


 The
Topic:
 Number
Systems

 Easier  A number
system is a way of counting things. It's a way of
identifying the quantity of something.

 Harder  A number
system is the set of symbols used to express
quantities as the basis for counting, determining
order, comparing amounts, performing calculations,
and representing value. It is the set of characters
and mathematical rules that are used to represent a
number. Examples include the Arabic, Babylonian,
Chinese, Egyptian, Greek, Mayan, and Roman number
systems. The ISBN and Dewey Decimal System are
examples of number systems used in libraries.
Social Security even has a number system.


 Development
of Counting Systems and Notations by M.I.
Woodcock
 http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/countsys.htm
 This module has been produced as a
distancelearning package. It is intended that the
student should read through the notes provided and
use the reading list and other History of
Mathematics links to answer further
questions.

 Links
to Information on Number Systems by S.
Alejandre from The Math Forum
 http://mathforum.org/alejandre/numerals.html
 This site connects to websites on Arabic,
Babylonian, Chinese, Egyptian, Greek, Mayan, and
Roman number systems.
 Related Website:
 2) Numbers and Number Theory Index from
University of St. Andrews,
Scotland
 http://wwwgroups.dcs.stand.ac.uk/~history/Indexes/Number_Theory.html
 See additional sites below in the Ancient
Number Systems

 Number
System from Kid's Online Resources,
College of the Redwoods
 http://www.kidsolr.com/math/numbersystem.html
 Designed for beginning computer students, this
site introduces binary, decimal, hexadecimal
systems and includes definitions and
conversions.
 Related Websites:
 2) Conversion Between Different Number Systems
http://www.cstc.org/data/resources/60/convexp.html
 3) Data Structures And Number Systems http://www.ibilce.unesp.br/courseware/datas/numbers.htm
 4) Digital Number System http://www.eelab.usyd.edu.au/digital_tutorial/chapter1/1_3.html
 5) Number Systems and Codes http://www.eelab.usyd.edu.au/digital_tutorial/chapter2/2_0.html

 Wise
Up! We Use Numbers All the Time from
British Broadcasting Corporation (BBC)
 http://www.bbc.co.uk/education/revisewise/maths/number/01_act.shtml
 The activity at this website is a review of our
base 10 number system. You can follow this up with
a fact sheet and an online test.



 Websites By Kids For Kids
 Abacus
Online (2000 ThinkQuest Internet
Challenge)
 http://library.thinkquest.org/C005843/
 This site explores the abacus, particularly the
Chinese (2/5) styled abacus or suan puan, and
contains information on its history, tutorials on
how to use it, and more.

 Do
We Really Know Dewey? (Silver Award, 1999
ThinkQuest Junior Project)
 http://tqjunior.thinkquest.org/5002/Melvil/melvil.htm
 This is a website created to teach kids about
the Dewey Decimal System. There are several levels,
so it could be used with different age groups. For
example, the "Alien" story and the "PreDew Review"
sections could be used with earlier elementary
levels. Middle grades could also learn a lot from
the "Let's Dew It" section. For those students who
are ready for more challenging information, there
is "Let's Dew it Again".

 Elementary
Number Theory (2001 ThinkQuest Internet
Challenge)
 http://library.thinkquest.org/C0124043/
 This is a site introducing elementary number
theory, including prime number, divisibility and
some Java games

 Integers
(2000 ThinkQuest Internet Challenge)
 http://library.thinkquest.org/C005090F/
 This site investigates the development of
number systems.

 Simply
Number Sense! (1998 ThinkQuest Internet
Challenge)
 http://library.thinkquest.org/17888/opening.shtml?tqskip1=1&tqtime=0710
 Have you hit the brick wall of confusion in
mathematics? Do your numbers have so many places
that you don't know what to call them? Does the
thought of decimals, fractions, and percentages
curl your hair? Brush up with this tutorial.

 Ancient Number Systems
 Babylonian
Numerals by J.J. O'Connor and E.F.
Robertson
 http://wwwgroups.dcs.standrews.ac.uk/~history/HistTopics/Babylonian_numerals.html
 The Babylonians inherited ideas from the
Sumerians and from the Akkadians. From the number
systems of these earlier peoples came the base of
60, that is the sexagesimal system. Yet neither the
Sumerian nor the Akkadian system was a positional
system, and this advance by the Babylonians was
undoubtedly their greatest achievement in terms of
developing the number system.
 Related Websites:
 2) Counting in Babylon by M. Fowler http://galileoandeinstein.physics.virginia.edu/lectures/babylon.html
 3) Cuneiform Numbers by D.J. Melville http://it.stlawu.edu/~dmelvill/mesomath/Numbers.html
 4) Sumerian and Babylonian Numerals by
M.I.Woodcock
 http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/sbn.htm

 Chinese
Numbers
 http://www.mandarintools.com/numbers.html
 While China has for many uses adopted the
Arabic numeral system familiar around the world, it
also still uses its native Chinese character number
system. The Chinese system is also a base10
system, but has important differences in the way
the numbers are represented.

 Egyptian
Numerals from History of Mathematics in
Africa
 http://www.saxakali.com/COLOR_ASP/historymaf5.htm
 The Egyptian numbering system was also based on
units of 10, but instead of relying on the position
of numbers to define their value, the Egyptians
used different images to represent different units
of 10.
 Related Websites:
 2) Egyptian Number Systems http://home.clara.net/beaumont/egypt/maths/egnosys.htm
 3) Egyptian Numerals by M.I. Woodcock http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/en.htm
 4) Hieroglyphic Numbers http://www.greatscott.com/hiero/num.html

 HinduArabic
Numerals by M.I. Woodcock
 http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/han.htm
 The Hindu system is a pure place value system,
that is why you need a zero. Only the Hindus within
the context of IndoEuropean civilizations have
consistently used a zero.

 Maya
Mathematics
 http://www.michielb.nl/maya/math.html
 Instead of ten digits like we have today, the
Maya used a base number of 20. (Base 20 is
vigesimal.) They also used a system of bar and dot
as "shorthand" for counting.
 Related Websites:
 2) Mayan Math by K.M. Strom http://www.hanksville.org/yucatan/mayamath.html
 3) Mayan Numbers http://www.niti.org/mayan/lesson.htm
 4) Mayan Number System by S. Jimenez http://www.geocities.com/CapeCanaveral/Launchpad/5752/
 5) Mayan Numerals from History of
Mathematics in Americas
 http://www.saxakali.com/historymam2.htm
 6) Mayan Numerical System http://members.tripod.com/~a_sheppard/

 Roman
Numerals 101 by O. Lawrence
 http://www.oliverlawrence.com/romans101/
 The Romans counted according to decimal
mathematics, just like we do, but with a different
style of writing. It is useful to know this method
of writing because we still run across these
numbers today.
 Related Website:
 2) Roman Numeration from Rome's Imperial
Forums
 http://www.capitolium.org/eng/ludi/numeri.htm

 More Websites on Number Systems
 Abacus:
The Art of Calculating with Beads
 http://www.ee.ryerson.ca:8080/~elf/abacus/index.html
 The abacus is a mechanical aid used for
counting. Addition, subtraction, division and
multiplication can be performed on a standard
abacus.
 Related Website:
 2) Abacus in Various Number Systems http://www.cuttheknot.com/blue/Abacus.shtml

 Base
Valued Numbers
 http://www.psinvention.com/zoetic/basenumb.htm
 The basic rules for a formalized base numbering
system involve ordering items, grouping ordered
items and then expressing the groups and items in a
consistent way. The way it represents the different
groups gives the numbering system an order of
magnitude.

 Binary
 How Does It Work? by K. Redshaw
 http://www.kerryr.net/pioneers/binary2.htm
 It's not so difficult! Binary numbers use the
same rules as decimal  the value of any digit
always depends on its position in the whole number.
It all gets down to bases. Decimal uses base ten
and Binary, on the other hand, uses base two.
 Related Website:
 2) Binary Number System http://www.mc.edu/courses/csc/110/module1.html

 First
PlaceValue Number System from A History
of Computers
 http://www.maxmon.com/1900bc.htm
 The decimal system is a placevalue system,
which means that the value of a particular digit
depends both on the digit itself and on its
position within the number.
 Related Section:
 2) Invention of the Abacus http://www.maxmon.com/1000bc.htm

 Numbering
Systems and Place Values
 http://members.aol.com/AmazingMazeMan/numberingsystems.html
 Learn about about large numbers and their place
values including ones up to trillions, tenths down
to trillionths; the American Numbering System;
Googol and Googolplex; and the British Numbering
System.

 Numeric
Systems
 http://members.tripod.com/numeric_systems/
 This website defines number systems, then
provides information about binary and the
hexadecimal system.

 Place
Value to 1,000: What Is It? from
MathSteps
 http://www.eduplace.com/math/mathsteps/2/a/
 Place value is the basis of our entire number
system. A place value system is one in which the
position of a digit in a number determines its
value.
 Related Website:
 2) All About Place Values by J.Banfill from
AAA Math http://www.aaamath.com/plc.html

 Understanding
Decimal, Binary, Hexadecimal from
Exploring MIDI
 http://nuinfo.nwu.edu/musicschool/links/projects/midi/pages/undstdbh.html
 This page summarizes three basic numbering
systems: decimal, binary, and hexadecimal.
 Related Websites:
 2) Binary/Octal/Decimal/Hexadecimal Conversion
http://www.mc.edu/courses/csc/110/module2.html
 3) Counting: Base 6, 12, 16 by S. Asplund from
The Math Forum
 http://mathforum.org/library/drmath/view/55739.html
 4) Hexadecimal Number System by E.
Østergaard http://www.danbbs.dk/~erikoest/hex.htm

 Understanding
Call Numbers
 http://www.hcc.hawaii.edu/education/hcc/library/callno.html
 Have you ever wondered how library books are
assigned their places on the shelves? Did you know
that the call number  the number placed on the
spine of the book  is a code which provides
valuable information about the book? This page will
provide an introduction to understanding and using
Library of Congress Classification call
numbers.
 Related Websites:
 2) Dewey Decimal Classification http://www.penrithcity.nsw.gov.au/Lib/ReaderServices/ddc.htm
 3) Dewey Decimal Classification System
http://www.tnrdlib.bc.ca/dewey.html#top
 4) Dewey Decimal System http://www.lis.uiuc.edu/~stoerger/dewey.html
 5) Dewey Decimal System http://www.monroe.lib.in.us/childrens/ddctable.html
 6) Let's Do Dewey http://www.mtsu.edu/~vvesper/dewey.html

 Websites For Teachers
 MacCandy
Factory Microworlds
 http://wwwrohan.sdsu.edu/faculty/jbowers/macpics/intro.htm
 The objective of this first program (Download
software at this site) is to engage students in the
activities of packing and unpacking to build a
sense of place value and ten as a composite
unit.

 Place
Value (Grades 14) from Midcontinent
Research for Education & Learning
(McREL)
 http://www.mcrel.org/resources/plus/math/place.asp
 Here is a collection of lesson plans and
activities for learning about place value.
 Related Lesson Plans:
 2) Fictional History of Place Value by B.B.
Jarrow http://www.iit.edu/~smile/ma9009.html
 3) Handson Role Play Activity: Counting the
Rice (Grades 28)
 http://www.arcytech.org/java/b10blocks/counting.html
 4) Place Value for Elementary Students
(Involving movement, music, and reflection) from
Southwest Educational Development Laboratory
http://www.sedl.org/scimath/compass/v03n02/place.html
 5) Place Value Game (Grades 18) by T. Sayre
http://www.lessonplanspage.com/MathPlaceValueGame18.htm

 Primary
Understanding and Use of Place Value by E.
Brzozowski from Hanson Park School
 http://www.iit.edu/~smile/ma9202.html
 This lesson examines some of the people that
have contributed to the development of modern
arithmetic (number systems); to provide a better
understanding of our base 10 number system and its
application to real life problems.

 Socratic
Method: Teaching by Asking Instead of by
Telling by R. Garlikov
 http://www.garlikov.com/Soc_Meth.html
 The is a transcript of a teaching experiment,
using the Socratic method, with a regular third
grade class in a suburban elementary school. The
experiment was to see whether I could teach these
students binary arithmetic (arithmetic using only
two numbers, 0 and 1) only by asking them
questions.

number

order

group

decimal

Pi

counting

place
value

integer

binary

arithmetic

order of magnitude

numeral

zero

golden
ratio

binary

negative number

positive number

infinity

natural number

decimal number system

calculate

numeration

hexadecimal

prime number

value

quantity

mathematics

base 10

"take a number"

number system




 Created by
Annette
Lamb and
Larry
Johnson,
7/02.
