The Abacus
Kathleen Allen
Thursday May 31, 2007
Presentation Focus
The Differences between Ancient and
Modern Day Abuci
History of the Abacus
How to Add and Subtract with the Abacus
Uses in the Classroom today
The Abacus vs. The Counting Board
The Counting Board is
the name for the Ancient
Abacus which were
used in the sand or on a
small wooden tablet
The Abacus is the name
for the modern day
counting devices which
used wooden frames
and beads to do
complicated
mathematical problems
Counting Board
Could be used in the sand,
or in a box, set of lines that
was used to place pebbles
in an order to keep track of
answers
Problems were solved in the
users head and transferred
to the sand
Salamis Tablet oldest
counting board still around
Made of Marble
History of the Abacus
Abacus comes from the
Greek word Abax which
means flat surface
Used to make large
calculations
First known Abacus is from
300 BC
One Form is the Roman
Hand Abacus, only five of
these remain and it is
believed that they were
used by the wealthy in
shops
Becoming Familiar with the Abacus
I-1
V-5
X - 10
L - 50
C - 100
D - 500
M - 1000
Addition with the Abacus
Set up 2734
MMDCCXXVII
on left side of
line
Set up 3874
MMMDCCCLX
XIIII on the right
side of the line
Solution
Push all of the beads/ counters to one side of
the line
Move the beads around to have them in the
appropriate locations working from the bottom
up
Solution 6611 MMMMMMDCXI
Subtraction with the Abacus
Place 2638
MMDCXXXVIII on the left
side of the counting board
Place 4321
MMMMCCCCXXI on the
right side of the counting
board
Do the two sides match up
for subtraction?
What can we do to make
the problem easier?
Solution
Remove the counters in pairs until you are
only left with counters on the left side
Answer 1783 -MDCCLXXXIII
Classroom Uses
There are many similarities
between the Counting Board and
The Base 10 Boards, you could
talk about these similarities with
students
Students can make an Abacus
by using popsicle sticks, beads
and rods
Resources
The History of the Abacus by J. M. Pullan,
Frederick A. Praeger, New York, 1968
The Abacus: The Art of Counting with Beads
http://www.ee.ryerson.ca:8080/~elf/abacus
How to Add and Subtract with a counting board
http://faculty.ed.umuc.edu/~swalsh/Math%20Arti
cles/CBAddition.html
The Ages of Mathematics Volume II Charles F.
Linn