Сценарий урока по английскому языку "Цифры, числа, математические действия",

1 План-конспект урока по теме «Цифры, числа, математические действия». Цель занятия: научить пользоваться математическими терминами на английском языке. Задачи: совершенствование навыков чтения и перевода по теме; совершенствование лексических навыков; развитие навыков говорения. Ход урока: 1. Организационный момент. Приветствие. Hello, dear friends. I am glad to see you! Our today’s lesson is about numerals, numbers, mathematical operations. But we'll start with the brief history of mathematics. Let's try to answer some questions. Where does the word mathematics come from and what does it mean? - The word mathematics comes from the Greek for science, learning and knowledge. What do you think Mathematics began with? - It began with number and counting. People needed to count their belongings. As society developed, numbers became more and more important for business dealings and taxation and it became especially important to be able to record numbers. What types of numerals do you know? - Right, Roman numerals and Arabic numerals. And here is a set of symbols for the main mathematical operations: + (plus) for addition, – (minus) for distraction, X (multiplication), : (division), = (equals). (But first we’ll start with checking of your homework.) 2. Проверка домашнего задания. (На дом было задано: прочитать текст и выполнить задания 1 и 2.) The word mathematics comes from the Greek for science, learning and knowledge. Mathematics began with number. 1) People needed to count their belongings. As society developed, 2) numbers became more and more important for business dealings and taxation and it became especially important to be able to record numbers. With writing, different ways of recording numbers developed in different countries, too. Roman numerals are a well-known example. In this system I is one and X is ten, so IX is one before ten, that is nine, and XI is eleven. It was not until the 16th century that the system of mathematical notation that we use today finally developed. It is a system that uses Arabic numerals (1, 2, 3 and so on) with a set of symbols + (plus), – (minus), = (equals) for example, along with letters, many of which are taken from the Greek alphabet. It is a system which is used by all mathematicians all over 2 the world. In fact, it has been said that mathematics is one of only two genuinely international languages; the other one is music. 3) What mathematicians study can be summed up as relating to four major fields. They look at quantities – how much or how many. 4) There is also the study of structure – how things are arranged together and the relationship between the parts. 5) Then there is the study of space, where mathematicians are interested in the shape of things. Finally, there is change and how things move, over time or through space. Quantity is mostly concerned with numbers. Mathematicians are interested in both natural numbers and integers. 6) Natural numbers are those which are greater than zero, while integers may be zero itself or more less than zero. There are four ways these may combine together; these are called operations. In arithmetic, we know the operations as addition (+), subtraction (-), division (:) and multiplication (x). For a fuller, more philosophical understanding of number and the operations that can be applied to them, mathematicians look to Number Theory. Задание 1. Составьте словосочетания из слов в левой и правой колонках. 1. To count 2. Business 3. To record 4. Roman 5. A set 6. Study of 7. Shape 8. natural a. of symbols b. of things c. numerals d. belongings e. structure f. dealings g. numbers h. numbers 1. Считать свои вещи 2. Ведение бизнеса 3. Записывать числа 4. Римские цифры 5. Набор символов 6. Изучение структуры 7. Формы тел 8. Натуральные числа Задание 2. Дополните предложения и переведите их. 1. People needed to count … 2. Numbers became more and more important for ………… 3. What mathematicians study can be summed up as ………… 4. There is also the study of structure …………. 5. Then there is the study of space, where …………. 6. Natural numbers are those which are greater than zero, while 3. Развитие навыков чтения. (The teacher: And now you are going to read a text to learn some facts of the development of the number system, but first let’s read and memorize the following words from the text and then do exercises 1 and 2) Задание 1. Ознакомление с новой лексикой. 3 A.D. – наша Эра B.С. – до нашей эры Babylonians – вавилонян Sumerians – шумеры Chinese – китайцы dynamic mathematics – динамическая математика shepherd – пастух sign – знак, символ milestone – веха pebbles – галька, булыжник records – записи evidence – доказательство, свидетельство achievements – достижения predecessors – предшественники to apply – применять contribute – внести вклад, принимать участие, содействовать tribes – племена to acquire – приобретать, усваивать counters – счетчики, считалки; counting – счет calculus – исчисление number pairs by points – система координат Задание 2. Подберите подходящие слова и составьте словосочетания. Переведите их. 1. the origin of number 2. important 3. progress of 4. arithmetical 5. in the distant 6. one of the greatest 7. the inventors 8. non-Euclidean a. past b. milestone c. of the calculus d. and counting e. geometry f. minds g. achievements h. civilization Задание 3. Найдите соответствующее окончание предложений. Переведите их. a. … inventors of the calculus. b. … masterpieces in 1. No one knows… 2. Counting represents a very 3. Historical records give evidence 4. This creation made possible… 5. important… of the astronomical and … Isaac Newton, one of the greatest minds, was one of the… greatest… 6. Lobachevsky created one of the mathematics – non-Euclidian geometry. civilization. c. … milestone in the progress of d. … when counting first began. e. … a great advance in science f. … arithmetical achievements of and mathimatics. the early Babylonians, Sumerians, and Chinese. 4 SOME FACTS OF THE DEVELOPMENT OF THE NUMBER SYSTEM Our present number system has not always been so fully developed as it is today. The number system is closely connected with early prehistoric man and with the most recent discoveries in atomic science. But there was a time when man didn’t know how to count. The origin of number and counting is hidden behind countless prehistoric ages. No one knows when the counting first began. Before man learnt count he probably used names or signs for each person or thing. It is believed that the early shepherds would call their sheep by names in order to determine if any of them were missing. 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 also in some cases, his toes. 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 learnt 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. One of the greatest mathematicians of recorded history was the Great Archimedes (287 – 212 B.C.) who developed a dynamic mathematics which could be applied to the laws of nature. The practical civilization of ancient Rome, great in many other fields, contributed little to mathematics. Going to the Renaissance period, we find the tribes of Moslem coming to Europe, bringing with them the culture of many civilizations, including a strange number system acquired from the Hindus. Only about 400 years ago a great French mathematician and philosopher Rene Descartes represented number pairs by points. This creation made possible a great advance in science and mathematics. Isaac Newton (1642 – 1727), one of the greatest minds, was one of the inventors of the calculus which is now studied by students who are seriously interested in mathematics or physical science. Few discoveries in the world of science can equal the discovery of Lobachevsky (1792 – 1856). Like Archimedes, Galileo, Copernicus and Newton, Lobachevsky is one of those who laid the foundation of mathematical science. Lobachevsky created one of the greatest masterpieces in mathematics – non-Euclidean geometry, one of the greatest achievements in mathematics. 4. Развитие навыков говорения. 5 Задание 4. Найдите в тексте ответы на вопросы. 1. What things did man use for counters? 2. What evidence do historical records of the early Babylonians, Sumerians and Chinese give? 3. Who developed a dynamic mathematics? 4. Who brought a strange number system to Europe? 5. What creation made possible a great advance in science and mathematics? 6. Who is one the inventors of the calculus? 7. Who created non-Euclidean geometry? 5. Развитие навыков аудирования. Специалисты утверждают, что счет как таковой возник благодаря необходимости понимать, каким запасом тех или иных вещей обладает человек. Изначально с этой целью использовались пальцы. Пальцы быстро сменились ракушками, палочками, зарубками и камушками. Для древних людей, пользующихся позиционной системой счисления, числа имели практическое значение. Они должны были обозначать реальное количество предметов или товаров, которые необходимо продать. Однако одно из чисел появилось намного позже всех остальных. Только после открытия этого нового числа стало возможным появление отрицательных чисел. Это число является уникальным, так как оно не может быть ни положительным, ни отрицательным. Сегодня всем известно, что долгота отсчитывается именно с меридиана под этим числом. А на шкале Цельсия это число разграничивает положительные и отрицательные температуры, являясь точкой замерзания воды. Компьютерная кодировка также основана на применении этого числа и единицы. О каком числе идет речь? Наше видео об этом числе. Посмотрим видео, а потом перескажем его содержание. Now you are going to watch a video. It is about one numeral, which was invented much later than others. https://www.youtube.com/watch?v=LQEuywkWa2U (After watching the video) So, let’s summarize what we have learnt from this video. (Индия – родина нуля. Большинство ученых считают, что история возникновения натурального числа и нуля обязана индийским ученым. Именно они подарили миру ту систему счислений, которой практически в неизменном виде мы пользуемся до сих 6 пор. Индийцы определили, что с помощью десяти цифр можно записать практически любое число и сделали эти знания достоянием просвещённых людей всего мира. ) 1. Cardinal Numbers – количественные числительные 6. Введение новой лексики.  279 – three hundred and seventy-nine  2,860 – two thousand eight hundred and sixty  5,084 – five thousand and eighty-four  470,000 – four hundred and seventy thousand  2,550,000 – two million five hundred and fifty thousand  3,000,000,000 – three billion 2. Ordinal numbers and dates – порядковые числительные и даты  4 January – the fourth of January / January the fourth  21 May – the twenty-first of May / May the twenty-first  1978 – nineteen seventy-eight  1908 – nineteen oh eight 3. Fractions and decimals – дроби и десятичные числа  1 ¼ - one and a quarter  1 1/3 – one and a third  1 ½ - one and a half  1 ¾ - one and three quarters  1.25 – one point two five  1.5 – one point five  0.7 – (nought) point seven  6.02 – six point oh two 4. Percentage - проценты  25% - twenty-five per cent  Odd numbers – 1, 3, 5, 7, 9 ..  Even numbers – 2, 4, 6, 8 .. 5. Telephone numbers – телефонные номера  707 159 94 05 – seven oh seven, one five nine, nine four, oh five 6. Закрепление новой лексики. Задание 6 Write the numbers. 1. The Celsius freezing point — ___________ 2. Days in April — ___________ 3. The number of letters in the English alphabet — ___________ 4. An unlucky number — ___________ 5. Teeth in the normal human mouth — ___________ 6. The number of years in a millennium — ___________ 7. The number of months in a year — ___________ 8. Days in December – ___________ 9. Degrees in a right angle — ___________ 10.Books in a trilogy — ___________ 11.Minutes in an hour — ___________ 7 12.Legs has an octopus — ___________ 13.The number of cents in a half-dollar — ___________ 14.Players in a soccer team — ___________ 15.Number of hours in a day — ___________ 16.Celsius boiling point — ___________ Задание 7. Write the correct ordinal number. (first, second, third, fourth, fifth, sixth, …) 1. Saturday is the __________ day of the week. 2. The ___________ month of the year is June. 3. The ___________month of the year is March. 4. In a competition the gold medal is for the________ place and the silver medal is for the__________ place. Задание 8. Choose the correct form. birth. century. 1. It happened in the middle of the twentyth/twentieth century. 2. I usually go to school by bus six/bus sixth. 3. He is now ranked hundred/hundredth in the world of tennis. 4. 1999 was the second hundred/the two hundredth anniversary of; Pushkin’s 5. The car changed the life of people in the 20th/the 20s century. 6. At least two third/two thirds of the novel is about the life of people in the 19th 7. He was the third/the thirdth to arrive. 8. 8 The USA ranks third/three in population. 9. 10.Vincent Van Gogh’s paintings are among the most famous of the 19 century / I am the one hundred and first/one hundredth and first in this huge line. the 19th century. Задание 9. And now let’s solve some mathematical problems. 1. A large box contains 18 small boxes and each small box contains 25 2. chocolate bars. How many chocolate bars are in the large box? It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.? 3. Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers? 4. Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and 5. a box of pens at $1.70. How much did Linda spend? John read the quarter of the time that Tom read. Tom read only two- fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read? 8 6. The distance between points A and B is 320 km. *How much does it take a car to cover the distance? *How much petrol is needed? *How much will it cost? speed – 80 km/h; petrol – 50 roubles per liter; 7. Подведение итогов урока. Выставление оценок. Объяснение домашнего задания. При создании урока использовались следующие источники: 1. Учебник MACMILLAN Guide to Science (Elena Kozharskaya и др.) 2. https://www.youtube.com/watch?v=LQEuywkWa2U 3. http://grammar-tei.com/uprazhneniya-na-chislitelnye-v-anglijskom- 4. https://www.syl.ru/article/350766/istoriya­chisla­nol­ego­svoystva 5. https://www.analyzemath.com/primary_math/grade_5/problems_sol.ht yazyke/ ml 6. https://yandex.ru/images/search?p=1&text=%D0%BA %D0%B0%D1%80%D1%82%D0%B8%D0%BD%D0%BA %D0%B8%20%D0%BD%D0%B0%20%D0%BC %D0%B0%D1%82%D0%B5%D0%BC %D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA %D0%B8%D0%B5%20%D1%82%D0%B5%D0%BC %D1%8B&pos=50&rpt=simage&img_url=https%3A%2F %2Fforexdengi.com%2Fattachment.php%3Fattachmentid %3D2256484%26stc%3D1%26d%3D1540993805&lr=213 7. http://curiosity101.com/a-brief-history-of-numbers-and-counting/ 8. https://yandex.ru/search/?lr=213&text=%D0%BA %D0%B0%D1%80%D1%82%D0%B8%D0%BD%D0%BA %D0%B8%20%D0%BD%D0%B0%20%D1%82%D0%B5%D0%BC %D1%83%20well%20done! МАТЕРИАЛ ДЛЯ УЧИТЕЛЯ – АУДИОСКРИПТ К ВИДЕО С ПЕРЕВОДОМ We may never know how the Indians came up with their number system, but we do know that they refined and perfected it creating the ancestors for the nine numerals we use across the world today. Many ranked the Indian system of counting as one of the greatest intellectual innovations of all time developing into 9 the closest thing we could call a universal language. But there was one number missing, and it was the Indians who would introduce it to the world. The earliest known recording of this new number dates from the 9th century that was probably in practical use for centuries before this strange new numeral is engraved on the wall of a small temple in the fort of Gwalior in central India. So here we are in one of the true holy sites of the mathematical world. and what I'm looking for is in this inscription written on the wall up here are some numbers and here's the new number it's zero it's astonishing to think that before the Indians invented it there was no number zero to the ancient Greeks it simply hadn't existed. Тhe Egyptians Mesopotamians and as we've seen the Chinese zero had been in use but as a placeholder, an empty space to show a zero inside a number. The Indians transform z-row from a mere placeholder into a number that made sense in its own right, a number for calculation, for investigation. This brilliant conceptual leap would revolutionize mathematics now with just 10 digits 0 to 9. It was suddenly possible to capture astronomically large numbers in an incredibly efficient way but why did the Indians make this imaginative leap? Well, we'll never know for sure but it's possible that the idea and symbol that the Indians use for 0 came from calculations they did with stones in the sand. When stains were removed from the calculation a small round hole was left in its place representing the movement from something to nothing. But perhaps there's also a cultural reason for the invention of 0. For the ancient Indians the concepts of nothingness and eternity were at the very heart of their belief system. In the religions of India the universe was born out of nothingness and nothingness is the 10 ultimate goal of humanity. So it's perhaps not surprising that a culture that so enthusiastically embraced the void should be happy with a notion of zero. The Indians even use the word for the philosophical idea of the void shunya to represent the new mathematical term zero. Возможно, мы никогда не узнаем, как индийцы придумали свою систему счисления, но мы знаем, что они усовершенствовали и усовершенствовали ее, создав предков для девяти цифр, которые мы используем по всему миру сегодня. Многие считают индийскую систему подсчета одним из величайших интеллектуальных нововведений всех времен, превращаясь в самое близкое, что мы можем назвать универсальным языком. Но пропало одно число, и именно индейцы представили его миру. Самая ранняя известная запись этого нового числа датируется 9 веком, который, вероятно, находился в практическом использовании на протяжении веков, прежде чем эта странная новая цифра была выгравирована на стене небольшого храма в форте Гвалиор в центральной Индии. Итак, мы находимся в одном из истинных святых мест математического мира. и то, что я ищу, в этой надписи, написанной на стене, вот некоторые цифры, и вот новое число, это ноль, удивительно думать, что до того, как его изобрели индейцы, у древних греков не было нуля, которого просто не было. т существовал. Египтяне, месопотамцы и, как мы видели, китайский ноль использовались, но в качестве заполнителя, пустого пространства, показывающего ноль внутри числа. Индейцы превращают z-строку из простого заполнителя в число, которое само по себе имеет 11 смысл, число для вычисления, для исследования. Этот блестящий концептуальный скачок произвел бы революцию в математике теперь всего с 10 цифрами от 0 до 9. Внезапно стало возможным запечатлеть астрономически большие числа невероятно эффективным способом, но почему индийцы сделали этот творческий скачок? Ну, мы никогда не узнаем наверняка, но возможно, что идея и символ, который индейцы используют для 0, были получены из расчетов, которые они сделали с камнями в песке. Когда пятна были удалены из расчета, на его месте осталась небольшая круглая дыра, представляющая движение от чего-то к ничему. Но, возможно, есть и культурная причина изобретения 0. Для древних индейцев понятия небытия и вечности лежат в основе их системы убеждений. В индийских религиях вселенная родилась из небытия, а небытие является конечной целью человечества. Так что, возможно, не удивительно, что культура, которая с таким энтузиазмом приняла пустоту, должна быть счастлива с понятием нуля. Индийцы даже используют слово для философской идеи void shunya, чтобы представить новый математический термин ноль.