Numeration - IELTS Reading Sample with Explanation
IELTS Reading sample on Numeration is taken from IELTS Cambridge test 6 Test 2. IELTS Reading contains four reading passages and a total of 40 questions to be answered in 60 minutes. Each answer is worth one point and the raw score is converted to a band score on a scale of 0-9.
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Numeration - IELTS reading sample discusses how the numbers came into practice, and how people learn to use them in their daily lives. It also tells the history of algebra and arithmetic. The IELTS reading sample on numeration discusses and contains two types of questions:
- Sentence completion with a suitable ending
- True/false/not given
The IELTS reading passage topics include subjects like environmental science, global politics, health and fitness, tourism, trade and commerce, etc.
Numeration - IELTS Reading Passage
- One of the first great intellectual feats of a young child is learning how to talk, closely followed by learning how to count. From earliest childhood, we are so bound up with our system of numeration that it is a feat of imagination to consider the problems faced by early humans who had not yet developed this facility. Careful consideration of our system of numeration leads to the conviction that, rather than being a facility that comes naturally to a person, it is one of the great and remarkable achievements of the human race.
- It is impossible to learn the sequence of events that led to our development of the concept of number. Even the earliest tribes had a system of numeration that, if not advanced, was sufficient for the tasks that they had to perform. Our ancestors had little use for actual numbers; instead, their considerations would have been more of the kind Is this enough? Rather than how many? When they were engaged in food gathering, for example. However, when early humans first began to reflect on the nature of things around them, they discovered that they needed an idea of numbers simply to keep their thoughts in order. As they began to settle, grow plants, and herd animals, the need for a sophisticated number system became paramount. It will never be known how and when this numeration ability developed, but it is certain that numeration was well developed by the time humans had formed even semi-permanent settlements.
- Evidence of early stages of arithmetic and numeration can be readily found. The indigenous peoples of Tasmania were only able to count one, two, many; those of South Africa counted one, two, two and one, two twos, two twos and one, and so on. But in real situations, the number and words are often accompanied by gestures to help resolve any confusion. For example, when using the one, two, many types of system, the word many would mean, Look at my hands and see how many fingers I am showing you. This basic approach is limited in the range of numbers that it can express, but this range will generally suffice when dealing with the simpler aspects of human existence.
- The lack of ability of some cultures to deal with large numbers is not really surprising. European languages, when traced back to their earlier version, are very poor in number, words and expressions. The ancient Gothic word for ten, tachund, is used to express the number 100 as tachund tachund. By the seventh century, the word teon had become interchangeable with the tachund or hund of the Anglo-Saxon language, and so 100 was denoted as hund teontig, or ten times ten. The average person in the seventh century in Europe was not as familiar with numbers as we are today. In fact, to qualify as a witness in a court of law a man had to be able to count to nine!
- Perhaps the most fundamental step in developing a sense of number is not the ability to count, but rather to see that a number is really an abstract idea instead of a simple attachment to a group of particular objects. It must have been within the grasp of the earliest humans to conceive that four birds are distinct from two birds; however, it is not an elementary step to associate the number 4, as connected with four birds, to the number 4, as connected with four rocks. Associating a number as one of the qualities of a specific object is a great hindrance to the development of a true number sense. When the number 4 can be registered in the mind as a specific word, independent of the object being referenced, the individual is ready to take the first step toward the development of a notational system for numbers and, from there, to arithmetic.
- Traces of the very first stages in the development of numeration can be seen in several living languages today. The numeration system of the Tsimshian language In British Columbia contains seven distinct sets of words for numbers according to the class of the item being counted: for counting flat objects and animals, for round objects and time, for people, for long objects and trees, for canoes, for measures, and for counting when no particular object is being numerated. It seems that the last is a later development while the first six groups show the relics of an older system. This diversity of number names can also be found in some widely used languages such as Japanese.
- Intermixed with the development of a number sense is the development of an ability to count. Counting is not directly related to the formation of a number concept because it is possible to count by matching the items being counted against a group of pebbles, grains of corn, or the counter's fingers. These aids would have been indispensable to very early people who would have found the process impossible without some form of a mechanical aid. Such aids, while different, are still used even by the most educated in today's society due to their convenience. All counting ultimately involves reference to something other than the things being counted. At first, it may have been grains or pebbles but now it is a memorized sequence of words that happen to be the names of the numbers.
Numeration – IELTS Reading Questions
Questions 1-5
Complete each sentence with the correct ending from A-G in boxes 1-5 on your answer sheet:
- was necessary in order to fulfill a civic role
- was necessary when people began farming
- was necessary for the development of arithmetic
- persists in all societies
- was used when the range of number words was restricted
- can be traced back to early European languages
- was a characteristic of early numeration systems
Q 1) A developed system of numbering
Supporting sentence: As they began to settle, grow plants, and herd animals, the need for a sophisticated number system became paramount.
Keywords: grow plants, sophisticated number system, semi-permanent settlements, Development System, Numbering
Location in the passage: Paragraph 2
Answer: B. was necessary when people began farming
Answer explanation: Towards the end of paragraph 2 it is mentioned that a developed system of numbering was necessary when people began farming. So, the reason behind the development of the number system is clear from this. In the supporting sentence, “they” refers to the ancestors. Grow plants and herd animals signifies farming. At the time of farming, the need for a sophisticated number system was mandatory for them.
Q 2) An additional hand signal
Supporting sentence: For example, when using the one, two, many types of system, the word many would mean, Look at my hands and see how many fingers I am showing you. This basic approach is limited in the range of numbers that it can express, but this range will generally suffice when dealing with the simpler aspects of human existence.
Keywords: additional, hand signal, Look at my hands, range, human existence
Location in the passage: Paragraph 3
Answer: E. was used when the range of number words was restricted
Answer explanation: In the third paragraph, it is mentioned that an additional hand signal was used when the range of number words was restricted. The use of hand signals along with their types are given in the last 4 lines of paragraph 3. The word “limited” in the passage shows the restriction. So the answer option “was used when the number of words was restricted” seems the most justified one.
Q 3) In seventh-century Europe, the ability to count to a certain number
Supporting sentence: The average person in the seventh century in Europe was not as familiar with numbers as we are today. In fact, to qualify as a witness in a court of law a man had to be able to count to nine!
Keywords: Not familiar with numbers, count to nine, seventh-century, Europe, ability, a certain number
Location in the passage: Paragraph 4
Answer: A. was necessary in order to fulfill a civic role
Answer explanation: According to the information given in paragraph 4 about seventh-century Europe, it looks like that the ability to count to a certain number was necessary in order to fulfill a civic role. From the supporting sentence, qualifying as a witness in the court of the law indicates a civic role. The phrase “Had to be able to” emphasizes that it was necessary. Therefore, the answer option of A is the most suitable for sentence completion tasks.
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Q 4) Thinking about numbers as concepts separate from physical objects
Supporting sentence: Perhaps the most fundamental step in developing a sense of number is not the ability to count, but rather to see that a number is really an abstract idea instead of a simple attachment to a group of particular objects.
Keywords: Specific word, notational system, arithmetic, thinking, numbers, concepts, separate from, physical objects
Location in the passage: Paragraph 5
Answer: C. was necessary for the development of arithmetic
Answer explanation: According to the 5th paragraph, there is a clear hint that Thinking about numbers as concepts separate from physical objects was necessary for the development of arithmetic. The term abstract ideas indicate the concepts and the particular objects can be considered as physical objects. The first step towards the development of the number system shows the steady growth in terms of arithmetic.
Q 5) Expressing number differently according to class of item
Supporting sentence: Traces of the very first stages in the development of numeration can be seen in several living languages today. The numeration system of the Tsimshian language In British Columbia contains seven distinct sets of words for numbers according to the class of the item being counted: for counting flat objects and animals, for round objects and time, for people, for long objects and trees, for canoes, for measures, and for counting when no particular object is being numerated.
Keywords: Tsimshian language, seven distinct sets, class of item, Expressing number, differently, class of item
Location in the passage: Paragraph 6
Answer: G. was a characteristic of early numeration systems
Answer explanation: From the second line of paragraph 6, it is clear that expressing numbers differently according to the class of item was a characteristic of early numeration systems. In the supporting sentence, there is a phrase “the very first stages in the development of numeration.” This particular phrase signifies the early stages in the development of numeration.
Questions 6-14
Do the following statements agree with the information given in the passage? In boxes 6-14 on your answer sheet, write:
TRUE: If the statement agrees with the information
FALSE: If the statement contradicts the information
NOT GIVEN: If no information is given on this
Q 6) For the earliest tribes, the concept of sufficiency was more important than the concept of quantity.
Supporting sentence: Even the earliest tribes had a system of numeration that, if not advanced, was sufficient for the tasks that they had to perform. Our ancestors had little use for actual numbers; instead, their considerations would have been more of the kind Is this enough?
Keywords: System of numeration, sufficient, is this enough
Location in the passage: Paragraph 2
Answer: True
Answer explanation: Second to the fifth line of paragraph 2 denotes that the ancient tribes considered numeration as a basis for sufficiency rather than measuring quantity. It means that the concept of sufficiency was more important and the concept of quantity was less important to the people of that time. It clearly aligns with the sentence given in the question, this is absolutely correct information.
Q 7) Indigenous Tasmanians used only four terms to indicate numbers of objects.
Supporting sentence: The indigenous peoples of Tasmania were only able to count one, two, many
Keywords: Early stages of arithmetic, indigenous, Tasmania, South Africa
Location in the passage: Paragraph 3
Answer: False
Answer explanation: According to the third line of the third paragraph, the indigenous Tasmanians were able to count one, two, and many. It means the Tasmanian indigenous could count only 3 items - one, two, and many. It contradicts with the number given in the question which makes the statement a false one. They could not use 4 items to indicate their belongings - instead, they use 3 items - one, two, and many.
Q 8) Some peoples with simple number systems use body language to prevent misunderstanding of expressions of numbers.
Supporting sentence: But in real situations, the number and words are often accompanied by gestures to help resolve any confusion. For example, when using the one, two, many types of system, the word many would mean, Look at my hands and see how many fingers I am showing you.
Keywords: One, two, two and one, gestures, some people, simple number systems, body language, prevent misunderstanding, expressions of numbers
Location in the passage: Paragraph 3
Answer: True
Answer explanation: Third and fourth lines of paragraph 3 mention that more than depending on numbers, the ancient people trusted bodily behaviors for numeration. They used body language so that the possibilities of a misunderstanding of number expressions can be prevented. It is not that they replace the numeric expressions with body language - rather, body language and numeric expressions go side by side. This is exactly what the sentence in the question says.
Q 9) All cultures have been able to express large numbers clearly.
Supporting sentence: The lack of ability of some cultures to deal with large numbers is not really surprising.
Keywords: All cultures, able to express, large numbers, clearly, Lack of ability, European languages
Location in the passage: Paragraph 4
Answer: False
Answer explanation: According to the first 3 lines of the fourth paragraph, the European language didn’t understand numbers. In the first line of the same paragraph, it is mentioned the lack of ability to understand large numbers was quite expecting. So, it was not at all very surprising that not all cultures have a clear perception of the large numbers.
Q 10) The word 'thousand' has Anglo-Saxon origins.
Keywords: word, thousand, Anglo-Saxon origins
Location in the passage: Paragraph 4
Answer: Not Given
Answer explanation: In the fourth paragraph, the author of the passage mentioned a number of numeric expressions and their origins. This paragraph mainly holds the origin of wordy expression of the numbers and their origin. In the same paragraph, as well as in the entire extract, one can find about the origin of 10-100; however, there is no information about the word “thousand”. So, it cannot be marked as true or as false.
Q 11) In general, people in seventh-century Europe had poor counting ability.
Keywords: Hund teontig, seventh century in Europe, In general, people in seventh-century Europe, poor counting ability
Location in the passage: Paragraph 4
Answer: True
Answer explanation: According to the 5th to 7th line of paragraph 4, 7th-century people in Europe didn’t have a proper idea of numeration. It is applicable to any average person of 7th century Europe. They were not very familiar with the number system and the method of counting. In other words, it can be mentioned that their ability of counting was very poor and incorrect. So, the given sentence is absolutely correct.
Q 12) In the Tsimshian language, the number for long objects and canoes is expressed with the same word.
Supporting sentence: The numeration system of the Tsimshian language In British Columbia contains seven distinct sets of words for numbers according to the class of the item being counted: for counting flat objects and animals, for round objects and time, for people, for long objects and trees, for canoes, for measures, and for counting when no particular object is being numerated
Keywords: Tsimshian language, British Columbia, class of the item, number, long objects, canoes, same word
Location in the passage: Paragraph 6
Answer: False
Answer explanation: The supporting sentence is line 2-6 of paragraph 6. Here it is clearly mentioned that 7 distinct sets of words. So, it can never be claimed that the long objects and canoes are expressed with the same words. These 7 distinct sets are created for the numbers and these were classified as per the type of item which needs to be counted. So, it will not be wrong that the Tsimshian language was rich enough and it makes the sentence of the question false.
Q 13) The Tsimshian language contains both older and newer systems of counting.
Supporting sentence: It seems that the last is a later development while the first six groups show the relics of an older system. This diversity of number names can also be found in some widely used languages such as Japanese.
Keywords: Being numerated, later development, older system, Tsimshian language, systems of counting
Location in the passage: Paragraph 6
Answer: True
Answer explanation: In paragraph 6, lines 5-7 denotes that the language contained both ancient and modern approaches. After providing the information about the seven diverse sets in the Tsimshian language, the author goes on to describe the relics of an older number system. The first six sets were the result of the older number system while the last one was the result of later development of number systems. It means the number system of the Tsimshian language was a combination of both old and modern number systems.
Q 14) Early people found it easier to count by using their fingers rather than a group of pebbles.
Keywords: Early people, easier, using their fingers, a group of pebble
Location in the passage: Paragraph 7
Answer: Not Given
Answer explanation: In the entire passage, there is no mention of the ease of using the pebbles and fingers for the purpose of counting. The last paragraph shows the possibility of counting the items by matching them and it can be done by using a group of pebbles, corns, or fingers. But the ease of these means for the early people is not given in the passage - therefore, this answer cannot be marked as true or as false.
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