This document provides a lesson on finding missing numbers in mathematical equations. It discusses different properties of operations like the commutative, associative, distributive, and identity properties. Examples of equations are provided and students are asked to determine the missing numbers by identifying which property is being used. Practice problems are included for students to solve. The goal is for students to understand how to use properties of operations to determine missing numbers in equations.

1. 1
Mathematics
Quarter 3 - Module 4: Week 4
Determines the Missing Term/s
in a Sequence of Numbers and
in an Equation
Department of Education Republic of the Philippines
4

2. 2
Lesson
1
Determine the Missing Term/s
in a Sequence of Numbers
When you do skip counting numbers by 2,3 and so on you can
form a pattern or a sequence. Aside from that you can identify the even
and odd numbers, get the factors and multiple of a number that can be
use in determining the missing term.
With this lesson you will be able to determine the missing term in
a given sequence by finding the sequence uses.
What’s In
A. Skip count by 3 from 6 to 36
1. List all even numbers
2. List all odd numbers
B. Skip count by 4 from 8 to 40
1. What are the factors of 4?
C. Skip Counting by 5 from 10 to 100
1.What are the multiples of 5?

3. 3
What’s New
Game: Odd or Even?
A. Identify each of the following number whether it is odd or even
number .
1.8
2.11
3.17
4. 24
5.33
Have you tried answering a number pattern with missing term?
What is It
Analyze each set of number.
1.8,10,12,____,____,18, 20
Odd and even numbers are used in number patterns

4. 4
2. 25, 29,_____,37,_____,45
3. 5,10, 15, ____, ____,30, 35
4.22, 25, 28, 31, ____, ____, 40
5.63, 57, 51, ____, 39, ____, 27
A
What’s More
Write the missing terms in each of the following number sequence.
1. 23, 25, 27, ____, ____,33 6.1, 5, 25,125,____,_____
2. 32, 37, ____, ____, 52, 57 7.1, 3, 9, 27, 81, _____
3. 42, 52, 62, ____, 82,____, 8. 1,10, 100, 1000, _____
4. 85, ____, 77, 73, ____, 65 9. 55, 54, 51, 46, ____, ____,
5. 1, 2, 4, ____, 11, ____ 10. 82, 78, 74, 70, ____,___
Can you see the pattern? What
are the missing terms?
A number sequence is a list of numbers arranged following a
pattern. Each number in the sequence is called term.
To find the missing term in a number sequence, you must first
figure out its pattern.

5. 5
What I Have Learned
What I Can Do
Find the missing term/s.
1. 5, 7, 11, 17, 25, ____
2. 7, 14, 21, 28, 35, _____
3. 3,4,7,8, 11, _____,____
4. 2, 3, 4, 5, _____, _____, _____
5. 6, 11, 16, 21, _____, _____, _____
6. 2, 7, 12, 17, _____, _____, _____
7. Nicole is writing a poem. She writes 6 words on the first line, 12 words
on the second line, 24 words on the third line, and 48 words on the
How do you find the missing term/s in a number
sequence?

6. 6
fourth line. If this pattern continues, how many words will Nicole write
on the fifth line?_____________________________________
8. Simoun saved ₱12.00 on Saturday, ₱15.00 on Sunday, ₱18.00 on
Monday, ₱21.00 on Tuesday, and ₱24.00 on Wednesday. If he
continues to save in the same pattern, how much will Simoun save next
Sunday?_____________________________
9. Roy visits his brother, John, every seventh day of the week.He
visited his brother last December 1, 2014 ,at what date will he visit his
brother for the third time?__________________________________
10. Lorna has a magic box. Anything she places inside the magic box
doubles every minute. If she placed an orange inside the box, how
many oranges would there be after 10 minutes?__________________
Post Assessment
Direction:
A. Find the missing term in a given number sequence.
1.43, 45, ____, 49, ____53
2.61, ___, 71, 76, ____, 86
3.67, 64, ____, 58, ____, 52

7. 7
4.6, 12,______,24, ______36
5.25, 24, ____,19, ___, 10
B. Follow the direction in each phrases.Write the sequence
being described.
1. With 10, as the first term, what is the 3rd
term in the sequence
multiples of 5?
Sequence:_____________________________ Answer:_________
2. With 30 as the first term in sequence. Add 4 to the next to get the
second term. Do the same to the next three terms. What is the fourth
term in the sequence?
Sequence:_____________________________ Answer:_________
3. If you skip count by 7, what will be the 7th
term in the sequence?
Sequence:_____________________________ Answer:_________
4. Starting with 16, count by 4 five times. What is the 5th
term in this
sequence?
Sequence:_____________________________ Answer:_________
5. If you skip count by 9,what will be the 10th
term in the sequence?
Sequence:_____________________________ Answer:_________

8. 8
Answer Key
What’s
new
A.
1.even
2.odd
3.odd
4.even
5.odd
B.
What
is
it
1.14,16
2.33,41
3.20,25
4.34,37
5.45,33
What
I
can
do
Whats
more
1.35
1.
29,
31,
33
2.42
2.
42,
47
3
.12,15
3
.72,
92,
4.
6,
7,
8
4.81,
69
5.
26,
31,
36
5.7,
16
6.
22,
27,
32
6.625,
3125
7.
96
7.243,729
8.
₱
36
8.100,000
9.
December
15,2014
9.39,
30
10.
20
oranges
10.66,
62
3.61,55
4.18,30
5.22,15
B.1
20
2.42
3.49

9. 9
What is the
missing number in
this equation?
45 + 80 = 80 + ___
I think it is 45. it
involves the
Commutative
Property of Addition
The order of the
addends does not
affect the sum.
45 + 80 = 80 + 45
125 =125
z
Lesson
2
Finds the Missing Number
in an Equation Involving
Properties of Operations
What’s In
What is an equation? An equation is a mathematical sentence stating
that two things are equal. These two things are separated by an equal
“=” sign.
Analyze these equations. Give the missing number.
Here is another example.
12 x 2 = x 12
24 = 24
Basic Number Properties

10. 10
1. Commutative Property- when two numbers are added the sum is
the same regardless of the order of the addends. Similarly, for
multiplication, when two numbers are multiplied the product is the
same regardless of the order of the factors.
Example: 4+2=2+4
4 x 2 = 2 x 4
2. Associative Property – when three or more numbers are added,
the sum is the same regardless of the grouping of the addends.
Similarly, in multiplication, when three or more numbers are
multiplied, the product is the same regardless of the grouping of
the factors.
Example: ( 2+3) + 4 = 2 ( 3+4 ) = 3 + (2 + 4)
(2 x 3) x 4 = 2 (3x 4) = 3 x (2 x 4)
3. Identity Property – The sum of any number and zero is the
original number. The product of any number and 1 gives the given
number. 0 is called the identity element of addition and 1 is the
identity element of multiplication.
Example: 5 + 0= 5
5 x 1 = 5
4. Distributive Property – The distributive property of multiplication
over addition can be used when you multiply a number by a sum.
Example: 5 ( 6+2 ) = 5x6 + 5x2
5 x 8 = 30 + 10
40 = 40
What’s New
Write on the circle the letter of the property used in each equation. Then
write the missing numbers.

11. 11
1. 30 x 5 = ___ x 30
2. ( 8 x 1 ) x 5 = ___ x ( ___ x 5 )
3. ___ + 246 = 246 + 369
4. ___ x ( ___ + 4 ) = ( 12 x 2 ) + ( 12 x 4 )
5. 2 x 194 = ___ x 2
6. 10 x ( 2 + 2 ) = (10 x 2) + (10 x ____)
7. 15 x 3 = ___ x 15
8. (3 x 2) x 4 = ___ x ( __ x 4 )
9. ( 7 + 4 ) + 5 = 7 +( __ + __ )
10. 15 x 2 = ___ x 15
What is It
Find the missing number in the following equations.
1. 36 + ___ = 29 + 36
2. 1 x 213 = ___ x 1
A. Commutative Property C. Distributive Property
B. Associative Property D. Identity Property

12. 12
3. ( 26 x 1 ) x 0 = ___ ( 1 x 0 )
4. ( 8 x ___ ) x 5 = ___ x ( 2 x 5 )
5. ___ x ( 3 x 2 ) = ( 40 x 3 ) + ( 40 x 2)
6. 3 x 4 = __ x 3
7. 2 ( 4x5 ) = ___ ( 2x4 )
8. 6 x ___ = 4 x 6
9. 4 ( 8x2 ) = ___ ( 8 x 4 )
10. 2 ( 4+3) = 2x__ + 3x2
What’s More
Find the missing number in the following equations:
1. 2 x ( 15 + 20 ) = ( __ x 15 ) + ( 2 x___)
2. 6 x 3 = 10 + 5 + ___
3. 42 + ( 63 + 200 ) = ( ___ + ___ ) + 200
4. 7 + 8 + 3 = 22 – ( 1 + ___ )
5. ( 16 x 5 ) x 4 = 8 x ( __ x 4)
6. (4 x 3) x2 = ___ (2x4)

13. 13
7. 6 x ( 5 + 10 ) = ( __ x 5 ) + ( 6 x___)
8. 10 x 5 = 35 + 15 + ___
9. 8 x 6) x4 = ___ (4x8)
10. (9 x3) x5 = ___ (3x9
What I Have Learned
Remember that:
In order to learn, understand and pass the activities, you should
study the pattern.
To find the missing number in an equation, determine the property
used in the number sentence such as: Commutative, associative,
Distributive and Identity.

14. 14
What I Can Do
Read the simple problem. Write the equation and solve.
1-2. There were15 kids at the party. 7 ate cake the rest ate ice cream.
How many kids ate ice cream?
Find the missing number in the following equation
Associative property
(13 + 6) + 5 = 13 + ( __ + __ )
19 + 5 = 13 + ( 6 + 5 )
19 + 5 = 13 + 11
24 = 24
( 5 x 6 ) x 4 = __ x ( __ x 4 )
30 x 4 = 5 x ( 6 x 4 )
120 = 120
Identity Property
48 + __ = 48
48 + 0 = 48
369 x __ = 369
369 x 1 = 369
Commutative
8x2 =2x8
16=16
Distributive Property
20 x ( 3 + 4 ) = ( 20 x __ ) + ( 20 x __ )
20 x ( 3 + 4 ) = ( 20 x 3 ) + ( 20 x 4 )
20 x 7 = 60 + 80
140 = 140

15. 15
3. 60 - ___ = 20 + 12
4. 12 x ( 3 + 9 ) = ( __ x3 ) + ( 12 x __ )
5.25 x 4 = ___ x 25
6.4 x 6 = ___ x 4
7. 5(7 + 4) = 5 x___ + 5 x ___
8.6 ( 8x3 ) = __ (6x3)
9.(4x5) = ___ (5x4)
10.(5+3) 7 = ___ (8)
Post Assessment
Direction:
Give the property used in each equation. Then, write the missing
numbers.
1. ( 8 + 15 )+ ( 4 + 9 ) = (4 +__ ) +( __ + 15 ) Property: __________

16. 16
1.
5
A
2.
8,
1
B
3.
369
A
4.
12,2
C
5.
194
A
6.
2,
C
7.
3
A
8.
2,3
B
9.
4,5
B
2. ( 5 + 4 ) x 6 = 6 x___ + ( 6 x ___ ) Property: _________
3. 30 + ___ = 90 + ____ Property: __________
4. 1 x 465 = ____ x 1 Property: __________
5. 87 + 63 = ____ + 87 Property: __________
6. 5 + _____ = 5 Property: __________
7. 1 x ____ = 80 Property: __________
8. 10 x ____= 2 x 10 Property: __________
9. 5 (6+ 5) = 5x ___+ 5 x 5 Property: __________
10. 6 +(10+5) = ____+(6+10) Property: __________
Answer Key

17. 17
What
is
it
1.
29
2.
213
3.
26
4.
2,8
5.
40
6.
4
7.
5
8.
4
9.
2
10.
What’s More
1. 2, 20
2. 3
3. 42,63
4. 3
5. 10
6. 3
7. 6,10
8. 0
What
can
I
do
1.
15,7
2.
8
3.
28
4.
12,9
5.
4
6.
6
7.
7,4
8.
8
9.
1
10.
7

18. 18
9. 6
10. 5
Post assessment
1. 9,8 commutative
2. 5,4 distributive
3. 90,30- Commutative
4. 465 - Commutative
5. 63 - Commutative
6. 0- Identity element for
addition
7. 80 –Identity element for
multiplication
8. 2- commutative
9. 6- Distributive
10. 5 Associative