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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
LEARNING PAPERS FOR CLASS V
TABLE
1
2 X 1 = 2
2 X 2 = 4
2 X 3 = 6
2 X 4 = 8
2 X 5 = 10
2 X 6 = 12
2 X 7 = 14
2 X 8 = 16
2 X 9 = 18
2 X 10 = 20
3 X 1 = 3
3 X 2 = 6
3 X 3 = 9
3 X 4 = 12
3 X 5 = 15
3 X 6 = 18
3 X 7 = 21
3 X 8 = 24
3 X 9 = 27
3 X 10 = 30
4 X 1 = 4
4 X 2 = 8
4 X 3 = 12
4 X 4 = 16
4 X 5 = 20
4 X 6 = 24
4 X 7 = 28
4 X 8 = 32
4 X 9 = 36
4 X 10 = 40
5 X 1 = 5
5 X 2 = 10
5 X 3 = 15
5 X 4 = 20
5 X 5 = 25
5 X 6 = 30
5 X 7 = 35
5 X 8 = 40
5 X 9 = 45
5 X 10 = 50
6 X 1 = 6
6 X 2 = 12
6 X 3 = 18
6 X 4 = 24
6 X 5 = 30
6 X 6 = 36
6 X 7 = 42
6 X 8 = 48
6 X 9 = 54
6 X 10 = 60
7 X 1 = 7
7 X 2 = 14
7 X 3 = 21
7 X 4 = 28
7 X 5 = 35
7 X 6 = 42
7 X 7 = 49
7 X 8 = 56
7 X 9 = 63
7 X 10 = 70
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
2
8 X 1 = 8
8 X 2 = 16
8 X 3 = 24
8 X 4 = 32
8 X 5 = 40
8 X 6 = 48
8 X 7 = 56
8 X 8 = 64
8 X 9 = 72
8 X 10 = 80
9 X 1 = 9
9 X 2 = 18
9 X 3 = 27
9 X 4 = 36
9 X 5 = 45
9 X 6 = 54
9 X 7 = 63
9 X 8 = 72
9 X 9 = 81
9 X 10 = 90
10 X 1 = 10
10 X 2 = 20
10 X 3 = 30
10 X 4 = 40
10 X 5 = 50
10 X 6 = 60
10 X 7 = 70
10 X 8 = 80
10 X 9 = 90
10 X 10 = 100
11 X 1 = 11
11 X 2 = 22
11 X 3 = 33
11 X 4 = 44
11 X 5 = 55
11 X 6 = 66
11 X 7 = 77
11 X 8 = 88
11 X 9 = 99
11 X 10 = 110
12 X 1 = 12
12 X 2 = 24
12 X 3 = 36
12 X 4 = 48
12 X 5 = 60
12 X 6 = 72
12 X 7 = 84
12 X 8 = 96
12 X 9 = 108
12 X 10 = 120
13 X 1 = 13
13 X 2 = 26
13 X 3 = 39
13 X 4 = 52
13 X 5 = 65
13 X 6 = 78
13 X 7 = 91
13 X 8 = 104
13 X 9 = 117
13 X 10 = 130
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
3
14 X 1 = 14
14 X 2 = 28
14 X 3 = 42
14 X 4 = 56
14 X 5 = 70
14 X 6 = 84
14 X 7 = 98
14 X 8 = 112
14 X 9 = 126
14 X 10 = 140
15 X 1 = 15
15 X 2 = 30
15 X 3 = 45
15 X 4 = 60
15 X 5 = 75
15 X 6 = 90
15 X 7 = 105
15 X 8 = 120
15 X 9 = 135
15 X 10 = 150
16 X 1 = 16
16 X 2 = 32
16 X 3 = 48
16 X 4 = 64
16 X 5 = 80
16 X 6 = 96
16 X 7 = 112
16 X 8 = 128
16 X 9 = 144
16 X 10 = 160
17 X 1 = 17
17 X 2 = 34
17 X 3 = 51
17 X 4 = 68
17 X 5 = 85
17 X 6 = 102
17 X 7 = 119
17 X 8 = 136
17 X 9 = 153
17 X 10 = 170
18 X 1 = 18
18 X 2 = 36
18 X 3 = 54
18 X 4 = 72
18 X 5 = 90
18 X 6 = 108
18 X 7 = 126
18 X 8 = 144
18 X 9 = 162
18 X 10 = 180
19 X 1 = 19
19 X 2 = 38
19 X 3 = 57
19 X 4 = 76
19 X 5 = 95
19 X 6 = 114
19 X 7 = 133
19 X 8 = 152
19 X 9 = 171
19 X 10 = 190
20 X 1 = 20
20 X 2 = 40
20 X 3 = 60
20 X 4 = 80
20 X 5 = 100
20 X 6 = 120
20 X 7 = 140
20 X 8 = 160
20 X 9 = 180
20 X 10 = 200
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
1) NUMBERS AND NUMERATIONS
• 4 Places in 4 digit numbers are
Thousand , Hundred, Tens , Ones
• 5 Places in 5 digit numbers are
Ten Thousand , Thousand , Hundred, Tens , Ones
• 6 Places in 6 digit numbers are
Lakh, Ten Thousand , Thousand , Hundred, Tens , Ones
Crores Periods Lakhs Periods Thousands Period Ones period
T. Crore Crore T. Lakh Lakh Ten Thousand Thousand Hundred Tens ones
4 0 1 3 8 6 9 4
1,38,694 = Four crore One lakh Thirty eight thousand Six hundred ninety four
International place value chart
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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
Place value and face value
• Place value of a digit in any number is the position of that digit in that number
• Face value of a digit is always the same digit itself .
Ex: Write place value and face value of 3 in the given number 23,456
solution : Place value is thousand i.e. 3 X 1000 = 3000 is the place value.
Face value of 3 is number itself i.e. 3
Comparison of numbers
• The number with more number of digits is always greater.
• If number of digits are same , start from the left and compare the digits until you find two different digits at the same place.
Forming the smallest and the greatest number
• For greatest : Arrange the numbers in descending order.
• For smallest : Arrange the numbers in ascending order.
If one of the digit is 0 so, put 0 at second place from left.
ROUNDING OFF NUMBERS
Nearest tens: 1) Digit at ones place less than 5, replace it by 0.
2) If it is greater than 5, replace it 0 and add 1 to the digit at ones place.
Ex. 73 rounds to 70
Nearest hundreds:1) Digit at ones place is replace by 0,look at digit at tens place.
2) If less than 5 replace it by 0.
3) If it is 5 or greater, replace it by 0 and add 1 to the digit at hundreds place.
5
4) The other digits will remain the same.
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
Ex. 743 rounds to 700
Nearest thousand:1) Digit at ones and tens place is replace by 0,look at digit at hundred place.
2) If less than 5 replace it by 0.
.3) If it is 5 or greater, replace it by 0 and add 1 to the digit at thousand place.
4) The other digits will remain the same.
Ex. 1589 rounds to 2000
ROMAN NUMERAL
Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum (or in some cases, the difference) of their values. The first ten Roman numerals are
I‐ 1 , V‐5 , X‐ 10 , L‐ 50 , C‐100 , D‐500 , M or K‐ 1000
1) When a symbol of lower value is placed on the left of a symbol of higher
value then its value is subtracted . Ex. IV – 4
2) When a symbol of lower value is placed on the right of a symbol of higher value then its value is added .
Ex.. V I– 6
3) For larger number a bar (‐) is used when its placed over a numeral its value is multiplied by 1000.
4) No symbol can be repeated more than three times. Repetition of Roman numerals means addition.
Ex : CCC, XXX.
5) The symbols V, L and D can never be repeated and never be subtracted.
• 1 Lakh = 100 thousands
• 10 Lakhs = 1 millions
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• 1 crore = 10 millions
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
• 10 crores = 100 millions
Test yourself :
• Write place value and face value of 9 in9,99, 89,232.
• Write 96,96,679 in expanded form.
• Write in Roman numeral : 1225 , 56560 , 36536
2) MULTIPLES AND FACTORS
• Even numbers: Numbers divisible by 2. Eg : 2,4,6
• Odd numbers: Numbers not divisible by 2. Eg: 3,5,7
• Prime number:Those numbers having only two factors , i.e., 1 and itself. Ex. 2,5
• Composite number: The numbers which have more than two factors. Ex. 4,12,15
• Co‐ prime : If two numbers do not have any other common factor except 1.
Ex. 7,10
• Two prime numbers whose difference is 2 are called twin prime numbers .
Ex. 3 and 5 , 5 and 7.
Test for Divisibility:
• By 2 : Last digit or digit at unit place of the number should be even number.
Ex: 482 , 588
• By 3 : The sum of the digits of the number should be divisible by 3.
Ex. 69 i.e. 6+9 = 15 (divisible by 3 ) means 69 is divisible by 3
• By 4: A number is divisible by 4 ,if the number formed by the tens and ones digits can be divided by 4 or is zero. Ex. 108
• By 5: Last digit of the number should be 0 or 5. Ex. 150, 10
• By 6: If a number is divisible by 2 as well as 3 so it is divisible by 6.
Ex. 12, 30
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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
• By 8: A number is divisible by 8 ,if the number formed by the hundreds, tens and ones digits can be divided by 8 or is zero.
Ex. 168, 80
• By 9: The sum of the digits of the number should be divisible by 9.
Ex. 54 i.e. 5+4=9(divisible by 9) means 54 is divisible by 9
• By 10: Last digit of the number should be 0. Ex. 20,60
Factors: A number is a factor of another large number if it divides the larger number exactly.
• 1 is factor of every number.
• A number is a factor of itself
Multiple : Multiple of any number is a number which can be exactly divided by that number.
Ex. 18 is a multiple of 9 because 18 is completely divisible by 9.
• A number can have unlimited multiples.
• Every number is multiple of itself .
• Multiple of a number is always greater than or equal to the number itself.
Prime Factorization : Expressing a composite number as the product of prime numbers
HCF:The HCF of two or more numbers is the greatest of their common factors.
Ex. 12 , 15 HCF =3
LCM: The LCM of two or more numbers is the smallest number which can be exactly divided by
each of the given numbers of their common factors. 6, 12 LCM is 24.
Methods: i). Multiple method ii ). Prime Factorisation method iii). Division method .
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Relation between HCF and LCM
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
First number X Second number = LCM X HCF.
• Every odd number is not a prime number.
• 2 is the smallest prime number.
• 3 is mallest odd prime number.
• 4 is the smallest composite number.
3) FRACTIONAL NUMBERS :
i) A fraction is the part of whole.
ii) A number in the form of p/q, in which number above the line segment ( ) is
numerator and the number below the line segment is denominator.
• Like Fraction: Fractions with same denominator.
• Unlike Fraction: Fractions with different denominators.
• Mixed fraction: Quotient X Reminder/ Divisor
• Improper fraction:(Whole number part X Denominator ) + Numerator/same denominator Lowest term: When the numerator and the denominator do not have any common factor other than 1.
Comparison of fractions :
Like Fraction:
We compare the numerators only and the fraction with the greater numerator is greater.
Ex. 85
> 83
Unlike Fraction: (with same numerator)
We compare the denominator only and the fraction with the greater denominator is greater.
Ex. 65 >
35
Unlike Fraction: (with different numerator)
First we change the unlike fractions to like fractions.
9
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
Multiplication of fractions:
Multiply the numerators .
Multiply the denominators.
Reduce to its simplest form.
Multiplicative inverse or reciprocal :
Numbers are multiplicative inverse of each other when their product is 1.
Ex. 2, ½
• 1 is only the number whose reciprocal is also 1.
• 0 has no reciprocal.
4) DECIMALS
A Decimal number consists two parts a whole part and decimal part.
Eg. 25.336 in which 25 whole part and 336 is a decimal part
Like and unlike decimals :
• The numbers those have same number of decimal places are like decimals .
Ex. 56.369
• The numbers those have different number of decimal places are like decimals .
Ex. 89.33
Multiplication
A) Decimal by whole
Do the multiplication by usual method and count the number of digits from the right equal to
the number of decimal places and put decimal point.
10
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
B) Decimal by decimal
Do the multiplication by usual method and count the number of digits from the right in both
the numbers and equal to the sum of the number of decimal places put the decimal point.
C) By 10,100,1000
When multiplication is by 10,100,1000 , then the decimal point is shifted towards the right
According to the number of zeros .
Division
A) Decimal by whole
Ex. 95.48 by 4
Do the division by usual method and when you reach at tengths place, put the decimal in the
Quotient just above the decimal in the dividend and proceed further in the same manner.
B) By 10,100,1000
When division is by 10, 100, 1000 , then the decimal point is shifted towards the left
according to the number of zeros .
5) BASIC GEOMETRICAL CONCEPTS
• Point : A point determines a definite position.
• Line: A line is a straight move with two arrow heads.
• Line Segment : It is a part of a line.
• Ray : A ray is a part of a line starting at a point and going endlessly in one direction.
Angle: An angle formed by two rays with the same initial point.
11
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
Name of an angle always consists three letters and the letter a the vertex always comes in between the two
letters. < AOB
O – Vertex , OB – Arm , OA‐ Arm .
Type of angles
a)Acute angle : Angle measure lies between 00 and 900
b)Right angle : An angle measure 900
c)Obtuse angle : Angle measure lies between 900 and 1800
d) Straight angle : Angle measures exactly 1800
e) Reflex angle: Angle measures more than 1800 and 3600
f) Complementary angles: If sum of the two angles is 900 andthey are said to be
complementary angles and each of the angle is called complement of other.
Ex. 500 and 400
g) Supplementary angles : If sum of the two angles is 1800 and they are said to be
supplementary angles and each of the angle is called supplement of other.
Ex. 1500 and 300
PARALLEL AND PERPENDICULAR LINES
Parallel lines:The lines in the same plane which do not intersect each other at any point called parallel lines. Symbol used to represent – ‘II’.
Ex. Opposite edges of a ruler , Steps of a ladder.
Perpendicular lines : Two lines which intersect each other at right angle
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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
Triangles : A triangle is a closed figure bounded by three line segment s.
It has 3 angles , 3 vertices , 3 sides.
. Types (on the basis of sides)
• Equilateral triangle :Triangle with all sides equal.
• Isoscales triangle: Triangle with two sides equal.
• Scalene triangle: Triangle with all three sides are of different length
Types (on the basis of angles)
• Acute angled triangle :Triangle with all three angles less than 900.
• Obtuse angled triangle: Triangle with one angle lies between 900 and 1800.
• Right triangle : Triangle one of whose angle is of 900.
Properties :
i) The sum of the angles of a triangle is 1800.(angle sum property)
Circle :
Locus of all those points which are equidistance from a fixed point.
Parts of the circle:
i) Radius: A radius of the circle is that line which joins centre of the circle with any point of the circle.
ii) Diameter : A diameter of the circle contains two radii of the circle.
Therefore, Diameter = 2 X radius.
iii) Semi circle: a diameter divides the circle into two halves,each is called semi circle.
iv) Circumference: The length of the boundary of a circle or its perimeter.
Circumference= 2 = 722
}
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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
v) Chord: A line segment joining two points on the circle.
vi) Arc: An arc is a part of the circle.
vii) Concentric circles : Two or more circles having same centre.
6) MEASUREMENT OF LENGTH,MASS AND CAPACITY
• System of measurement is known as metric system.
• A unit which majority of the people use as a basic unit of measurement is called a standard unit
Conversions: To convert a bigger into smaller unit , we multiply by 10,100 or 1000
Ex. 14m into cm = 14 X 100 =1400 cm
To convert a smaller into bigger unit , we divide by 10,100 or 1000
Ex. 14m into km = 14 /1000 =0.014 km
7) AREA AND PERIMETER
Perimeter- The length of the boundry of the closed figureis called its perimeter.
Area: Amount of surface covered by a figure.
Perimeter = 2(L + B) Perimeter = 4 X side
Area = Length X Breadth Area = Side X side
Breadth= LengthArea
Length=
BreadthArea
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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
8) SOLID FIGURES
Figures which can be touch are known as solid figures
Edges‐ 12 , vertices‐ 8 , Faces‐ 6
VOLUME :The space which an object is occupies or a box can be hold.
Volume of cuboid = length x breadth x height(cubic unit)
Length =Breadth
Area
Breadth = LengthArea
Volume of a cube = Edge X Edge X Edge (cubic unit)
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MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
9) TIME
a) Half an hour= 21 X 60 = 30 minutes
b) Quarter of an hour = 41X 60 = 15 minutes
c) Three Quarters of an hour = 43
x 60 = 45 minutes
d) 1 day = 24 hr.
e) 1 hr = 60 min
f) 1 min = 60 seconds
g) Time from 12 o’ clock noon to 12 o’ clock mid night is shown by letters pm (post meridian)
h) Time from 12 o’ clock midnight to 12 o’ clock noon is shown by letters am (ante meridian)
Conversion: Hours to mins multiply by 60
Minutes to seconds multiply by 60
Minutes to Hours divide by 60
Seconds to minutes divide by 60
CALENDER
• 1 year = 12 months
• 1 week = 7 days
• 1 year = 52 weeks.
The earth completes one round around the sun in 365and ¼ days. But ¼ th day is not counted in
every year
16
. Thus in four years this ¼ th day adds upto 1 day. This one day is added in every fourth year . This year is called a leap year. So a leap year has 366 days.This additional day is counted in the monh of February. Therefore ,a leap year is a year which has 29 days.
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
10) TEMPERATURE
• The degree of measurement of temperature is degree (0).
• The normal human body temperature is 370C.
• Freezing Point of water is 00C or 320F.
• Boiling Point of water is 1000C or 2120F
Conversion
1) 0 C into 0F
• Multiply by 9
• Divide by 5
• Add 32
2) 0 F into 0 C
• Subtract 32
• Multiply by 5
17
• Divide by 9
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
11) SYMMETRY
Symmetry is when one shape becomes exactly like another if you flip, slide or turn it.
Rotational Symmetry
With Rotational Symmetry, the shape or image can be
rotated some amount and it still looks the same.
This image can be rotated to three different positions and it
would look the same.
Order of rotational symmetry: The number of times a figure matches itself or
can be rotated to get the original shape .
Reflection symmetry : A type of symmetry where one half is the reflection of the other half.
In the figure the black line is known as the line of reflection
Line of reflection : A reflection is the transformation that results from flipping a figure across a line,
called line of reflection.
18
MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V
12) DATA HANDLING
Data : A data is a collection of facts and figures
Pictograph: A pictograph shows the information in the form of pictures and symbols.
Tally Marks: Representation of numbers in the form of vertical lines.
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