Lekcja 2 B

SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: Teresa Olechowska
DLA LEKTORA
Lekcja 2 B
______________________________________________________________________________________________
MATHEMATICS
INTRODUCTION (in the class):
Explain that in this part they are going to tackle the mathematical concepts of powers, roots
and matrices. The introduction and TASK 1 should not take more than 5 minutes.
Think and try to match the answers to the following questions:
1. What does it mean, when we say x squared? d
2. What does it mean when you see the following:
16 b
3.
4.
5.
6.
a.
b.
c.
d.
e.
What is a matrix? f
What do matrices consist of? c
How can matrices be added? a
How can matrices be multiplied? e
By adding corresponding elements - only if they have the same order.
It means the square root of sixteen and it equals 4.
Elements (numbers/letters), rows and columns.
Then the 2 is called the power or index.
If the number of elements in the columns of one matrix equals the number of elements in the rows of
the other matrix.
f. It is an array of numbers or letters in the shape of a rectangle.
Key: 1d; 2b; 3f; 4c; 5a; 6e
INPUT – HOMEWORK
TASK 2
When checking this task, just point out that there are several ways of reading the powers, i.e.
“squared, cubed, but - to the power of [number], or to the nth power”.
Knowing that:
a x a² = a³ (a times a squared is equal to a cubed)
a³ x a² = a (a cubed times a squared is equal to a to the power of five, or a to the fifth power )
a. practice reading out the following:
1. a² + b² a squared plus b squared
2. x² + y³
x squared plus y cubed
3. p
p to the power of four / to the fourth power
4. xⁿ
x to the power of n / to the nth power
b. Can you solve the following equations:
1. 4a² + 2a² = ?6a²
2. 4a² - 2a² = ?2a²
3. 4a² x 2a² = ? 8a
4. 4a² ÷ 2a² = ? 2
TASK 3
Point out the plural of the word index > indices.
Complete the following statements about procedure:
1. When multiplying two numbers which have been raised to certain powers e.g. n³ (n cubed) and n (n
to the fifth), we add the indices .
2. When we wish to raise a power to a power, the indices must be multiplied . In the above case the
answer is n¹.
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: Teresa Olechowska
DLA LEKTORA
Lekcja 2 B
______________________________________________________________________________________________
To learn more you can visit the YouTube site:
http://www.youtube.com/watch?v=qOn-NW_lsvE&feature=related
Key: 1. cubed; to the; indices; 2. raise; to; indices; multiplied.
TASK 4
Before checking the answers, again underline that there are different ways of reading the
roots, i. e. a square root, a cube root, but the nth root. However, some people also say the
second root and the third root.
Why "Root" ... ?
When you see "root" think:
"I know the tree, but what is the root that produced it?"
Example: in √9 = 3 the "tree" is 9, and the root is 3.
http://www.mathsisfun.com/numbers/nth-root.html
Knowing that:
is called the radical sign;
64 means the square root of 64;
27 means the cube root of 27;
x means the fifth root of x.
If we want to find the root in the following example, we must divide the index by the root:
Practice reading out the following, and then express them in more simple terms:
1. √x²;
2. √4x;
3. √a²b²
4. ∜mn
5.
b³
6.
a³
7. √16b²
If you want to learn and practice more, check the YouTube sites:
http://www.youtube.com/watch?v=PlZZ6ZZJBg4
Key:
1. x;
2.2 x²;
3. ab;
4. mn;
5. b;
6. 2a²;
7. 4b.
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: Teresa Olechowska
Lekcja 2 B
______________________________________________________________________________________________
TASK 5
While checking in class - it is worth mentioning that in Polish language we have the same
rules.
Words which retain their original Greek or Latin forms make their plurals according to the rules of Greek
and Latin.
-us > -i
-is > -es
-um
-ix
-a
-on
-ices
-ex
Supply the proper plurals of the words in the brackets.
1. The new (syllabus) syllabi will be drawn up according to different (criterion) criteria.
2. These (index) indices must be multiplied.
3. (Matrix) matrices can be added if they have the same order.
4. He agreed that these were strange (phenomenon) phenomena .
5. Television and newspapers are the mass (medium) media .
Key: 1. syllabi; 2. indices; 3. matrices; 4. phenomena; 5. media
TASK 6
1. Now add two matrices:
a
4
1
7
5
2
8
3
6
9
+
b 3
5
6
1
4
9
7
2
8
=
2. And multiply the following two matrices:
b 3 1
a 2 0 3 x
2 1
- 1 3 1
1 0
=
If you want to learn more - visit:
http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php
http://www.youtube.com/watch?v=sYlOjyPyX3g
Key:
1. addition:
7 6 10
6 6
8
13 17 17
2. multiplication:
(2 x 3 + 0 x 2 + 3 x 1)
(2 x 1 + 0 x 1 + 3 x 0)
9 2
=
(- 1 x 3 + 3 x 2 + 1 x 1) (- 1 x 1 + 3 x 1 + 1 x 0)
4
3
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: Teresa Olechowska
DLA LEKTORA
Lekcja 2 B
______________________________________________________________________________________________
CLASSWORK CHECKING
TASK 7
When you check their homework – which should take only a few minutes, you can control how
they have got the result of addition or multiplication. The questions in TASK 7 are for some
discussion about mathematical concepts in general. The discussion can be serious or a
humorous one – it depends on the group.
TASK 7
Discuss the following questions:
1. Can numbers or other mathematical concepts be said to exist?
2. Are numbers ‘discovered’ or ‘invented’ (Leopold Kronecker said that “God made the integers. All
else is the work of men”)?
3. Taking negative numbers into consideration – has anyone seen ‘minus one cow’?
1.
2.
3.
4.
5.
6.
7.
BIBLIOGRAPHY
A Mathematical Dictionary, Jason, R.E., Pergamon Press, 1979
Alex’s Adventures in Numberland, Bellos, Alex, Bloomsbury, 2010
Computer Adventures in Lingua Land, Olechowska, Teresa, Rouba, Wojciech, WSiP, 1992
English for Basic Maths, Blackie, David, Nelson, 1978
Lingua Land Kappa Land, Olechowska, Teresa, WPW, 1986
Mathematics and the Imagination, Kasner, Edward, Newman, James, Penguin Books, reprinted 1979
MINI anglojęzyczne – EAP & ESP, Olechowska, Teresa, wydanie własne, 2012
http://dictionary.reference.com
http://www.purplemath.com/modules/radicals.htm
http://www.mathsisfun.com/numbers/nth-root.html
http://en.wikibooks.org/wiki/Primary_Mathematics/Powers,_roots,_and_exponents
http://www.youtube.com/watch?v=qOn-NW_lsvE&feature=related
http://www.youtube.com/watch?v=PlZZ6ZZJBg4
http://en.wikipedia.org/wiki/Matrix_multiplication
http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php
http://www.youtube.com/watch?v=sYlOjyPyX3g
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