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Ateneo de Zamboanga University
Grade School Unit
PAASCU Level III Accredited
ALTERNATIVE ACADEMIC ACTIVITIES IN MATHEMATICS
Grade Four
I. LEARNING OBJECTIVE
At the end of the lesson the students are expected to find the Prime factorization of a
number.
II. TIME FRAME
October 16, 2013
III. LESSON
PRIME FACTORIZATION
References
Domingo, E. C. & Apistar, E. M. (2009). Integrative Mathematics. Quezon City,
Philippines: Sibs Publishing House, Inc.
Ani M. Guerrero, Darwin M. Guerrero, Loly Ong (2009). Beyond Math. 927 Quezon
Avenue, Quezon City, Philippines: Phoenix Publishing House, Inc.
Socao, J. (2009). Math World 4. Quezon City, Philippines: C & E Publishing, Inc.
Gannaban, O. (2009). Skills Enhancer in Mathematics 4. Santa Anna Manila,
Innovative Educational Materials, Inc.
IV. LEARNING EXPERIENCE
RECALLING OF SOME
MATHEMATICAL CONCEPTS
Factors – two or more numbers multiplied to come up with a product.
Ex.
3 x 5 = 15;
8 x 5 = 40;
3 and 5 are the factors of 15
8 and 5 are the factors of 40
Prime number – is a number that has only two distinct factors – 1 and the number
itself
Ex.
Number/Product Factors
5
7
1x5
1x7
Number of
factors
2
2
Composite number – is a number with more than 2 distinct factors.
Ex.
Number/Product Factors
Number of
factors
1x4
2x2
1x8
2x4
4
8
3 (1, 4, 2)
4 (1,8, 2, 4)
LET’S TRY THIS ACTIVITY
SIEVE OF ERATOSTHENES ACTIVITY
Sieve of Eratosthenes was invented by a Greek mathematician. It is a method to find
the prime numbers less than 100.
INSTRUCTIONS
Use the table below. Follow each step carefully to be able to answer the
questions below. (Steps 1 and 2 are done.)
STEPS:
1. Draw a triangle in number 1.
2. Encircle number 2.
3. Cross out all the numbers which are divisible by 2 (multiples of 2).
4. Encircle number 3.
5. Cross out all the numbers which are divisible by 3 (multiples of 3).
6. Encircle number 5.
7. Cross out all the numbers which are divisible by 5 (multiples of 5).
8. Encircle number 7.
9. Cross out all the numbers which are divisible by 7 (multiples of7).
10. Encircle and color the remaining numerals using light colors.
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
Answer the questions based on the given chart.
1. What kind of numbers were encircled? ______
2. What kind of numbers were crossed out? _____
3. What is the only even prime number? ______
Answers:
1. All the encircled numbers are prime numbers.
2. All the crossed out numbers are composite numbers.
3. The only even prime number is 2.
Patricia made sampaguita garlands. Each garland has 7
flowers. How many flowers are there in 10 garlands?
There are 70 flowers in 10 garlands because 7 x 10 = 70.
What kind of a number is 70?
Why is 70 a composite number?
Can we write 70 as the product of prime numbers?
All the factors of the given composite numbers which are prime numbers are
called prime factors.
Here are the two ways of expressing a number as a product of prime factors.

Using Factor Tree:
70
7
7
X
10
X
2
X
-
Write the number at the top of the factor tree. ( 70 )
-
- Write any factor pair of the number. ( 7 x 10 )
( except 1 and the number itself)
5
- Continue factoring the composite numbers until all the
numbers at the tip of the factor tree are prime.
The prime factors of 70 are 2 x 5 x 7.

Using Continuous division
2 70
- Divide 70 by any of its prime factors. ( 70 ÷ 2 = 35)
5 35
- Divide 35 by any of its prime factors. ( 35 ÷ 5 = 7)
7
- The quotient is already a prime number.
The prime factors of 70 are 2 x 5 x 7.
POINTS TO REMEMBER
A Prime Factor is a prime number which is a factor of a given
whole number.
Prime Factorization is the process of finding the prime factors
of a composite number.
Identify the prime factors of the given numbers.
A. Using factor tree
9
18
x
x
x
24
x
x
x
x
6
x
B. Using Continuous division
2
12
2
3
32
2
16
2
2
54
63
50
Ateneo de Zamboanga University
Grade School
PAASCU Level III Accredited
ACTIVITY 1
Name: _______________________________________ Score: ________________
Section : ______________________________________ Date : _________________
A. Find the prime factorization of the following composite numbers using factor tree
method.
9
12
x
x
36
x
x
x
x
x
x
x
x
x
x
x
x
x
x
272
48
4
x
2
x
x
x
2
x
x
x
x
B. Find the prime factorization of the following composite numbers using continuous
division method.
1.
27
2.
4.
105
56
3.
5.
196
102
Ateneo de Zamboanga University
Grade School
PAASCU Level III Accredited
ALTERNATIVE ACADEMIC ACTIVITIES IN MATHEMATICS
Grade Four
I. LEARNING OBJECTIVES
At the end of the lesson, the students are expected to:
a. find the Greatest Common Factor (GCF) of a given set of numbers; and
b. solve word problems involving Greatest Common Factor (GCF).
II. TIME FRAME
October 17, 2013
III. LESSON
Greatest Common Factor
References
Domingo, E. C. & Apistar, E. M. (2009). Integrative Mathematics.
Quezon City, Philippines: Sibs Publishing House, Inc.
Ani M. Guerrero, Darwin M. Guerrero, Loly Ong (2009). Beyond Math. 927 Quezon
Avenue, Quezon City, Philippines: Phoenix Publishing House, Inc.
Socao, J. (2009). Math World 4. Quezon City, Philippines: C & E
Publishing, Inc.
IV. LEARNING EXPERIENCE
Ms. Agustin makes necklaces using cultured South Sea
pearls. She has 24 small pearls and 30 big pearls to use. For each
necklace, she wants to have a combination of small and big pearls.
What is the greatest number of necklaces that she can make if
each necklace will have the same design and there will be no
leftover pearls?
1. What is being asked in the problem?
2. What are the given facts?
3. How can we solve the problem?
To answer the problem, we need to find the greatest number that can divide both
24 and 30. Hence, we need to find the Greatest Common Factor or GCF of 24
and 30.
The following are the different methods on how to find the Greatest Common
Factor or GCF.
a. Listing Method
 List down all the given factors of each of the given numbers..
Example:
24 { 1, 2, 3, 4, 6, 8, 12, 24}
30 {1,
2, 3, 5, 6, 10, 15, 30}
 Identify the common factors from the given list.
Example:
24 { 1, 2, 3, 4, 6, 8, 12, 24}
30 { 1, 2, 3, 5, 6, 10, 15, 30}
The common factors are 1, 2, 3 and 6.
 Identify the Greatest Common Factor of the numbers from the list.
Example:
24 { 1, 2, 3, 4, 6, 8, 12, 24}
30 { 1, 2, 3, 5, 6, 10, 15, 30}
The Greatest Common Factor of 24 and 30 is 6.
b. Prime Factorization
 Express the prime factorization for each using the factor tree.
Factor Tree
30
5
X
24
6
6
2 X
3
3
X
X
2
24 = 2 x 2 x 2 x 3
30 =
2x3x5
 Bring down the common prime factors.
24 = 2 x 2 x 2 x 3
30 =
2x3x5
GCF =
2X3
 Multiply the common prime factors to get the GCF.
2x3=6
Greatest Common Factor: 6
4
2 X
2
LET’S PRACTICE
1. Find the GCF of the following numbers
a. Listing Method
1. 16 =
25 =
GCF = ___________
2. 12 =
30 =
GCF = ___________
3. 18 =
24 =
GCF = ___________
4. 15 =
45 =
GCF = ___________
5. 54 =
81 =
GCF = ___________
b. Prime Factorization
1.
12
18
X
X
X
12 = ___________________
18 = ___________________
GCF = ___________________=_____
X
2.
8
16
X
X
X
X
X
8 = ___________________
16 = ___________________
GCF = ___________________=_____
APPLY YOUR SKILLS
Directions: Solve the following word problems.
1. Miguel has 24 red marbles and 40 blue marbles. He wants to put an equal
number of marbles in small boxes without mixing the two kinds. What is the
greatest number of marbles he can place in each box if he uses all the marbles?
2. Ramon has 2 pieces of yarn. The orange yarn measures 36 cm. The violet
yarn measures 27 cm. If he wants to cut each yarn into smaller pieces of equal
length, what is the longest possible measure of each small piece?
Ateneo de Zamboanga University
Grade School
PAASCU Level III Accredited
ACTIVITY 2 – A and B
Name: ___________________________________ Score: ________________
Section : ________________________________ Date : _________________
A. Use any method to find the GCF of each of the following.
1.
8 , 12
______
2.
56 , 48
______
3.
32 , 24
______
4.
64 , 16
______
5.
18 , 36
______
B. Solve the following word problems.
1. Sony has 64 boxes of crayons and 80 boxes of pencils. He wants to give
these to the pupils in a public school. If he packs the items separately with
each box having the same number of crayons and pencils, what is the
greatest number of boxes he can place in each package?
2. Dexter helps the librarian in arranging the books in the school library during
dismissal. He was asked to put 50 science fiction books and 75 reference
books in shelves, with each shelf having the same number of books. What is
the most number he can place in each shelf without combining the kinds of
books?
Ateneo de Zamboanga University
Grade School
PAASCU Level III Accredited
ALTERNATIVE ACADEMIC ACTIVITIES IN MATHEMATICS
Grade Four
I. LEARNING OBJECTIVES
At the end of the lesson, the students are expected to:
a. find the Least Common Multiple of a given set of numbers; and
b. solve the word problems involving Least Common Multiple (LCM).
II. TIME FRAME
October 18, 2013
III. LESSON
Least Common Multiple
References
Domingo, E. C. & Apistar, E. M. (2009). Integrative Mathematics. Quezon
City, Philippines: SibsPublishing House, Inc.
Ani M. Guerrero, Darwin M. Guerrero, Loly Ong (2009). Beyond Math. 927
Quezon Avenue, Quezon City, Philippines: Phoenix Publishing House, Inc.
Socao, J. (2009). Math World 4. Quezon City, Philippines: C & E
Publishing, Inc.
IV. LEARNING EXPERIENCE
Jose and Melissa are OFWs in the United Kingdom. Jose goes
home to the Philippines every 6 months while Melissa goes home
every 8 months. This month, they both went home to the Philippines.
After how many months will they be in the country in the same
month again?
How will you solve the problem?
You may perform skip counting to solve the problem.
JOSE
From this
month
6
12
18
24
30
36
MELISSA
From this
month
8
16
24
32
You can see from the illustrations above that Jose and Melissa
will go home in the same month again after 24 months.
You actually solved for the least common multiple (LCM). When
you skip 6 and 8, you obtained the multiples of 6 and 8.
What is Least Common Multiple (LCM)?
Least Common Multiple (LCM) is the smallest number that is divisible
by
the given number.
Methods on how to solve for Least Common Multiple (LCM)
1. Listing Method
List all the nonzero multiples of 3 and 9 and identify their common multiples.
From these common multiples choose the least.
Multiples of 3:
Multiples of 9:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
9, 18, 27, 36, 45, 54, 63, 72, 81, 90
Common multiples: 9, 18, and 27
Least common multiple = 9
So the LCM of 3 and 9 is 9.
2. Prime Factorization
Express the prime factorization of each number through factor tree.
15
10
2
X
3
5
X
5
Steps:
 List the prime factorization of each number.
10 = 2 x 5
15 = 3 x 5
 Encircle the common prime factors.
10 = 2 x 5
15 = 3 x 5
5 is the common prime factor of 10 and 15.
Bring down the common factors and the
other prime factors.
10 = 2 x 5
15 =
5x 3
LCM = 2 x 5 x 3
 Multiply the common prime factor with the
other prime factors. Their product is the
LCM of the given numbers.
2 x 5 x 3 = 30
Therefore, the LCM of 10 and 15 is 30.
LET’S PRACTICE
A. Find the LCM of the following numbers;
c. Listing Method
1. Multiples of 8 =
Multiples of 40=
LCM = _____
2. Multiples of 4 =
Multiples of 15 =
LCM = _____
3. Multiples of 16 =
Multiples of 40 =
LCM = _____
4. Multiples of 18 =
Multiples of 36 =
LCM = _____
5. Multiples of 7 =
Multiples of 11 =
LCM = _____
d. Prime Factorization
1.
6
X
33
X
6 = ___________________
33 = ___________________
LCM = ___________________= _____
9
2.
25
X
X
9 = ___________________
25 = ___________________
LCM = ___________________=_____
3.
12
15
X
X
X
12 = ___________________
15 = ___________________
LCM = ___________________=_____
4.
20
24
X
X
X
X
20 = ___________________
24 = ___________________
LCM = ___________________=_____
X
5.
56
27
X
X
X
X
X
56 = ___________________
27 = ___________________
LCM = ___________________=_____
ENHANCE YOUR SKILLS
Directions: Solve the following word problems.
1. Oliver has a collection of compact discs. He can arrange these into equal piles of 12,
or 16 compact disc per pile. What is the smallest possible number of compact discs that
Oliver has?
2. Aaron washes the family car every 6 days, and does gardening work every 9 days. If
he did both activities on September 1, when is the next date that he will do both on the
same day again?
Ateneo de Zamboanga University
Grade School
PAASCU Level III Accredited
Activity A and B
Name: _______________________________________ Score: ________________
Section : ______________________________________ Date : _________________
A. Use any method to find the LCM of each of the following.
Pair of Numbers
a.
3, and 6
b.
4 and 8
c.
9, and 15
d.
10 and 20
e.
7 and 21
f.
10 and 15
g.
3 and 4
h.
12 and 18
i.
3 and 18
j.
4 and 8
Least Common Multiple
(LCM)
B. Solve the following word problems.
1. Felix and Rowald work in Zamboanga. Felix goes home to the province every
three months while Rowald goes home every four months. If they both went
home last December 2008, what is the next date they will go home at the same
time?
2. What is the smallest multiple of seven that is divisible by thirteen?