МЕТ_1к_1ч

26.You want to ask your friend to do something for you. Use the prompts below to make questions, as in the example. Use the Future Continuous.

1.You want your friend to solve this mathematical problem.

Will you be solving this mathematical problem?

2.You want your friend to explain the difference between the words "equation" and "expression".

3.You want your friend to translate this sentence.

4.You want your friend to prove the theorem.

5.You want your friend to describe the table.

6.You want your friend to clarify the term "limit".

7.You want your friend to explain the rule.

8.You want your friend to look for some information about the difference between mathematics and arithmetic.

27.Choose the correct answer.

1.By the end of May, Tom will have studied / will have been studying English for a year.

2.By June, Kate will have been finishing / will have finished studying at the University.

3.Hopefully, they will have learned / will have been learning everything by the time they sit the exam.

4.By 7 o'clock, I will have been studying / will have studied mathematics for three hours.

5.By Monday, we will have written / will have been writing an essay about mathematics.

28.Put the verbs into the correct present tense.

1.The people in each country ........................ (to translate) algebra into their own spoken language.

2.Algebra .................... (to pass) three stages in its development.

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3.Common language .................. (to be) a product of social development.

4.Power of transformation ....................... (to lift) algebra above the level of a convenient shorthand.

5.The history of symbols "+" and "−" ...................... (to illustrate) the point.

29.Put articles where necessary.

1.… common language is … product of … social development.

2.… algebra, … language of … mathematics, consists mostly of … signs and symbols.

3.… algebra is one and … same throughout … civilized world.

4.… algebra in … broad sense of… term, deals with … operations upon … symbolic forms.

5.… Cartesian notation not only displaced … Vietan one, but has survived to this day.

6.It is … symbolic language that is one of … basic characteristics of … modern mathematics.

30.Translate into English.

A.

1.Алгебра – це точна, стисла та універсальна наука.

2.Скорочення перетворилося на символ.

3.В своєму розвитку алгебра пройшла декілька ступенів.

4.Сучасна алгебра об’єднує велику кількість самостійних дисциплін.

5.Метод аналізу математичних моделей посідає провідне місце серед інших методів дослідження.

6.Для стародавніх греків математика була насамперед геометрією. А

тому над дверима Академії, де Платон навчав своїх учнів, був напис:

"Нехай сюди не входить ніхто, хто не знає геометрії".

7.Архімед за допомогою математичних розрахунків сконструював багато різноманітних механізмів, які настільки допомагали у війні проти

римлян при облозі Сиракуз, що Марцелло сказав: "Треба припинити

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війну проти геометра". Пізніше тільки зрада допомогла римлянам

увійти до Сиракуз.

8.Знання математики допомогли французу Вієту розкрити шифр у листуванні іспанського короля Філіппа II під час війни Франції з Іспанією. Таким чином він прискорив перемогу Франції. За це іспанська інквізиція оголосила Вієта чаклуном і присудила його до спалення на вогнищі.

9.Леонардо да Вінчі назвав механіку "раєм математичних наук".

10.Чи знаєте ви, що теорему Піфагора називали "ослячим мостом"? Учнів,

що запам’ятовували теорему без розуміння, називали віслюками,

оскільки вони не могли перейти через міст − теорему Піфагора.

11.Чи знаєте ви, що зібрання творів Леонарда Ейлера становить 75

великих томів, і якщо кожного дня переписувати по десять годин його роботи, то не вистачить 76 років?

B.

П'єр Ферма

(1601-1665)

П'єр Ферма − видатний французький математик, один із основоположників аналітичної геометрії і теорії чисел. Він є автором робіт в області теорії ймовірності, оптики, численних нескінченно-

малих величин. У 1637 році П'єр Ферма сформулював так звану "Велику теорему Ферма", яка була доведена американським математиком Ендрю Уайлсом лише у 1995 році.

Теорема стверджує, що для будь-якого

натурального n>2 i xyz<>0 рівняння хn+уn=zn не можна розв’язати в цілих

(і раціональних) числах.

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SPEAKING

31.Discuss the following questions.

1.What counting systems do you know?

2.Analyse the advantages of the 12 system (used in UK and US) over the decimal system and vice versa.

3.What problems must the Romans have had with their system?

4.What are the specialized uses of Roman numerals today?

5.Could we manage just cardinal numbers, rather than having both cardinal and ordinal?

32.Work in pairs. Many people think that the words 'arithmetic' and 'mathematics' mean the same. Student A and Student B are talking about the difference between mathematics and arithmetic. Role play the conversation. Use role and cue cards (Appendix 3).

33.Work in pairs. You are an outstanding mathematician and your knowledge of the history of mathematics is deep. Your student asks you about the creation of the quadratic formula. Act out the conversation using information from the text "WHO CREATED THE QUADRATIC FORMULA?" (see the EXTRA READING section to Unit 7). Cover the following points:

mathematical problems;

creators of the quadratic formula;

the formula moves to Europe;

the importance of the formula.

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34.A. Look at the portraits of famous mathematicians, match the portraits with the names and tell your groupmates about their contribution to science.

Euclid of Megara & Alexandria, Joseph-Louis Lagrange, Sofya Vasilyevna Kovalevskaya, James Clerk Maxwell, Augusta Ada King Byron, Gottfried Wilhelm von Leibniz

B. You want to create an Internet site about the greatest mathematicians of all times. First, you need to write a list of the greatest mathematicians (not less than 10) and tell your groupmates shortly about their contribution to mathematics. Continue the list: Archimedes, Carl Gauss,

........, ......., ......... .

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C. You are Pythagoras of Samos. Two of your students want to prove the Pythagorean theorem in different ways. Be ready to prove the theorem using the figure and the statement below.

The Pythagorean theorem:

The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

35.A. You are a mathematician at Oxford University. It is your first lecture. The theme of your lecture is: "Mathematical Thinking". Cover the topic using the following notes:

mathematical thinking is important as a way of learning mathematics;

definition (a process through which a mathematical point of view is developed);

application (support science, technology, economic life and development in an economy);

a wide range of skills and abilities necessary for solving problems (deep mathematical knowledge; general reasoning abilities; knowledge of heuristic strategies; helpful beliefs and attitudes (e.g. an expectation that maths will be useful); personal attributes such as confidence, persistence and organisation; skills for communicating a solution);

four fundamental processes:

specializing – trying special cases, looking at examples

generalizing − looking for patterns and relationships

conjecturing – predicting relationships and results

convincing – finding and communicating reasons why something is true.

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B. Prepare a short talk for your groupmates. Choose the topic from the given: "Maya numerals", "Babylonian numerals", "Quipus".

LISTENING

You are going to listen to some information about mathematics. Be ready to do the following tasks:

36.Before you listen, check if you know the meaning of the words: abstract quantities, measurement, recognizing, simplicity, systematic study, engineering.

37.Decide whether the facts from the text are true (T) or false (F).

1.The word "mathematics"comes from the Latin "math".

2.The term "mathematics" meant "astrology" in English until 1700.

3.Mathematicians resolve the truth or falsity of conjectures by the mathematical proof.

4.The research in Maths required to solve some problems.

5.The earliest uses of Maths were, besides the others, in painting, recording of time, medicine.

6.There is no such a notion as "pure mathematics".

38.Complete the sentences.

1.Mathematicians deal with the study of … .

2.Prehistoric people knew how ... .

3.Maths is used all over the world as an essential … .

4.It is known that Maths often inspired by one area … .

5.… in Maths are valued.

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WRITING

39.Write 5 sentences using abbreviations or shortenings from Exercise 5.

40.A. Complete the phrases using your own variants.

1.Mathematics is … .

2.Arithmetic is … .

3.A language is … .

4.Geometry is … .

5.A symbol is … .

6.Geometric Algebra is ... .

7.Number Theory is ... .

B. Write our equivalents to the numbers and measures in the suggested

joke. Use Appendix 8.

A Joke

A boy (enters a grocer’s shop) – A pound of sugar at 90 pence, a pound of butter at one pound and 80 pence, a pound of cheese at two pounds and 20 pence, two pounds of tea at five and six a pound. If I give you 20 and 6, how much would you give me a change?

Grocer (writing it all down) − 13 pounds. And why?

Boy – Please, give me that bill. It’s my homework for tonight. Thank you.

41.Write an essay (100−120 words) that ends:

"As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection."

J.-L. Lagrange.

Follow this structure:

Introduction

Paragraph 1 (state the topic)

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Main Body

Paragraphs 2-3 (viewpoints, examples)

Conclusions

Final paragraph (summarise).

PROBLEM-SOLVING

42.Try to solve curious problems and puzzles (see the PROBLEM-SOLVING section to Unit 7).

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Unit 8: RECREATIONAL MATHEMATICS

Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

Stephen Hawking

WARM-UP

1. What is recreational mathematics?

Label the pictures below with the names: Sudoku, Rubik’s cube, tangrams, origami, Towers of Hanoi. Have you ever tried any of these? Which of these do you think is the most difficult to do? Why?

2.Do you agree with the English puzzlist and mathematician Henry Dudeney who wrote: "A good puzzle, like virtue, is its own reward."? Why (not)?

3.What do you think about numerology? Do you agree with Sir Thomas Browne who "… admired the mystical way of Pythagoras, and the secret magic of numbers"? Why (not)? Do you believe that numbers have mystical significance? Give your reasons.

4.What magic figures do you know? Why are they called magic?

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