Importance of Zero

Date: 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