gemdas

MATHEMATICS 6

QUARTER 2 WEEK 7

DAY 1

R E V I E W

Directions: Evaluate the following
expressions.
1. (3 + 5) × 2
2. 22 + 3 x 3
3. 4 × (6 ÷ 2) + 9
4. (10 – 3) x 32
5. 75 x 2 + (12 x 4)

Draw a thermometer for
each item on your answer

sheet. Then show the
given temperature on
each thermometer.

1) _______ 2) _______
3) _______ 4) _______

5) _______

1) Freezing point of water

2) Boiling point of water

3) Normal body temperature
4) 41 degrees below normal
body temperature

5) 8 degrees below freezing
point

DESCRIBING

THE SET

OF INTEGERS

DESCRIBING SET OF INTEGERS

The set of positive and negative
numbers including zero is called the
set of integers. (Perez, 2016).
Integers are numbers with no
fractional parts and no decimals.

DESCRIBING SET OF INTEGERS

a. Positive Numbers. These are the
counting or natural numbers such as
1, 4, 67, 90, and so on. These can be
written with or without the positive
sign (+). They are well represented by
the set {1, 2, 3,…} or {+1, +2, +3,…}.

DESCRIBING SET OF INTEGERS

b. Zero. It is a very special number.
It is halfway between -1 and +1 on the
number line. It shows that there is no
amount. It is neither positive nor
negative. It is represented by the
symbol (0).

DESCRIBING SET OF INTEGERS

c. Negative Numbers. These have
values less than 0. These are
preceded by a negative sign (-).
These are represented by the set
{-1,-2,-3,…}.

DESCRIBING SET OF INTEGERS

Figures 1 and 2 represent how counting
or positive numbers, zero and negative
numbers comprise integers.

DESCRIBING SET OF INTEGERS

• When counting or
positive numbers {1, 2,
3,…} are combined with
zero (0), they make up
the set of whole
numbers {0, 1, 2, 3,…}.

DESCRIBING SET OF INTEGERS

• When whole numbers
are combined with
negative numbers, they
make up the set of
integers {…,-3, -2, -1, 0,
1, 2, 3,…}.

DESCRIBING SET OF INTEGERS

• On the number line,
the positive integers are
the numbers found at the
right of zero and the
negative integers are the
numbers found at the
left of zero.

DESCRIBING SET OF INTEGERS

• Zero is the point of

origin or the boundary
between the positive
and negative
numbers.

DESCRIBING SET OF INTEGERS

• The arrow heads of
the number line tell us
that the series extends
infinitely in opposite
directions.

Real-Life Situations that Make Use of Integers

Real life situations can be represented by
integers. Let us read the following word
problem.

Real-Life Situations that Make Use of Integers

Noe actively participates in the distribution
of learning activity sheets for his son, Manny.
He uses his bicycle to reach the school every
week to avoid physical contact with others.

After a quarter of doing this, he lost 5

kilograms. How will Noe represent

this using an integer?

Real-Life Situations that Make Use of Integers

A loss of 5 kilograms can be represented

by negative five or -5.

On the other hand, if he gained 5 kilograms,

it can be represented by positive five (+5) or five

(5). Thus, the term ‘loss’ is represented by a

negative number while the term ‘gain’ is

represented by a positive number. Here are

other terms associated with negative

and positive numbers.

Real-Life Situations that Make Use of Integers

NEGATIVE

POSITIVE

loss

gain

below

above

withdraw

deposit

backward

forward

downward

upward

south

north

west

east

dropped

rise

down

up

left

right

Real-life Situations

Integers

a. 25 degrees above
zero

=
+25 or 25

b. 8 steps backward

=

-8

c. Deposited Php1 500 =

+1 500 or 1 500

d. Dropped 8 meters

=

-8

e. sea level

=
0

Real-Life Situations that Make Use of Integers

Maryx, a hospital nurse forgot on what floor she
would find her Personal Protective Equipment
(PPE). With no one to ask for directions, she
rode the elevator up to the 10th floor. Then she
went down 5 floors and went up again 4 floors.
Still, she could not find the right floor. So she

went up again 3 floors, then down again
8 floors and decided to stop for a while.

On what floor did Maryx stop?

Real-Life Situations that Make Use of Integers

In solving this word problem, remember that
positive numbers are at the right of zero and
negative numbers are at the left of zero. We
can use the number line to find what floor the

messenger stopped. It is important to take
note of the given data by representations

using the number line.

Real-Life Situations that Make Use of Integers

Real-Life Situations that Make Use of Integers

Real-Life Situations that Make Use of Integers

Answer:

Since this is the last movement of
Maryx, therefore, she stopped at the

4th floor.

A C T I V I T Y 1

Directions: Ana loves word hunt
puzzles. Help her find 10 words
involving integers in the following.
Words are arranged in horizontal,
vertical or diagonal forms. List down
your answers.

A C T I V I T Y 1

P O S

I

T

I

V E Z B Q L X Q M P

Z V A J H D

I

N T E G E R A T

Z

A E M M A N U E L R R S Y C M X
M N R O L A N G N N E S A

I

S R

I

A

I

O

I

M T A Q A A Z N L P V

L N G R R F Z T Z X T X Q E Z M
E N H N E X M

I

C H E P K G Q

I

T A T L

L M V V X Q R A

I

N E R

G H A M Y A Z E Q U A L

Z A B

I

C O M P A R E X V

I

C T O R C A

O J

A D E Y C H R

I

S T

I

N E M

A S S E S S M E N T

Directions: Write CORRECT if the
statement is true and INCORRECT
if the statement is false.

___________ 1. The nearer the
positive number is from zero, the
larger is its value.

A S S E S S M E N T

___________ 2. Positive numbers are
represented by the set {1, 2, 3,…}.

___________ 3. Negative numbers are
represented by the set {-1, -2, -3,…}.

A S S E S S M E N T

___________ 4. Negative numbers, zero
and positive numbers make up the set of
integers.

___________ 5. Negative numbers are
always less than positive numbers.

MATHEMATICS 6

QUARTER 2 WEEK 7

DAY 2

R E V I E W

Directions: Write an integer to describe each
situation.
1) withdrew ₱20 000.00 from her savings
account
2) absent from school for 15 days
3) received ₱50 000.00
4) spent a total of ₱10 000.00 for medicine
5) a gain of 7 kg

Write the integer that
matches each point.

1) A

2) B

3) C

4) D

5) E

DESCRIBING

THE SET

OF INTEGERS

DESCRIBING SET OF INTEGERS

The set of positive and negative
numbers including zero is called the
set of integers. (Perez, 2016).
Integers are numbers with no
fractional parts and no decimals.

DESCRIBING SET OF INTEGERS

a. Positive Numbers. These are the
counting or natural numbers such as
1, 4, 67, 90, and so on. These can be
written with or without the positive
sign (+). They are well represented by
the set {1, 2, 3,…} or {+1, +2, +3,…}.

DESCRIBING SET OF INTEGERS

b. Zero. It is a very special number.
It is halfway between -1 and +1 on the
number line. It shows that there is no
amount. It is neither positive nor
negative. It is represented by the
symbol (0).

DESCRIBING SET OF INTEGERS

c. Negative Numbers. These have
values less than 0. These are
preceded by a negative sign (-).
These are represented by the set
{-1,-2,-3,…}.

DESCRIBING SET OF INTEGERS

Figures 1 and 2 represent how counting
or positive numbers, zero and negative
numbers comprise integers.

DESCRIBING SET OF INTEGERS

• When counting or
positive numbers {1, 2,
3,…} are combined with
zero (0), they make up
the set of whole
numbers {0, 1, 2, 3,…}.

DESCRIBING SET OF INTEGERS

• When whole numbers
are combined with
negative numbers, they
make up the set of
integers {…,-3, -2, -1, 0,
1, 2, 3,…}.

DESCRIBING SET OF INTEGERS

• On the number line,
the positive integers are
the numbers found at the
right of zero and the
negative integers are the
numbers found at the
left of zero.

DESCRIBING SET OF INTEGERS

• Zero is the point of

origin or the boundary
between the positive
and negative
numbers.

DESCRIBING SET OF INTEGERS

• The arrow heads of
the number line tell us
that the series extends
infinitely in opposite
directions.

Real-Life Situations that Make Use of Integers

Real life situations can be represented by
integers. Let us read the following word
problem.

Real-Life Situations that Make Use of Integers

Noe actively participates in the distribution
of learning activity sheets for his son, Manny.
He uses his bicycle to reach the school every
week to avoid physical contact with others.

After a quarter of doing this, he lost 5

kilograms. How will Noe represent

this using an integer?

Real-Life Situations that Make Use of Integers

A loss of 5 kilograms can be represented

by negative five or -5.

On the other hand, if he gained 5 kilograms,

it can be represented by positive five (+5) or five

(5). Thus, the term ‘loss’ is represented by a

negative number while the term ‘gain’ is

represented by a positive number. Here are

other terms associated with negative

and positive numbers.

Real-Life Situations that Make Use of Integers

NEGATIVE

POSITIVE

loss

gain

below

above

withdraw

deposit

backward

forward

downward

upward

south

north

west

east

dropped

rise

down

up

left

right

Real-life Situations

Integers

a. 25 degrees above
zero

=
+25 or 25

b. 8 steps backward

=

-8

c. Deposited Php1 500 =

+1 500 or 1 500

d. Dropped 8 meters

=

-8

e. sea level

=
0

Real-Life Situations that Make Use of Integers

Maryx, a hospital nurse forgot on what floor she
would find her Personal Protective Equipment
(PPE). With no one to ask for directions, she
rode the elevator up to the 10th floor. Then she
went down 5 floors and went up again 4 floors.
Still, she could not find the right floor. So she

went up again 3 floors, then down again
8 floors and decided to stop for a while.

On what floor did Maryx stop?

Real-Life Situations that Make Use of Integers

In solving this word problem, remember that
positive numbers are at the right of zero and
negative numbers are at the left of zero. We
can use the number line to find what floor the

messenger stopped. It is important to take
note of the given data by representations

using the number line.

Real-Life Situations that Make Use of Integers

Real-Life Situations that Make Use of Integers

Real-Life Situations that Make Use of Integers

Answer:

Since this is the last movement of
Maryx, therefore, she stopped at the

4th floor.

A C T I V I T Y 2

Directions: Write an integer to
describe each situation.
1) Prince deposited ₱186.00 in his
Aflatoun account.

2) The delegates are moving 3
kilometers east.

A C T I V I T Y 2

3) Evelyn is gaining 9-kilogram weight.

4) A withdrawal of ₱1 500.00 was made
by Darnelle from her bank account.

5) Loren has a fever. His body
temperature is 39◦C.

A S S E S S M E N T

Directions: Plot on the number line
the integer described in each of the
following situations.

1) a temperature decreased by 6◦C

2) lost 4 kilograms after getting sick

A S S E S S M E N T

3) going 18-kilometer elevation
upstream

4) move 3 steps backward

5) consumed 30 liters of fuel

6) temperature reading of 99◦C

A S S E S S M E N T

7) an additional of 15 points in Math quiz

8) walk 7 kilometers down the valley

9) 42 feet below sea level

10) stands at approximately 35 meters
east

MATHEMATICS 6

QUARTER 2 WEEK 7

DAY 3

R E V I E W

Directions: Use a number line to identify the
integers being described.
1. An integer that is 8 units to the right of -5.
2. What integer is 10 units to the left of +4?
3. 15 units to the right of 0
4. 7 units to the right of -19
5. An integer that is halfway between
+14 and -2 on a number line

Read the given situations
below. Write an integer to
represent each situation.
1) May gained 2 pounds
after a month of taking

food supplement.

2) Ann moves 4 steps

backward as she dances.

3) Mr. Cruz deposited

P2 000.00.

4) Ray stretches his arms
10 cm. upward to reach
the fruit of the guava tree.

5) Jean withdrew the
amount of P1 500.00

from her savings account.

COMPARING INTEGERS
WITH WHOLE NUMBERS,

FRACTIONS,

AND DECIMALS

COMPARING INTEGERS

During the Math Camp, Gia and her

team is going to solve a challenge. Their
task is to compare -2 with the numbers

given below:
{2, 0.5 1

𝟏
𝟒}

If you are a member of the team, how
would you compare the given numbers?

COMPARING INTEGERS

When comparing integers with whole
numbers, fractions, and decimals, the
one that is on the right direction of the

number line has greater value.

COMPARING INTEGERS

Study the following.
Let us plot the numbers (-2, 2, 0.5, 1

𝟏
𝟒)

on the number line.

COMPARING INTEGERS

A. Compare the integer -2 and the whole
number 2.
Since -2 can be found to the left of 2;
therefore, -2 is less than 2. Let us use a
relation symbol to compare the two numbers.

-2 < 2

COMPARING INTEGERS

B. Compare the integer -2 and the decimal
number 0.5.
Since -2 can be found to the left of 0.5;
therefore, -2 is less than 0.5. Let us use a
relation symbol to compare the two numbers.

-2 < 0.5

COMPARING INTEGERS

C. Compare the integer -2 and the mixed number
𝟏
𝟒.

Since -2 can be found to the left of 1

1
4; therefore, -2

is less than 1

1
4.

Let us use a relation symbol to compare the two
numbers.

-2 < 1

𝟏
𝟒

COMPARING INTEGERS

Here is another example:
Plot the following numbers on the number line and
study how the pair of numbers are compared.
(-4, -2.5, 1, 1

3
4 , -3)

A C T I V I T Y 3

Directions: Below are pair of numbers for
you to compare. Choose the appropriate
relation symbol >,<, or = to make the
expression true.

A C T I V I T Y 3

1) +9 1/2

2) 0.36 -6

3) 1/3 +2

4) 0 -9

5) -5 -5.8

A S S E S S M E N T

Directions: Read carefully each
situation and write the correct answer
in your notebook.
1. In a number line, Jean plotted 0.15
and -15. Which is higher?

2. Which is lower, -2 or 3/4?

A S S E S S M E N T

3. How would you compare
15 and +15?

4) Which is greater, 0.7 or +1?

5) Which is lesser, 1 or 0.25?

MATHEMATICS 6

QUARTER 2 WEEK 7

DAY 4

R E V I E W

Directions: Below are pair of numbers to be
compared. Use the following relational
symbols <,> or =.
1) 25 0.25 3) -1 1/8

2) 7 1.5 4) +98 7 1/8

5) 27 -29.16

Use the number line to

compare the numbers below.

_____1. Which is greater, -2
or 7?
_____ 2) Which is greater,
1/2 or +3?

_____ 3) Which is greater,
-6 or 4.25?

_____ 4) Which is lesser, 2
or -4?

_____ 5) Which is lesser, 5
1/2 or -6?

COMPARING INTEGERS
WITH WHOLE NUMBERS,

FRACTIONS,

AND DECIMALS

COMPARING INTEGERS

During the Math Camp, Gia and her

team is going to solve a challenge. Their
task is to compare -2 with the numbers

given below:
{2, 0.5 1

𝟏
𝟒}

If you are a member of the team, how
would you compare the given numbers?

COMPARING INTEGERS

When comparing integers with whole
numbers, fractions, and decimals, the
one that is on the right direction of the

number line has greater value.

COMPARING INTEGERS

Study the following.
Let us plot the numbers (-2, 2, 0.5, 1

𝟏
𝟒)

on the number line.

COMPARING INTEGERS

A. Compare the integer -2 and the whole
number 2.
Since -2 can be found to the left of 2;
therefore, -2 is less than 2. Let us use a
relation symbol to compare the two numbers.

-2 < 2

COMPARING INTEGERS

B. Compare the integer -2 and the decimal
number 0.5.
Since -2 can be found to the left of 0.5;
therefore, -2 is less than 0.5. Let us use a
relation symbol to compare the two numbers.

-2 < 0.5

COMPARING INTEGERS

C. Compare the integer -2 and the mixed number
𝟏
𝟒.

Since -2 can be found to the left of 1

1
4; therefore, -2

is less than 1

1
4.

Let us use a relation symbol to compare the two
numbers.

-2 < 1

𝟏
𝟒

COMPARING INTEGERS

Here is another example:
Plot the following numbers on the number line and
study how the pair of numbers are compared.
(-4, -2.5, 1, 1

3
4 , -3)

A C T I V I T Y 4

Directions: Below are pair of numbers for
you to compare. Choose the appropriate
relation symbol >,<, or = to make the
expression true.

A C T I V I T Y 3

1) -5 10

2) +9 -1/8

3) -7

0.7

4) -15 -15.5

5) 0.5 1/2

A S S E S S M E N T

1) -1.5 +5

2) -7 - 1.5

3) 1/17

-6

4) +9 -4.9

5) +27 29.17