- •Contents
- •Передмова
- •We are students at donetsk national university
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •Student Dima Loboda
- •Student Dasha Klimova
- •Student Nastya Savchuk
- •Student profile
- •L earn mathematics in English Cardinal and ordinal numbers
- •1. Read the text about two arithmetical operations and do the exercises that follow it Basic arithmetical operations. (Addition & subtraction)
- •What’s your best friend like?
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •Who’s their ideal partner?
- •L earn mathematics in English
- •1. Read the text and do the exercises below it Basic arithmetical operations (Multiplication & division)
- •A day in the life of a student
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •I. Look through the text and do the tasks
- •Learn mathematics in English
- •I. Read the text and do the exercises below it. Advanced arithmetical operations
- •What’s your university like?
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Donetsk national university
- •The University of Sheffield
- •1. Find a partner from the other group. Tell each other the information you read about one of the universities
- •Fractions
- •The city I live and study in
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Learn mathematics in English
- •Mixed numbers
- •Mathematics is the queen of scienses
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words:
- •“`A mathematician is a machine for converting coffee into theorems”. /Paul Erdos/
- •L earn mathematics in English
- •Equivalent fractions
- •Reciprocals and the "invisible denominator"
- •The language of mathematics
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words
- •L earn mathematics in English
- •Statistics is very serious!
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words:
- •Statistics is very serious!
- •Get to know a typical computer
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Get to know a typical computer
- •Computer without a program is just a heap of metal!
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary.
- •2. Key words
- •We can’t imagine modern computing without them
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •I. Read the following texts and do the tasks Alan Turing
- •Tim Berners-Lee
- •He has left mathematicians enough to keep them busy for five hundred years
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary.
- •2. Key words
- •I. Read the text and do the tasks niels henric abel
- •Getting to know each other better
- •II. Swap charts with b. Ask a to explain the information in his/her chart. Ask for more information
- •III. Explain your answers to b
- •Mood graph
- •A time for everything
- •Expert opinion
- •Vocabulary
- •Vocabulary
- •What’s your body age?
- •I. Read the questionnaire and answer the questions below, adding or subtracting the numbers after your answer from your actual age
- •How many friends can you share problems with?
- •15. Have you taken antibiotics in the past five years?
- •II. Check your score
- •If you're younger than your years
- •I. Look at your partner’s answers. Ask for more information, for example: What is your worst diet habit? How much time do you have for yourself?
- •II. Some ways to lower our body age are given below. Read it and give your partner some good advice starting with the following words: I think you should…
- •Donetsk national university
- •Inspires students’ enthusiasm for learning
- •An ideal teacher
- •Is a well-educated person has a good sense of humor is a polite and a punctual person delivers interesting lectures
- •Numbers
- •I. Mind–map’ numbers’. When you read this ‘mind-map’, you’ll meet words that are new to you. First try to guess their meaning and then look them up in a dictionary.
- •II. Answering and explaining
- •III. Playing a trick with numbers
- •IV. The ‘Terribly Stressed‘ game
- •I. Use this mind-map ‘Four basic operations in Mathematics’ as a topic activator to speak about the basic operations in Arithmetic
- •III. Reading, writing and saying numerical expressions
- •3. Look at each numerical expression written in symbols and signs. Then say it in words. Your partner will listen to see if you repeat correctly and correct your incorrect answers
- •I. Use this mind-map ‘Algebra’ as a topic activator to speak about Algebra (its origin and some facts from its history)
- •II. Match each numerical expression in the left column with the equivalent expression in the right column
- •Look at the expressions written in words and write them in mathematical notation (in symbols)
- •III. Read the following inequalities aloud. Your partner will check your answers
- •I. Mind-map ‘Geometry’. Use this map to speak about geometry (its meaning, the history of its development, its application). Add more information you know
- •II. Working with geometric terms. Demonstrate your knowledge of geometric terms. Work in pairs (a/b)
- •The language of mathematics
- •Practice set 12
- •III. Draw your mood graph or graph with your marks showing changes during the week or a month (semester). Explain it to your partner
- •Some facts from the history of mathematics education
- •I. Read the article and mark the sentences t (true), f (false) or ng (not given)
- •Do you know that…
- •II. Search for some information about one of these mathematics teachers and share it with other students. Make a table of the most important facts of his/her biography
- •Ancient sources of information
- •I. Choose from (a-j) the one which best fits each of (1-7). There are two choices you do not need to use.
- •II. Tell your partner about these famous papyri
- •III. Find some information about Mathematics of ancient civilizations and share it with other students (e.G. The Maya calendar, the ancient numeration systems)
- •The history of the symbols for plus and minus
- •I. Read the article. Guess the meaning of the highlighted words. Check with the teacher or your dictionary
- •II. Read the article again. Say what events the following years refer to:
- •III. Tick (√) the things the article says
- •IV. Read the facts listed below. In pairs, discuss which one is the most surprising do you know that...
- •V. Find some information on the history of the mathematical symbols. Give a presentation to the students of your group
- •Statistics
- •I. Match the words with their definitions:
- •II. Decide if the given statements are true (t) or false (f) according to the text
- •III. Search for information about one of the scientists listed below and then give a presentation
- •Important contributors to statistics
- •Degrees and diplomas in statistics
- •III. Do you know anything about awards in Statistics in your country or abroad?
- •Why is there no nobel prize in mathematics?
- •I. Read the text. Seven sentences have been removed from it. Choose from the choices (a- I) the one which fits each gap (1-7). There are two choices you do not need to use
- •III. Work in pairs. Tell your partner why Nobel decided against a Nobel Prize in mathematics
- •Major awards in mathematics
- •The obverse of the Fields Medal
- •The reverse of the Fields Medal
- •A. Fields medal
- •III. Look at these words. Why are they important in this text?
- •B. Abel prize
- •IV. Focus on these words. Why are they important in the text?
- •VI. Compare the major awards in Mathematics with the Nobel Prize by using like (similar to) or unlike (different from) in the sentences
- •V. Search for more information on the following topics on the Internet and share it with other students
- •Abel Prize Laureates
- •Fields medalist
- •I. Decide if the given statement is true (t) according to the text, if it is false (f) or if the information is not given (ng) in the text (Work in pairs)
- •II. Number these events in the order they happened. Look at the Reading
- •III. Interview your partner about this great mathematician (Work in pairs)
- •IV. Ask and answer the following questions in pairs
- •II. Match the number with its symbolic meaning:
- •III. Answer the questions below and then ask for more information (Work in pairs)
- •Do you know that…
- •IV. Find information on the Internet and give a presentation of the number you are interested in (brings you good or bad luck)
- •Text 10
- •Reading and Speaking
- •Number and reality
- •I. Match the word with its meaning:
- •II. Work in pairs. Decide if the sentences 1- 7 are t (true) or f (false)
- •A strong mathematical component
- •I. Choose from (a-j) the one which best fits each of (1-6). There is one choice you do not need to use
- •II. Match choices (a-d) to (1-4)
- •III. In pairs, find and then say what events the following years refer to:
- •IV. Do you know an artist (a writer) having a strong mathematical component in his/her creative work? Search for information on the Internet and give a presentation on the subject
- •Reading and Speaking fractal
- •I. Match the words with their meanings:
- •II. Choose from (a-f) the one which best fits each of (1-5). There is one choice you do not need to use
- •III. Work in pairs. Tell your partner about fractal
- •IV. On the Internet search for information about applications of fractals and then share your information with other students
- •Healthy computer work
- •Match the words with their meanings:
- •I I. Read the article once and then decide if the following guidelines are true, false or are not mentioned in the text above
- •III. Team work. Work out the main rules for operating the computer. The winner is to give clear recommendations for young people working on the computer. The first one is given for you
- •IV. Ask and answer the questions (Work in pairs)
- •Computers can do wonders
- •I. Match the words with their meanings
- •II. Decide if the following statements are true or false (t/f) by referring to the information in the text
- •III. Work in pairs. Tell your partner about the most surprising facts from the article
- •IV. Search for information about ‘computer wonders’ on the Internet and give a presentation about new computer developments (e.G. Robots)
- •Watching ‘how did mathematics begin? (a cartoon)
- •I. Answer the following questions:
- •II. Tell the class about the most interesting facts you have learned from the cartoon. Do you agree with the information mentioned in the cartoon? Add more information about the development of numbers
- •Recommendations and some useful phrases for giving presentations
- •Introduction
- •Introducing your subject
- •If you make a mistake, start your sentence again.
- •If you can’t remember a word, use another one.
- •Conclusion
- •Inviting questions
- •Questions
- •Wording mathematical signs, symbols and formulae
- •Answer keys
- •References
I. Choose from (a-j) the one which best fits each of (1-7). There are two choices you do not need to use.
A. Some problems may present a challenge even to modern students; e.g. ‘Find the volume of a cylindrical granary of diameter 9 and height 10 cubits.’
B. One ought not to underestimate the contributions of these ancient civilizations to the development of geometry.
C. The ancient Indians and Chinese, however, used very perishable writing materials (bark bast and bamboo) and due to the lack of primary sources we know nothing about Mathematics in ancient India and China.
D. Babylonian Maths refers to any Maths of the people of Mesopotamia from the days of the early Sumerians until the beginning of the Hellenistic period.
E. The Rhind papyrus is a collection of arithmetical, geometrical and miscellaneous problems, including some area and volume applications.
F. Nevertheless, early Egyptians surveyors realized that a triangle with sides of lengths 3, 4 and 5 units is a right triangle.
G. The solution is expressed only in terms of the necessary computational steps for the given numerical values: height of 6 and the bases of sides 4 and 2.
I. Babylonian Mathematics merged with Greek and Egyptian Maths to give rise to Hellenistic Mathematics.
J. Although it contains only 25 problems, it is similar to the Rhind papyrus.
II. Tell your partner about these famous papyri
1. A (Book closed): Tell about the Rhind papyrus.
B (Book open): Help and add more information.
2. B (Book closed): Tell about the Moscow papyrus.
А (Book open): Help and add more information.
III. Find some information about Mathematics of ancient civilizations and share it with other students (e.G. The Maya calendar, the ancient numeration systems)
Text 3
Reading and Speaking
The history of the symbols for plus and minus
T he symbols of elementary arithmetic are considered to be algebraic, most of them being transferred to the numerical field only in the 19th century. When we study the genesis and development of the algebraic symbols of operation, therefore, we include the study of the symbols in arithmetic. Some idea of the status of the latter in this respect may be obtained by looking at almost any of the textbooks of the 17th and 18th centuries. Hodder in 1672 wrote "note that a + (plus) sign signify Addition, and two lines thus = Equality, or Equation, but a X sign thus, Multiplication," no other symbols being used. His work was the first English arithmetic to be reprinted in the American colonies in Boston in 1710. Even Recorde (c1510-1558), who invented the modern sign of equality, did not use it in his arithmetic, the Ground of Arts (c1542), but he used it in his algebra only in 1557.
T here is some symbolism in Egyptian algebra. In the Rhind papyrus we find symbols for plus and minus. The first of these symbols represents a pair of legs walking from right to left, the normal direction for Egyptian writing, and the other a pair of legs walking from left to right, opposite to the direction for Egyptian writing.
The earliest symbols of operation that have come down to us are Egyptian. In the Ahmes Papyrus (c1550 B.C.) addition and subtraction are indicated by these symbols on the left and right above respectively.
T he Hindus at one time used a cross placed beside a number to indicate a negative quantity, as in the Bakhshali manuscript of possibly the 10th century. With this exception it was not until the 12th century that they made use of the symbols of operation. In the manuscripts of Bhaskara (c1150) a small circle or dot is placed above a subtrahend as illustrated for -6, or the subtrahend is enclosed in a circle to indicate 6 less than zero.
I n Europe the word plus, used in connection with addition and with the Rule of False Position was not known before the latter part of the 15th century.
T he use of the word minus as indicating an operation occurred much earlier, in the works of Fibonacci (c1175-1250) in1202. The bar above the letter simply indicated an omission. In the 15th century, this third symbol was also often u sed for minus, but most writers preferred the other variations.
I n the 16th century the Latin races generally followed the Italian school, using the letters p and m, each with the bar above it, or their equivalents, for plus and minus. However, the German school preferred these symbols, neither of which is found for this purpose before the 15th century. In a manuscript of 1456, written in Germany, the word "et" is used for addition and is generally written so that it closely resembles the modern symbol for addition. There seems little doubt that the sign is merely a ligature for "et", much in the same way that we have the ligature "&" for the word "and."
T he origin of the minus sign has been more of a subject of dispute. Some have thought that it is a survival of the bar above the three symbols for minus as listed above. It is more probably that it comes from the habit of early scribes of using it as a shorthand equivalent of "m." Thus Summa became Suma with the bar above the letter u, and 10 thousand became an X with the bar above the letter. It is quite reasonable to think of the dash (-) as a symbol for "m" (minus), just as the cross (+) is a symbol for "et".
There were other various written forms for plus and minus, as in piu (Italian), mas (Spanish), plus (French) and et (German) for plus and as in de or men (Italian), menos (Spanish), moins (French) for minus.