lesson plan multiple and factors.ppt v 3
DESCRIPTION
Lesson plans for primary teachers to teach multiples and factors to grade 5 studentsTRANSCRIPT
Lesson plans
HCF and LCMBy
Kavita Grover
1Class 5-Multiples &Factors, LCM &HCF
LESSON PLAN BREAK-UPLesson plan
Setting/time Slide # Topic
1 Classroom/30 mins Multiples
2 AV room/45 mins Composite and prime numbers
3 Class room/60 mins Divisibility rules, factorization/
4 AV room/45 mins Exponents and prime factorization
5 Class rooom/45 mins Class test
6 AV room/45 mins LCM
7 AV room/45 mins LCM
8 Class room/60 mins HCF
9 AV room/45 mins HCF
10 Class rooom/45 mins Class test
Content• Learning objectives• Multiples• Prime and composite numbers• Test of divisibility• Factors• Factorization and index notation• LCM
Prime FactorizationShort Division
• HCFPrime FactorizationShort DivisionFactor treeVenn Diagram
Class 5-Multiples &Factors, LCM &HCF 3
Learning ObjectivesThe student will be able to :• Differentiate between the terms
factors and multiples composite and prime numbers LCM and HCF
• Lists the multiples and factors of composite numbers• Express factors as index notations• Calculates the HCF and LCM of 2 or 3 digit numbers using
Number trees Prime factorization Long division method Venn Diagram
Class 5-Multiples &Factors, LCM &HCF 4
Multiples
• Multiples of a number can be made by multiplying the number by any whole number.
• 1X12=12• 2X12 = 24• 3 X12 =36• 4X12=4812, 24, 36, 48, 60, 72, 84,
96,108,120….are multiples of 12
1 x 10 = 10, 2 x 10 = 20, 3 x 10 = 30, 4 x 10 = 40, 5 x 10 = 50, 6 x 10 = 60, and so on ...
5Class 5-Multiples &Factors, LCM &HCF
Multiples
• 5 10 15 20 25 30 35 40 45 50 55
6Class 5-Multiples &Factors, LCM &HCF
A clock is set to ring at every 5th minute. Will it ring 55 minutes later?
Multiples• Is 12 a multiple of 3?
If you multiply 3 by 4 you get 12, so 12 is a multiple of 3.
• Is 15 a multiple of 3?3 x 5 = 15. So 15 is a multiple of 3, (and also of 5).
• Is 21 a multiple of 6?21 is not a multiple of 6 because you can't make 21 by multiplying 6 by any whole number.6 x 3 = 18 and 6 x 4 = 24 but there is no whole number between 3 and 4 that could give us an answer of 21.
What are the first five multiples of 13?
13 x 1 =13
13 x 2 = 26
13 x 3 = 39
13 x 4 = 52
13 x 5 = 65
13, 26, 39, 52, 6513, 26, 39, 52, 65
8Class 5-Multiples &Factors, LCM &HCF
Find the Missing Multiples
• 6, 12, 18, ____, ____
• ___, 6, 9, 12, ____, ____, 21
• ___, 24, 36, 48, 60, ____
24 30
3 15 18
12 72
9Class 5-Multiples &Factors, LCM &HCF
Composite and Prime numbers
10Class 5-Multiples &Factors, LCM &HCF
1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100
Prime Numbers• A prime number is a positive integer that has exactly
two positive integer factors, 1 and itself.• For example, if we list the factors of 28, we have 1,
2, 4, 7, 14, and 28. That's six factors.• If we list the factors of 29, we only have 1 and 29.
That's two factors. So we say that 29 is a prime number, but 28 isn't.
11Class 5-Multiples &Factors, LCM &HCF
Composite Numbers• A Composite Number can be divided evenly by numbers
other than 1 or itself. • Example: is 6 a Prime Number or Composite Number?
• 6 can be divided evenly by 2, or by 3, as well as by 1 or 6:
• 6 = 1 × 66 = 2 × 3
• So 6 is a Composite Number
12Class 5-Multiples &Factors, LCM &HCF
Factors• Factors are the numbers you multiply
together to get a product or a factor is a number that exactly divides another number without leaving a remainder.
• 12 can be written as the product of 2 x 6 or 2 x 6 = 12
13Class 5-Multiples &Factors, LCM &HCF
2 and 6 are the factors of 12
12 is the multiple of its factors 2 and 6
FACTORSThe factors of 12 are:
– 1 x 12
– 2 x 6
– 3 x 4
– 4 x 3
– 6 x 2
– 12 x 1
• 12 can be divided evenly by 1, 2, 3, 4, 6 and 12:– 1 × 12 = 12
– 2 × 6 = 12
– 3 × 4 = 12
• So 12 is a Composite Number
• The factors of 12 are 1, 2, 3, 4, 6, and 12
Class 5-Multiples &Factors, LCM &HCF 14
Factors
15Class 5-Multiples &Factors, LCM &HCF
• For example, the product 24 has several factors.
• 24 = 1 x 24• 24 = 2 x 12• 24 = 3 x 8• 24 = 4 x 6• So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Divisibility rules
• A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.• A number is divisible by 3 if the sum of the digits is divisible
by 3.• A number is divisible by 4 if the number formed by the last
two digits is divisible by 4.• A number is divisible by 5 if the last digit is either 0 or 5.• A number is divisible by 10 if the last digit is 0.• A number is divisible by 8 if the number formed by the last
three digits is divisible by 8.• A number is divisible by 9 if the sum of the digits is divisible
by 9.• A number is divisible by 6 if it is divisible by 2 AND it is
divisible by 3.
16Class 5-Multiples &Factors, LCM &HCF
Writing facors
The factors of 48 are
1 x 48 2 x 243 x 164 x 126 x 8
Another way of writing factors is:Write your first pair of factors with a reasonable space between them, then move on to the next pair until you have them all.This way, when you get to the 6,8 pair, you can stop because 7 is not a factor and you already have 8 in your list.
17Class 5-Multiples &Factors, LCM &HCF
Exponential Notation or Index Notation
• 4cm x 3cm= 12 cm square• When a number is multiplied by itself several
times, we express the product in the given form:
• 3x3=32 = three raised to the power 2• 4 x 4 x4 x 4 x 4= 4 5= 4 raised to the power 5• 8 7= 8 x 8 x 8 x 8 x 8 x 8 x 8• 2 x 2 x 2 x 4 x 4 = (2 x 2 x 2) x (3 x 3) =23 x 42
Class 5-Multiples &Factors, LCM &HCF 18
Exercise 11) Write in the exponential form.a) 5 x 5 x 5=b) 10 x 10 x 10 x 10=c) 6 x 6 x 6 x 6 x 6=d) 2 x 2 x 3 x 3=e) 8 x 8 x 8 x 4 x 4 x 4 x 4 1) Write in the product form.a) 8 7 =b) 6 3 x 11 4 =
Class 5-Multiples &Factors, LCM &HCF 19
Factorization & Exponents
• 60=1x60 60=2x30 60=3x20 60=4x15 60=5x12 60=6x10
20Class 5-Multiples &Factors, LCM &HCF
60
Factorization & Prime Factorization• The factor
pairs for 60 are• 60=1x60
60=2x30 60=3x20 60=4x15 60=5x12 60=6x10
60
2 30
Composite number
3 10
Composite number
2 5
60 is written as the product of its prime factors60 = 2 x2 x 3 x 5
FACTOR TREE
• 60=4x15 =2x2 x3 x5
60
4 15
3 5
22
Prime factorization through short division
60
30
15
2
2
3
5 51
The prime factors of 60 are
2x2x3x5
2, 3, and 5 are all prime numbers, so we have prime factored 60. All we have to do now is neaten our answer up a bit. It is customary to write prime factorizations in increasing order, that is with the smallest numbers first.
Prime Factorization
24Class 5-Multiples &Factors, LCM &HCF
So the prime factorization of 910 is 2x5x7x13
• Now let us try another example: 910
Least common Multiple-LCM• A cold drink truck visits Rita's neighbourhood
every 4 days and Amul ice cream truck visits her neighborhood every 5 days. For the month of June on which day will both the trucks visit on the same day?
25Class 5-Multiples &Factors, LCM &HCF
1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30
Least common Multiple-LCM• In the given problem we have to first find the multiples of
both the numbers. • Cross out the multiples that are common. (20 and 40)• Which multiple is the least-20• Both the trucks will visit the neighbour hood on 20 June or
after 20 days.
Truck Days of visit
1 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,...
2 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,...
26Class 5-Multiples &Factors, LCM &HCF
Exercise -Find the LCM of 18 and 24.
Multiples of 18 18, 36, 54, 72, 90, 108, 126, 144,…
Multiples of 24 24, 48, 72, 96, 120,144, ….
• Common multiples of 18 and 24 are 72 and 144 • The least common multiple of 18 and 24 is 72. • LCM = 72
Highest Common Factor-HCFFind the HCF of 60 and 72
,1815
2
60 ,72
30 ,36
5 ,6
2
3 ,1815
2
60 ,72
30 ,36
5 ,6
2
3
The common factors of 60 and 72 are 2 x 2 x 3The HCF of 60 and 72 =2x2x3=12
Uncommon factors
HCF by prime factorization
Factors of 60Factors of 72
LCM of 60 and 72
• To find the LCM of 60 and 72 we multiply all the factors.
• 2x2 x3x5x6 = 336
• So the HCF of 60 and 72 is 12 and
• LCM is 336
,1815
2
60 ,72
30 ,36
5 ,6
2
3
Find the HCF of 56 and 48– Prime Factor Tree for 56 • Prime Factor Tree for 48
56
2
2
28
14
2 7
56 is all the prime numbers 2 x 2 x 2 x 7 multiplied together
48
2
2
24
12
2 6
2 3
48 is the prime numbers 2 x 2 x 2 x 2 x 3 multiplied together
Look for common factors in both trees
Multiply them together =
x
x
48
2
2
24
12
2 6
2 3
56
2
2
28
14
2 7
2
2
2
88 is the biggest number that goes into both 56 and 48
So it is the Highest Common Factor
Finding the Highest Common Factor
HCF through Prime Factorization• The prime factors of : 56 = 2 x 2 x 2 x 7 48 = 2 x 2 x 2 x 2 x 3 The prime numbers that are common are: 2x2x 2= 8So the HCF of 56 and 48 is 8
HCF & LCM as a diagram
2
2 2
7
3
53
5
Write the common prime factors of both 504 and 700 here .The HCF =2X 2 X 7=28
Write the other PRIME FACTORS of 504 in the 504 circle
Write the other PRIME FACTORS of 700 in the 700 circle
504 700
The LCM is found by multiplying all the numbers from the circles
504 = 2 x 2 x 2 x 3 x 3 x 7700 = 2 x 2 x 5 x 5 x 7
The four different ways to find the HCF
504
2
2 2
7
3
53
5
700
,1815
2
60 ,72
30 ,36
5 ,6
2
3
The prime factors of : 56 = 2 x 2 x 2 x 7 48 = 2 x 2 x 2 x 2 x 3 The prime numbers that are common are: 2x2x 2= 8So the HCF of 56 and 48 is 8
x
x
48
2
2
24
12
2 6
2 3
56
2
2
28
14
2 7
2
2
2
8