity 4; Back to Stirling Comparing Maya numbers and our numbers Place value in our numbers; Building bigger numbers; Calculator activity 4 Counting on odometers Observing how numbers change; Calculator activity 5 Translating our numbers into Maya [workpage 7; Calculator activity 6; workpage 8] Picturing very large numbers [Workpage 9] Other number systems Calculator activity 7; Base systems; Calculator activity 8, 9; Up and down or sideways The Maya long count calendar Calendar activity 1, 2, and 3; An even longer count Maya number challenges Challenge 1, 2, 3, 4, 5, 6, and 7 Using the software, How to play Glyph trek Getting started; Playing the game; Decode; Esc key; quit Using the software, Maya Calculator Getting started; Input #; New base; Quit Using the software, Maya Calendar Getting started; Input date; Print; Quit . Teacher's guide: Introduction Follows the student guide contents Workpages 1-9 Calculator activities 1-9 Calendar activities 1-3 Challenges 1-7 Workpages answers Calculator activities answers Calendar activities answers Challenges answers Teacher utilities Apple II, working with your computer Apple IIGS, control panel settings What happens if ? WINGS warranty. Student book: A charter to the past Where's Mimi? If I can do this A tomb in the jungle Habla usted Mayan? and Who's a Maya? Sweating it out A light in the dark Underwater gardens As the Earth turns The underworld Performing under pressure and Here comes the Fizz The incredible shrinking head A stone puzzle Dig this Feeling the pressure Cracking the code Secret messages and Maya math Written in stone The quest begins Whose pot is it? and A pot is worth a thousand words The ancient farm A Road to danger Mini beasts A scorpion tale A friendly village Dear diary Curandera Discoveries The plot thickens Up a tree Found and lost Stamp it! In the canopy The fate of a king Time travel One stone at a time Maya stela Glossary. Specifications: 3 computer disks (Apple II) : sound, color ; 5.25 in. + 3 backup disks (Apple II ; 5.25 in.) + 1 student guide (130 pages : color illustrations ; 28 cm.) + 1 teacher's guide (approximately 197 pages, loose-leaf : illustrated ; 28 cm.) + 1 student book (160 pages : color illustrations ; 28 cm.) Equipment: System requirements: Apple--Apple II family of computers (128K); specific hardware requirements not noted in source materials. Availability: As of: 1994. Sunburst Communications Inc. (distributor) 101 Castleton Street, P.O. Box 100 Pleasantville, NY 10570-9961 Telephone no.: 914/747-3310 (call collect) Toll-free no.: 800/321-7511 NOTE: All software packages and print materials are available for individual purchase. 1 learning module (Maya math): ; Order no.: 3407-MG (5.25 in. disk Apple) or 6366-MG (3.5 in. disk Apple) ; $79.00 1 videodisc/Apple software package (includes Overview guide, software and manual, 3 learning modules and 30 student books): ; Order no.: 405002-MG ; $1650.00 Funding: National Science Foundation (NSF) United States Department of Education Added Entries: Auclair, Joan. (Computer graphics) Bobash, Kirk. (Programmer) Driggs, Lorin A. (Editor) Gibbon, Samuel Y. Jr. (Software designer) Honey, Margaret. (Software designer) Lampert, Magdalene. Robinson, Shari. (Software designer) Smallberg, Ralph. (Writer, Software designer) Sullivan, Dennis (Software programmer) Bank Street College Project in Science and Mathematics. Bank Street College of Education. National Science Foundation (NSF). (Funding source) Sunburst Communications, Inc. (Distributor) United States Department of Education. (Funding source) WINGS for Learning, Inc. (Publisher) -Doctor Jodi, The Math Forum |
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