8. NUMBERS AND MEASUREMENTS 1. Introduction. Discuss these questions in small groups. a)Do you like learning English? What other languages can you speak? At what level? b) Describe some interesting teacher you had at secondary school. c)Do you like mathematics and physics? Are you good at it? What is difficult about it? d) What are some things that a biologist needs to calculate? An astronomer? A physicist? A geologist? What about a chemist? e)“Mathematics is the father of all sciences.”, “Everything in science has its origin in mathematics.”, Mathematics is the most primary science.” Do you agree with these statements? Why? Why not? f) What could you calculate or measure in this classroom? Think of weight, volume, temperature, size… g) Do you know any magical/lucky/unlucky numbers? Have you heard of numerology? Do you trust it? READING NUMBERS: 0 zero / nought (in mathematics) / „o“ (in telephone numbers) 25 twenty-five 1. the first 135 one hundred and thirty-five 2. the second 1258 one thousand two hundred and fifty-eight 5. the fifth 2 000 000 two million 26. the twenty-sixth 26 / 11 the twenty-sixth of October October the twenty-sixth 2. Work in pairs. Find out this information: a) What´s your name and surname? Can you spell it? b) How old are you? When were you born? c) In which year of your study are you? d) What´s your phone number? e) What´s your address? Include the postal code. f) How many brothers and sisters do you have? Can you spell their names? g) How many students are there in this class? h) Can you read these numbers? : 2654 4000 25 158 264 3 000 000 25. 78. SIMPLE ARITHMETICS Look at the way we say these examples: 4 + 4 = 8 four and (plus) four is / equals eight 9 − 2 = 7 nine minus two is seven 5 × 5 = 25 five times five is twenty-five or five multiplied by five is twenty-five 8 ÷ 4 = 2 eight divided by four is two Here are some more arithmetical symbols. Notice how to say them. 2^2 two squared square root of … - 2^3 minus (negative) two cubed cube root of … 2^4 two to the power of four π pi log[10]7 log of seven to the base ten x=3(a+b) x equals three, bracket a plus b, bracket This is how we say fractions a half a third one thousandth/one over a thousand a quarter three fifths one hundredth/ one over a hundred three quarters two and a half 35 10 thirty-five over ten Look at this example 5 + 4 = … How much is five and four? Five and four is nine. 3. Work in pairs. Ask and answer questions about these in the same way. a) 12 − 6 = … d) = … g) = … b) 9 × 5 = … e) h) 2^4 = … c) 30 ÷ 6 = … f) 9^2 = … i) π = … Look at this example: Add six to seven. Now multiply by four. Subtract four. Divide by twelve. What is the answer? Four. 6 + 7 = 13, 13 × 4 = 52 52 − 4 = 48 48 ÷ 12 = 4. 4. Work in pairs to do these exercises. One of you should ask the questions. The other should give the answers without looking at the paper. See how quickly you can 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 two. Multiply by 10. What is the answer? c) Add six to eight. Multiply by 10. What is the answer? d) Take 50% of the students in your class. Multiply by 2. Divide by 4. What is the answer? FRACTIONS AND DECIMALS Notice how we say the decimals. Read these examples. = 0.5 (nought point five / zero point five) = 1.75 (one point seventy five) = 3.8 (three point eight) = 0.874 (nought point eight seven four) and the measurements: 0.643 g = (nought) point six four three of a gramme 1.385 cm = one point three eight five centimetres 1 km = 0.621 miles : one kilometre equals nought point six two one miles 5. Change these fractions into decimals. Read it aloud with a neighbour. a) = c) = b) = d) = 6. Work with a neighbour. Describe these numbers: Example: a) One kilometre equals one thousand meters or ten to the power of three. One decimetre equals one tenth of a meter or ten to the power of minus one. a) kilo- one thousand: 1 km = 1000 m 10^3 b) deci- one tenth: 1 dm = m 10^−1 c) centi- one hundredth: 1 cm = m 10^−2 d) milli- one thousandth: 1 mm = m 10^−3 e) micro- one millionth: 1 μm = m 10^−6 f) nano- one thousand millionth: 1 nm = m 10^−9 PERCENTAGES 7. 65% (per cent) of our body weight is oxygen. Use the diagram to make more sentences. READING SIMPLE EQUATIONS^1: Here are some common compounds, their names and FORMULAS: NaCl – sodium chloride H[2]SO[4] – sulphuric acid ZnSO[4] – zinc sulphate C[6]H[6 ] - benzene ZnO – zinc oxide HCl – hydrochloric acid Na[2]CO[3] – sodium carbonate NH[3] - ammonia CO[2 ] - carbon dioxide NaOH – sodium hydroxide These formulas are useful for writing EQUATIONS. [] Example: HCl + NaOH → NaCl + H[2]O We spell as: H Cl plus Na OH gives Na Cl plus H[2]O We read as: hydrochloric acid reacts with sodium hydroxide to form sodium chloride and water. combines with 8. Complete these equations: a) CuO + H[2 ]→ ……………………………… (copper oxide reacts with hydrogen to form copper and water) b) Na[2]CO[3] + 2 HCl → ………………………….. (sodium carbonate reacts with 2 molecules of hydrochloric acid to form sodium chloride, carbon dioxide and water) c) Zn + 2HCl → …………………………… (zinc reacts with 2 molecules of hydrochloric acid to form zinc chloride and hydrogen) 9. Express these equations in words: 1. 2 Na + Cl[2 ]→ 2 NaCl ................................................................................................... .................... 2. ZnO + H[2]SO[4 ]→ 2 ZnSO[4] + H[2]O ................................................................................................... 3. 2 Na + 2 H[2]O → 2 NaOH + H[2 ................................................................................................... ........................................................] 10. Watch the video lecture about pH calculation given by Dr.Goldwhite.^2 Listen and write down the calculation. Then watch it for the second time and note down the important words and phrases. Finally, try to describe the calculation in pairs. Useful vocabulary: acid (n ) - kyselina base (n) – zásada obtain (v) – získat strongly acidic (adv+adj) – silně kyselé basic (adj) - zásadité species (n) - vzorek concentration of a solution (n) ion (n) - iont relate to (v) – vztahovat se k … – koncentrace roztoku relationship (n) - vztah 11. HOMEWORK – UNITS OF MEASUREMENT a) Make 10 sentences from the table below. a) Example: The height of large objects is measured in metres. The height volume area width surface area length radius cross-sectional area diameter circumference of large small very small minute cylindrical objects is measured in m cm mm μm m^3 cm^3 mm^3 m^2 cm^2 mm^2 km distance between places Help: Units of measurements and their abbreviations kilometre km metre m decimetre dm centimetre cm millimetre mm square metre m^2 cubic metre (metre cubed) m^3 micrometre μm = („micron“) b) Say whether the following statements are true or false. Correct the false statements. a) Duration is measured in degrees Centigrade T/F b) The second is a unit of time T/F c) Speed is measured in kilograms per hour. T/F d) The watt is a unit of electrical charge. T/F e) Density is measured in grams per metre cubed. T/F f) The gram is a unit of mass. T/F g) Liquid measurements are made in litres, or cubic decimetres. T/F Help: Other measurements and their units: electric current ampere (amp) electric power watt (W) electric resistance ohm (Ω) electric potential difference volt (V) temperature degrees Centigrade (°C) mass gram (g), kilogram (kg) weight (the force of gravity on mass) newton (N). kilonewton (kN) speed kilometres per hour (km/h) (km.h^−^1) density kilograms per cubic metre (kg/m^3) (kg.m^−3) time (duration) second (s), minute (min), hour (h) fluid capacity litre (l) = cubic decimetre (dm^3) concentration molar (mole/liter) ^ For more units and their abbreviations visit http://www.jbc.org/site/misc/itoa.TI.xhtml Sources: Lesson based on Bates, Martin and Dudley-Evans, Tony: Nucleus of General Science. Longman 1990. ^1Adapted from Cihová, Jarmila et al. Angličtina pre študentov chémie. Bratislava: Univerzita Komenského, 2003. ^ 2Available at http://www.youtube.com/watch?v=LZk1_yzF9js. Accessed 29th October 2010 Week 8 – Numbers and Measurements - Vocabulary four and (plus) four is / equals eight čtyři plus čtyři se rovná osm nine minus two is seven devět mínus dva je sedm five times five is twenty-fine / five multiplied by five is twenty-five pět krát pět je dvacet pět eight divided by four is two osm děleno čtyřmi je dva two squared dva na druhou minus (negative) two cubed mínus dva na třetí two to the power of four dva na čtvrtou square root of … druhá odmocnina cube root of … třetí odmocnina three quarters tři čtvrtiny a third třetina one thousandth/one over a thousand jedna tisícina / jedna lomeno tisíc How much is five and four? Kolik je pět plus čtyři? one thousand two hundred and fifty-eight tisíc dvěsta padesát osm add (v) přičíst subtract (v) odečíst One kilometre equals nought point six two one miles. Jeden kilometr se rovná nula celá šedesát dva mil. 7. 65 per cent of our body weight is oxygen. 7,65 procent těledné váhy je kyslík. Hydrochloric acid reacts with sodium hydroxide to form sodium chloride and water. Kyselina chlorovodíková reaguje s hydroxidem sodným a vytvoří chlorid sodný a vodu. sodium chloride chlorid sodný carbon dioxide oxid uhličitý sulphuric acid kyselina sírová sodium hydroxide hydroxid sodný sodium carbonate uhličitan sodný acid (n ) / acidic (adj) kyselina / kyselý base (n) / basic (adj) zásada / zásaditý obtain a species (v) získat vzorek formula (n) vzorec equation (n) rovnice ion (n) iont relate to (v) / relationship (n) vztahovat se k / vztah concentration of a solution (n+prep+n) koncentrace roztoku The height of large objects is measured in metres. Výška velkých předmětů se měří v metrech. surface area (n+n) povrch width (n) šířka length (n) délka square metre (adj+n) metr čtvereční cubic metre (metre cubed) (adj+n) metr krychlový electric current (adj+n) elektrický proud electric power(adj+n) elektrický výkon electric resistance (adj+n) elektrický odpor kilometres per hour kilometry za hodinu Temperature is measured in degrees Centigrade (n+n) Teplota se měří ve stupních Celsia.