METHODS OF TEACHING

Профильное обучение “Information technologies”

Тексты для чтения и развития навыков устной речи для учащихся профильных 11-х классов

UNIT 1

Learning to count

Did you ever try to imagine what the world would be like if no one had ever learned how to count or how to write numbers? We are so in the habit of using numbers that we rarely think of how important they are to us.

For example, when we open our eyes in the morning we are likely, first of all, to look at the clock, to see whether it is time to get up, but if people had never learned to count there would be no clocks. We should know nothing of hours or minutes or seconds. We could tell time only by the position of the sun or the moon in the sky; we could not know the exact time under the best conditions, and in stormy weather we could only guess whether it was morning or noon or night.

The clothes we wear, the houses we live in, and the food we eat, all would be different if people had not learned how to use numbers. All day long we either use numbers ourselves, or we use things that other people have made by using numbers.

It has taken thousands of years for people to learn how to use numbers or the written figures which we call “numerals”. For a long time after men began to be civilized such simple numbers as two and three were all they needed. For larger numbers they used words in their various languages which corresponded to such expressions of our own as “lots” of people, a “heap” of apples, a “school” of fish, and a “flock” of sheep. For example, a study of thirty Australian native languages showed no number above four, and in many of these languages there were number names for only one and two, the larger numbers being expressed simply as “much” or “many”.

1. Answer the following questions.

1. What would the world be like if people had never learned how to count or how to write numbers?

2. What was the role of fingers in the process of learning how to count?

3. What kind of words did people use for larger numbers?

4. What did a study of thirty Australian languages show?

 2. Complete the following sentences.

1. We are so in the habit of using numbers that we rarely think of …

2. If people had never learned to count we could tell the time only by …

3. If people had not learned how to use numbers …

4. It has taken thousand of years for people to learn how to use numbers or …

5. A study of thirty Australian languages showed no number above four, and in many of these languages there were number names for …

3. Express in English.

1. Мы так привыкли пользоваться числами, что мы редко задумываемся о том, насколько они важны для нас.

2. Людям потребовались тысячи лет, чтобы научиться пользоваться числами.

3. Очень долго люди обходились числами два и три.

4. Для больших чисел они использовали такие слова как множество людей, груда яблок, стая рыб, стадо овец.

UNIT 2

Scales of counting

You know that the Latin word “digit” means “finger”. Because we have five fingers on each hand, people began, after many centuries, to count by fives. Later they found it more convenient to count by tens, using the fingers of both hands. We still use this “scale“ in counting; that is, we count to ten; then by ten tens; then to ten times ten tens; and so on.

In early days people often counted on a scale of three or four instead of ten, and sometimes other number scales were used. Because we have ten toes as well as ten fingers, some people counted fingers and toes together and used a number scale of twenty. In at least one tribe the people said “man finished” for this number. The French in early times counted by twenty (vingt). Even today they say “four twenties” (“quatre vingt”) for eighty, and “four twenties and ten” (“quatre vingt dix”) for ninety; it was not long ago that they went as far as “nineteen twenties” for three hundred eighty. In the English language, also this plan was used for a long time; as when we said, “The days of a man’s life are three score years and ten”, the word “score” meaning twenty.

There is also much evidence that twelve is often used as a scale in counting; as 12 inches = 1 foot; 12 ounces = 1 pound (old style); 12 pence = 1 shilling; 12 units = 1 dozen; and 12 lines = 1 inch. There are certain advantages in using a scale of twelve; because 1/3 of 12 pence = 4 pence, whereas 1/3 of 10 cents = 3.3333 + cents – a difficult number to work with.

Whatever scale we use, we need as many digits as the scale contains. For example, in our scale of ten we need ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. If we used a scale of eight, we should need 0, 1, 2, 3, 4, 5, 6, 7, and we would write eight as 10 (1 eight and no units); nine would be 11 (1 eight and 1 unit); sixteen would be 20 (2 eights and no units); and so on. If we were brought up with such a system it would be just as easy as our scale of ten; in some respects it would be even easier because eight is more easily divided into fourths and eighths (fractions that are often needed) than ten.

1. Answer the following questions.

1. What does the word “digit” mean in Latin?

2. Why did people begin to count by fives or by tens?

3. What kind of “scale” do we still use in counting?

4. What other number scales were used by people in early days?

5. In what ways did the French count in early times?

6. What are the advantages of using a scale of twelve?

7. Is the number of digits we need for counting on different scales the same?

8. What digits should we need if we used the scale of eight, for example?

9. Why in some respects would it be even easier to use the scale of eight?

2. Complete these sentences using words from the text. The first letter of each word is given to help you.

1. Digits means f______ in Latin.

2. Later people found it more c______ to count by tens.

3. In early days people often counted on a scale of three or four i_____ of ten.

4. There are many e___________ that twelve are often used as a scale in counting.

5. There are c___________ advantages in using a scale of twelve.

6. In some r_______ would it be even easier to use the scale of eight?

Key: 1. fingers; 2. convenient; 3. instead; 4. evidences; 5. certain; 6. respects

3. Complete the following sentences.

1. Because we have ten toes as well as ten fingers, some people counted fingers and toes together and used ________

2. Whatever scale we use, we need as many digits as _________

3. If we used the scale of eight, we should need ___________

4. If we were brought up with a scale of eight it would be just as easy as _____

UNIT 3

Naming the numbers

Number names were among the first words used when people began to talk. They were needed in speaking of days, sheep, men, and all sorts of things that people had to deal with in their everyday lives.

Some of these words have probably not changed a great deal in many thousands of years. This list shows how similar some of the number names are in several different languages.

How did it come about that these words are so much alike in all these different languages?

Find India on the map. In ancient days the people who lived in this country spoke a language known as Sanskrit. Some of these people travelled west to Greece and Italy, and to other European lands farther north and west. The language spoken by the people who lived in these countries later are called by different names (Latin, Greek, German, and so on); but they are grouped together in a class known as Indo-European languages because the very beginning of many of words in each language came from the ancient Sanskrit. For instance, the Sanskrit word for seven was “septa”. You can see by looking at the chart how the other names for seven have grown out of this Sanskrit word. If you are interested in tracing the history of the number names, you can find out a great deal about it in any large dictionary.

1. Answer the following questions.

1. What language did the people who lived in ancient India speak?

2. Where did some of these people travel?

3. What are the Indo-European languages?

4. Where did many of the words in each Indo-European language come from?

2. Arrange the following words in pairs of synonyms:

rarely, call, age, for example, agree with, century, seldom, for instance, name, correspond, convenient, suit, evidence, divide, suitable, proof, multiply.

3. Express in English:

1. Названия для чисел были среди первых слов, когда люди начали разговаривать.

2. Как же случилось, что эти слова так сильно похожи в разных индо-европейских языках?

3. Вы можете найти много об истории названий чисел в любом большом словаре.

UNIT 4

Reserved For God

The number “one” was looked upon by some ancient peoples as being different from other numbers. In the old Hebrew and Arabic languages counting began with two, one being reserved for God alone, as in the expressions: “There is one God“, or “God is one”.

Even in Europe in the early days, zero (0) and one (1) were not called digits, because zero was not considered a number and one was looked upon as the source of all numbers and not as a number itself. Writers of that time applied the name “digits” only to the eight numerals from 2 to 9. Nowadays, however, the first ten numerals, beginning with 0, are usually called digits.

Ordinals

It is a curious fact that in many languages the words meaning “first” and “second” do not come from the words meaning “one” and “two”.

Also, it is easy to see that the word “second” is not related to the word “two”. All this goes to show that early people did not connect “the second boy” with “two boys”. It was not until the human race had developed considerably that people began to see the relationship and to relate “third” to “three”, and “fourth” to “four”.

SepteM, Octo, NoveM, Decem

(One Hypotheses)

Don’t these Latin number names remind you of the names of the last four months in our year? You may wonder why the name of the our ninth month (September) begins with septem (seven), our tenth month (October) with octo (eight), and so on with November and December. The reason is that the calendar year could, of course, begin with any month that people might choose. In the Latin World, which included about all the Western Europe at the time the present months were named, the year was often taken as beginning in March. When this was done, the seventh month was September and the tenth was December.

1. Answer the following questions.

1. How was the number “one” looked upon by some ancient people?

2. What were “zero” and “one” considered to be in ancient Europe?

3. Why are the words “first” and “second” not related to the words “one” and “two”?

4. Why does the name of our ninth month, (September) begin with septem (seven), our tenth month (October) with octo (eight) and so on?

2. Arrange these words in pairs of synonyms:

form, a few, principal, in particular, shape, wish, main, several, in general, want, suppose, except, though, assume, wait for, although.

3. Arrange these words as pairs of antonyms:

whole, different, real, abstract, adding, indifferent, fractional, concrete, certain, like, easy, unreal, subtracting, uncertain, unlike, difficult.

4. Complete these sentences using words from ex. 2 and 3.

1. It is interesting to know how some of the numerals of today came to have their present __________.

2. Why are any numbers called “______” and others “_____”?

3. I’m going to tell you a few things about such matters as _______ and _________.

4. The idea of number separated itself from the objects counted and thus became an ______ idea.

5. As this abstract idea came into contact with the needs of everyday life it became more and more ______.

Key: 1. shape; 2. whole, fractional; 3. adding, subtracting; 4. abstract; 5. real.

Compiled by Youdif Boyarskaya,
School No. 814, Moscow