Name of Pupil: ________________________________ Grade and Section: ________

Name of Teacher: _____________________________

Pasay-M6- Q2-W4-D1

DEPARTMENT OF EDUCATION, NATIONAL CAPITAL REGION

SCHOOLS DIVISION OF PASAY CITY

MODULE IN MATHEMATICS 6
Quarter 2 / Week 4/ Day 1

Objective: Describes the exponent and the base in a number expressed in exponential notation.

YOUR LESSON FOR TODAY!

Exponential Notation is commonly found in algebraic terms, expressions, and equation.

Exponents are used to shorten or condense repeated multiplication

4 ● 4 ● 4 = 𝟒𝟑
exponent
base
The term 𝟒𝟑 is written using exponential notation, 4 is the base and 3 is the exponent.
The exponent or power, indicates the number of times that the factor or base, is multiplied.
Exponential Notation
For any natural number n,

𝒃𝒏 𝒎𝒆𝒂𝒏𝒔 𝒃 ● 𝒃 ● 𝒃 ● 𝒃 ●….𝒃

n factors

x = 𝑥1 𝑖𝑓 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑛𝑜 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 𝑔𝑖𝑣𝑒𝑛, 𝑖𝑡 𝑖𝑠 𝑡𝑜 𝑡ℎ𝑒 1𝑠𝑡 𝑝𝑜𝑤𝑒𝑟

x ● x = 𝑥 2 𝑥 𝑡𝑜 𝑡ℎ𝑒 2𝑛𝑑 𝑝𝑜𝑤𝑒𝑟 𝑜𝑟 𝑥 𝑠𝑞𝑢𝑎𝑟𝑒𝑑
x ● x ● x = 𝑥 3 𝑥 𝑡𝑜 𝑡ℎ𝑒 3𝑟𝑑 𝑝𝑜𝑤𝑒𝑟 𝑥 𝑐𝑢𝑏𝑒𝑑
x ● x ● x ● x = 𝑥4 𝑥 𝑡𝑜 𝑡ℎ𝑒 4𝑡ℎ 𝑝𝑜𝑤𝑒𝑟
x ● x ● x ● x ● x = 𝑥 5 𝑥 𝑡𝑜 𝑡ℎ𝑒 5𝑡ℎ 𝑝𝑜𝑤𝑒𝑟

Let’s Explore

EXAMPLE 1
Write 3 x 3 x 3 x 3 in the exponential notation. Then, evaluate.
Solution:
The base is 3. Since 3 used as a factor four times, the exponent is 4. Therefore,

3 x 3 x 3 x 3 = 𝟑𝟒 = 81
 Name of Pupil: ________________________________ Grade and Section: ________
Name of Teacher: _____________________________

EXAMPLE 2
Evaluate each expression.

a. 54 = 5 𝑥 5 𝑥 5 𝑥 5 5 is used as a factor 4 times.

= 625

b. 39 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 3 is used as a factor 9 times.

= 19, 683

c. (−4)5 = (-4) x (-4) x (-4) x (-4) x (-4) -4 is used as a factor 5 times

= - 1024 An odd power of a negative number is negative.

EXAMPLE 3
Evaluate each expression if x = 2, y = 5, and z = 6.

1. y + 𝑥 2 = 5 + 22 Substitute the given values of the variables.

=5+4 Evaluate 22 (2 x 2 = 4). Then, add.
=9

2. 𝑧 3 − 𝑦 2 = 63 − 52 Substitute the given values of the variables.

= 216 – 25 Evaluate 63 (6𝑥6𝑥6 = 216)𝑎𝑛𝑑 52 (5𝑥5 = 25). Then, subtract.

= 191

3. 2𝑥 3 = 2(2)3 Substitute the given values of the variables.

= 2(8) Evaluate 23 (2𝑥2𝑥2 = 8). Then, multiply

= 16

Let’s Practice!

Practice no. 1

DIRECTION: Express each of the following using exponential notation. Match

column A to column B

COLUMN A COLUMN B

i. 6x6 a. 42 x 52

ii. 3x3x3 b. 62

iii. 5x5x5x7x7 c. 33

iv. 4x4x5x5 d. 32 x 84

v. 3x3x8x8x8x8 e. 53 x 72
 Name of Pupil: ________________________________ Grade and Section: ________
Name of Teacher: _____________________________

Let’s Practice!

Practice no. 2

DIRECTION: Expand each of the following exponential notations. Then evaluate.

Example: 𝟒𝟑 = 𝟒 𝒙 𝟒 𝒙 𝟒 = 𝟔𝟒

a. 63 = _____________________________________________________

b. 95 = _____________________________________________________

c. 54 = _____________________________________________________

d. 28 = _____________________________________________________

e. 37 = _____________________________________________________

Remember
o The exponent tells the number of times the base is used as a factor.

o A number is called a power when it is written in exponential form.

o Any nonzero number with a zero exponent is equal to 1

o Any number raised to the exponent 1 is equal to the number itself.

o The number of zero found after the digit 1 in a power of 10 corresponds to

the exponent of 10
Example: 100 000 = 10 x 10 x 10 x 10 x 10 = 105
 Name of Pupil: ________________________________ Grade and Section: ________
Name of Teacher: _____________________________

Let’s Practice!

Practice no. 3

DIRECTION: Evaluate each expression.

Example: 𝟐𝟐 + 𝟑𝟐 = (2x2) + (3x3)
=4+9
= 13

1. 53 + 42 =

2. 25 - 33 =

3. 23 x 24 =

4. 33 + 43 + 53 =

5. 83 - 73 =

Integrated the Development of the Following Learning Skills:

Integrated The Development of the Following Learning Skills:

Communication Creativity Critical Thinking
1. Following directions 1. Problem solving 1. analysis
2. Reasoning 2. interpretation
3. Responding to ideas 3. Problem solving
Collaboration
Cooperative brainstorming, exchange of ideas
Character
1. Accuracy
2. Perseverance
Evaluation:
3. Honesty
4. Patience
Evaluation:

Directions: Write each of the following in expanded form and find its value.

Exponential Expanded Form Value

Notation
𝟏𝟎𝟓

(−𝟕)𝟒

𝟏𝟔𝟒

𝟗𝟔

(−𝟑)𝟑

Reference for further enhancement:

1. https://www.youtube.com/watch?v=j_Eb5FsgJLY
2. 21st Century Mathletes Grade 6 textbook, pages 174 to 179.
3. Primary Mathematics K to 12 Grade 6 worktext

Prepared by:
Oliver Dizon
Teacher 2 - PBES
Name: _______________________________Grade and Section: _____________
Name of Teacher: ______________________

Pasay-M6-Q2- W4-D2

DEPARTMENT OF EDUCATION, NATIONAL CAPITAL REGION

SCHOOLS DIVISION OF PASAY CITY

MODULE IN MATHEMATICS 6
Quarter 2 / Week 4/ Day 2

OBJECTIVE: Gives the value of numbers expressed in exponential notation.

YOUR LESSON FOR TODAY:

In giving the value of numbers expressed in exponential notation:

 An exponential graph is a graph in which the relationship between the
variables involves on expression in which one of the variables appears as an
exponent. The word is often used in connection with “exponential growth” to
indicate that its rate of change is always increasing.
 Exponent notation is a way of indicating how a number (or symbol) must be
operated on by using another number written as a superscript to the first; this
second number is called an exponent. When the exponent is a positive whole
number, that number indicates how many of the first number or symbol must
be multiplied together: When the exponent is a fraction, it indicates that a root
has to be found.
Examples: A2 = A x A 53 = 5 x 5 x 5 = 125 91/2 = √9 = 3
 Base in exponential notation the base is the number (or symbol) upon which
the exponent is to operate.
Examples: In A2, y-1, 34, 10X A, y, 3, and 10 are all the bases
 Positive exponent – A positive exponent is an exponent which is greater than
zero.
 Zero Exponent – A zero exponent is an exponent which is equal to zero. Any
number (except zero) raised to a zero exponent is equal to 1.
Examples: 10 = 1; 20 = 1; 50 = 1; (any number)0 = 1; x0 = 1
 Negative exponent – An exponent having a negative value indicates that a
reciprocal has to be taken before the exponent is applied to the base.
1 1 1 1
Examples: x-1 = 𝑥, x-2 = 𝑋 2, 2-3 = 23 = 8
 When two or more numbers are multiplied, each number is called a factor. An
exponent is used to show how many times the factor or base is multiplied.
 An exponent is a shorthand way to show how many times a number, called
the base, is multiplied by itself. A number with an exponent is said to be
“raised to a power” of that exponent.
Name: _______________________________Grade and Section: _____________
Name of Teacher: ______________________

Example: 24 2 to the fourth power

= 2 x 2 x 2 x 2 = 16

Factors
4 Exponent
2 Base

 The number of unit cubes that the large cube has can be determined by
finding the product of the length, the width, and the height of the cube or 4 x 4
x 4. The numerical expression of 4 x 4 x 4 contains three fours. This is a
repeated multiplication, a short way to write 4 x 4 x 4 is 4 3. The expression 43
means the third power of 4. It is read as “four to the power of three”; “four to
the third power”; or “four cubed”.

In the expression 43, the number 4 is called the base and the number
written at the upper right corner is called the exponent. The exponent tells
how many times the based is used as a factor. The base is the factor being
repeated. The expression 43 is called the exponential form.

 Exponents are also useful when writing powers of ten. Numerical expressions
such as 100, 101, 102 and so on are called power of 10

 A power of equals the number 10 multiplied by itself for a given number of

times.
Example: 100,000 = 10 x 10 x 10 x 10 x 10
There are five zeros in 100,000 so 10 is multiplied by itself 5 times. Thus, to
write 100,000 in exponential form or notation we have, 10 x 10 x 10 x 10 x 10
= 100,000 = 105

Do you see the relationship between the exponent in a power of 10 and the
number of zeros in the standard form of the number?

We read numbers in exponential form as follows:

100 is read as “ten to the zeroth power”
101 is read as “ten to the first power”
102 is read as “ten to the second power” or “ten squared”
103 is read as “ten to the third power” or “ten cubed”
104 is read as “ten to the fourth power”
105 is read as “ten to the fifth power”
Name: _______________________________Grade and Section: _____________
Name of Teacher: ______________________

Let’s Explore!
A. Answer the following
1. 53 written in standard form is 125 since 53 = 5 x 5 x 5 = 125
2. 34 written in standard form is 81 since 34 = 3 x 3 x 3 x 3 = 81

3. 10 x 10 x 10 x 10 x 10 written in exponential form is 105.

4. 9 x 9 x 9 x 9 x 9 x 9 x 9 written in exponential form is 9 7
5. 1,000,000,000 written in exponential form is 109
1,000,000,000 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

B. Evaluate each of the following expressions for n = 5

1. n3 (5)3 or 5 x 5 x 5 = 125
2. 2 x n4 2 x (5)4 or 2 x 5 x 5 x 5 x 5 x 5 = 2 x 625 = 1250
0
3. n x n 2 (5)0 x (5)2 = 1 x 5 x 5 = 1 x 25 = 25
Find the value of N
4. 16 = 4 n 2 n
4 =4 n=2
5. 64 = 2n 2 x 2 x 2 x 2 x 2 x 2 = 2n
26 = 2 n n = 6

ARE YOU READY TO PRACTICE?

Any clarification to my discussion? If none bring out your pen and paper and
enjoy answering the following exercises.

PRACTICE EXERCISE 1:
A. Write each in exponential form
1. 3 x 3 x 3 x 3 x 3 =
a. 34 b. 30 c. 35 d. 36
2. (a+b) x (a+b) x (a+b) x (a+b) x (a+b) =
a. (a+b)4 b. (a+b)0 c. (a+b)5 d. (a+b)3
3. (x+y)2 x (x+y)3 x (x+y)4 =
a. (x+y)24 b. (x+y)5 c (x+y)9 d. (x+y)12
(𝑎+𝑏)5 (𝑎+𝑏)9
4. x (𝑎+𝑏)7 =
(𝑎+𝑏)2
a. (a+b)4 b. (a+b)3 c. (a+b)2 d. (a+b)6
(𝑥+𝑦)2 (𝑥+𝑦)5 (𝑥+𝑦)8
5. x (𝑥+𝑦)6 x (𝑥+𝑦)10 =
(𝑥+𝑦)3
1 1 1 1
a. (𝑥+𝑦)2
b. (𝑥+𝑦)3 c. (𝑥+𝑦)4 d. (𝑥+𝑦)5
Name: __________________________Grade and Section: _____________
Name of Teacher: ______________________

PRACTICE EXERCISE 2:
Find the number x that will make each sentence true
1. 16 = 4x a. 2 b. 3 c. 4 d. 5
2. 1,024 = 2 2x a. 5 b. 6 c. 7 d. 4
3. 729 = 93x a. 1 b. 2 c. 3 d. 4
4. 15,625 = 5x+3 a. 3 b. 4 c. 5 d. 6
5. 100,000 = x 5 a. 100 b. 1,000 c.10 d. 10,000

PRACTICE EXERCISE 3:
Evaluate each expression where a = 2, b = 3, and c = 5
1. a3 + b2 = a. 17 b. 18 c. 16 d. 19
2. 5 + a4 = a. 21 b. 27 c. 18 d. 9
3. b – (a + c ) =
4 4 2 a. 39 b. 40 c. 41 d. 42
4. 10 x c3 x a2 x b = a. 1,500 b. 500 c. 150 d.15,000
2 3
5. (7 x b ) + (3 x a ) = a. 87 b. 67 c. 77 d. 97

Integrated the Development of the Following Learning Skills:

1. Follow the simple direction
2. Be honest in solving
3. Accuracy and speed in solving equation
4. Communication
5. Observe time management

Remember Key Ideas

In giving the value of numbers expressed in exponential notation: A number in

exponential form has a base and exponent. The base is the repeated factor. The
exponent tells the number of times the base is to be multiplied by itself.
 Any nonzero number with a zero exponent is equal to 1.
 Any number raised to the exponent 1 is equal to the number itself.
 The number of zeros found after the digit 1 in a power of 10 corresponds to
the exponent of 10.

EVALUATION
Answer the following equation and show your solution
1. 15,625 = 5x+3 a. 3 b. 4 c. 5 d. 6
(𝑥+𝑦)2 (𝑥+𝑦)5 (𝑥+𝑦)8
2. x x (𝑥+𝑦)10 =
(𝑥+𝑦)3 (𝑥+𝑦)6
1 1 1 1
a. (𝑥+𝑦)2 b. (𝑥+𝑦)3 c. (𝑥+𝑦)4 d. (𝑥+𝑦)5
3. 729 = 93x a. 1 b. 2 c. 3 d. 4
Name: __________________________Grade and Section: _____________
Name of Teacher: ______________________

4. 3 x 3 x 3 x 3 x 3 =

34 b. 30 c. 35 d. 36
5. If a = 2, b = 3, and c = 5, what is the value of the following equation?
(7 x b2) + (3 x 93) + (5 x b0) = N
a. 87 b. 92 c. 77 d. 82

Prepared by:

Mr. Rafael S. Divinagracia Jr.

Andres Bonifacio Elementary School

References:
1. Our World of Math 6 pp. 8-11
2. Math Hour Skillbook 6 pp. 40-43
3. MSA Elementary Algebra pp. 32-35
4. Mathematics in Action 6 pp. 60-61
5. Barron’s Mathematics Study Dictionary pp. 47 and 62
Name: ________________________________ Grade and Section: _____________
Name of Teacher: ______________________

Pasay-M6-Q2- W4-D3

DEPARTMENT OF EDUCATION, NATIONAL CAPITAL REGION

SCHOOLS DIVISION OF PASAY CITY

MODULE IN MATHEMATICS 6
Quarter 2 / Week 4/ Day 3
OBJECTIVE: Interprets and explains the Grouping, Exponent, Multiplication,
Division, Addition, Subtraction (GEMDAS) rule.

YOUR LESSON FOR TODAY:

Rules in solving more than one arithmetic operation:
 Simplify the operation in grouping symbols. Start from the innermost grouping
symbol.
 Evaluate exponential expressions.
 Multiply and divide in the order they appear from left or right.
 Add and subtract in the order they appear from left or right.
GEMDAS rule means Groupings symbols, Exponents, Multiplication, Division, Addition
and Subtraction.

LET’S TRY THESE!

Example:

Hazel and Eden are both working on the Value of the expression:
14 + 7 x 6 – 8 ÷ 2 . However, they have different answers. Hazel answered 59, while
Eden answered 52. Of the two pupils, who answered correctly?

EXPLORE
In a series of operations without grouping symbols, multiplication and division are
performed first from left to right, followed by addition and subtraction, whichever comes
first from left to right.
Thus, to solve 14 + 7 x 6 – 8 ÷ 2,
Multiplication: 14 + 7 x 6 – 8 ÷ 2
Division: 14 + 42 – 8 ÷ 2
Addition: 14 + 42 – 4
Subtraction: 56 – 4
Answer: 52
Therefore, Eden got the correct answer by following the MDAS rule.
Name: ________________________________ Grade and Section: _____________
Name of Teacher: ______________________

EXPLAIN
A series of operations may also involve grouping symbols and exponents. In
solving series of operations, the following rules can be used:
RULE 1: Simplify the operations inside the grouping symbols first.
Grouping symbols are always done from the innermost set outward.
RULE 2: Evaluate exponential expressions.
RULE 3: Multiply and divide in the order they appear from left to right.
RULE 4: Add and subtract in the order they appear from left to right.
This is what we now call the GEMDAS rule (Grouping symbols, Exponent,
Multiplication, Division, Addition and Subtraction).
The multiplication symbol x may be omitted in a multiplication expression involving
grouping symbols.
Examples:
1. 3 x (8 + 42) may be written as 3(8 + 42)
2. 23 x (122 – 52) may be written as 23(122 – 52)
3. (2 + 3 + 8 ÷ 2) x (16 – 4 x 3) = (2 + 3 + 8 ÷ 2) (16 – 4 x 3)
Let us apply the GEMDAS rule:

Example 1 Simplify: 2 + (7 x 3) – 5
=2+7x3–5 Multiply 7 and 3 First.
= 2 + 21 – 5 Add and subtract from left to right.
= 18
Answer: 18
Example 2 Simplify: 3 x 4 ÷ (7 – 5) – 12 ÷ 4
= 3 x 4 ÷ (7 – 5) – 12 ÷ 4 Simplify first the expression inside the
parenthesis.
= 3 x 4 ÷ 2 – 12 ÷ 4 Then, perform the multiplication
and division from left to right.
= 12 ÷ 2 – 12 ÷ 4
=6–3 Subtract.
=3
Answer: 3
Name: ________________________________ Grade and Section: _____________
Name of Teacher: ______________________

Example 3 Simplify: 7 + [2(12 – 5) + 32] – 18 ÷ 3

= 7 + [2(12 – 5) + 32] – 18 ÷ 3 Simplify first the expression inside the
parenthesis.
= 7 + [2(7) + 32] – 18 ÷ 3 Next, multiply 2 and 7 inside the bracket.
= 7 + [14 + 32] – 18 ÷ 3 Add the number inside the bracket.
= 7 + 46 – 18 ÷ 3 Perform the division. Divide 18 by 3.
= 7 + 46 – 6 Then, add and subtract the numbers from
left to right.
= 47
Answer: 47

Example 4 Simplify 4 + [-1(-2-1)]

= 4 + [-1(-2-1)] Simplify first expression inside the parenthesis.
= 4 + [-1(-3)] Next, simplify the expression inside the square bracket.
= 4 + (3) Perform the indicated operation. In this case, we
have addition
=7
Answer: 7

Example 5 Simplify: 5 – [(4 + 2 • 23 ) ÷ 10 ].

= 5 [(4 + 2 • 23 ) ÷ 10] Simplify first the expression with
exponent.
= 5 – [(4 + 2 • 8) ÷ 10] Next, multiply the expression inside the
parenthesis.
= 5 – [(4 + 16) ÷ 10] Perform addition to simplify the
expression inside the parenthesis.
= 5 – (20 ÷ 10) Divide 20 by 10
=5–2 Subtract.
=3
Answer: 3
 Name: ________________________________ Grade and Section: _____________
Name of Teacher: ______________________

Example 6 Simplify: 42 – 4 • 32 + 2(5-2)3

= 42 -4 • 32 +2(5 - 2)3 Simplify first expression inside the
parenthesis.
= 42 – 4• 32 + 2(3)3 Simplify expression with exponent.
= 42 – 4 • 9 + 2(27) Perform multiplication.
= 42 – 36 + 54 Subtract and add the numbers.
= 60
Answer: 60

ARE YOU READY TO PRACTICE?

How to interpret and explain the Grouping, Exponent, Multiplication, Division,
Addition, Subtraction (GEMDAS)? Do you find it easy? If yes, proceed to the next
activities. If not you can go back to our examples. Are you excited to do more exercises?
Ready….set….solve…enjoy doing the activities.

PRACTICE EXERCISE 1

Explain on how to solve the following expression.

1. 45 ÷ 9 + (23 – 14)

2. (10 + 4) + 23 + 75

3. (17 – 2) + (18 ÷ 3)

4. 92 ÷ 9 x (4 + 8) - 6

5. [11 x 13 – (5 x 7)] ÷ 9 + 6

Before you proceed to the next exercises, REMEMBER that:

Rules in solving more than one arithmetic operation:

 Simplify the operation in grouping symbols. Start from the innermost grouping
symbol.
 Evaluate exponential expressions.
 Multiply and divide in the order they appear from left or right.
 Add and subtract in the order they appear from left or right.

Continue with your final activities. Enjoy and happy working!

Name: ________________________________ Grade and Section: _____________
Name of Teacher: ______________________

PRACTICE EXERCISE 2

How to get the correct answer of the following?

1. 2 + (3 x 6) – 16

2. 2(1 + 2 + 3) ÷ 2

3. 64 ÷ (42 x 22) + 5

4. 7 + [(30 – 5 x 5) ÷ 5]

5. [(15 - 3 x 3) – (18 ÷ 9)] + 5

PRACTICE EXERCISE 3

Interpret the following expression.

1. 56 - (5 + 10) x 3

2. (24 ÷ 6) x 2 + 50

3. 50 (100 ÷ 25) – 2 + 13

4. (9 x 7) + (14 – 2 ) – (7 + 8)

5. 3 x [4 – 2 x (10 -8) + 12 ÷ 6 x 1]

Integrated the Development of the Following Learning Skills:

1.) Communication
a.) Understanding of words/vocabulary:
group, exponent, multiplication, division, subtraction, addition, rule

b.) Following instructions/directions.

2. Critical Thinking 3. Creativity 4. Collaboration 5. Character
a.) Problem solving a.) Problem Solving a.) Teamwork a.) Honesty
b.) Data Analysis b.) Work independently
c.) Evaluation

EVALUATION

Explain on how to solve the following expression.

1. 40 ÷ 8 + (25 – 12)
2. 12 x 65 + (34 -11)
3. 14 + 7 x 6 – (42 ÷ 2)
4. 4 x 4 ÷ (7 – 5) – 12 ÷ 4
5. 42 – 4 • 32 + 2(5-1)3

Prepared by:
EUFROCINA MELODY D. CORTEZ
References for Further Enhancement:
Books: 21st Century Mathematics 6 pp.180-183
Hands On Math pp.42-43
Realistic Math 6 pp. 55-57
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________ Pasay – M6-Q2- W4-D4

DEPARTMENT OF EDUCATION, NATIONAL CAPITAL REGION

SCHOOLS DIVISION OF PASAY CITY

MODULE IN MATHEMATICS 6
Quarter 2 / Week 4 / Day 4

OBJECTIVE: Performs two or more different operations on whole numbers without

exponent and grouping symbols.

YOUR LESSON FOR TODAY:

 In a series of operations involving addition, subtraction, multiplication and
division, the operations multiplication or division should be done first in
order from left to right. The operations addition or subtraction are carried
out next. In performing a series of operations, the MDAS rule is applied.
MDAS refers to multiplication, division, addition and subtraction.

TRY TO DISCOVER
Example 1.
3 + 4 × 2 = 7 × = 14

Micah Josh

Solution : Micah Josh

3+4x2 3+4 x2
= 3+8 =7x2
= 11 = 14
Who is correct? Is it Micah or Josh? Why?
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

The student who got the correct answer is Micah, it should be 11. Micah followed
the rule in solving expression having 2 different operations. Between addition and
multiplication, multiplication should be done first before addition.

Example 2.
10 + 12 ÷ 4 -6 x 2
10 + 12 ÷ 4 - 6 x 2 First, divide
10 + 3 - 6 x 12 Next multiply
10 + 3 - 12 Then, add
13 - 12 Lastly, subtract

Example 3.
100 – 42 + 9 x 3 - 10 ÷ 2
100 – 42 + 9 x 3 - 10 ÷ 2 First, do the multiplication
100 - 42 + 27 - 10 ÷ 2 Next, do the division
100 – 42 + 27 - 5 Then, subtract from left to right
58 + 27 - 5 Do the addition from left to right

85 - 5 Finally, do the subtraction.

80

ARE YOU READY TO PRACTICE?

Is today’s lesson clear to you? If not, go back to the discussion, try other
numbers and solve them. If our lesson is clear to you, then you are now ready for more
practices.
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

PRACTICE EXERCISES 1.
Perform the following operations below. Match column A with column B Write
only the letter on the space provided.
A B
_________1. 2x 3 +4 A. 73
_________ 2. 35 – 6 x 3 B. 17
_________3. 48 ÷ 12 + 8 C. 15
_________4. 20– 12 ÷ 2 D. 14
_________ 5. 76 - 8 + 5 E. 12
F. 10

PRACTICE EXERCISES 2.
Study each expression. What operation should be done first? Write + , - , x or
÷ in the blank and perform the operation. Write the final answer inside the box.
_____1. 15- 42 ÷ 7 + 3 x 6
Answer

_____2. 11 + 7 x 12 – 8 ÷ 5
Answer

____ 3. 14 + 4 x 7 – 2
Answer

____ 4. 27 ÷ 3 + 6 x 8
Answer

____ 5. 56 ÷ 8 + 3 x 6
Answer
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

POINTS TO PONDER:
To find the value of a mathematical expression following the
MDAS rule, perform the steps outlined below.

 M Perform first multiplication or division from left to right, or

 D whichever comes first.

 A Then, perform addition or subtraction from left to right, or

 S whichever comes first.

PRACTICE EXERCISES 3:
Perform this game with relatives of your age. The one who can tell the answer
ahead of others wins the game. Ready, get set, go…..

Do you know
the name of our
spaceship kids?

Find out the name of our spaceship by performing the operations below. After
getting N, find its equivalent letter in the box. The word you will be able to form out of
these letters is the name of our spaceship.

The name of our spaceship is ____________________________

Name :__________________________Grade and Section : _____________
Teacher : __________________________

1. 12 – 3 + 18 ÷ 6 x 3
2. 7 x 9 -3 + 8 A = 68 M = 45
3. 18 – 12 ÷ 6 + 7
4. 9x9÷3–9+6 T = 24 E = 18
5. 16 ÷ 4 x 5 – 7 + 5
R = 23 H = 21

S = 52

Integrated the Development of the Following Learning Skills:

Communication Critical Thinking

1. Following instructions/directions 1. Analyzing situations and

2. Understanding messages determining appropriate
3. Responding to ideas responses
4. Reasoning 2. Problem solving

Creativity Character

1. Problem solving 1. Perseverance

2. Creating models 2. Honesty

EVALUATION:
Perform the following operations. Write your final answer inside the circle.

1. 4 x 15 ÷ 5 + 6 – 4
2. 90 ÷ 9 x 2 -3 + 8
3. 60 + 48 ÷ 2 x 5
4. 7 – 3 + 45 ÷ 3 x 5
5. 9÷3x7–6+8

Prepared by :

ANGELITA M. GILO
VABES

References for Further Enhancement:

Making connections in Math 6 pp 18-22
21st Century Mathletes pp 180-183
Lesson Guides in Elem. Math 6 2003 pp 34-39
https://youtu.be/Ux5ty2Hlf04
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________ Pasay- M6-Q2- W4-D5

DEPARTMENT OF EDUCATION, NATIONAL CAPITAL REGION

SCHOOLS DIVISION OF PASAY CITY

MODULE IN MATHEMATICS 6
Quarter 2 / Week 4 / Day 5

OBJECTIVE : Performs two or more different operations on whole numbers with

exponent and grouping symbols.

YOUR LESSON FOR TODAY:

 An expression is a combination of numbers, operation signs, and grouping
symbols. Grouping symbols show which operation should be done first.
Three commonly used grouping symbols are parentheses, ( )brackets
[ ], and braces { }. When you perform an expression you first do all the
operations inside the grouping symbols, followed by the exponents, then
multiplication and/or division ( from left to right ), and finally addition and/or
subtraction ( from left to right ). This is called the GEMDAS rule.
TRY TO DISCOVER
Example 1.

48 ÷ (6 – 2) + 𝟑𝟐

My
answer My answer
is 15! is 21!
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

Let us evaluate the expression 48 ÷ (6 − 2) + 32

Solution:

48 ÷ (6 − 2) + 32 Subtract the numbers inside the parentheses

= 48 ÷ 4 + 32 Simplify the expression with exponent

= 48 ÷ 4 + 9 Divide
= 12 + 9 Add
= 21

Example 2. Simplify 32 x (7 - 2)2

Solution:

32 x ( 7 -2 )2 Do the operation inside parentheses

= 32 x 52 Simplify the expressions with exponents

= 9 x 25 Multiply
= 225

Example 3. Evaluate 5 x [24 ÷ 22 ×(10 − 8)] ÷ 10

5 x [24 ÷ 22 ×(10 − 8)] ÷ 10 Do the operations inside the grouping symbols

Start from the innermost parentheses

= 5 x [ 24 ÷ 22 × 2 ] ÷ 10 Simplify the expression with exponent

= 5 x [ 24 ÷ 4 ×2 ] ÷ 10 Do the operations inside the bracket from

= 5 x [ 6 ×2 ] ÷ 10 left to right; divide and multiply

= 5 x 12 ÷ 10 Multiply, and finally divide
= 60 ÷ 10
= 6

ARE YOU READY TO PRACTICE?

Is today’s lesson clear to you? If not, go back to the discussion, try other
numbers and solve them. If our lesson is clear to you, then you are now ready for more
practices.
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

PRACTICE EXERCISES 1.
Perform the following operations.

1. 6 + ( 2 x 7 + 52 )
2. ( 4 x 32 ) + ( 3 x 10 )
3. ( 8 ÷ 2 ) + 23
4. ( 82 + 136 ) ÷ 102
5. ( 18 + 6 ) x 32

PRACTICE EXERCISES 2.
Look at each expression. Decide what operation should be done first, then solve
for the answer.

1. ( 9 + 4 ) x ( 23 – 3) = _____________________

2. ( 27 ÷ 3 ) x 52 + 12 = _____________________

3. 102 – ( 32 + 42 ) x 22 = ______________________

4. 6 x ( 2 x 7 + 52 ) = ______________________

5. ( 15 – 5 )3 ÷ ( 8 + 2 ) 2 = _______________________

POINTS TO PONDER:
To find the value of a mathematical expression, we follow the order of
performing mathematical operations called the GEMDAS rule.

 G Perform first the operation within the grouping symbols

(Parentheses, brackets, and braces.)

 E Simplify the expressions with exponents

 M Perform first multiplication or division from left to right, or

 D whichever comes first.

 A Then, perform addition or subtraction from left to right, or

 S whichever comes first.
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

PRACTICE EXERCISES 3:
Match column A with column B. Write only the letter.
Perform this game with relatives of your age. The one who can tell the answer
ahead of others wins the game. Ready, get set, solve…..
COLUMN A COLUMN B

1) 9 + 4 - ( 10- 7)2 A. 109

2) (15-6) + ( 4 – 1 ) x 23 B. 33

3) 3 x [( 4 𝑥 8 ) ÷ 8]
C. 24

4) 6 x ( 2 x 7 + 52 )
D. 10

5) 5 x [4 + 3 − ( 22 + 1)]
E. 4
Name :_____________________________ Grade and Section : __________________
Teacher : __________________________

Integrated the Development of the Following Learning Skills:

Communication Critical Thinking
1. Following instructions/directions 1. Analyzing situations and
2. Understanding messages determining appropriate
3. Responding to ideas responses
4. Reasoning 2. Problem solving
Creativity Character
1. Problem solving 1. Perseverance
2. Honesty

EVALUATION:
Perform the following operations. Write your final answer on the space
provided.

1. (9 − 5) + (32 ×5) = ________________________

2. 4 × (15 − 32 ) + 16 = _______________________

3. (20 − 5 ) + [(3 ×42 ) + 7 ] = _________________

4. 10 × [32 + 23 ×(102 − 20)] = ________________

5. 3 ×[56 − 52 ×( 10 − 8) + 9 ÷ 3×2 ] = __________

Prepared by :

ANGELITA M. GILO
Villamor Airbase Elem. School

References for Further Enhancement:

Realistic Math 6 pp 167-172

Soaring 21st Century Mathematics 6 pp 28-30
Lesson Guides in Elem. Math 6 2003 pp 28-33
https://youtu.be/dAgfnK528RA