Arabic Republic of Egypt Ministry of Education Book Sector
Mathematics Fifth Primary
2012-2013
غري مرصح بتداول هذا الكتاب خارج وزارة الرتبية والتعليم
5
Student's Book First Term
Authors Mr. Omar Fouad Gaballa Prof.Dr. Afaf Abo-ElFoutoh Salah Dr. ,ZZHT >HZÄ 9V\WOHLPS Mr. 4HOTV\K @HZZLY (S ROH[PLI Mr. :LYHÄLT ,SPHZ :RHUKLY
Revised by Mr. /\ZZLPU 4HOTV\K /\ZZLPU Counsellor of Mathematics M.O.E
Issued: 2009 D.N: 11224/2009 ISPN: 978-977-6294-15-8
ﺑﺴﻢ ﺍﷲ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ Dear students:
It is extremely great pleasure to introduce the mathematics book for fifth primary. We have been specially cautious to make learning mathematics enjoyable and useful since it has many practical applications in real life as well as in the other subjects. This gives you a chance to be aware of the importance of learning mathematics, to determine its value and to appreciate the mathematicians roles. This book sheds new lights on the activities as a basic objective. Additionally, we have tried to introduce the subject simply and excitingly to help attaining mathematical knowledge as well as gaining the patterns of positive thinking skills which pave your way to creativity. This book is divided into units, each unit contains lessons. Colors and pictures are effectively used to illustrate some mathematical concepts and the properties of figures. Lingual level of previous study has also been taken into consideration. Our great interest here is to help you get the information by yourself in order to develop your self-learning skills. Calculators and computer sets are used when there’s a need for. Exercises, practices, general exams, Activities, unit test, general tests, and final term tests attached with model answers have been included to help you review the curriculum completely. Eventually, we hope getting on the right track for the benefits of our students as well as for our dearest Egypt hoping bright future to our dearest students. Authors
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Contents First Term: Unit one: Fractions Lesson One :
Approximating to the nearest hundredth and thousandth . .. . 4
Lesson Two:
Comparing fractions .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 10
Lesson Three:
Multiplication: Multiplying fractions and decimal numbers by 10, 100, 1000 15
Lesson Four:
Multiplying a fraction or a decimal number by an integer number .. 17
Lesson Five:
Multiplying common fractions . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 19
Lesson Six:
Multiplying decimal fractions .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 20
Lesson Seven: Division: (1) Dividing fractions .. .. .. .. .. .. .. .. .. .. .. .. .. .. 23 Lesson Eight: (2) Dividing fractions and decimal numbers by 10, 100, 1000 .. .. 25 Lesson Nine:
(3) Dividing an integer by a 3-digit number without having a remainder
27
Lesson Ten:
(4) Division by a decimal fraction and by a decimal number . .. 29
General Exercises .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 36 Activity .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 39 Unit Test .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 40
Unit Two: Sets Lesson One :
What is a set? .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 42
Lesson Two:
Mathmatical expression of a set .. .. .. .. .. .. .. .. .. .. .. .. .. .. 44
Lesson Three: Belonging of an element to a set . .. .. .. .. .. .. .. .. .. .. .. .. .. 47 Lesson Four:
Types of sets .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 49
Lesson Five:
Equal sets . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 51
Lesson Six:
Inclusion and subsets .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 53
Lesson Seven: Intersection of two sets .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 56 Lesson Eight: Union of two sets .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 59
Lesson Nine:
The universal set .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 61
Lesson Ten:
The complement of a set .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 63
Lesson Eleven: The difference of two sets .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 65 General Exercises .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 67 Activity .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 69 Unit Test .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 70
Unit Three: Geometry Lesson One
The Circle .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 72
Lesson Two:
Drawing a triangle given the lengths of its three sides .. .. .. 76
Lesson Three:
Drawing line segements from the vertices of a triangle perpendicular to its opposite sides .. .. .. .. .. .. .. .. .. .. .. .. .. 79
General Exercises .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 83 Activity .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 85 Unit Test .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 86
Unit four: Probability Lesson One:
Experimental Probability .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 88
Lesson Two:
Theoretical Probability .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 91
General Exercises .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 94 Activity .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 95 Unit Test .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 96 General Exams .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 97 Answers
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 100
List of Symbols C
Set of counting numbers
G
Less than or equal to
E
Set of even numbers
=
Equal to
O
Set of odd numbers
≠
Not equal to
P
Set of prime numbers
Open curve
∅ or { }
Null set or empty set
Closed curve
∈
Belonging
Circle
∉
Not belonging
r
radius
⊂
Inclusion
r
Approximate ratio
⊄
Not inclusion
AB
Line segment A B
⋃
Union
AB
Ray A B
⋂
Intersection
AB
Straight line A B
U
Universal set
d
Angle
X`
Complement set
X-Y
X difference Y
m (d B) P (E)
Measure angle (B), m (dB) Probability of event P
N
Set of natural numbers
/
Congruent
>
More than
b
Triangle
H
More than or equal to
<
Less than
(X, Y)
Ordered pair X, Y
P (E)
(X, Y)
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The Complement of a set
Think and discuss
you will learn If the set of the music team at school is:
☺ To find the
U= {Magdy, Yasser, Fayez, Lila, Souad}
complement of a set. U
Then, the set of boys in the team X. X
X= {Magdy, Yasser , Fayez}
✗ Yasser
✗ Lila
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✗ Magdy
✗ Fayez
✗
X = { ...................... } Therefore, the set x is the complement of the set x. Complete X ∪ X = ... , X ∩ X = ..... If the universal set
Key Terms
U ✗
U = {1, 2, 3, 5, 6, 8, 9}
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6
9
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A ✗
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3
5
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1
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2
8
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The complement of a set A with regard to the set U is A where: A ∪ A = U , A ∩ A = ∅
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1 Look at the opposite Venn diagram then complete: U
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A = ............
2 Look at the opposite Venn diagram then complete: U
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Find each of the following sets:
Ma
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X
B
Y
C
XțY
D
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E
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F
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Exercise General Exercises 1 Place the suitable symbol Ǻ , ǻ , ɴ or ɶ in the blanks: A
8 ..... {5, 7}
B
{3} ..... {1, 3, 2}
C
2 ..... {22, 44}
D
{1, 2} .....The set of prime numbers
E
Ƿ ..... {0}
F
(X ț Y) ..... X
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B
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C
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D
{1, 2, 4} - {2, 4, 6} = ..........
E
If 4 Ǻ {2, X, 7}, then X = ..........
3 Choose the true sentence from the parentheses: A
{1, 7} .......... {0, 1, 2, 3, 4, ...}
B
X - X = ..........
C
If {2, 5, 7} = {5, A, 2} then A = .......... (2 or 5 or 7 or 0)
D
{5} - {1, 2, 5} = ..........
E
The number of subsets for the set {5} is ......
(Ǻ or ǻ or ɴ or ɶ)
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5 Describe the colored section in each of the following shapes: X
X
U
Y
X X
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Test
Unit Test 1 Place the suitable symbol Çş or Çť or É´ or Éś in the blanks to make each of the following sentences true: A
{52} ....... {2 , 5}.
B
{3} ....... {1, 3}.
C
5 ....... the set of the digits in the number 2513.
D
4 ....... {44}.
2 /RRN DW WKH RSSRVLWH 9HQQ GLDJUDP WKHQ ÂżQG HDFK RI WKH IROORZLQJ A
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E
Y
F
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U Y
X 5
1
4
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3
3 Choose the correct answer from the parentheses
6
7
in each of the following sentences: A
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B
ǡ ....... {0}
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C
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D
X - X = .......
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E
If a Çş X then a ....... X
(Éś or Çť or Çş or É´)
4 Write down what the colored section in each of the following Venn diagram represents: U
U
Y
X
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U
Y
Y
X
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....................
5 IF U = { 1, 2,3, 4, 5, 6, 7 }, X = { 1, 2, 3, 4} and Y = {1, 2, 5, 6} Write down each of the following sets using the listing method:
Ma
A
XČ&#x153;Y
B
XČ&#x203A;Y
C
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D
X
E
Y
D
(X Č&#x203A; Y )
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Fifth Prima ry
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3-3 Third: The altitudes of the obtuse triangle:
In the opposite figure, ABC is a triangle whose angle C is obtuse . Follow the same previous steps: Draw
AD
9 BC .
and similarly
BE
9 AC ,
CF
9 AB
F
D
Note that
1
B C
The altitudes of the triangle are the segments: AD , AD , BE ,
BE
,
E
CF .
CF intersect at
one point which is located outside the triangle ABC.
Practice 1
Draw the triangle ABC in which AB = 5cm, BC = 6cm, m (dB) = 120° . Then, draw AD perpendicular to BC , and measure the length of AD . Draw also BE perpendicular to AC and measure the length of
BE .
Are AD and BE intersected at one point?
2
Draw the rectangle ABCD in which AB = 3cm, BC = 5cm, then label the point X Ǻ DA where AX = 2cm. How many locations can be labeled for the point X on the ray DA . Draw the traingle XBC then draw XY perpendicular from X to BC .
Ma
Can you know the length of XY without measuring it by a ruler?
the mat ics -
82 82
Fifth Prima ry
Exercises
General Exercises 1 Put ( ) for the true sentence and ( ) for the false one: A
The length of the diameter of a circle > the length of any chord which doesn't pass throught its center. (
)
The right triangle has only one altitude.
(
)
The line segments drawn from the vertices of the acute triangle perpendicular to the opposite sides intersect at one point inside the triangle.
(
)
D
Only one diameter can be drawn from any point on the circle.
(
)
E
The diameter of the circle divides it into two equal halves.
(
)
B C
2 Draw a circle whose center is N and diameter is 6cm. Then draw the diameter AB and the chord AC in the circle. Draw BC . Use the portractor to measure d ACB then draw CD 9 AB that intersects it at D and the circle at E, then choose the correct answer: A
The triangle ABC is ........
B
CE is .... in the circle (chord - diameter - radius).
C
The intersection point of the perpendicular line segments drawn from the
(right triangle - acute traingle - obtuse traingle)
vertices of the triangle ABC to the opposite sides is
(C - D - E)
3 Draw a circle whose center is M and radius 4cm then draw two radii
MX , MY
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Fig. (1)
Fig. (2)
Fig. (3)
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Fig. (2)
Fig. (3)
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Test Four Complete the following: (1) ∅ .................... {a , b} (2) 6.35 + 17.025 = .................... to the nearest
1 100
(3) It is .................... that the sun rises from the west. (4) As throwing a fair die once , then the probability of appearing a number less than 3 is .................... (5) The altitudes of the right angled triangle intersect at ....................
Choose the correct answer : (1) 63.598 A
(2) 3
63.60 to the nearest part of ....................
10
1 2
÷
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B
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C
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D
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C
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∈
(5) The chord which passes through the centre of the circle is called .................... A
a diameter
B
C
A
Arrange ascendingly: 0.6 ,
B
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