Download Mathematics in Mesopotamia

12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Mathematics in Mesopotamia By Vickie Chao
1
Do you like mathematics? No matter what your answer may be, you are not alone. Mathematics is
a challenging subject. Its basic concepts began to emerge when the world's very first civilization took
root in Mesopotamia more than 5,000 years ago. Back then, the Sumerians developed a unique
numeral system, using a base of sixty. In scientific terms, that system is called a sexagesimal system.
Since the Sumerians counted things with sixty as a unit, they had the same symbol ( ) for 1 and 60.
And they would express 70 (
) as, literally, the sum of 60 ( ) and 10 ( ). Likewise, they would express 125 (
) as the sum of two units of 60 ( ) and one unit of 5
( ).
2
Today, our decimal numeral system uses ten, not sixty, as a base unit. But that is not to say that
the Sumerians' invention became obsolete. As a matter of fact, it still plays a critical role in our
everyday life. For example, have you ever wondered why an hour has 60 minutes and a minute has
60 seconds? Have you ever thought about why a full circle has 360 degrees? As it turns out, that was
how the Sumerians kept track of their time. And that was how they defined a full circle.
3
When the Sumerians first came up with their numerals, they did not have a specific symbol for
zero. If they needed to inscribe, say, 506 on a clay tablet, they would simply put a blank space
between the symbols of 5 ( ) and 6 ( ). This way of denoting zero could be quite confusing and
problematic. Neither the Sumerians nor other people in Mesopotamia (most notably, the Babylonians)
were able to come up with a solution at the time. This issue would remain unsolved until around 500
A.D. when the Indians developed the Arabic numerals that we are still using today.
4
Even though the Sumerians and the Babylonians did not have a full grasp of zero, they did
introduce a groundbreaking concept ­ positional or place value. Let's compare two numbers ­ 25 and
52. The symbol "5" of the first number means 5 units, whereas "5" of the second number means 50.
So, for every position a digit moves to the left, it is increased by a power of 10. This way of notation is
for the Arabic numerals. But since both the Sumerians and the Babylonians used a sexagesimal
system, each of their digits would be increased by a power of 60 as it moved along to the left. To
express a large number like 18,247, they would inscribe . The left­most digit equals to 5 times
60 times 60, or 18,000. The middle digit equals to 4 times 60, or 240. And the right­most digit equals
to 7.
5
With their advanced knowledge in numerals, people in Mesopotamia were excellent
mathematicians. When applied to their daily life, they developed formulas to calculate weights, areas,
volumes, and wages. Students from that time needed to study mathematics at school, too. They had
to learn how to do addition, subtraction, multiplication, division, and fractions. During the reign of
Hammurabi (1792 B.C. ­ 1750 B.C.) of the 1st dynasty of Babylon, there were even specific laws
addressing issues such as interests and loans. Because of those codified rules, we know that people
in Mesopotamia were the ones who established the world's first banking system. Without mastering
mathematics, that would be entirely impossible!
Copyright © 2016 edHelper
http://www.edhelperblog.com/cgi­bin/vspec.cgi
1/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Name _____________________________
Date ___________________
Mathematics in Mesopotamia
1. Which of the following about mathematics in 2. How many minutes did the Sumerians say an
Mesopotamia is correct?
hour has?
The Sumerians counted things with
30
twelve as a unit.
60
People in Mesopotamia used a dot to
90
denote zero.
15
The Sumerian numeral system is
commonly known as the Arabic numerals.
People in Mesopotamia said a full circle
is equal to 360 degrees.
3. How would people in Mesopotamia inscribe
10,925?
12 x 30 x 30 + 4 x 30 + 5
6 x 30 x 60 + 2 x 60 + 5
5 x 36 x 60 + 4 x 30 + 5
3 x 60 x 60 + 2 x 60 + 5
4. Which of the following statements is correct?
Mathematics began to take shape at the
same time that the world's first civilization
started to emerge in Mesopotamia.
Hammurabi was an Assyrian King.
People in Mesopotamia developed their
numerals around 500 A.D.
People in Mesopotamia did not apply
mathematics to their daily life.
5. How would the Sumerians write 65?
6. Who invented the world's first banking
system?
The Babylonians
The Chinese
The Arabs
The Indians
http://www.edhelperblog.com/cgi­bin/vspec.cgi
2/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Name _____________________________
Date ___________________
Mathematics in Mesopotamia
7. Which two Sumerian numerals used the same 8. How would a Sumerian express the result of
symbol?
80 minus 73?
1 and 30
1 and 10
1 and 32
1 and 60
9. Given that the Sumerians used a sexagesimal 10. Knowing that the Sumerian numeral system
system, how many days a year do you think a
was a positional one, which large number
Sumerian calendar had?
does translate to?
436
925,392
500
1,742,149
360
872,903
247
1,548,305
http://www.edhelperblog.com/cgi­bin/vspec.cgi
3/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Name _____________________________
Date ___________________
Mathematics in Mesopotamia
Compare and contrast the Sumerian numeral system and the Arabic numeral system.
http://www.edhelperblog.com/cgi­bin/vspec.cgi
4/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Mathematics in Mesopotamia By Vickie Chao
scientific
knowledge
issue
digit
literally
units
digits
calculate
issues
subtraction
numeral
compare
numerals
power
notation
unsolved
banking
value
unit
Directions: Fill in each blank with the word that best completes the reading comprehension.
Do you like mathematics? No matter what your answer may be, you are not alone. Mathematics is a
challenging subject. Its basic concepts began to emerge when the world's very first civilization took root in
Mesopotamia more than 5,000 years ago. Back then, the Sumerians developed a unique
(1) _______________________ system, using a base of sixty. In (2) _______________________ terms, that
system is called a sexagesimal system. Since the Sumerians counted things with sixty as a unit, they had the
same symbol ( ) for 1 and 60. And they would express 70 (
) as, (3) _______________________ , the sum
of 60 ( ) and 10 ( ). Likewise, they would express 125 (
(4) _______________________ of 5 (
) as the sum of two units of 60 ( ) and one
).
Today, our decimal numeral system uses ten, not sixty, as a base unit. But that is not to say that the
Sumerians' invention became obsolete. As a matter of fact, it still plays a critical role in our everyday life. For
example, have you ever wondered why an hour has 60 minutes and a minute has 60 seconds? Have you ever
thought about why a full circle has 360 degrees? As it turns out, that was how the Sumerians kept track of their
time. And that was how they defined a full circle.
When the Sumerians first came up with their numerals, they did not have a specific symbol for zero. If they
needed to inscribe, say, 506 on a clay tablet, they would simply put a blank space between the symbols of 5 (
) and 6 (
). This way of denoting zero could be quite confusing and problematic. Neither the Sumerians nor
other people in Mesopotamia (most notably, the Babylonians) were able to come up with a solution at the time.
This (5) _______________________ would remain (6) _______________________ until around 500 A.D.
when the Indians developed the Arabic (7) _______________________ that we are still using today.
Even though the Sumerians and the Babylonians did not have a full grasp of zero, they did introduce a
groundbreaking concept ­ positional or place (8) _______________________ . Let's
(9) _______________________ two numbers ­ 25 and 52. The symbol "5" of the first number means 5
(10) _______________________ , whereas "5" of the second number means 50. So, for every position a digit
moves to the left, it is increased by a power of 10. This way of (11) _______________________ is for the
Arabic numerals. But since both the Sumerians and the Babylonians used a sexagesimal system, each of their
(12) _______________________ would be increased by a (13) _______________________ of 60 as it
moved along to the left. To express a large number like 18,247, they would inscribe http://www.edhelperblog.com/cgi­bin/vspec.cgi
. The left­most
5/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
digit equals to 5 times 60 times 60, or 18,000. The middle (14) _______________________ equals to 4 times
60, or 240. And the right­most digit equals to 7.
With their advanced (15) _______________________ in numerals, people in Mesopotamia were excellent
mathematicians. When applied to their daily life, they developed formulas to (16) _______________________ weights, areas, volumes, and wages. Students from that time needed to study mathematics at school, too. They
had to learn how to do addition, (17) _______________________ , multiplication, division, and fractions.
During the reign of Hammurabi (1792 B.C. ­ 1750 B.C.) of the 1st dynasty of Babylon, there were even specific
laws addressing (18) _______________________ such as interests and loans. Because of those codified rules,
we know that people in Mesopotamia were the ones who established the world's first
(19) _______________________ system. Without mastering mathematics, that would be entirely impossible! Copyright © 2016 edHelper
http://www.edhelperblog.com/cgi­bin/vspec.cgi
6/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Name _____________________________
Date ___________________ (Key 1 ­ Answer ID # 0555807)
Crack the code! Write the real word that each of the codes represent. Each letter in the real word has
been changed to another letter. For example, a B in the code might really mean C. Once you figure out the
code for one letter, the same code is used for all the words on this sheet.
Code: A C D E F G H J K L O P Q R S T U V X Y Z
Letter: T D U C S
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ODACAVDO UVRVFVYCAVDO UCFUTFCAL FLKA­XDZA SVQHA­XDZA USVAVUCF LEGSLZZ PVQVA GDZVAVDO ZTJASCUAVDO http://www.edhelperblog.com/cgi­bin/vspec.cgi
7/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Mathematics in Mesopotamia ­ Answer Key
1 People in Mesopotamia said a full circle is equal to 360 degrees.
2 60
3 3 x 60 x 60 + 2 x 60 + 5
4 Mathematics began to take shape at the same time that the world's first civilization started to emerge in
Mesopotamia.
5 6 7 The Babylonians
1 and 60
8 9 10 360
1,548,305
http://www.edhelperblog.com/cgi­bin/vspec.cgi
8/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Mathematics in Mesopotamia
By Vickie Chao
Answer Key
Do you like mathematics? No matter what your answer may be, you are not alone. Mathematics is a
challenging subject. Its basic concepts began to emerge when the world's very first civilization took root in
Mesopotamia more than 5,000 years ago. Back then, the Sumerians developed a unique (1) numeral system,
using a base of sixty. In (2) scientific terms, that system is called a sexagesimal system. Since the Sumerians
counted things with sixty as a unit, they had the same symbol ( ) for 1 and 60. And they would express 70 (
) as, (3) literally , the sum of 60 ( ) and 10 ( ). Likewise, they would express 125 (
) as the sum of two units of 60 ( ) and one (4) unit of 5 (
).
Today, our decimal numeral system uses ten, not sixty, as a base unit. But that is not to say that the
Sumerians' invention became obsolete. As a matter of fact, it still plays a critical role in our everyday life. For
example, have you ever wondered why an hour has 60 minutes and a minute has 60 seconds? Have you ever
thought about why a full circle has 360 degrees? As it turns out, that was how the Sumerians kept track of their
time. And that was how they defined a full circle.
When the Sumerians first came up with their numerals, they did not have a specific symbol for zero. If they
needed to inscribe, say, 506 on a clay tablet, they would simply put a blank space between the symbols of 5 (
) and 6 ( ). This way of denoting zero could be quite confusing and problematic. Neither the Sumerians nor
other people in Mesopotamia (most notably, the Babylonians) were able to come up with a solution at the time.
This (5) issue would remain (6) unsolved until around 500 A.D. when the Indians developed the Arabic
(7) numerals that we are still using today.
Even though the Sumerians and the Babylonians did not have a full grasp of zero, they did introduce a
groundbreaking concept ­ positional or place (8) value . Let's (9) compare two numbers ­ 25 and 52. The
symbol "5" of the first number means 5 (10) units , whereas "5" of the second number means 50. So, for every
position a digit moves to the left, it is increased by a power of 10. This way of (11) notation is for the Arabic
numerals. But since both the Sumerians and the Babylonians used a sexagesimal system, each of their
(12) digits would be increased by a (13) power of 60 as it moved along to the left. To express a large
number like 18,247, they would inscribe . The left­most digit equals to 5 times 60 times 60, or 18,000.
The middle (14) digit equals to 4 times 60, or 240. And the right­most digit equals to 7.
With their advanced (15) knowledge in numerals, people in Mesopotamia were excellent mathematicians.
When applied to their daily life, they developed formulas to (16) calculate weights, areas, volumes, and
wages. Students from that time needed to study mathematics at school, too. They had to learn how to do
addition, (17) subtraction , multiplication, division, and fractions. During the reign of Hammurabi (1792 B.C.
­ 1750 B.C.) of the 1st dynasty of Babylon, there were even specific laws addressing (18) issues such as
interests and loans. Because of those codified rules, we know that people in Mesopotamia were the ones who
established the world's first (19) banking system. Without mastering mathematics, that would be entirely
impossible!
http://www.edhelperblog.com/cgi­bin/vspec.cgi
9/10
12/15/2016
www.edhelperblog.com/cgi­bin/vspec.cgi
Answer Key 0555807
Key # 1
Crack the code! Write the real word that each of the codes represent. Each letter in the real word has been
changed to another letter. For example, a B in the code might really mean C. Once you figure out the code for
one letter, the same code is used for all the words on this sheet.
Code: A C D E F G H J K L O P Q R S T U V X Y Z
Letter: T A O X L P H B F E N D G V R U C I M Z S
1. 2. ODACAVDO NOTATION UVRVFVYCAVDO CIVILIZATION 3. UCFUTFCAL CALCULATE 4. FLKA­XDZA LEFT­MOST 5. SVQHA­XDZA RIGHT­MOST 6. USVAVUCF CRITICAL 7. LEGSLZZ EXPRESS 8. PVQVA DIGIT 9. GDZVAVDO POSITION 10. ZTJASCUAVDO SUBTRACTION http://www.edhelperblog.com/cgi­bin/vspec.cgi
10/10