Read the text and say why Math is one of the most important subjects at school.



Educators consider mathematics as one of the best media for the development of thinking skills. The often-heard opinion that a person who is good in mathematics could be a good chess player does not refer to computational ability but rather to reasoning ability. In the process of teaching mathematics, the teacher must be able to seize opportunities for developing the skills of reasoning, for developing in the children habits of organized thinking.

Mathematics should not be regarded as an isolated body of knowledge. The teacher should be able to see mathematics in the environment and in other disciplines. This is pedagogically important, since the teacher must use or provide experiences or situations that are the starting points for children to discover and develop the inherent mathematics. In technical language, we say that a physical situation is used to introduce and develop a "mathematical model" of the reality of the situation. On the other hand, the teacher who can readily see mathematics in the environment may be able to point to those different situations to which similar mathematical descriptions apply.

National drives and politics impact curricular programmes inmathematics. The teacher should become aware of national goals and policies and should then seek to bring about a closer relation between what is taught in the classroom and what is learned and done outside of it in terms of these national efforts, at least within the childs surroundings or community. Examples might include development of the countryside, better nutrition improved health and sanitation, and population education. Economics oriented activities may be simulated in the classroom.

Special teaching plans are needed to help a child understand "volume", not only as something upon the button of a radio set, which is within the childs experience, but also as a mathematical concept of the quantity of space occupied. Again, the younger children usually think of multiplication as repeated addition. They, therefore, may find it confusing to conceptualize 3/4 x 1/4, where repeated addition does not apply. The sensitive teacher who anticipates this difficulty would plan her teaching strategy to broaden the idea of multiplication before confusion arises. A similar situation arises when children are drilled in subtraction to use the following language:

10 take away 1 is 9. 10 take away 2 is 8. 10 take away 3 is 7.

The drill emphasizes the "take away" idea of subtraction to the exclusion of comparison (i.e., how much more, or how much less), which also invokes subtraction.


Read the text and be ready to tell about the most important milestones in the history of the number system.

Some facts on the development
of the number system


Counting represents a very important milestone in the progress of civilization. Of course there were no number names at first; so counters were used. For counters man used sticks, pebbles, his fingers, and in some instances, his toes also. In fact the word calculus comes from the Latin, meaning pebble; our numerals are called digits from the Latin, meaning finger.

It is possible to mention only a few important achievements in the history of mathematics. Historical records give evidence of the astronomical and arithmetical achievements of the early Babylonians, Sumerians, and Chinese. Somewhere in the distant past man learned that number was useful for civilized living. As early as 5,700 B.C. predecessors of the Babylonians had calendar and a type of practical arithmetic.

Only about 300 years ago a great mathematician and philosopher, Rene Descartes (1596-1650), represented number pairs by points. This creation made possible the great advance in science and mathematics during the eighteenth century. In 1642 one of the greatest minds of all time Isaac Newton was born (1642-1727). Newton was one of the inventors of the calculus which is now studied by college students who are seriously interested in mathematics or physical science.

Like Archimedes, Galileo, Copernicus and Newton, Lobachevsky (1792-1856) is one of those who laid the foundations in science. Lobachevsky created one of the greatest masterpieces of mathematics non-Euclidean geometry.

Our number system uses only the symbols 0, 1, 2, 9; it has base ten and positional notation. Thus any integer can be expressed with these symbols in various combinations and arrangements. The base of our system is ten. Ten is probably the base because we have ten fingers and the fingers were used in the early stages of counting.

It is not known when or by whom zero (nought) was invented. Historians thinks that zero was introduced by the Hindus or the Babylonians not later than in the ninth century A.D. and probably as early as the second century B.C. The invention of zero and our number system is one of the greatest achievements of the human race, without which the progress of science, industry, and commerce could be impossible. This new system was introduced in Europe by Arabs, or Moslems, at about the beginning of the tenth century. These new numbers were used, and finally, after about five centuries, the decimal system won the battle.


Read the text and say how the witty vizier managed to cheat the king. Make use of the vocabulary list:


desire ;

to fulfill ;

chessboard ;

grain ;

wheat ;

bushel , ᒺ;

to be in debt .


You probably know that the game of chess so popular nowadays all over the world comes from India. According to an old legend it was invented by king Shirhams vizier Sissa Ben Dahir and presented to the king by the latter. The King was very pleased and asked Sissa Ben whether he could do anything to thank him for the present. His viziers desire seemed quite easy to fulfill. He asked the king to give him a grain of wheat to put on the first square of the chessboard, and two grains to put on the second square, and four grains to put on the third square and eight grains to put on the fourth and so on doubling the number for each square that came next. He said he wanted the grains to cover all 64 squares of the board.

The king thought his vizier did not ask too much for what he had done and said that he would certainly give him what he asked for. And he told his men to bring a large bag full of wheat.

But when the counting began, with 1 grain for the first square, 2 for the second, 4 for the third and so on, the bag was emptied before the twentieth square was covered with wheat. More bags were brought before the king but the number of grains needed increased so rapidly that the king soon saw he would not be able to keep his word.

The thing is that a bushel of wheat contains about 5,000,000 grains. The king had, certainly, no idea of it and did not expect that he would have to give 4000 billion bushels to Sissa Ben.

Since the world production of wheat averages about 2,000,000,000 bushels a year, the amount of wheat asked by the vizier qualed the worlds wheat production for the period of some two thousand years.

Thus king Shirham found that he either had to remain constantly in debt to his vizier or cut his head off. He thought it best to choose the latter alternative.


Read the text and be ready to answer the questions:

1. Which mobile computer (laptop or notebook) is considered to be technically smaller in size?

2. What is the average weight of a notebook computer?

3. Why did the notebook originally weigh less than the laptop?

4. Why is the size of portable computers decreasing nowadays?

5. What are the reasons the term "laptop" is becoming used not so often?

6. What mobile computers are becoming mainstream devices?

7. Why arent netbooks perfect yet?


Nowadays, we cannot imagine our life without computers and the fact is that they have become so important that nothing can replace them. They seem to be everywhere today. Since 1948 when the first real computer has been invented our life has changed so much that we can call it real digital revolution.

First computers differed from today's ones. They were so big that they occupied whole rooms or buildings being relatively slow. They were not faster than modern simple watches or calculators. Nowadays they are also used by scientist and they may also be as big as the old ones but they are millions times faster. They can perform many complex operations simultaneously and scientist practically can't do without them. Thanks to them people have an access to various information. Gathering data has never been simpler than now. They are not only used in laboratories but also in factories to control production. Sometimes computers make other computers.

But not only in science and industry computers are being used. Thanks to them modern medicine can diagnose diseases faster and more thoroughly. Also in banking system computers have become irreplaceable. Furthermore, architects, designers and engineers can't imagine their work without computers. These machines are really everywhere and we depend on them also in such fields as criminology.

Moreover, computers are wide-spread in education. Except their classic tasks such as administration and accountancy they are used in process of learning. Firstly, they store data which help students to gain information. Secondly, thanks to special teaching techniques and programs they improve ours skills of gaining knowledge. They have become so popular that not knowing how to use them means to be illiterate.

Of course there is also dark side of computer technology because every invention brings us not only benefits but also threats.


1. Computers save storage place. Imagine how much paper would have to be used, how many trees would have to be cut just to store information which is today on hard disks, CDs, and memory cards.

2. Computers can calculate and process information faster and more accurate than a human.

3. Computers improve our office work

4. We can communicate with whole world very fast and cheap using the Internet.

5. Computers are user-friendly. We can watch videos and listen to the music having only a PC. We can also buy a laptop which is smaller, and use it outside anywhere we want.



1. Computers are dangerous to our health. Very often parents want to have a rest and don't draw enough attention to how long their children use computer.

2. Computers sometimes break down and you can lose your data. If you have the Internet connection you have to be particularly careful and download anti-virus programs.

3. Violence and sex. The main threat to younger users of computers is the Internet pornography and bloody games.

4. Another threat is that you can be computer addict.

Computers are practically irreplaceable and we can't make without them any more. They are everywhere: at our homes, schools, at work, in our cars.




Read the text and decide if the following statements are true (T) or false (F).

1. Hardware is known as something you can actually touch.

2. The pages and the ink of a book are the hardware analogy.

3. The main memory refers to physical memory that is internal to the computer.

4. There are two different types of memory: the main memory and the random access memory.

5. Devices which can be connected to the CPU are known as

6. A keyboard is the most commonly used output device.

7. To display the processed data an input device is used.

8. Mass storage devices retain data even when the computer is turned off.


Is there really a difference between a laptop and notebook computer? For most people shopping for a mobile (or portable) computer today, the short answer is "no". In fact, the difference between a laptop and notebook today is mainly what the manufacturer chooses to call its product. Technically and traditionally, the difference between the two is a matter of size.

Notebook computers typically weigh less than six pounds and are small enough to fit easily in a briefcase. Laptop computers are small enough too that they can sit on your lap. Nowadays, laptop computers are more often called notebook computers, though technically laptops are somewhat larger in size than notebooks.

The laptop was originally designed to be similar to a desktop, but be small and light enough. For this reason, years ago, a laptop had more features than notebooks did, but the tradeoff was it was also a larger and heavier than a notebook. This is because the notebook style of portable computers was for mobility, not just portability. To be a more mobile device, the notebook was a thinner design and it weighed less than the laptop, simply because it didn't come packed with features and multiple devices and drives.

Today technology allows devices to be smaller and better for mobile computing by design, so the size of portable computers is decreasing.

Another reason the term "laptop" is becoming used not often is because a portable "comparable to desktop" system today could easily lead to heat discomfort if left on your lap for long periods of time. By calling a laptop a notebook, it also removes the association that the portable device is well-suited to being used only on your lap.

People often call their notebook a laptop and use the two words interchangeably. However, most mobile computer manufacturers stopped using the term "laptop" completely; they use the term "notebook."

At present netbooks are a new category of laptops. It's an inexpensive, lightweight machine which is powerful enough for the basic, day-to-day, Internet-based tasks that people use a regular laptop for.

At the same time, today's netbooks aren't perfect. Since they are such small, inexpensive devices, they include processors, memory, and hard disks several generations behind the ones found in regular notebooks. Even so, the potential is there for netbooks to become mainstream devices.


Read the text and then fill in the gaps in the sentences.

1. A ______ is a program written in one of the high-level languages.

2. A program written in a high-level language must be interpreted into ______ before the computer reads and processes it.

3. A program designed to perform a specific task is called an _______.

4. The ______ is the program produced when the original program has been converted into machine code.

5. A _____ is a program that converts a high-level language into machine code.

6. The systems program which fetches required systems routines and links them to the object is known as the _______.

7. The _______ is the program directly executable by the computer.

The Main Pieces of Hardware

Hardware refers to objects that you can actually touch, like disks, disk drives, display screens, keyboards, printers, boards, and chips. In contrast, software is untouchable. Software exists as ideas, concepts, and symbols, but it has no substance.

Books provide a useful analogy. The pages and the ink are the hardware, while the words, sentences, paragraphs, and the overall meaning are the software. A computer without software is like a book full of blank pages you need software to make the computer useful just as you need words to make a book meaningful.

The most important item of hardware is the CPU (Central Processing Unit). This is the electronic unit at the center of the computer system. It contains the processor and the main memory.

The processor is the brain of the computer. It does all the processing and controls all the other devices in the computer system.

The main memory is the part of the computer where programs and data being used by the processor can be stored. It refers to physical memory that is internal to the computer. The word main is used to distinguish it from external mass storage devices such as disk drives. Another term for main memory is RAM.

RAM (pronounced ramm, acronym for random access memory) is a type of computer memory that can be accessed randomly; that is, any byte of memory can be accessed without touching the preceding bytes. RAM is the most common type of memory found in computers and other devices, such as printers.

All the other devices in the computer system, which can be connected to the CPU, are known as peripherals. These include input devices, output devices and storage devices.

An input device is a peripheral, which enables information to be fed into the computer. The most commonly used input device is a keyboard.

An output device is a peripheral, which enables information to be brought out of the computer, usually to display the processed data. The most commonly used output device is a monitor or VDU (Visual Display Unit). Another common output device is a printer. This prints the output of the CPU onto paper.

A mass storage device is a peripheral used for the permanent storage of information. It has a much greater capacity than the main memory. Mass storage is distinct from memory, which refers to temporary storage areas within the computer.

Unlike main memory, mass storage devices retain data even when the computer is turned off. The main types of mass storage are various disks. These are the main pieces of hardware of any computer system whether a small "micro" or a large mainframe system.


Read the text and make a list of the main programming languages. What languages werent mentioned in the text?


Computers are known to provide capability to make rapid calculations, compare and make decisions, and send messages through communication links to geographically scattered places, etc.

The organization of these capabilities into a system which is capable of solving problems and realizing aims depends on computer programs. The process of telling a computer what to do and how to do is called programming. The set of instructions is known as the program.

Programs are considered to be an integral part of computer systems: they have been given the name "software" to indicate that they are distinct from but parallel to the "hardware".

More exactly, software includes not only the computer programs but also their documentation and the training required for people to use total system and operate and maintain the programs.

Computers can deal with different kinds of problems if they are given the right instructions for what to do. Instructions are first written in one of the high-level language, e.g. FORTRAN, COBOL, ALGOL, PL/I, PASCAL, or C, depending on the type of program, and it cannot be processed by the computer until it has been compiled, which means interpreted into machine code .Usually a single instruction writtenin a high-level language, when transformed into a machine code, results in several instructions. Here is a brief description of some of the many highlevel languages:

FORTRAN acronym for FORmula TRANslation. This language is used for solving scientific and mathematical problems. It consists of algebraic formulae and English phrases. It was introduced in the United States in 1954.

COBOL acronym for Common Business-Oriented Language. This language is used for commercial purposes. COBOL, which is written using English statements, deals with problems that do not involve a lot of mathematical calculations. It was first introduced in 1959.

ALGOL acronym for ALGOrithmic Language .Originally called IAL, which means International Algebraic Language. It is used for mathematical and scientific purposes. ALGOL was first introduced in Europe in 1960.

PL/I Programming Language I. It was developed in 1964 to combine features of COBOL and ALGOL. Consequently, it is used for data processing as well as scientific applications.

BASIC acronym for Beginners Allpurpose Symbolic Instruction Code. It was developed in 1965 at Dartmouth College in the United States for use by students who require a simple language to begin programming.

C developed in the 1970s to support the UNIX operating system. C is a highly portable generalpurpose language.

Other such languages are APL (developed in 1962), PASCAL (named after Blaise Pascal and developed in 1971), LISP and PROLOG, both of which are used for work in artificial intelligence. LOGO is a development of LISP which has been used to develop computerbased training (CBT) packages.

When a program written in one of these highlevel languages is designed to do a specific type of work such as to calculate a companys payroll or calculate the stress factor on a roof, it is called an applications program. Institutions either purchase these programs as packages or commission their own programmers to write them to meet the specifications of the users.

The program produced after the source program has been converted into machine code is referred to as an object program or object module. This is done by a computer program called the compiler, which is unique for each computer.

The compiler is a systems program which may be written in any language, but the computers operating system is a true systems program which controls the central processing unit (C P U), the input, the output, and the secondary memory devices. Another systems program is the linkage editor, which fetches required systems routines and links them to the object module (the source program in machine code). The resulting program is then called the load module, which is the program directly executable by the computer. Although systems programs are part of the software, they are usually provided by the manufacturer of the machine.

Unlike systems programs, software packages are sold by various vendors and not necessarily by the computer manufacturer. They are a set of programs designed to perform certain applications which conform to the particular specifications of the user.

Summarize the information on different high-level computer languages by completing the table below.

Language Date of development Purpose Characteristics
    Mathematical and scientific  
      Combines features of COBOL and ALGOL
    To support Unix operating system  




Read the text and make a list of software terms which are new for you. Give the definitions to these terms.


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