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Lesson 6: NUMBERS
I. Discuss the questions below
1. Is it Maths or Math? Choose the correct verb form: Mathematics give/gives you wings.
2. “Mathematics is the father of all sciences.” Do you agree? Can you think of other
metaphors for mathematics? What about maths in relationship to physics?
3. Why do you think some ancient people believed mathematics to be mysterious? Why do
you think certain numbers were considered magical?
4. What could you calculate or measure (express in numbers) in this room?
5. What are the things that these people need to calculate?
a. physicist
b. biologist
c. astronomer
d. geologist
e. chemist
II. a) Give an example of a cardinal, ordinal, decimal, even, odd, irrational and prime
number. What does it mean to round a number up/down?
b) Read these numbers or fractions:
0.2
0.05
2479 (ordinal number)
549495009 (telephone number of your teacher – call in emergency)
2,053
2.053
1800
1 415 605
2 000 000 000
1/3; ¾; 2/5; 14/15
III. Listening: How big is a billion?
(https://www.youtube.com/watch?annotation_id=annotation_215752&feature=iv&src_vid=SbZCECvoaTA&v=
C-52AI_ojyQ)
Listen and watch the video on the different systems, then summarise the main points.
IV. 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-fine
or five multiplied by five is twenty-five
8 ÷ 4 = 2 eight divided by four is two
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Here are some more arithmetical symbols. Notice how to say them.
22
two squared √ square root of …
- 23
minus (negative) two cubed √
3 cube root of …
24
two to the power of four π pi
log107 log of seven to the base ten x=3(a+b) x equals three, bracket a
plus b, bracket
V. Work in pairs. Solve these maths problems.
a) 125 − 69 = … d) √16= … g) √27
3
= …
b) 9 × 5 = … e) 4 + 7
1
5
=. .. h) 24
= …
c) 30 ÷ 6 = … f) 92
= … i) π = …
Look at this example:
Add six to seven. Now multiply by four. Subtract four. Divide by twelve. What is the answer?
6 + 7 = 13, 13 × 4 = 52 52 − 4 = 48 48 ÷ 12 = ?
Work in pairs. Write down graphical image of the problems below, then take turns in saying them
aloud and finding the answer (one of you should say the equation and 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 3. What is the answer?
VI. Using letters as symbols, write a formula for each relationship. The first one is done
for you.
1. Work is the product of force times the distance through which the force acts.
w=f x d
2. The volume of a cube is calculated by multiplying the length times the width
times the height.
3. Power is the rate at which work is done; it is computed by dividing work by
time.
4. Kinetic energy is calculated as one half the product of the mass times the
velocity squared.
VII. Read the following formulas:
1. N = kg.
m.
s-2
2. v = u + at
3. s = ut + at2
VIII. Mill´s constant
(http://www.numberphile.com/videos/mills_constant.html)
Listen and watch the video on Mill´s constant. What is it used for? Why do the presenters
find it special? Does it have any limitations?
Lesson adapted from: A. Rozkošná (Sources: Bates, Martin and Dudley-Evans, Tony: Nucleus of General Science. Longman
1990. Zemanová, A. Angličtina pre fyzikov. )
http://www.numberphile.com/
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GRAMMAR REVISION: COUNTABLE/ UNCOUNTABLE NOUNS
I. Divide the words below into two categories: countable and uncountable nouns
metre, science, molecule, knowledge, nitrogen, information, radius, second,
heat, fraction, time, petroleum, research, change, object, ion, light, substance,
matter, energy, electron, advice
II. Complete the sentences below with “many”or “much”
1. How ___________years ago were the Universe and space-time created?
2. How ___________time does it take the Earth to go around the Sun?
3. How___________ seconds are there in one day?
4. How ___________ of the Universe do we know today?
5. How ___________ planets are there in the solar system?
6. How ___________ liquid does a beaker contain?
7. How ___________energy would you need to boil 10 litres of water?
8. How ___________ nitrogen does the atmosphere contain?
9. Do you find __________ useful information about quantum physics on the Internet?
10. Will we exploit ____________ more nuclear energy in the future than we do today? What do
you think?
Now answer these questions.
III. Complete the sentences with “little”, “a little”, “few”, “a few”
1. As very _____________ research has been done in the field, we still have no antidote to the
disease.
2. Doing just _____________ research threw up some very useful information.
3. Only _____________ scientists were invited to take part in the project. That is probably why
it was not successful.
4. The project team consists of _____________ well-known chemists.
Week 6 – 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
acceleration zrychlení, akcelerace
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
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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.
approximate přibližný
round off zaokrouhlit
diameter průměr
velocity rychlost
resistance odpor
el.charge elektrický náboj
angle úhel
density hustota; propustnost
obtain a species (v) získat vzorek
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
temperature (n) teplota
degree Centigrade (n+n) stupeň Celsia
kilometres per hour kilometry za hodinu
Second is a unit of time. Sekunda je jednotka času.