The document outlines a mathematics tutorial for 6th graders focusing on the whole number system. It starts with a pre-test on topics such as place

1. SOLANO NORTH ELEMENTARY SCHOOL
AUGUST 3, 2019
EDGAR H. ANOS
DISCUSSANT
MTAP-DepEd Saturday
Program in Mathematics for
Grade VI
SESSION 1

2. Session 1
Whole Number System
Math Song:

3. Pre-Test
Give what is asked
1. Write in words 30 501 047.
2. Write in standard form: 5 x 105 + 6 x 104 +
3 x 103 + 5 x 102 + 2 x 10 + 9 .
3. The following are prime numbers except,
2, 3, 5, 7, 9, 11, 13, 17, 19
4. 800 is how many times lesser than 80 000?
5. What is the standard form of 23 x 32 x 5?

4. Pre-Test
6.What is the GCF of 12 and 18?
7. The LCM of 8 and 12.
8. The prime factors of 180.
9. Which of the following is greater?
34 or 43 ?
10. Which of the following is not correct?
22 x 3 x 5 = 60
24 x 33 = 133
22 x 32 x 52 = 900

5. A

6. Answers
1. Thirty million, five hundred one thousand,
forty-seven
2. 563 529
3. 9
4. 100 times
5. 360
6. 6
7. 24
8. 2x2x3x3x5 or 22 x 32 x 5
9. 34
10. 24 x 33 = 133

7. Introduction
Place Value of Whole Numbers
Our numeration system is called the decimal number
system (“deci” means 10)because it makes use of ten
symbols to form numbers.
The decimal number system makes use of Hindu-
Arabic numerals that the value of a number depends
on the place values the digits use in a number.
Each place or position that a digit holds in a number has
a value ten times the value of the place at its right

8. Place Value Chart
Billions Millions Thousands Units
Hundreds
Tens Ones
Hundreds
Tens Ones
Hundreds
Tens Ones
Hundreds
Tens Ones
P E R I O D S
P L A C E V A L U E S
D I G I T P L A C E M E N T

9. Place Value Chart
I. Writing numbers in words
1. Thirteen thousand, one hundred ninety five
2. Two hundred seven thousand, six hundred thirty
3. Eight million, one hundred thirty –seven thousand,
five hundred thirty-nine
4. seventy-six million, one hundred four thousand, two
hundred sixty-five
5. Six hundred thirty-nine million, eight hundred
seventy-one thousand, two hundred twenty-three

10. Place Value Chart
I. Writing numbers in words
5. Five billion, ninety-two million, four hundred forty-
one thousand, seven hundred thirty-six

11. Place Value Chart
II. Writing numbers in standard form
1. 8 475
2. 30 656 213
3. 40 823
4. 756 345
5. 5 016 899

12. Writing Expanded notation in standard form
4 628
4 000 = 4 x 103
600 = 6 x 102
20 = 2 x 101
8
Thus:
4 628 = 4 x 103 + 6 x 102 + 2 x 101 + 8 (place-value
expanded form) or
= 4 000 + 600 + 20 + 8 ( value-expanded form)

13. Writing Expanded notation in standard form
850 609
800 000 = 8 x 105
50 000 = 5 x 104
600 = 6 x 102
9
Thus:
850 609 = 8 x 105 + 5 x 104 + 6 x 102 + 9 or
= 800 000 + 50 000 + 600 + 9

14. II. B. Writing Expanded notation in standard
form
1. 40 925
2. 863
3. 287 927
4. 35 569
5. 7 895 738

15. Expressing Exponential Form in
Standard Form
 Base – is the number used as a factor
 Exponent – indicates how many times the
base is multiplied to itself
 Product is the standard form of an
exponential expression
Ex. 23 = 2 x 2 x 2 = 8
112 = 11 x 11= 121
105 = 10 x 10 x 10 x 10 x 10=100 000

16. Identifying how many times a number is
lower or greater than on its place value
900 900
= 900 000 is 100 times greater than 900
= 900 is 100 times lesser than 900 000
2 020
= 2 000 is 100 times greater than 20
= 20 is 100 times lesser than 2 000

17. III. Identifying how many times a number is
lower or greater than on its place value
1. 1oox greater
2. 10 000x greater
3. 1 000x lesser
4. 10 000x lesser
5. 10x lesser
6. 10x greater

18. Odd , Even and Prime Numbers
 ODD numbers are NOT divisible by 2
 EVEN numbers are divisible by 2
Prime Number
Is a number which has only 2 factors; 1 and
itself
Prime numbers below 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

19. IV. Expressing a number as a sum of
two prime numbers
 Choose from the following list of prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
1. 35
= 5+7+23
2. 21
= 19 + 2
= 2+2+17

20. Factor
A number that evenly divides
another number
An amount by which another
amount is multiplied or divided
Any of the numbers or symbols in
mathematics that when
multiplied together form a
product

21. Pair share: List all the factors of
the following:
 15
 36
 125
 75
 48
 13
Answers: 15: 1, 3, 5, 15 36: 1,2,3,4,6,9,12,36
125: 1, 5, 25, 125 75: 1, 3,5,15,25,75
48:1,2,3,4,6,8,12,24,48 13: 1, 13

22. Prime Factorization
Expressing a composite
number as a product of its
prime factors

23. Finding prime factors by
continuous division method
36
36 ÷ 2 =18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

24. Finding prime factors by
continuous division method
2 36
2 18
3 9
3
36 = 2 x 2 x 3 x 3 or
22 x 32

25. Finding prime factors by factor-
tree method
48
2 x 24
2 x 12
2 x 6
2 x 3
48 = 2 x 2 x 2 x 2 x 3 or
24 x 3

26. V. Work by Pair: Give the Prime Factors
B. 1. 96
2. 42
3. 81
4. 56
5. 144
6. 108
7. 420
8. 1260
= 2 x 2 x 2 x 2 x 2 x 3 or 25 x 3
= 2 x 3 x 7
= 3 x 3 x 3 x 3 or 34
= 2 x 2 x 2 x 7 or 23 x 7
= 2 x 2 x 3 x 3 x 3 or 22 x 33
= 2 x 2 x 3 x 5 x 7 or 22 x 3 x 5x7
= 22 x 32 5 x 7
= 2 x 2 x 2 x 2 x 3 x 3 or 24 x 32

27. Finding GCF and LCM
Greatest Common Factor (GCF)
- is the largest divisor of the
numbers in a set
Least Common Multiple (LCM)
- is the smallest number that can be
divided by each number in a set

28. Finding GCF by continuous division
method
24 and 36
24 ÷ =
36 ÷ =
Common factors = 2 x 2 x3
GCF = 2 x 2 x 3 = 12
12
18
÷
÷
2
2
=6
=9
÷
÷
3
3
=2
=3
2
2

29. Finding LCM by continuous division
method
24 and 36
24 ÷ =
36 ÷ =
Common factors = 2 x 2 x 3
Uncommon Factors (end part)= 2 x 3
LCM (common x uncommon factors)
= 2 x 2 x 3 x 2 x 3
= 72
12
18
÷
÷
2
2
=6
=9
÷
÷
3
3
=2
=3
2
2

30. VI. Give the GCF of each set of numbers
1. 20 & 36
2 20 36
2 10 18
5 9
GCF = 2 x 2 = 4
LCM = 2 x 2 x 5 x 9 = 180
VI. Give the GCF of each set of numbers

31. VI. Give the GCF of each set of numbers
2. 18 & 54
3. 32 & 56
4. 44 & 88
5. 63 & 84
6. 150 & 225
GCF= 22 x 3 x 3= 18
GCF= 2 x 2 x 2 = 8
GCF= 2 x 2 x 11 = 44
GCF= 3 x 7 = 21
GCF= 3 x 5 x 5= 75

32. VII. Give the LCM of each set of numbers
1. 12 & 15
3 12 15
2 4 5
2 5
GCF = 3= 3
LCM = 3 x 2 x 2 x 5 = 60

33. VI. Give the LCM of each set of numbers
2. 14 & 18
3. 32 & 56
4. 36 & 48
5. 27 & 63
6. 48 & 54
LCM = 2 x 3 x 3 x 7= 126
LCM = 2 x 2 x 2 x 2 x 2 x 3= 96
LCM = 2 x 2 x 2 x 2 x 3x 3= 144
LCM = 3 x 3 x 3 x 7= 189
LCM = 2 x 2 x 2 x 2 x 3 x 3 = 432

34. Expressing a number as a sum of two
prime numbers
 Choose from the following list of prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
ex. 32
= 13 + 19 or 29 + 3
64
= 3 + 61 or 47 + 17

35. Work by Group
Answer problem solving part in
10 minutes( 1-5 )