Numeration - IELTS Reading Answers & Explanations
From Cambridge IELTS 06 Academic Reading Test 2 · Part 3 · Questions 27–40
Reading Passage
You should spend about 20 minutes on Questions 27-40, which are based on Reading Passage 3 below.
Numeration
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 developing the concept of number. Even the earliest of 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 number 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 type 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 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 memorised sequence of words that happen to be the names of the numbers.
Questions
Questions 27–31 Matching Sentence Endings
Complete each sentence with the correct ending, A-G, below.
A. was necessary in order to fulfil a civic role.
B. was necessary when people began farming.
C. was necessary for the development of arithmetic.
D. persists in all societies.
E. was used when the range of number words was restricted.
F. can be traced back to early European languages.
G. was a characteristic of early numeration systems.
Questions 32–40 True / False / Not Given
Do the following statements agree with the information given in Reading Passage 3?
TRUE if the statement agrees with the information
FALSE if the statement contradicts the information
NOT GIVEN if there is no information on this
Answers & Explanations Summary
| # | Answer | Evidence | Explanation |
|---|---|---|---|
| Q27 | B | As they began to settle, grow plants and herd animals, the need for a sophisticated number system became paramount | Excerpt/Passage Explanation: The passage explains that when people started to live in permanent spots to farm and look after animals, they absolutely needed a high-level system for counting. Answer Explanation: The answer means that having a complex and advanced way to use numbers was required once humans started living in one place and farming. Reason For Correctness: The correct answer is B because the passage states that as early humans began to settle down, grow crops, and raise animals (which are the activities of farming), having a sophisticated or 'developed' number system became very important. The text uses the word 'paramount' to show how necessary this system became. |
| Q28 | E | 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 type of system, the word many would mean, Look at my hands and see how many fingers I am showing you | Excerpt/Passage Explanation: The passage explains that when people have only a few words for numbers, they use hand movements and fingers to show exactly how many things they are talking about. Answer Explanation: The answer E means that hand signals were used as a tool when a language only had a small number of words to describe amounts. Reason For Correctness: The correct answer is E because the passage notes that some early groups of people had very limited counting systems, using only words like 'one', 'two', and 'many'. To avoid confusion when using such a 'limited' or restricted range of words, they would use hand gestures—like showing a specific number of fingers—to clarify exactly what they meant. The word 'gestures' in the text serves as a synonym for 'hand signal', and 'limited' explains the word 'restricted'. |
| Q29 | A | In fact, to qualify as a witness in a court of law a man had to be able to count to nine | Excerpt/Passage Explanation: The passage explains that in the 600s (the seventh century) in Europe, if a man wanted to be a witness in a legal case, he was required to prove he could count up to the number nine. Answer Explanation: The answer means that in Europe many years ago, a person had to know how to count to a specific number to perform a duty for their community, like speaking in a court of law. Reason For Correctness: The correct answer is A because the passage states that in seventh-century Europe, a man needed to be able to count to nine to 'qualify as a witness in a court of law'. Being a witness in court is a type of civic role or duty. This shows that even a very basic ability to count was a requirement for participating in legal or public activities at that time. |
| Q30 | C | 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 | Excerpt/Passage Explanation: The passage says that when a person can think of a number word as its own thing, without thinking about a specific object, they can then start to create number systems and study math. Answer Explanation: The answer means that people needed to learn how to think about numbers on their own, without looking at real things, before they could start doing math. Reason For Correctness: The correct answer is C because the passage explains that the first step toward arithmetic (math) is being able to think of a number as its own word or idea. For example, instead of thinking only about "four birds," a person must understand the word "four" by itself. The text says that once a person can think of a number independently from an object, they are ready to develop number systems and "arithmetic." |
| Q31 | G | 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 | Excerpt/Passage Explanation: The passage explains that the Tsimshian language has seven different ways to say numbers based on the group or 'class' the object belongs to. It mentions that almost all of these groups are leftovers from an 'older system' from the past. Answer Explanation: The answer means that using different words for numbers based on the type of object being counted is a feature found in very old systems of counting. Reason For Correctness: The correct answer is G because the passage gives an example of a language (Tsimshian) that has many different ways to name the same number depending on what kind of thing is being counted (like flat objects, round objects, or people). It says these differences are 'relics of an older system,' meaning it was a common trait or 'characteristic' of early ways people counted. |
| Q32 | TRUE | 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 | Excerpt/Passage Explanation: The passage explains that early people didn't use specific numbers very much. Instead, when they were collecting food, they only thought about whether they had enough food to survive, not the specific total amount they had. Answer Explanation: The answer means that ancient people cared more about having what they needed than knowing the exact total count of things. Reason For Correctness: The correct answer is TRUE because the passage explains that early humans (our ancestors) did not really need exact numbers for their daily lives. For example, when they were looking for food, they focused on whether they had "enough" (which means sufficiency) rather than asking "how many" (which means quantity). The text explicitly contrasts these two ideas to show what was more important to them. |
| Q33 | FALSE | The indigenous peoples of Tasmania were only able to count one, two, many | Excerpt/Passage Explanation: The passage tells us that these people had a very simple way of counting that only included three words: the word 'one', the word 'two', and the word 'many'. Answer Explanation: The answer is FALSE because the statement says they used four words to count, but the text says they only used three words. Reason For Correctness: The correct answer is FALSE because the passage states that the indigenous peoples of Tasmania used the words 'one, two, many' to count. This equals a total of three terms. Since the question claims they used four terms, the information in the statement contradicts the information provided in the passage. |
| Q34 | TRUE | But in real situations the number and words are often accompanied by gestures to help resolve any confusion | Excerpt/Passage Explanation: The passage explains that in real life, when people talk about numbers, they often use hand or body movements at the same time to make sure the other person understands them clearly and doesn't get confused. Answer Explanation: The answer means that the statement correctly matches the information given in the book about how some people with simple ways of counting use their bodies to communicate. Reason For Correctness: The correct answer is TRUE because the passage mentions that when people use simple counting systems (like saying 'one, two, many'), they often use 'gestures' to help people understand exactly what they mean. In this context, 'gestures' is a synonym for 'body language', and 'resolve any confusion' is a synonym for 'prevent misunderstanding'. |
| Q35 | FALSE | The lack of ability of some cultures to deal with large numbers is not really surprising | Excerpt/Passage Explanation: The passage says it is expected that some groups of people were not able to count or use very big numbers. Answer Explanation: The answer means it is not true that every group of people in history could count to high numbers or describe big amounts well. Reason For Correctness: The correct answer is FALSE because the passage states that some groups of people did not have the words or skills to talk about large numbers. For instance, it mentions that some cultures only had words for "one, two, many," and even old European languages were not very good at expressing big numbers. This directly contradicts the idea that all cultures could express large numbers clearly. Key phrases to look for are "lack of ability" and "some cultures" in relation to "large numbers." |
| Q36 | NOT GIVEN | 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 | Excerpt/Passage Explanation: The passage explains the old words used for 'ten' and 'one hundred' in the Anglo-Saxon language, but it says nothing about the word ‘thousand’. Answer Explanation: The answer is NOT GIVEN because the reading text does not provide any information about where the word 'thousand' comes from. Reason For Correctness: The correct answer is NOT GIVEN because, although the passage talks about the history of number words like 'ten' and 'one hundred' in the Anglo-Saxon language, it never mentions the word 'thousand' or its origin. Since the text does not give us this specific information, we cannot say if the statement is true or false. To find this answer, a learner should look for keywords like 'thousand' and 'Anglo-Saxon' and compare what the text says. |
| Q37 | TRUE | 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 | Excerpt/Passage Explanation: The passage says that people in seventh-century Europe did not know numbers as well as modern people do. It gives an example that to be a witness in court, a person only had to know how to count to nine. Answer Explanation: The answer means that most people living in Europe during the seventh century (the 600s) were not very good at counting or using numbers compared to people today. Reason For Correctness: The correct answer is TRUE because the text clearly states that the average person during that time was "not as familiar with numbers" as people are now. To support this, it mentions that a man only needed to be able to count to nine to be allowed as a witness in court. This low requirement suggests that a general "poor counting ability" was common, as being able to count only to nine is considered a very basic skill today. |
| Q38 | FALSE | 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 | Excerpt/Passage Explanation: The passage shows that the language uses seven separate groups of words for counting different things. In the list provided, 'long objects and trees' and 'canoes' are mentioned as two different categories, meaning they utilize different words. Answer Explanation: The answer FALSE means that the statement is incorrect according to the information provided in the passage. Reason For Correctness: The correct answer is FALSE because the passage explains that the Tsimshian language has seven 'distinct' or different groups of words for counting. It lists 'long objects and trees' as one group and 'canoes' as a separate group. If they have distinct sets of words for different groups, they do not use the same word for both. |
| Q39 | TRUE | 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 | Excerpt/Passage Explanation: The passage states that the Tsimshian language has seven ways to count. Six of these ways are part of an old system, and the seventh way was developed more recently. Answer Explanation: The answer is TRUE because the passage explains that the Tsimshian language uses groups of words for counting that come from two different times: some are very old, and one is newer. Reason For Correctness: The correct answer is TRUE because the text describes the Tsimshian language as having seven different sets of words for numbers. It specifically says that the first six groups are 'relics of an older system' and the seventh group is a 'later development.' In this context, 'later development' means it is a newer system. Because the language has both 'older' and 'later' (newer) parts, the statement is correct. Key synonyms to note are 'relics' for things from the past and 'later development' for something created more recently. |
| Q40 | NOT GIVEN | 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 | Excerpt/Passage Explanation: The passage explains that counting can be done by pairing the items you are counting with other objects like small stones, corn seeds, or fingers, but it does not say which of these is easier to use. Answer Explanation: The answer is NOT GIVEN because the passage does not provide information to determine if using fingers was easier than using pebbles. Reason For Correctness: The correct answer is NOT GIVEN because, although the text mentions that early people used "pebbles," "grains of corn," or "fingers" as tools to help them count, it never compares these methods. It does not state that one method was "easier" than the others; it simply lists them as options that were essential for people who could not yet count using abstract numbers. |