The History of Mathematics - BBC doc (parti) http://www.voutube.com/watch?v=WD 1 CXzTbUtA Listen to and watch the video, then fill in the missing expressions in the statements. 1) In his studies of maths, the speaker is especially interested in.............. 2) Give examples of patterns and sequences which occur in the world. 3) The most basic concepts of maths are......................................... 4) Also animals understand......................................................... 5) People around the Nile river started to settle around......................... 6) The most important event in Egypt was........................................ 7) People used this event for......................................................... 8) People of Egypt needed to calculate or measure................................ 9) Egyptians used their...................for measurements. 10) It was important to know the area of farmer's land so that it could be........... 11) The first numbers in history were.................................................... 12) They used a....................number system because they used their 10 fingers. 13) There was, however, no concept ofa................................................... 14) Million minus .1 has.................characters in total. 15) The.......................................is the most important mathematical document form ancient Egypt. 16) The speaker demonstrates how to calculate............................................ 17) The interesting thing is that the second number is described in....................... NUMBERS AND MEASUREMENTS SIMPLE ARITHMETIC Look at the way we say these examples four and four is eight nine minus two is seven live times five is twenty-five five multiplied by live is twenty-five eight divided by four is two 4+4-8 9-2 - 7 5x5 - 25 8-5-4 = 2 or 1. Now read these aloud a) 12+7 =19 b)!5-r3 = 5 c) 6x2 = 12 d) 23-6 = 17 e)9-3 = 6 f)6+3 »9 g) 28-M = 7 h) 8x9 = 72 i) 3x8 « 24 j) 12-4 - 8 ARITHMETIC Here are some more arithmetical symbols. Notice how to say them. 21 two squared 23 two cubed 2* two to the power of four a pi y/ square root ^ cube root This is how we say fractions i a half J a third i a quarter ' | three fifths i three quarters 2| two and a half 1. Now read these aloud 5J. 2|. 104. i If. 4i | Look at this example 5+4 How much is five and four? Five and four is nine. 2. Ask and answer questions about these in the same way. Work with a friend. e) ^16 = ... i) ^27 r» a) 12-6 = b) 9x5 = . c) 30+6 «= d) 4) + 6£ = f) 4 + 7* = ... g) 33+6$ - ... h) 9* - . .. j) 2* = k) jt = .., I) 2i-i-2 = ... FRACTIONS AND DECIMALS Parts of a whole number can be expressed as fractions or as decimals. Here are some fractions with decimal equivalents. Notice how we say the decimals: \ = 0-5 (nought point live) 11 = 1-75 (one point seven five) = 3-8 (three point eight) ■fijfo = 0874 (nought point eight seven four) and the measurements: 0643 g = point six four three of a gramme 1-385 cm = one point three eight five centimetres. 1. Change these fractions into decimals a) i b) 4$ c) 6J d) 7) e) ,7„ Look at the way we xay this example I km 0621 miles one kilo metre equals nought point six two one miles *. PERCENTAGES We can express parts of a full quantity as percentages ("/„). Look at this example 65 % (per cent) of our body weight is oxygen. 2% cnlciiim 3% nitrogen -10% hydrogen 1 % other elements 1. Now use the diagram to make more sentences about the composition oflhe body. Make a similar diagram and sentences about the composition of the atmosphere. MENTAL ARITHMETIC ---- Mental arithmetic is done in your head, not on paper. Practice in mental arithmetic will help you to think quickly in English. Look at this example Add six to seven. Now multiply by Tour. Subtract four. Divide by twelve. What is the answer? Four. Here »the process in numbers and symbols: 6 + 7 = 13, 13 x 4 - 52 52-4-48,48+12-4. I. Now work with a friend to do these exercises. One of you should hove his book open and ask the questions. The other should have his Iwok closed and gin the answers. See how quickly you am do it. a) Multiply 7 by 9. Add 9. Divide by 6. Subtract 3. What is the answer? b) Subtract 8 from 24. Divide by 2. Add 2. Multiply by 10. What is the answer? c) Take the average of 20. 24, 26 and 30. Multiply by 10. What is the answer? d) Take 50% of the pupils in your class. Multiply by 2. Divide by 4. What is the answer? c) Divide 20" by5. Multiply by 9. Add 32. What is the answer? f) Multiply 7 by 4. Add 20. Subtract 6. Divide by 6. What is the answer? g) Take the square root or 36. Add 14. Multiply by 5. Subtract I. What is the answer? h) Take the square root of 81. Add the square root of 16. Multiply by 12. Divide by 4. What is the answer? i) Calculate the volume of a.rectangular solid with a length of 10 cm. a height of 8 cm and a width of 5 cm. j) What is the length of a box which has a volume of 144 cc. a height of 4 cm and a width of 3 cm? Section 1 One-dimensional and two-dimensional shapes 1. Look at these: a point a straight lint • curvtd line an angle The letter 'E* has one vertical line and three horizontal lines. It also has four angles. Which of these letters are described below? D, M, C, H, F, L, Z, B. a) A letter with 2 horizontal lines and I vertical line. b) A letter with 1 curved line and no straight lines. c) A letter with 2 curved lines and I vertical line. d) A letter with 2 parallel vertical lines, 1 horizontal line and 4 angles. e) A letter with 2 vertical lines and 2 diagonal lines. Now write sentences describing these signs: + the equals sign the plus tign X " -i- the multiplication tign the division sign 2. Look at these figures and answer tbe questions: the minus sign TT PI P-141S9) O □ □ A a circle a square aractangla a triangle eeami-cacJe a) Which figure is curved? b) Which figures have parallel sides? c) Which figure always has equal sides? d) Which figure may have equal sides? c) Which figure has 3 angles? 0 Which figure has a curved side and a straight side? Now make sentences from the table: Example: A coin is shaped like a circle. It is circular in shape. A coin square. I rectangular 1 A ruler b shaped like a rectangle. circular in A set square A protractor semi-circle, triangle. It is square semi-circular shape. A chess-board circle. triangular -. k— . uMtirai line • horizontal line a diagonal Ho* Unitl Studying at University Lesson 1 - Making New Friends Functions: 1. introduction oneself - informal 2. identifying oneself (previous studies, current studies) 3. introducing others - informal 4. asking for / giving information Vocabulary: interests, likes, dislikes, life style, higher education Task 1: a) Prepare some questions for your partner to learn more about him / her. Try to be original. b) Decide what you would like to tell the others about yourself (something interesting, attractive, amazing something they will remember) Task 2: a) Work in pairs. Ask and answer questions about each other. Také notes to be able to introduce your partner to the others, b) In front of the class introduce your partner to the others. Task 3: Read and listen to the text about Libor Novák, a student of Masaryk University in Brno. Libor Novák, a student talks about himself. Hello. My name is Libor Novák and I come from Jeseník, a small town with a population of about 10,000, in the mountains of nothem Moravia but I'm currently living and studying in Brno. I study Chemistry at the Faculty of Science, which is very demanding but I am enjoying the challenge. I'm in the second year of a five year course which means that next year I'll be able to start specializing by choosing options in those areas which interest me most. Before coming here I attended the grammar school in Jeseník where my favourite subjects were Mathematics and Chemistry. On the other hand, I found languages more difficult and had to put in a lot of extra work to pass my school/ leaving exams. At the moment I am living in the halls of residence in Komirov although next year I will have to leave and find a place to stay privately since there are not enough rooms for all the students who want them. I share a double room with another student from Jihlava called Radek Kašpar who studies Geology. He would have studied Physics if it had been possible but he didn't get a high enough mark in his ef trance exams. n Task 4: Complete the questions about Pavel Zemanek. 1. Where..................................from? 2. What....................................do? 3. What...................................research...........? 4. Why...................................updating his C. V. ? 5. What.................................. like to do? 6. Where................................living? 7. Who 8. Why he he to share a flat............? to share a flat? Task 5: Listen to the text about Pavel Zeminek and answer the questions (task 4). Task 6: Work in pairs. Ask and answer questions about Libor Novik. Task 7: Grammar revision - the present simple & the present continuous Task 8: Vocabulary from task 3 and task S Task 9: a) Prepare a short talk about an imaginary student of the Faculty of Science. b) Work in groups of 4 - 5, tell the others about your student, choose the best, tell the class c) Choose the most original talk. k THINKING ABOUT LANGUAGE QUESTIONNAIRE 37 . student each student in the udents to complete at correspond to their * discuss their previous^ :ner. Take a quick cer inaire again and to plafl t will be true of the i partner: are the two : ry different? e whole group. ce to find out about perience, and the hich may be very vain :nt culture. It will alsoj •mething about the do on the course and tivities that they find the completed , it will help you build LEARNING A LANGUAGE: EXPERIENCE AND EXPECTATIONS Think about your previous experience of learning a language. Tick y) the sentences that are true for you: 1 Learning a language involves hard work Q is interesting Q is difficult □ is frustrating Q is painful Q is confusing Q is boring Q can be a lot of fun □ 2 When I am speaking a foreign language I: feel shy □ fee| confident □ feel frustrated □ feel challenged □ feel stupid □ feel happy □ is easy comes naturally requires a lot of memorization feel embarrassed feel tongue-tied feel as if I am a 3 Learning a language in class involves: reading a passage and answering questions translating a passage reading literature - writing grammar exercises doing a project learning about British culture learning grammar rules dictation listening to the teacher acting a play or a dialogue memorizing passages snaking a-TV or radio-programme reading aloud •earning lists of vocabulary □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ □ different person □ frequent teste role play, mime, and drama □ following a textbook □ making a newspaper □ letter writing □ practising speaking in pairs or groups . .. , • •"•>. v. ,i w- <-kk Uj..... listening to a tape and answering questions □ □ games □ repeating in chorus □ practising pronunciation □ class discussion and debates □ songs □ writing stories or essays ^ □ St!90 baCk t0 the be9'nnin9 of me questionnaire. Mark with a cross (x) the nces that you expect will be true of the language course you are about to follow.