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*