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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 left-most digit equals to 5 times 60 times 60, or 18,000. The middle digit equals to 4 times 60, or 240. And the right-most 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 ? 2015 edHelperName _____________________________Date ___________________Mathematics in Mesopotamia1.??Which of the following about mathematics in Mesopotamia is correct???People in Mesopotamia used a dot to denote zero.??The Sumerian numeral system is commonly known as the Arabic numerals.??The Sumerians counted things with twelve as a unit.??People in Mesopotamia said a full circle is equal to 360 degrees.2.??How many minutes did the Sumerians say an hour has???15??60??30??903.??How would people in Mesopotamia inscribe 10,925???5 x 36 x 60 + 4 x 30 + 5??6 x 30 x 60 + 2 x 60 + 5??3 x 60 x 60 + 2 x 60 + 5??12 x 30 x 30 + 4 x 30 + 54.??Which of the following statements is correct???People in Mesopotamia did not apply mathematics to their daily life.??Hammurabi was an Assyrian King.??Mathematics began to take shape at the same time that the world's first civilization started to emerge in Mesopotamia.??People in Mesopotamia developed their numerals around 500 A.D.5.??How would the Sumerians write 65?????????6.??Who invented the world's first banking system???The Arabs??The Indians??The Babylonians??The Chinese?Name _____________________________Date ___________________Mathematics in Mesopotamia7.??Which two Sumerian numerals used the same symbol???1 and 10??1 and 60??1 and 32??1 and 308.??How would a Sumerian express the result of 80 minus 73?????????9.??Given that the Sumerians used a sexagesimal system, how many days a year do you think a Sumerian calendar had???436??500??360??24710.??Knowing that the Sumerian numeral system was a positional one, which large number does??translate to???925,392??1,742,149??872,903??1,548,305?Name _____________________________Date ___________________Mathematics in MesopotamiaCompare and contrast the Sumerian numeral system and the Arabic numeral system.?Mathematics in Mesopotamia?By Vickie Chao??dynastynumeralsconceptcompareobsoletesexagesimalright-mostinscribesubtractionnumeralcalculatemultiplicationconceptslikewiseunsolvedsolutionremainDirections:??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?(1)??_______________________?? 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?(2)??_______________________?? 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 ().?(3)??_______________________??, they would express 125 () as the sum of two units of 60 () and one 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?(4)??_______________________??. 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?(5)??_______________________??, 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?(6)??_______________________?? at the time. This issue would?(7)??_______________________???(8)??_______________________?? until around 500 A.D. when the Indians developed the Arabic 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?(9)??_______________________?? - positional or place value. Let's(10)??_______________________?? 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?(11)??_______________________???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?(12)??_______________________???. The left-most digit equals to 5 times 60 times 60, or 18,000. The middle digit equals to 4 times 60, or 240. And the?(13)??_______________________?? digit equals to 7.?????With their advanced knowledge in numerals, people in Mesopotamia were excellent mathematicians. When applied to their daily life, they developed formulas to?(14)??_______________________?? weights, areas, volumes, and wages. Students from that time needed to study mathematics at school, too. They had to learn how to do addition,?(15)??_______________________??,(16)??_______________________??, division, and fractions. During the reign of Hammurabi (1792 B.C. - 1750 B.C.) of the 1st?(17)??_______________________?? 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 ? 2015 edHelper?Name _____________________________Date ___________________Mathematics in Mesopotamia1.??Which of the following about mathematics in Mesopotamia is correct???People in Mesopotamia used a dot to denote zero.??The Sumerians counted things with twelve as a unit.??People in Mesopotamia said a full circle is equal to 360 degrees.??The Sumerian numeral system is commonly known as the Arabic numerals.2.??How many minutes did the Sumerians say an hour has???30??15??60??903.??How would people in Mesopotamia inscribe 10,925???5 x 36 x 60 + 4 x 30 + 5??6 x 30 x 60 + 2 x 60 + 5??3 x 60 x 60 + 2 x 60 + 5??12 x 30 x 30 + 4 x 30 + 54.??Which of the following statements is correct???Hammurabi was an Assyrian King.??People in Mesopotamia developed their numerals around 500 A.D.??Mathematics began to take shape at the same time that the world's first civilization started to emerge in Mesopotamia.??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 Arabs??The Indians??The Babylonians??The Chinese?Name _____________________________Date ___________________Mathematics in Mesopotamia7.??Which two Sumerian numerals used the same symbol???1 and 10??1 and 60??1 and 32??1 and 308.??How would a Sumerian express the result of 80 minus 73?????????9.??Given that the Sumerians used a sexagesimal system, how many days a year do you think a Sumerian calendar had???247??436??360??50010.??Knowing that the Sumerian numeral system was a positional one, which large number does??translate to???1,548,305??925,392??872,903??1,742,149?Name _____________________________Date ___________________?(Key 1 - Answer ID # 0422037)Fill in the missing letter.Hint: Cross off each letter from this list after using it.??r??i??o??o??g??g??i??t??l??d??u??a??a??s??i??m??n??z??e??a??a??s??e??r??o1.??ri____ht-most2.??insc____ibe3.??calcu____ate4.??addit____on5.??ma____hematics6.??obsol____te7.??co____pare8.??po____ition9.??nume____al10.??co____cept11.??subtr____ction12.??iss____e13.??sex____gesimal14.??p____wer15.??expre____s16.??uns____lved17.??knowle____ge18.??lit____rally19.??rei____n20.??s____lution21.??not____tion22.??critic____l23.??civili____ation24.??multipl____cation25.??bank____ng?????Mathematics in Mesopotamia - Answer Key1????People in Mesopotamia said a full circle is equal to 360 degrees.2????603????3 x 60 x 60 + 2 x 60 + 54????Mathematics began to take shape at the same time that the world's first civilization started to emerge in Mesopotamia.5????6????The Babylonians7????1 and 608????9????36010????1,548,305?Mathematics in MesopotamiaBy 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?(1)??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?(2)??numeral???system, using a base of sixty. In scientific terms, that system is called a?sexagesimalsystem. 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 ().?(3)??Likewise??, they would express 125 () as the sum of two units of 60 () and one 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?(4)??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?(5)??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?(6)??solution???at the time. This issue would?(7)??remain???(8)??unsolved???until around 500 A.D. when the Indians developed the Arabic 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?(9)??concept???- positional or place value. Let's?(10)??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?(11)??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?(12)??inscribe???. The left-most digit equals to 5 times 60 times 60, or 18,000. The middle digit equals to 4 times 60, or 240. And the?(13)??right-most???digit equals to 7.?????With their advanced knowledge in numerals, people in Mesopotamia were excellent mathematicians. When applied to their daily life, they developed formulas to?(14)??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,?(15)??subtraction??,?(16)??multiplication??, division, and fractions. During the reign of Hammurabi (1792 B.C. - 1750 B.C.) of the 1st?(17)??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!Answers to Reading Comprehension Questions1????People in Mesopotamia said a full circle is equal to 360 degrees.2????603????3 x 60 x 60 + 2 x 60 + 54????Mathematics began to take shape at the same time that the world's first civilization started to emerge in Mesopotamia.5????6????The Babylonians7????1 and 608????9????36010????1,548,305?Answer Key 0422037Key # 11.??right-most2.??inscribe3.??calculate4.??addition5.??mathematics6.??obsolete7.??compare8.??position9.??numeral10.??concept11.??subtraction12.??issue13.??sexagesimal14.??power15.??express16.??unsolved17.??knowledge18.??literally19.??reign20.??solution21.??notation22.??critical23.??civilization24.??multiplication25.??banking???? ................
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