- •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
L earn mathematics in English
1. Read the text and do the exercises below it Basic arithmetical operations (Multiplication & division)
In spoken English, 4 × 2 = 8 is, ‘Four multiplied by two equals eight’ or ‘Four times 4 equals eight’. This arithmetic operation is called multiplication. The result of this operation is the product. Thus, if four is multiplied by two, the product is eight.
In spoken English, 8 : 2 = 4 is, ‘Fight divided by two equals four’. This arithmetical operation is called division. The result of this operation is called the quotient, Thus, if twelve is divided by two, the quotient is six.
Exercise 1
Study the following questions and the answers
Q. If 10 is divided by 2, what is the quotient?
A. If 10 is divided by two, the quotient is 5.
Q. If 90 is added to 10, and the sum is divided by two, what is the quotient?
A. If 90 is added to ten, and the sum is divided by two, the quotient is 50.
Q. If 500 is subtracted from 560, the difference is divided by 30, then 2 is added to the quotient, what is the sum?
A. If 500 is subtracted from560, the difference is divided by 30, then 2 is added to the quotient, the sum is 4.
Exercise 2
Practise asking your classmates similar questions and giving similar answers about the sums listed below
394 : 2 =
64 : 4 =
(40 + 20) : 3 =
(15 + 17) × 2 =
(41 3) : 19 =
Exercise 3
Make up your own questions to ask your classmates
Unit 3
A day in the life of a student
Vocabulary
1. Guess the meaning of these international words. Check with your teacher or a dictionary
Finally, double, period, salad, soup, practice, politics, sandwich, minute, absolutely
2. Key words
To crawl To go off For a while |
Повзати, півільно пересуватися Лунати (про гудок, дзвінок будильника) Деякий час |
To rush |
Кинутися, мчати |
To have a snack |
Перекусити на ходу |
Canteen |
Їдальня |
Nap (to have a nap) |
Короткий сон, дрімота (задрімати) |
Roughly |
Грубо, приблизно |
To surf the Internet |
Шукати інформацію в Інтернеті |
Immediately |
Негайно, одразу |
Rather strange |
Досить дивно |
Reading
I. Look through the text and do the tasks
A day in the life of a student
Student Stas Kovalenko |
Student Lesya Borisova |
At 7.30 a.m. my alarm goes off. It is very loud. I need that to wake me up. I stay in bed for a while, but finally crawl out of bed at about 7.45. As my classes begin at 8 o’clock I don’t have time to do morning exercises or have breakfast (and don’t often have anything for breakfast, you know, I’m living in a hall of residence) – I just quickly wash my face, dress and rush to the university. My faculty isn’t far from my hall of residence – it’s only a five-minute walk from it. I study at the faculty of mathematics. Usually we have three or four double periods a day which finish at 12.35 or 2 p.m. After the first double period I have a snack in a snack bar and after classes I have lunch in our student canteen or we cook something for lunch in a hall of residence by ourselves. It’s often fried potatoes with meat or fish, some salad or soup. I like borsch very much, but I can’t make it. After lunch I have a nap and then have football practice for the faculty team. I do my homework in the evening. It takes three or four hours. My homework always gets done at roughly 11 p.m. After that I either surf the Internet or chat with my friends. You know I like my hall of residence mainly because of the number of friends I have there. We talk about politics, girls, our teachers, football, everything! I go to bed late after midnight, so it’s not easy to wake up in the morning |
I usually get up at 6 in the morning. You may ask me why I get up so early. Well, the thing is, I live in Makeevka, and it takes me more than an hour to get to my university. I‘m not hungry in the morning, but my mother always makes me eat something. I often have fried eggs, tea or coffee and a sandwich for my breakfast. I leave home at 7 a.m. and take a trolley-bus to the bus station where I take a bus to Donetsk. I arrive at university five or six minutes before classes. I don’t like being late. It’s rather strange that students living in a dormitory which is near the university are often late. I usually enjoy university if I cope with my university work. I hate feeling left behind. I take a course in applied mathematics. My course is interesting, but some subjects are very difficult, and Calculus is the most difficult of all. It takes me two or three hours to do my homework in Calculus. I do my homework immediately after dinner when I come home after classes at about 3.30 p.m. All my homework takes roughly five hours. So at about 9 p.m. I can relax. I either watch TV or play computer games. I sometimes go out with my boyfriend, but I always try to go to bed at 11 p.m. because having a good sleep is very important to me. When I was at school I went to a swimming-pool twice a week, but now I have absolutely no time for any sports. It’s much harder to study at the university than at school! |
Task 1. Read the text again and find the information required
The time the students get up.
The reason why Stas doesn’t have breakfast and Lesya does.
How they get to their university.
Who sleeps in the afternoon.
Who usually plays sports.
Whose homework takes longer.
The reason why Stas likes his dormitory.
The time they go to bed.
Task 2. Join the sentences with either … or
Example
After that I sometimes surf the Internet and I sometimes chat with my friends.
After that I either surf the Internet or chat with my friends.
I sometimes have coffee and I sometimes have tea for my breakfast.
In the afternoon I sometimes play football and I sometimes do my homework.
In the evening I sometimes watch TV and I sometimes go out with my friends.
After the first double period I sometimes have a sandwich and I sometimes eat in a student canteen.
On Saturday evenings we sometimes go to the cinema and we sometimes play cards.
Task 3. Read Stas’ story and write ten questions that the interviewer might have asked him
Examples
What time do you get up?
Do you like getting up?
Task 4. Share your questions with a partner. Have you got any similar questions? Write down those which are different from yours
Speaking
Task 1. Interview your partner using the list of questions you made in the previous task. Ask additional questions if you want to.
Task 2. Tell your class-mates about the most interesting facts from the day of your partner