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### Importance of Zero

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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
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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
Audience:
Elementary school teachers
Middle school teachers
Parents
Secondary teachers
Supervisors
Teacher educators
Teachers
Resource Type:
Activities
Print materials
Reference materials
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;
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
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
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;
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;
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;

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
Index
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:
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.
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
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
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
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

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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