DLP-MATH-6.docx

I. OBJECTIVES
A. Content
Standards
The learner demonstrate understanding of order of operations,
ratio and proportion, percent, exponent, and integers.
B. Performance
Standards
The learner is able to apply knowledge of order of operations, ratio
and proportion, percent, exponent, and integers in mathematical
problems and real-life situations.
C. Learning
Competencies/
Objectives/ LC
Code
Expresses one value as a fraction of another given ratio and vice
versa. (M6NS-IIa-129)
1. Express one value as a fraction of another given their ratio and
vice versa.
2. Write ratio in three different ways.
II. CONTENT Expressing one’s value as a fraction of another given ratio and
vice versa.
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
Pages
Mathematics Curriculum Guide for Grade 6 p. 190
2. Learner’s
Materials Pages
21st
Century Mathletes 6 LM p. 82 - 87
3. Textbook Pages Mathematics for Everyday Use 6 p. 128 - 129
4. Additional
Materials from
Learning (LR)
Portal
Lesson Guide in Elementary Mathematics Grade 5 - Rational
Numbers: Ratio and Proportion p. 1-5
B. Other Learning
Resources
Lesson Guide in Elementary Mathematics Grade 6 p. 289 - 293
IV. PROCEDURES Teacher’s Activity Pupils’ Activity
A. Reviewing
previous lesson or
presenting the new
lesson.
Mental Computation:
1. 3÷
3
7
= N 2.
3
4
÷
1
2
= N
3.
1
5
÷ 6 = N 4. 8 ÷
1
2
= N
5. 1
1
3
÷ 4
Possible answer.
1. 7
2.
3
2
or 1
1
2
3.
1
30
4. 10
5.
1
23
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date
and Time: Week 1, Day 1 Quarter: SECOND

B. Establishing a
purpose for the
lesson.
Ask the pupils to compare the
things in the classroom
according to their number or
quantity.
For example, the number of
chairs compare to the number
of tables, the number of shoes
to the number of slippers and
so, on. Have them write the
ratios of these sets of objects
on the board.
Pupils answer may vary.
C. Presenting
examples/
instances of the
new lesson
In Mr. Cambangay’s class,
there are 12 boys and 10 girls.
Compare the number of girls to
the number of boys and vice
versa.
Guide the pupils to show the
relationship of the number of
boys to the number of girls.
Ask: How will you write the
comparison of the number of
boys to the number of girls
using fraction? Is there another
way of writing it? How?
Possible answer.
12
10
Yes in colon (:) and in words.
D. Discussing new
concepts and
practicing new
skills #1
To compare, let us use the
concept of ratio. Ratio is a
comparison of two quantities.
If there are 12 boys and 10
girls, we can say that 12 is to
10. Other ways to express
such comparison is by writing
them using a colon, 12:10 or
writing them in fraction from,
12/10. Therefore, comparing
the number of boys to the
number of girls can be
expressed as: 12 is to 10,
12:10, or
12
10
. Even if the ratio is
in fractional form, we say
twelve is to ten.
Possible answer.
12:10
Twelve is to ten
12
10
E. Discussing new
concepts and
practicing new
skills #2
Ratio is the spoken language of
arithmetic. It is a way of
comparing two or more
quantities having the same
units – the quantities may be
Possible answer.

separate entities or they may
be different parts of a whole.
We can write ratio of a and b in
three ways:
Word form  a is to b
Colon form  a:b
Fraction form  a/b
The order of which ratio is
expressed is important.
Therefore, the order of the
terms in a ratio must
correspond to the order of the
objects being compared.
Ivy has some yellow and red
beads. (Present this using
blocks)
Yellow Beads:
Read Beads:
Ask: The ratio of the number of
read beads to the number of
yellow beads is ___:___
Two is to five,
2:5
2
5
F. Developing
mastery (Leads to
Formative
Assessment 3)
Compare the number of
vowels to consonants and vice
versa in the word
MATHEMATICS, in word,
colon and fraction forms.
Vowels: A, E, and I  3
Consonants: M.T,H, C and S 
5
Ratio of vowels to consonants:
Word form: 3 is to 5
Colon form: 3:5
Fraction form:
3
5
Ratio of consonants to vowels:
Colon form: 5:3
Fraction form:
5
3
G. Finding practical
applications of
concepts and skills
in daily living
There are 10 buses in a station
and each bus has 6 wheels,
what is the ratio of buses to
wheels?
Colon form: 10:6
Fraction form:
10
6

Write your answer in three
ways.
H. Making
generalizations and
abstractions about
the lesson
What is ratio?
What are the three ways of
writing ratio?
Ratio - is a way of comparing two
or more quantities having the
same units – the quantities may
be separate entities or they may
be different parts of a whole.
The three ways of writing ratio
are:
Word form, colon form and
fraction form.
I. Evaluating
Learning
Write a ratio for each of the
following using the three ways
of writing ratio.
1. 4 apples compared to 5
guavas.
2. Eight compared to 28.
3. There are five kites to
seven boys.
4. Four squares
compared to 3 circles.
5. 2 flowers compared to
3 leaves.
Answer for number 1
a) Word form: 4 is to 5
b) Colon form: 4:5
c) Fraction form:
4
5
Answer for number 2
a. Word form: 8 is to 28
b. Colon form: 8:28
c. Fraction form: 8/28
Answer for number 3
b. Colon form: 5:7
Answer for number 4
b. Colon form: 4:3
Answer for number 5
b. Colon form: 2:3

J. Additional
activities for
application or
remediation
1.
2.
3. 4 wins to 2 losses in
basketball
4. 10 decimeters to 10
centimeters
5. 6 weeks to 12 days
Possible answer.
1. 8:6, 8/6, 8 is to 6
2. 10:8, 10/8, 10 is to 8
3. 4:2, 4/2, 4 is to 2
4. 100:10, 100/10, 100 is to 10
5. 42:12, 42/12, 42 is to 12
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
additional activities
for remediation
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners
who continue to
require remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
F. What difficulties
did I encounter

which my principal
or supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover which
I wish to share with
other teachers?

I. OBJECTIVES
A. Content
Standards
The learner demonstrate understanding of order of operations, ratio
and proportion, percent, exponent, and integers.
B. Performance
Standards
C. Learning
Competencies/
Objectives/ LC Code
Finds how many times one value is as large as another given their
ratio and vice versa. (M6NS-IIa-130)
1. Find how many times one value is as large as another given their
ratio and vice versa.
2. Write ratio in simplest form.
II. CONTENT Finding how many times one value is as large as another given their
III. LEARNING
RESOURCES
A. References
Pages
2. Learner’s
Materials Pages
21st
3. Textbook Pages Mathematics for Everyday Use 6 p. 130 - 132
4. Additional
Materials from
Learning (LR) Portal
B. Other Learning
Resources
A. Reviewing
previous lesson or
presenting the new
lesson.
Teacher conducts a review in
finding the GCF. Let the pupils do
this mentally.
Give the GCF using drill board.
1. 15 and 60
2. 24 and 18
3. 16 and 40
4. 49 and 28
5. 35 and 50
Possible answer.
1. 15
2. 6
3. 4
4. 7
5. 7
School: Grade Level: VI
Teacher: Learning Area: MATHEMATICS
Teaching
Date and
Time: Week 1, Day 2 Quarter: SECOND

B. Establishing a
purpose for the
lesson.
Ask the pupils about their favorite
drink for snacks, like calamansi
juice, tea, etc. Tell them that
Calamansi Juice is good because of
its nutritious value.
Pupils will share what their
favorite drink for snack is.
(Answers may vary.)
C. Presenting
examples/ instances
of the new lesson
Teacher presents this problem
situation.
Mother is preparing Calamansi
Juice:
a) For each glass of Calamansi
Juice, 5 pieces of Calamansi are
needed.
b) If she makes 2 glasses, how many
pieces of calamansi are needed?
c) If she makes 3 glasses, how many
pieces of calamansi are needed?
Analyze the problem by asking the
following questions:
a) What is asked?
b) What are the given facts?
What strategies may be used to
answer the problem?
Possible answer.
a. The number of calamansi
needed in making 2 glasses
of calamansi juice.
b. The number of calamansi
needed in making 3 glasses
of calamansi juice.
D. Discussing new
concepts and
practicing new skills
#1
Illustrate the problem using blocks.
a)
Glass:
Calamansi:
b)
Glass:
Calamansi:
c)
Glass:
Calamansi:
E. Discussing new
concepts and
Ask: Possible answer.

#2
1. How many pieces of Calamansi
are there in a glass of Water in a? In
b? In c?
2. Which of these ratios is expressed
in lowest term/simplest form? Why?
Pupils write the ratios for
question number 1.
a. (
1
5
or 1:5)
b. (
2
10
or 2:10)
c. (
3
15
or 3:15)
2. (1:5)
F. Developing
mastery (Leads to
Formative
Assessment 3)
Reduce the following ratios in
lowest term. Choose the letter that
corresponds to the ratio in simplest
form.
E = 3:4 I = 1:2 R = 2:9
T = 15:4 G = 1:6 N = 5:6
S = 1:4
4:8 15:18 30:8 18:24
6:27 15:20 8:32 60:16
7:14 25:30 4:24
What is the hidden word?
____________________________
Possible answer.
I = 1:1
N = 5:6
T = 15:4
E = 3:4
R = 2:9
E = 3:4
S = 1:4
T = 15”4
I = 1:2
N = 5:6
G = 1:6
G. Finding
practical
applications of
concepts and skills
in daily living
Study the table below and answer
the question after it.
Things Quantity Costs
Stamps 10 Php50
Patches 15 Php180
Bookmark 20 Php300
Diary 12 Php300
In simplest form, express the
following ratio of:
a) stamps to patches
b) bookmark to patches
c) diary to patches
d) bookmark to stamps
e) diary and stamps
Possible answer.
a. 10:15 = 2:3
b. 20:15 = 4:3
c. 12:15 = 4:5
d. 20:10 = 2:1
e. 12:10 = 6:5

H. Making
generalizations and
abstractions about
the lesson
The teacher will ask the pupils the
following question:
Can a ratio be expressed in lowest
terms? How?
Possible answer.
Yes. By dividing the ratio by its
common factor.
I. Evaluating
Learning
Reduce these ratios in simplest
form.
1) 10:12
2) 9:15
3) 18:24
4) 21:27
5) 40:50
Possible answer.
1. 5:6
2. 3:5
3. 3:4
4. 7:9
5. 4:5
J. Additional
activities for
application or
remediation
Express the given ratio to simplest
or lowest terms.
a. 8 hours to 10 hours
b. 40 minutes to 1 hours
c. 25 centavos to 1 peso
d. 2 dozen to 18 things
e. 18 boys to 16 girls
Possible answer.
a. 8:10 = 4:5
b. 40:60 = 4:6
c. 25:100 = 1:4
d. 24:18 = 4:3
e. 18:16 = 9:8
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
for remediation
C. Did the remedial
lessons work? No. of
learners who have
caught up with the
lesson
D. No. of learners
who continue to
require remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
did I encounter
which my principal or
supervisor can help
me solve?
G. What innovation
or localized

materials did I
use/discover which I
wish to share with
other teachers?

I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives/ LC
Code
Finds how many times on value is as large as another given their ratio
and vice versa. (M6NS-IIa-130)
1. Find how many times one value is as large as another given their
2. Write ratio in simplest form.
II. CONTENT Writing ratio to lowest term.
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide Pages
2. Learner’s
Materials Pages
21st
3. Textbook
Pages
Mathematics for Everyday Use 6 p. 130 - 132
4. Additional
Materials from
Learning (LR)
Portal
B. Other
Learning
Resources
IV.
PROCEDURES
Teacher’s Activity Pupils’ Activity
A. Reviewing
previous lesson
or presenting
the new lesson.
Teacher conducts a review on
reducing fractions to lowest
terms. Let the pupils do this
mentally.
Reduce these fractions to
lowest terms.
8/10, 12/15, 18/30, 3/9, 6/20
Possible answer.
a. 8/10 = 4/5
b. 12/15 = 4/5
c. 18/30 = 3/5
d. 3/9 = 1/3
e. 6/20 = 3/10
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date

B. Establishing
a purpose for
the lesson.
Present the picture on the
board:
Ask: What is the ratio of the
number of blue cubes to the
number of red cubes?
Possible answer.
6:12 or 1:2
C. Presenting
examples/
instances of the
new lesson
Let us now place the cubes in
groups of 2.
What is the ratio?
Place the cubes in groups of 3
What is the ratio?
Finally, group them into 6s.
What is the ratio?
Say: 6:12, 3:6, 2:4 and 1:2 are
called Equivalent Ratios. 1:2 is
the ratio in the Simplest Form
Possible answer.
3:6
2:4
1:2
D. Discussing
new concepts
and practicing
new skills #1
Take a look at the ratio 12:8.
How do we write it in simplest
form?
Step 1: Divide 12: 8 by the
common factor 2 to get 6:4
Step 2: Divide 6:4 by the
common factor 2 to get 3:2
12:8
÷ 2 ÷ 2
6:4
÷ 2 ÷ 2
3:2
Possible answer.
Divide 12 and 8 by common factor
which is 4 to get 3:2.
3:2 cannot be divided exactly by a
common factor thus 3:2 is the ratio in
simplest form.

The ratio 3:2 cannot be divided
exactly by a common factor to
get another equivalent ratio.
Thus, 3:2 is the ratio in
Simplest Form
E. Discussing
new concepts
and practicing
new skills #2
Present this example:
There are 9 papayas and 15
pineapples. What is the ratio in
simplest form?
9:15
÷3 ÷3
3:5
The ratio of papaya to
pineapple is 3:5
F. Developing
mastery (Leads
to Formative
Assessment )
A Volleyball Team won 8
games out of 12 games it
played.
a) Write the ratio of wins to
games played.
b) Write the ratio of wins to
losses.
c) Write the ratio of losses to
games played.
Possible answer.
a. 8:12 = 2:3
b. 8:4 = 2:1
c. 4:12 = 1:3
G. Finding
practical
applications of
concepts and
skills in daily
living
In a Grade VI Mathematics
class, there are 27 boys and 21
girls.
a) Write the ratio of boys to
girls.
b) Write the ratio of girls to
boys.
c) Write the ratio of girls to the
whole class.
d) The ratio of boys to the whole
class.
Possible answer.
a. 27:21 = 9:7
b. 21:27 = 7:9
c. 21:48 = 7:16
d. 27:48 = 9:16
H. Making
generalizations
and abstractions
about the lesson
The teacher will ask the pupils
the following question:
How do we express ratio in
simplest form?
Possible answer.
We express ratio in simplest form by
dividing it to its common factor.
I. Evaluating
Learning
Write each of the following
ratios in simplest form:
Possible answer.

1) 12:18
2) 25:10
3) 21:56
4) 20:25
5) 30: 54
1. 2:3
2. 5:2
3. 3:8
4. 4:5
5. 5:9
J. Additional
activities for
application or
remediation
Express each rate in lowest
terms.
1. 36:18
2. 48:6
3. 5760:12
4. 468:9
5. 504:14
Possible answer.
1. 2:1
2. 8:1
3. 480:1
4. 52:1
5. 36:1
V. REMARKS
VI.
REFLECTION
A. No. of
learners who
earned 80% in
the evaluation
B. No. of
learners who
require
additional
activities for
remediation
C. Did the
remedial
lessons work?
No. of learners
who have
caught up with
the lesson
D. No. of
learners who
continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did these
work?
F. What
difficulties did I
encounter which
my principal or

supervisor can
help me solve?
G. What
innovation or
localized
materials did I
use/discover
which I wish to
share with other
teachers?

I. OBJECTIVES
A. Content
Standards
The learner demonstrate understanding of order of operations, ratio and
proportion, percent, exponent, and integers.
B. Performance
Standards
The learner is able to apply knowledge of order of operations, ratio and
proportion, percent, exponent, and integers in mathematical problems
and real-life situations.
C. Learning
Competencies/
Objectives/ LC
Code
Finds how many times one value is as large as another given their ratio
and vice versa. (M6NS-IIa-130)
1. Express ratio in lowest term.
2. Find the rate.
II. CONTENT Expressing ratio in lowest term.
III. LEARNING
RESOURCES
A. References
Pages
2. Learner’s
Materials Pages
21st
3. Textbook Pages 21st
4. Additional
Materials from
Learning (LR)
Portal
Lesson Guide in Elementary Mathematics 6 p. 293 - 297
B. Other Learning
Resources
Mathematics for Everyday Use 6 p. 130 – 132.
A. Reviewing
previous lesson or
presenting the new
lesson.
Ask: What is a ratio?
Give example of ratio.
Possible answer.
Ratio is a comparison of two qualities
which can be written in colon, word or
fraction form.
(answers may vary)
B. Establishing a
purpose for the
lesson.
A motorist traveled 240 km in 3
hours. What is the speed of the
motorist?
Solution:
Possible answer.
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date

240 𝑘𝑚
3 ℎ𝑜𝑢𝑟𝑠
= N
240km
3 hours
The motorist has a constant
speed of 80 km/hour.
What do you call the
comparison of the distance and
the time travelled by the
motorist?
80 km/hr
C. Presenting
examples/
instances of the
new lesson
There are instances when the
terms of the ratio do not have
the same units or
classifications.
For example, 60 kilometers to
an hour of 60 kilometers per
hour. This special ratio is called
rate.
Rate is the comparison of two
quantities but may have
different units of measures and
their ratio has a unit of
measure.
Pupils will listen to the discussion.
D. Discussing new
concepts and
practicing new
skills #1
Present this example:
Joshua scored 168 points in 7
basketball games. Express in
lowest terms, the average rate
of the number of points that
Joshua scored in every game.
Rate =
168 𝑝𝑜𝑖𝑛𝑡𝑠
7 𝑔𝑎𝑚𝑒𝑠
=
24 𝑝𝑜𝑖𝑛𝑡𝑠
1 𝑔𝑎𝑚𝑒
= 24 points per game.
Notice that in the above
example, the two terms do not
have the same classification;
that is, points and games. In
this instance, we have to use
rate.
Pupils will listen and participate in the
discussion by solving on their seat the
problem presented.
Possible answer.
24 points per game
= 80 km/hr

E. Discussing new
concepts and
practicing new
skills #2
Joana can type 288 words in 8
minutes. How many words can
she type per minute?
Rate =
288 𝑤𝑜𝑟𝑑𝑠
8 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
=
1 𝑚𝑖𝑛𝑢𝑡𝑒
= 36 words/minute
Possible answer.
36 words/minute
F. Developing
mastery (Leads to
Formative
Assessment 3)
Ask the pupils to find the rate
and express it to lowest term if
possible.
a) If Luisa can type 440 words
in 8 minutes, what is her rate of
typing?
b) If 30 green oranges cost
Php100, at what rate are the
oranges sold?
Possible answer.
55 words per minute
Php10 for 3 oranges
G. Finding
practical
applications of
concepts and
skills in daily
living
Answer the following:
a) A Mitsubishi Montero vehicle
can travel 900 km on 75 liters of
diesel. Write the rate of liters of
diesel used to kilometers
traveled.
b) A machine can produce 156
items in 12 minutes. Write the
rate of the number of items
produced to the number of
minutes.
Possible answer:
a.
900 𝑘𝑚
75 𝑙𝑖𝑡𝑒𝑟𝑠
= 12km/liters
b.
156 𝑖𝑡𝑒𝑚𝑠
=13 items/min
H. Making
generalizations and
abstractions about
the lesson
Teacher will ask:
What is rate?
Possible answer.
Rate is the comparison of two quantities
but may have different units of measures
and their ratio has a unit of measure.
I. Evaluating
Learning
Express each rate in lowest
term.
1. The ratio of 112 persons to
16 tables.
2. the ratio of Php306.00 to 9 m
cloth
3. The ratio of 312 m to 13
seconds
4. The ratio of Php6,480.00 to
12 families.
Possible answer:
1. 7 person/table
2. Php34/m
3. 1,140
4. Php540.00/family
5. 46 students/bus

5. The ratio of 368 students to 8
buses.
J. Additional
activities for
application or
remediation
Find the unit rate and express
the answer to lowest term if
possible.
a) 700 kilometers in 5 hours
b) 150 stools in 2 weeks
c) 300 words in 5 minutes
d) Php48 for 8 ball pens
e) Php275 for 2
3
4
𝑘𝑔 of
chicken.
Possible answer.
a. 140km/hr
b. 75 stools/week
c. 60 words/minute
d. Php6/ball pen
e. Php100/kg.
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
for remediation
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners
who continue to
require remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
did I encounter
which my principal
or supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover which
other teachers?

I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
proportion, percent, exponent, and integers in mathematical problems and
real-life situations.
C. Learning
Competencies/
Objectives/ LC
Code
Expresses one value as a fraction of another given ratio and vice versa.
(M6NS-IIa-129)
Finds how many times on value is as large as another given their ratio and
vice versa. (M6NS-IIa-130)
Answer weekly test.
II. CONTENT Expressing one value as a fraction of another given their ratio and vice
versa and finding how many times one value is as large as another given
their ratio and vice versa.
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide Pages
2. Learner’s
Materials Pages
21st
Century Mathletes p. 82-91
3. Textbook
Pages
21st
Century Mathletes p. 82-91
4. Additional
Materials from
Learning (LR)
Portal
B. Other Learning
Resources
IV.
PROCEDURES
A. Reviewing
previous lesson
or presenting the
new lesson.
Have a quick review on writing
ratio in three ways, that is;
Word form, Colon form, fraction
form, writing ratio in lowest term
and expressing ratio in lowest
term
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date

B. Setting of
Standards.
Ask. What are the things that
you need to do in answering
the test?
Possible answers.
1. Read and follow the directions.
2. Answer silently.
3. Cover your paper.
4. Don’t talk with your seatmates.
5. Don’t cheat.
6. If you’re done, review your answer.
C. Giving of
instruction and
distribution of test
papers.
Read the instruction in
answering the test.
Distribute the test papers.
D. Test Proper Supervise the pupils in
answering the test.
A. Write a ratio for each of the
following in three ways.
1. 4 wins to 2 losses in
basketball
2. 3 months to 8 weeks
3. 24 girls to 18 boys
4. 8 melons to 36 fruits
5. 6 weeks to 12 days
B. Express ratios in lowest
terms.
1. 5:15
b. 21:27
3. 2:14
4. 25:100
5. 60:16
C. Find the rate.
Jay can type 324 words in 9
minutes. How many words can
he type per minute?
Possible answer.
A.
1. 4 is to 2, 4:2, 4/2
2. 3 is to 8, 3:8, 3/8
3. 24 is to 18, 24:18, 24/18
4. 8 is to 36, 8:38, 8/36
5. 6 is to 12, 6:12, 6/12
B.
1. 1:3
2. 7:9
3. 1:7
4. 1:4
5. 15:4
C.
Rate =
=
1 𝑚𝑖𝑛𝑢𝑡𝑒
= 36 words/minute
E. Checking of
Test paper and
recording of
scores.
The teacher will post the
answer on the board and record
pupils score.
Pupils will check the test papers.
F. Additional
activities for
Solve the following problems. Possible answer.

application or
remediation
1. The ratio of ducks to chicken
in the farm is 3:5. The total
number of chickens and ducks
together is 72. If 6 chickens
have shown symptoms of flu
and had to be removed from the
farm, what is the new ratio of
ducks to chickens?
Solution:
Ducks = 3
Chicken = 5
Total = 72
3:5 = 72
3n+5n = 72
8𝑛
8
=
72
8
N= 9
(Ducks) 9 x 3 = 27
(Chicken) 9 x 5 = 45
So, 45 – 6 = 39
The new ratio of ducks to chicken is
now 9:13.
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80%
in the evaluation
B. No. of learners
who require
additional
activities for
remediation
C. Did the
remedial lessons
work? No. of
learners who
have caught up
with the lesson
D. No. of learners
who continue to
require
remediation
E. Which of my
teaching
strategies worked
well? Why did
these work?
F. What
difficulties did I
encounter which
my principal or
supervisor can
help me solve?
G. What
innovation or
localized

materials did I
use/discover
which I wish to
share with other
teachers?

I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
proportion, percent, exponent, and integers in mathematical problems and
real-life situations.
C. Learning
Competencies/
Objectives/ LC
Code
Defines and illustrates the meaning of ratio and proportion using concrete
or pictorial models. M6NS-IIb-131
Sets up proportions for groups of objects or numbers and given situations.
M6NS-IIb-132
1. Defines and illustrates the meaning of ratio and proportion using
concrete or pictorial models.
2. Sets up proportions for groups of objects or numbers and given
situations
3. Value carefulness in doing the activities
II. CONTENT Forming ratio and proportion
III. LEARNING
RESOURCES
A. References
Pages
2. Learner’s
Materials Pages
21st
4. Additional
Materials from
Learning (LR)
Portal
B. Other Learning
Resources
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date and
Time: WEEK 2, DAY 1 Quarter: SECOND

A. Reviewing
previous lesson or
presenting the new
lesson`.
Give the fractional part of the
shaded portion.
Possible answer.
a. 2/8 or ¼
b. 6/15 or 2/5
c. 1 ¼
d. 5/10 or ½
e. 8/16 or 1/2
B. Establishing a
purpose for the
lesson.
Look around your room.
What are the things you find
inside?
Answers may vary.
C. Presenting
examples/
instances of the
new lesson
1. Let the pupils count the
number of boys and girls.
Guide the pupils to show the
relationship of the number of
boys to the number of girls.
Example: 25/28 25 is the first
term boy, 28 is the second term
girls
Possible answer.
25:28

Ask: Is there another way of
writing it? How?
2. Let the pupils count other
objects/things.
Let them give/write the ration in
2 ways (colon and fraction
form)
Ask: Did you count the
objects/things correctly? Why?
What will you do if you are
given objects to use/
manipulate? How will you
handle them?
Yes. 25/28
D. Discussing new
concepts and
practicing new
skills #1
The teacher will show a
problem.
Ronald bought 3 pencils for 10
pesos at Elen’s School Supply
Store. Ruby bought 6 pencils
for 20 pesos. Give the ration of
the pencils to the amount of
money of each child.
1. What did Ronald and Ruby
buy? How many pencils did
each of them buy? How
much did each of them
pay?
2. What are being compared
in the problem? Write the
ratios in 2 ways
3. How many ratios did you
write?
4. What can you say about
the two ratios? Why?
5. How can we write the two
ratios to show the equality
in two ways?
6. What do you call two equal
ratios?
1. Ronald and Ruby buys pencil. Ronald
buys 3 pencils while Ruby buys 6
pencils. They pay P10.00 and P20.00
pesos each.
2. The number of pencils and its price.
3:10 and 6:20
3. There are two ratios.
4. The two ratios are equal.
5. 3:10::6:20
6. Two equal ratios are called proportion.
E. Discussing new
concepts and
practicing new
skills #2
The ratio of chairs to tables is 8
to 2 or 4 to 1.
Let the pupils write in 2 ways.
Possible answer.
8:2::4:1
8
2
=
4
1

Let them identify the terms,
means and extremes.
F. Developing
mastery (Leads to
Formative
Assessment 3)
Let the pupils answer it by pair.
Illustrate and give the ratio of
the following in two different
ways( colon and fraction):
1. 4 squares to 3 circles
2. 2 flowers to 3 leaves
3. 5 crayons to 4 books
4. 2 basketball to 8 tennis
balls
5. 6 apple to 7 guavas
1. 4:3, 4/3
2. 2:3, 2/3
3. 5:4, 5/4
4. 2:8, 2/8
5. 6:7, 6/7
applications of
concepts and skills
in daily living
Find the ratio and proportion of
the following.
1. There are 10 busses at gas
station. If each bus has 6
wheels, what is the ratio of
busses to wheels?
2. Every quarter each student
submits 2 projects in EPP.
Give the ratio of projects to
quarters.
3. There are 3 caimito trees
and 4 mango trees in Mang
Tino’s orchard. While in Mr.
Trazona’s orchard, there
are 6 caimito trees and 8
mango trees. Give the ratio
of the mango to caimito
trees in each orchard then
write a proportion.
Possible answer.
1. 10/6, 10:6
2. 2/1, 2:1
3. 4:3, and 8:6
H. Making
generalizations and
abstractions about
the lesson
What is a ratio? Proportion?
What are the ways in writing
ratio/ proportion?
Possible answer.
Ratio is a way of comparing two or more
quantities having the same units.
The three ways in ratio are: word form,
colon and fraction form.
I. Evaluating
Learning
Write the ratio and proportion
for each of the following:
1. 6 apples to 18 children.
2. Eight compared to 28.
3. There are 5 kites to seven
boys.
4. In a t-shirt factory, each box
contains 3 t-shirts. Give the
ratio of boxes to t-shirts.
5. In a camping, each boy
scout was given 4 hotdogs.
If there are 5 boy scouts, 20
Possible answer.
1. 6:18, 6/18
2. 8:28, 8/28
3. 5:7, 5/7
4. 1:3, 1//3
5. 1:4=5:20

hotdogs were cooked. Write
the proportion.
J. Additional
activities for
application or
remediation
Form ratio/proportion for the
following using 2 different
ways.
1) 7 to 8
2) 3 to 5 is equivalent to 6 to
15
3) two barangays to 13 348
people
4) one boat to 3 people is
equal to 6 boats to 18 people
5) 45 members of Glee Club to
30 members of Dance Club
Possible answer.
1. 7:8, 7/8
2. 3:5 = 6:15
3. 2 : 13 348
4. 1 :3 = 6:18
5. 45:30
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
for remediation
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners
who continue to
require remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
did I encounter
which my principal
or supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover which
other teachers?

I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives/ LC
Code
Find a missing term in a proportion (direct, inverse and partitive)
M6NS-IIb-133
4. Find a missing term in a direct proportion.
5. Solve for the missing term in a direct proportion.
II. CONTENT Finding a missing term in a direct proportion.
III. LEARNING
RESOURCES
A. References
Pages
2. Learner’s
Materials Pages
21st
4. Additional
Materials from
Learning (LR)
Portal
B. Other Learning
Resources
Lesson Guide in Elementary Mathematics Grade 6 – Ateneo de
Manila University, 2010
A. Reviewing
previous lesson or
presenting the new
lesson.
What is ratio? Give examples. Answers may vary.
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date and
Time: WEEK 2, DAY 2 Quarter: SECOND

B. Establishing a
purpose for the
lesson.
The teacher will show an equation and ask
questions.
1 mango:12 pesos = 4 mangoes: 48 pesos
What have you observed from the given
equation?
Notice that as the number of mangoes
increases, the payment also increases.
Why do you think so?
Answers may vary.
C. Presenting
examples/
instances of the
new lesson
Mr. Cambangay bought 9 different kinds of
bread for Php324.00. At the same price,
how much will she pay for the 15 different
breads?
To solve this problem, write equal ratios.
Let n be the price of 15 different kinds of
bread
9
324
=
15
𝑛
To solve the problem of Mr. Cambangay:
9
324
=
15
𝑛
9 x n = 324 x 15
9n = 4860
9𝑛
9
=
4860
9
n = 540
Therefore, he has to pay Php540.00 for
15 different kinds of bread.
Possible answer.
N = 540
D. Discussing new
concepts and
practicing new
skills #1
When two ratios are equal, a proportion is
formed.
A proportion is a statement of equality
between two ratios. Each part of a
proportion is a term. The first and the last
terms are called extremes while the
second and the third terms are called
means.
In the proportion
9
324
=
15
𝑛
or 9:324= 15: n,
9 and n are the extremes. While 324 and
15 are the means.
Pupils will listen
attentively to the
discussion.

In a proportion, the cross product of equal
ratios are equal.
If
𝑎
𝑏
=
𝑐
𝑑
, then ad = bc.
Thus, the product of the means is equal to
the product of the extremes.
a:b = c:d
If in a given proportion a term is missing, it
can be solved using cross multiplication.
Tell whether the ratios form a proportion.
a.
6
14
,
3
7
6
14
=?
3
7
Write the proportion
6 x 7 =? 14 x 3 Form cross products
42 =/ 42 Multiply.
Answer: The ratios form a proportion.
b. 6:9 = 8:n
6 x n = 9 x 8
6𝑛
6
=
72
6
n = 12
Answer: The ratios form a proportion.
E. Discussing new
concepts and
practicing new
skills #2
The above problems are examples of
direct proportion. In direct proportion, as
one quantity increases, the other quantity
increases at the same rate and vice versa.
F. Developing
mastery (Leads to
Group Activity Possible answer:
Means
Extremes

Formative
Assessment)
The teacher will present a problem on the
board and let the group answer it.
Arlene and her mother also sells hotcakes
on weekends. Mother’s recipe need 3 eggs
to make 5 hotcakes. Arlene wants to make
25 hotcakes. How many eggs will she
need?
1. Let the group illustrate their solution
on the board.
2. Check if the groups wrote the
correct proportions for the
problems.
3. Again, guide the pupils in finding
the missing term or element.
4. Ask questions to elicit the rule for
finding the missing element in a
proportion.
Eggs Cakes
3 5
6 10
9 15
12 20
15 25
Another solution using
proportion.
3 = 5
n 25
3 x 25 = n x 5
75 = 5n
5 5
n = 15
applications of
concepts and skills
in daily living
At the school canteen:
a. 3 pieces of pad paper cost 50
cents.
21 pieces of pad paper cost _____.
b. 4 colored pencils cost Php25.00.
12 colored pencils cost ________.
c. 2 boiled bananas cost Php3.50.
10 boiled bananas cost ________.
Possible answer:
a. 3 = 50
21 n
3 x n = 21 x 50
3n = 1050
3 3
n = 350
b. 4 = 25
12 n
4 x n = 12 x 25
4n = 300
4 4
n = 75
c. 2:10::3.50:n
2 x n = 10 x 3.5
2n = 35
2 2
n = 17.5
H. Making
generalizations and
abstractions about
the lesson
What is proportion?
Define direct proportion.
Possible answer.
A proportion is a
statement of equality
between two ratios.
Each part of a
proportion is a term.
The first and the last
terms are called

extremes while the
second and the third
terms are called
means. The product of
the means is equal to
the product of the
extremes.
Direct proportion on
the other hand is a
proportion that as one
quantity increases, the
other quantity increase
at the same rate and
vice versa.
I. Evaluating
Learning
A. Find the missing term and tell whether it
is a direct proportion or not.
1.
2
3
=
4
𝑛
2.
12
15
=
𝑛
5
3.
𝑛
7
=
24
28
4.
28
𝑛
=
2
3
B. Analyze the problem and write a
proportion to solve it.
1. A car travels 72 km on 8 liters of
gasoline. At the same rate, about how far
can it travel on 10 liters of gasoline?
Possible answer.
A.
1. 2 x n = 3 x 4
2n = 12
2 2
n = 6, direct
proportion
2. 12 x 5=15 x n
60 = 15n
15 15
n = 4, direct
proportion
3. n x 28=7 x 24
28n = 168
28 28
n = 6, direct
proportion
4. 28 x 3 = n x 2
84 = 2n
2 2
n = 42, direct
proportion
B.
72
𝑛
=
8
10
72 x 10 = n x 8
720 = 8n
8 8

n = 90
J. Additional
activities for
application or
remediation
Solve each proportion.
1.
5
12
=
35
𝑛
2.
39
2
=
𝑛
4
3.
27
𝑛
=
9
5
4.
𝑛
4
=
24
6
5.
3
𝑛
=
24
40
Possible answer.
1. 5 x n=12 x 35
5n = 420
5 5
n = 84
2. 39 x 4 = 2 x n
156 = 2n
2 2
n = 78
3. 27 x 5 = n x 9
135 = 9n
9 9
n = 15
4. n x 6 = 4 x 24
6n = 96
6 6
n = 16
5. 3 x 40=n x 24
120 = 24n
24 24
n = 5
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
for remediation
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners
who continue to
require remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
did I encounter

which my principal
or supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover which
other teachers?
I.
OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives/ LC
Code
M6NS-IIb-133
1. Find a missing term in an inverse proportion.
2. Solve for the missing term in an inverse proportion.
3. Be generous enough to care for the less fortunate and the
needy.
II. CONTENT Finding a missing term in an inverse proportion.
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide Pages
2. Learner’s
Materials
Pages
21st
3. Textbook
Pages
4. Additional
Materials from
Learning (LR)
Portal
BEAM LG Grade 6 – Module 11, page 26.
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date
and Time: WEEK 2, DAY 3 Quarter: SECOND

B. Other
Learning
Resources
Lesson Guide in Elementary Mathematics Grade 6 – Ateneo de Manila
University, 2010
IV.
PROCEDURES
A. Reviewing
previous lesson
or presenting
the new
lesson`.
Review on direct proportion.
The teacher will show to the pupils the
following problem involving direct
proportion.
1.
𝑛
8
=
9
24
3.
9
4
=
𝑛
16
2.
6
𝑛
=
18
21
4.
5
3
=
25
𝑛
5.
𝑛
8
=
15
24
Possible answer.
1. 3
2. 7
3. 36
4. 15
5. 5
B. Establishing
a purpose for
the lesson.
Ask pupils if they have visited some
places that care for the physically
handicapped, aged or orphans. Discuss
the importance of these places, and the
value of helping our less fortunate
brothers.
Today, we’re going to learn a new type of
proportion; inverse proportion.
Answers may vary.
C. Presenting
examples/
instances of the
new lesson
An orphanage has enough bread to feed
30 orphans for 12 days. If 10 more
orphans are added, how many days will
the same amount of bread last?
Solution:
(Orphans) (Days)
𝑂𝑟𝑖𝑔 𝑛𝑜.
𝑁𝑒𝑤 𝑛𝑜.
=
𝑁𝑒𝑤 𝑛𝑜.
𝑂𝑟𝑖𝑔 𝑛𝑜.
(Orphans) (Days)
Therefore:
30
40
=
𝑛
12
40n = 30 x 12
40n = 360
n =
360
40
n = 9
Possible answer.
N = 9

Therefore, their supply of bread will only
last for 9 days if additional 10 orphans will
be admitted to the orphanage.
D. Discussing
new concepts
and practicing
new skills #1
In inverse proportion, when one quantity
increases, the other quantity decreases,
and vice versa. We can also say that in an
inverse proportion, the quantities change
in opposite directions, that is, as one
quantity increases, the other decreases.
It takes Kevin 20 minutes to ride his
bicycle at 20kph from home to the grocery
store. To shorten his travel time to 16
minutes for the same distance, how fast
should he cycle?
Solution:
Let the desired speed be x kph. Then we
have the following table.
Speed (kph) 20 X
Time (in minutes) 20 16
Hence,
𝑥
20
=
20
16
16 * x = 20 * 20 - Give the cross product
16x = 20*20 - Divide both sides by 16
16𝑥
16
=
400
16
Answer: Kevin should cycle at 25kph.
Notice that the faster the bike is driven,
the less time is required to reach the
destination.
Possible answer.
Kevin should cycle at
25kph.
E. Discussing
new concepts
and practicing
new skills #2
The above problems are examples of
inverse proportion. In an inverse
proportion, one quantity increases as the
other quantity decreases at the same rate
and vice versa.
Speed varies inversely with time of travel
because the faster we go, the shorter time
of travel.

F. Developing
mastery (Leads
to Formative
Assessment)
Group Activity
The teacher will present a problem on the
board and let the group answer it.
If 4 farmers can plow a 3-hectare land in
6 days, how long will 8 farmers do it?
Possible answer.
Solution:
4
8
=
𝑛
6
4 x 6 = 8 x n
24
8
=
8𝑛
8
n = 3
G. Finding
practical
applications of
concepts and
skills in daily
living
Solve the following problem in inverse
proportion.
1. A house contractor has enough money
to pay 8 workers for 15 days. If he adds 4
more workers, for how many days can he
pay them at the same rate?
2. Five people can finish painting a wall in
5 hours. If only 2 people are available,
how many hours do they have to work to
finish the same job?
Possible answer.
1.
8
12
=
𝑛
15
8 x 15 = 12 x n
120 = 12n
12 12
n = 10
2.
5:2::n:5
2 x n = 5 x 5
2n = 25
2 2
n = 12.5 hours
H. Making
generalizations
and
abstractions
about the
lesson
What is an inverse proportion? Possible answer.
An inverse proportion is a
proportion that when one
other quantity decreases,
and vice versa. We can also
say that in an inverse
proportion, the quantities
change in opposite
directions, that is, as one
other decreases.
I. Evaluating
Learning
A. Find the missing term in the following
inverse proportion.
1.
40𝑘𝑝ℎ
𝑛
=
60𝑚𝑖𝑛𝑢𝑡𝑒𝑠
Possible answer:
A.
1.

2.
𝑛
90
=
8
20
3.
24
28
=
𝑛
7
4.
12
𝑛
=
6
10
B. Analyze the problem and solve for the
missing term.
1. A house contractor has enough money
to pay 16 workers for 30 days. If he adds
8 more workers, for how many days can
he pay them at the same rate?
40 x 60 =n x 50
2400 = 50n
50 50
n = 48
2.
20 x n = 90 x 8
20n = 720
20 20
n = 36
3.
n x 28 = 7 x 24
28n = 168
28 28
n = 6
4.
12 x 10 = n x 6
120 = 6n
6 6
n = 20
B.
16:24::n:30
16 x 30 = 24 x n
480 = 24n
24 24
n = 20
J. Additional
activities for
application or
remediation
Solve for the value of n.
1.
16
𝑛
=
4
3
2.
𝑛
20
=
2
5
3. 15:30 = 12: n 4. n:125 = 3:5
5. n:16 = 5:4
Possible answer:
1. 16 x 3 = n x 4
48 = 4n
4 4
n = 12
2. n x 5 = 20 x 2
5n = 40
5 5
n = 8
3. 15:30::12:n
15 x n = 30 x 12
15n = 360
15 15

n = 24
4. n:125 = 3:5
n x 5 = 125 x 3
5n = 375
5 5
n = 75
5. n:16 = 5:4
n x 4 = 16 x 5
4n = 80
4 4
n = 20
V. REMARKS
VI.
REFLECTION
A. No. of
learners who
earned 80% in
the evaluation
B. No. of
learners who
require
additional
activities for
remediation
C. Did the
remedial
lessons work?
No. of learners
who have
caught up with
the lesson
D. No. of
learners who
continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did these
work?
F. What
difficulties did I
encounter
which my
principal or

supervisor can
help me solve?
G. What
innovation or
localized
materials did I
use/discover
which I wish to
share with
other teachers?

I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives/ LC
Code
M6NS-IIb-133
1. Find a missing term in a partitive proportion.
2. Solve for the missing term in a partitive proportion.
3. Accept things given with an open heart.
II. CONTENT Finding a missing term in a partitive division.
III. LEARNING
RESOURCES
A. References
Pages
2. Learner’s
Materials Pages
21st
4. Additional
Materials from
Learning (LR)
Portal
BEAM LG Grade VI Module 11
B. Other Learning
Resources
https://bit.ly/30yipsn
A. Reviewing
previous lesson or
presenting the new
lesson
(5 minutes)
What is a direct proportion?
How would you set up the
proportion?
A direct proportion state as
one quantity increases the
other quantity increases at
the same rate and vice
versa.
School: Grade Level: VI
Teacher: Learning Area: Mathematics
Teaching Date
and Time: Week 2, Day 4 Quarter: 2nd
Quarter

B. Establishing a
purpose for the
lesson
(10 minutes)
The teacher will show 21 popsicle
sticks.
Ask: How are we going to divide it in
to 3 groups if the popsicle sticks are
not even?
The teacher will show how and
explain further as they go on to
another examples.
Answers may vary.
C. Presenting
examples/
instances of the
new lesson
(10 minutes)
The teacher will example of partitive
proportion.
A class has 56 students. The ratio of
girls to boys is 4:3. How many are
girls? boys?
What is asked in the problem?
What are the given facts?
What type of proportion is this?
-The number of boys and
girls in a class.
- 56 students
- Students will be
divided in the ratio 4:3
D. Discussing new
concepts and
practicing new
skills #1
PARTITIVE PROPORTION
The word "part" (noun) may be
defined as a division or portion of a
whole. As a verb it means to divide
into parts. The word "partitive" is an
adjective derived of the word "part"
and it means restricted to a part of a
whole.
Partitive Proportion is a proportion
applied to dividing a given quantity
into two or more parts, which shall be
in a given ratio, one to another. The
terms of the given ratio or ratios, may
be called the proportional terms.
In a partitive proportion, a whole is
divided into parts that are
proportional to the given ratio.
Possible answer.

Steps in solving partitive proportions:
• Add together all the given
proportional terms. 4 + 3 = 7
• Multiply the total number of students
by each proportional term. Divide the
product by the sum of the
proportional terms. (56 x 4) ÷ 7 = 32
(56 x 3) ÷ 7 = 24
Therefore, there are 32 girls and 24
boys in a class
E. Discussing new
concepts and
practicing new
skills #2
What number we can multiply to 4
and 5 to get 72?
4:5 = 72
4n + 5n = 72
9n = 72
n = 72 ÷9
n = 8
4(8) + 5(8) = 72
32 + 40 = 72
Try to answer this! (By Pair)
Find the missing terms in the partitive
proportion
1. 5:3 = 56
2. 1:2:3 = 48
3. 3:4 = 3500
1. 5n = 35
3n = 21
2. n = 8
2n = 16
3n = 24
3. 3n = 1500
4n = 2000
F. Finding practical
applications of
concepts and skills
in daily living
The teacher will group the pupils and
let them answer the following.
1. Two numbers are in the ratio of
3:4. Their sum is 105. Find the two
numbers.
2. The sum of two numbers is 430. If
the ratio is 4:6, find the smaller
number.
3. The ratio of yellow flowers to white
flowers is 5:6. If there were 88
flowers in all. How many are yellow/
white?
Possible answer.
1. 3n = 45
4n = 60
2. 4n = 172
3. 5n = 40
6n = 48
G. Making
generalizations
What is partitive proportion?
How do we find the missing terms?
What are the steps?
Possible answer.

and abstractions
about the lesson
Partitive Proportion is a
proportion applied to dividing
a given quantity into two or
more parts, which shall be in
a given ratio, one to another.
The terms of the given ratio
or ratios, may be called the
proportional terms
Steps in solving partitive
proportions: • Add together
all the given proportional
terms.
• Multiply the total number of
students by each
proportional term. Divide the
product by the sum of the
proportional terms.
H. Evaluating
Learning
(15 minutes)
Solve and find the missing terms
involving partitive proportion.
1. The ratio of the three sides of a
triangle is 1:2:3. What are the
measurements of each sides if the
perimeter of the triangle is 120 cm?
2. Ronald draws three lines in
different colors, red, yellow and
green. Their lengths are in the ratio of
1:3:5. The yellow line is 18. How long
is the green line? The red line?
3. The total weight of Maria, Juan
and Jose is 112 kg. Their weight are
in the ratio of of 3:1:4. What is
Maria’s weight? How much heavier is
Jose than Juan?
Possible answer.
1. n= 20 2n = 40 3n =
60
2. red = 6 green = 30
3. Maria = 42 kg
Jose = 56 kg
Juan = 14 kg
- 42kg
I. Additional
activities for
application or
remediation
1. Ruby, Diana and Jane are
business partners. They agreed to
divide their profits in the ratio of 1:2:3.
How much should each receive if the
total profit is 6000 pesos?
2. Divide a 72m rope into 3 with the
ratio 1:2:5, What is the measure of
each rope?
Possible answer.
1. Ruby = Php1000
Diana = Php2000
Jane = Php3000
2. 9m, 18m, 45m
V. REMARKS

VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require
for remediation
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners
who continue to
require
remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
did I encounter
which my principal
or supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover which
other teachers?

I.
OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives/ LC
Code
Defines and illustrates the meaning of ratio and proportion using
concrete or pictorial models. M6NS-IIb-131
Sets up proportions for groups of objects or numbers and given
situations. M6NS-IIb-132
M6NS-IIb-133
II. CONTENT Find a missing term in a proportion (direct, inverse and partitive)
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide Pages
2. Learner’s
Materials
Pages
21st
Century Mathletes 6 TX p. 92 - 97
3. Textbook
Pages
4. Additional
Materials from
Learning (LR)
Portal
Lesson Guide in Mathematics 6 p. 3012 - 307
B. Other
Learning
Resources
IV.
PROCEDURES
A. Reviewing
previous lesson
or presenting
the new lesson.
Have a quick review on
defining and illustrating the
meaning of ratio and
proportion, setting up
proportions for groups of
objects or numbers and given
situations and finding the
School:
Grade
Level: VI
Teacher:
Learning
Area: MATHEMATICS
Teaching Date
and Time: Week 2 Day 5 Quarter: SECOND

missing term in a direct,
inverse and partitive
proportion.
B. Setting of
Standards.
Ask. What are the things that
you need to do in answering
the test?
Possible answers.
1. Read and follow the directions.
2. Answer silently.
3. Cover your paper.
4. Don’t talk with your seatmates.
5. Don’t cheat.
6. If you’re done, review your answer.
C. Giving of
instruction and
distribution of
test papers.
Read the instruction in
answering the test.
D. Test Proper Supervise the pupils in
answering the test.
A. Find the missing term in a
proportion.
1.
3
𝑛
=
9
15
2.
𝑛
6
=
6
4
3.
5
11
=
35
𝑛
4. 3:x = 6:10
5. 3:4 = 27:x
B. Find the missing term in
the following proportion
(direct, inverse and partitive)
1. The ratio of the areas of 2
squares is 1:4. The area of
smaller square is 36 cm
square. How long is each
side of the bigger square?
2. The ratio of 2 numbers is
3:5. The larger number is 30.
What is the smaller number?
3. The ratio of cats to dogs is
6:5. There are 495 dogs and
cats in a certain barangay.
a. How many cats are there?
b. How many dogs are there?
Possible answer.
A.
1. n = 5
2. n = 9
3. n = 77
4. x = 5
5. x = 36
B.
1. The area of the bigger square is 144
cm square.
2. The smaller number is 18.
3.
a. There are 270 cats
b. There are 225 dogs
4.
a. 72

4. Three numbers are in the
ratio 2:5:7. If their sum is 504,
what are the three numbers?
a. First number
b. Second number
c. Third number
b. 180
c. 252
E. Checking of
Test paper and
recording of
scores.
answer on the board and
record pupils score.
F. Additional
activities for
application or
remediation
V. REMARKS
VI.
REFLECTION
A. No. of
learners who
earned 80% in
the evaluation
B. No. of
learners who
require
additional
activities for
remediation
C. Did the
remedial
lessons work?
No. of learners
who have
caught up with
the lesson
D. No. of
learners who
continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did these
work?
F. What
difficulties did I
encounter
which my

principal or
supervisor can
help me solve?
G. What
innovation or
localized
materials did I
use/discover
which I wish to
share with
other teachers?

School Grade Level SIX
Teacher Learning Area MATHEMATICS
Teaching
Dates Time Week 3 day 1
Quarter 2nd
QUARTER
1.OBJECTIVES
A. Content Standards :
The learners demonstrate understanding of order of operations , ratio and proportion ,
percent, exponent and integers .
M6NS-IIc-134
B. Performance Standards :
The learner is able to apply knowledge
of order of operations , ratio and proportion , percent,
exponent and integers in mathematical problems
and real life situations
C. Learning Competencies / Objectives
 Solve word problems involving direct proportion
 Write proportions correctly
 Practice diligence and industry 134
M6NS – IIc – 134
II. CONTENT : Solving Word Problem Involving Direct Proportion
III. LEARNING RESOURCES
A. References
1. CG in Mathematics 6 pp 190-191
2. Learners Material 21st
Century Mathletes TB
Job Cards, puzzle pieces
3. Additional Materials from Learning Resource portal
Lesson Guide in Mathematics 6 ( ATENEO ) pp284-287
(uploaded at http://lrmds.deped.gov.ph)
B. Other Learning Resources Activity cards, video presentation, slide deck
presentation on direct proportion
IV. PROCEDURES Teachers Activity Pupils Activity
A. Reviewing
previous
lessons
 Conduct a drill on
finding the missing
term in a proportion
 One contestant will
represent each group

 (group contest)
 Prepare set of
flashcards written
with
3: n = 6 :10
3 :4 = 27: N
N:9 = 12;18
 Set a standard
 Answer orally and make
one step forward if first to
answer.
B. Establishing
a purpose
for
the lesson
 Introduce the lesson
and set classroom
rules.
 Motivate the children
by guessing what do
the children doing in
the picture (slide
show)
 Ask: which of the
pictures can you do by
yourself?
 Listen to the teacher
 Watch the video
 Call some pupils to
answer
C. Presenting
Examples/
Instances of
new lessons
Present this problem:
Ben and Roy sell newspapers
on weekends to earn extra
money. For every 3
newspapers that Ben sells, Al
sells 5. If Roy sold 15
newspapers, how many did Al
sell?
Analyze the problem:
a) What is being asked?
b) What are given?
c) Illustrate the problem ?
 Watch the video
D. Discussing
new
concepts
and
Practicing
new
skills # 1
 Illustrate the problem
using blocks
 Explain the illustration
 Set up a proportion
BEN 3 15
ROY 5 N
BEN : ROY = BEN : ROY
3 : 5 = 15 : N
 the teacher will
explain that the
proportion is called a
direct proportion as
the number of
newspaper that Ben
sells increases, the
number of

newspapers that Roy
sells also increases.
E. Discussing
new
concepts
and
Practicing
new
skills #2
 Present another
problem and let each
group work for the
answer.
 Give directions on
what to do.
 The sign on the store
window says
“magazine for sale,
buy 3 take 2” How
many magazines will I
buy if I want to take 10
magazines for free?
 Check if they were
able to write the
proportion correctly.
 Work in group
.
 Have them show their
solution on their white
board.
F. Developing
Mastery
Leads to
Formative
Assessment
# 3
 Present another word
problem and let them
work by pair:
 At the school canteen:
a) 3 pcs of pad paper
cost 45 cents, 21
pieces of pad
paper cost
_______
b) 4 colored pencil
costs 25.
c) 12 colored pencils
cost _______
d) 2 boiled bananas
cost 3.50
e) 10 boiled
bananas cost
____
 Let them show their
solution on their tag
board and be check
by the teacher
 Work by pair
 Let them show their
solution
G. Finding
practical
applications of
concepts and skills in
Daily living
 This is for an
individual output. Let
them read and solve
the problem on their
tag board.
 Reporting method.
Each group should
have a representative
to do the reporting of
his /her output
 Read and solve the word
problem given
 Reporting of his/ her
output
 The pupils are encourage
to interact

 A) a motorist travels
275 km in 5 hours.
How far can he travel
in 9 hours at the same
speed?
Proportion _________
Answer
____________
B) Two buses can
transport 130 people.
how many buses are
needed to transport
780?
Proportion ________
Answer ___________
H. Making
generalizations
and
abstractions
about the lesson
 The teacher will ask
the following
questions:
 What are the
steps in
solving
problems
involving
Direct
Proportions?
 What must you
remember
when setting a
direct
Proportion?
Answer the teacher’s question
I. Evaluating
Learning
The teacher will give 5 item
test. Read and solve. Write
your answer on the blank.
1.At the rate of 3 items per
100 how much will 12 items
costs?
Proportion ______
Answer _________
2) A car travels 72 km on 8
liters of gasoline. At the same
rate, about how far can it
travel on 11 liters of gasoline?
Proportion ________
Answer ____________
3) The ratio of duck eggs to
chicken eggs in an egg store
is 2 : 7 . If there are 312 duck
eggs in a store, how many
chicken eggs are there?
Answer the activity in
1
2 sheet of
paper

Proportion ______________
Answer _________________
4 ) The Ratio of men to
women working for a
construction company is 10 :
3 if there are 21 women in
the construction company,
how many men are there ?
Proportion ________
Answer ___________
5 ) The ratio of the Areas of
2 squares is 1 : 4 The area of
the smaller square is 36 𝑐𝑚2
.
How long is each side of the
bigger square?
Proportion _____________
Answer _______________
J. Additional
activities for
applications
and
remediation
 Teacher prepares
another set of activity.
 Write a proportion for
each problem, Then
find the missing term:
1. The ratio of 2
numbers is 3 ; 5 . The
larger number is 30.
What is the smaller
number?
2. There are 3 teachers
to 125 pupils during
the school program.
How many teachers
were there if there are
2500 pupils? The ratio
of male teachers to
female teachers in our
school is 2 :9. If there
are108 female
teachers, how many
teachers are male?
 Answer the activity at
home .
V. REMARKS
VI. REFLECTION
A. No. of
learners who
earned
80% in the
evaluation

B. No. of
learners who
require
additional
activities for
the
remediation
C. Did the
remedial
lessons
work?
No. of
learners who
have
caught up
with the lesson
D. No. of
learners who
continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did this
work?
F. What
difficulties
did I
encounter
which My
principal
or supervisor
can help me
solve?
G. What
innovation or
localized
materials did
I used /
discover
which I wish
to share with
other
Teachers

IV. PROCEDURES:
A. Reviewing previous lesson of presenting the new lesson
Teacher’s Activity Pupil’s Activity
Form 4 teams of equal number of members. With
the use of a flash cards, the 4 teams will play the
game, the members will have to write their answers
on the board, the first to write the correct answer will
have a corresponding point for their team
Do: What is Asked for
What is 25% of 30?
Forty is what percent of 200?
18 is 30% of what number?
300 is 20% of what number?
What is 52% of 250?
Actively participates in the
activity
7.5
0.20
60
1500
130
School Grade Level SIX
Teaching
Dates Time Week 3 day 1
Quarter 2nd
QUARTER
I. OBJECTIVES
A. Content Standards
The learner is able to demonstrate understanding of solving
word problems on percent of increase and decrease
B. Performance Standards
The learner is able to apply knowledge in solving word
problems on percent of increase and decrease
C. Learning Competencies/
Objectives
Write the LC code for each
Solves Percent problems such as percent of
Increase/decrease (discounts, original price, rate of
discount, sale price, marked-up price) commission, sales
tax, and simple interests.
M6NS-IIe-144
Cognitive: Solve word problems involving finding the
percent of increase/decrease on discounts
Affective: Use Money Wisely
Psychomotor: Write the solutions of word problems on
percent of increase/decrease on discounts
II. CONTENT
Solving Word Problems Involving Increase and
Decrease of Discounts
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages Lesson guide in Elementary Mathematics
2. Learner’s Materials pages
3. Textbook pages 21st
Century Mathletes pp. 122-129
4Additional Materials from
Learning Resource
(LR) portal
B. Other Learning
Resources

B. Establishing a purpose for the lesson
The table shows the population of the two largest
cities in the Philippines. By about what percent did
the population in each city increase from 2000 to
2010? Which city had the greater percent of change
in population?
City 2000 2010
Manila 1 581 082 1 652 171
Quezon 2 173 831 2 761 720
(Guide the pupils to come up with a solution for the
problem.)
Unsatisfactory response
C. Presenting examples/instances of the new lesson
Present the Bar Graph:
Reads and analysis the bar
graph, takes down notes on
the important data presented
in the graph…
D. Discussing new concepts and practicing new skills #1
Group Activity:
Form 4 group, with equal number of members, each
group will answer questions on how to find the
percent of increase in the population of Manila and
Quezon City for ten years.
Guide the pupils to
Present the questions:
1. Which City do you think have the highest increase
of population for ten years?
2. What operation are you going to use to solve for
the answer?
3. How are we going to solve for the increase in
population of Manila City? Quezon City?
activity
0
500000
1000000
1500000
2000000
2500000
3000000
2000 2010
Manila and Quezon City Population
Manila Quezon City

Explain:
To determine which City had the greater percent of
change in its population, find the increase in
population of each city in percent for us to compare
them.
Guide the pupils to perform the step by step
procedure in solving the problem:
Step 1:
Subtract the total population of Manila City in 2000
from 2010
1 652 171 – 1 581 082 = 71 089
Step 2:
Divide the difference with the total population of
Manila City in year 2000
71 089 ÷ 1 581 082 = 0.045
(Rounded to the nearest thousandths)
Step 3:
Multiply the quotient by 100%
0.045 x 100% = 4.5%
Manila’s percent of increase is about 4.5%
Instruct the pupils to do the same steps in order for
them to solve for the percent of change in population
in Quezon City.
Explain:
A percent of change indicates how much a quantity
increases or decreases with respect to the original
amount. Whenever there is a change (increase or
decrease), it can be expressed as a percent of
increase or of a decrease. If the new amount or
value is greater than the original amount or value,
the percent of change is called percent of
increase. If the new amount or value is less than
the original amount or value, the percent of change
is called percent of decrease.
To find the percent of change, use the following
formula:
Percent of change=
Amount of Increase or decrease
Original Amount

E. Discussing new concepts and practicing new skills #2
Group Activity:
Present the problem:
At a local bookstore, Jane makes ₱500.00 a week
working part-time. Last week, she received
₱550.00. what was the percent of increase in
Jane’s salary last week?
Ask the group to answer the following questions:
1. what is asked?
2. what are the given facts?
Guide the pupils to find the answer, allow them to
solve for the answer with the help of their
groupmates. Each group will be given time to show
their solution on the blackboard, they will have to
explain their answers in front of the class.
3. what is the percent of change in Jane’s salary?
The percent of change in
Jane’s salary
She earns ₱500.00 per week.
Her salary is raised to ₱550.00
last week
10%
F. Developing Mastery (leads to formative assessment 3)
Complete the table. For percent of change, indicate
whether the change is an increase or a decrease.
Round your answer to the nearest hundredths (if
rounding is needed)
Original
Quantity
New
Quantity
Difference
Percent
of
Change
1. 10 20
2. 25 75
3. 42 24
4. 100 300
5. 89 33
6. 256 500
7. 667 243.25
8. 999 673.50
9. 1,245.50 900
10. 2,456.30 15,000
Pupils actively participates in
the activity. Take turns in
finding the answers on the
presented table
G. Finding Practical applications of concepts and skills in daily living
Solve Each problem:

1. Due to typhoon, the harvest of cabbage in
Baguio this month decreased from 125 tons to 80
tons, what is the percent of decrease?
2. the price of a kilo of galunggong increased from
73.00 to 85.00 per kilo. Find the percent of increase
3. there were 12 pupils in a Grade 6 class who
failed in the first quarterly exam. In the last
quarterly test, only 5 failed. What is the decrease in
failure?
H. Making generalizations and abstractions about the lesson
How do you solve for percent of increase and
decrease?
Use the formula:
Percent of change=
Amount of Increase or decrease
Original Amount
I. Evaluating Learning
Analyze and solve the problem:
1 following the raise in cost of health insurance by
Philhealth, 250 out of 3000 employees of a
company dropped their health coverage. What
percent of the employees cancelled in their
insurance?
2. A man invested an amount of money in a fund
that earns 5% interest in a year. After how many
years will his money be doubled?
3. A manager of a bank has an annual salary of
₱430,200.00. He also receives 8% raise in his
annual salary. How much will be his new monthly
salary next year?
V. Remarks:
VI. Reflection:
A. No. of learners achieve 80%: ____
B. No. of learners who require additional activities for remediation: ___
C. Did the remedial lessons work? ___
D. No. of learners who have caught up the lesson: ___
E. No. of learners who continue to require remediation: ___
F. Which of my teaching strategies worked well? Why did these work? ___
G. What difficulties did I encounter which my principal or supervisor help me solve?
H. What innovation or localized materials did I used/discover which I wish to share with other
teacher? ___

I. OBJECTIVES
The learner demonstrates understanding in
solving word problems involving
increase/decrease on discounts, original price,
rate of discount, sale price, marked up price.
The learner is able to apply knowledge of in
rate of discount, sale price, marked up price
Objectives
Solves percent problems such as percent of
increase/decrease (discounts, original price, rate
of discount, sale price, marked up price)
commission, sales tax, and simple interests.
M6NS-IIe-144
Cognitive: solve word problems involving finding
the increase/decrease on discounts, original price,
rate of discount, sale price and marked up price
Affective: Use money wisely
Psychomotor: write the solution of word
problems on percent of increase/decrease on
discounts, original price, rate of discount, sale
price and marked up price
II. CONTENT
Solving Word problems involving Percent of
Increase/Decrease in discounts, original price,
rate of discount, sale price and Mark up Price
III. LEARNING
RESOURCES
A. References

IV.
PROCEDURES:
The pupils of Lundagin Elementary School had an
educational trip. One of the places they visited
was Lukban, Quezon. While the group was going
around the place the attention of some pupils was
caught by the signs in one of the stalls. 15% off,
10% off, and 12% off. Can you tell what the signs
mean?
Unsatisfactory Response
Allow the pupils to read the problem aloud. Then
give them time to read it silently.
Fritz is selling ethnic sandals from his father’s
factory. One day, he decided to rent a stall in a
market to sell his products. A costumer can get a
10% discount for each pair of ethnic sandals if he
buys 3 pairs. Each cost ₱1,000.00, each exclusive
of the 12% VAT (Value Added Tax). For every pair
of sandals that Fritz can sell, he gets 40% of the
profit and the rest will be used for the payment of
other expenses. If he gets his sandals from his
father’s factory at 650.00 each, how much is Fritz’s
total gain amount if he sells 120 ethnic sandals?
How much will be remitted to BIR for the 12% vat?
Reads and analyze the
problem
Group Activity:
Let the pupils discuss the presented problem
among their groupmates, guide them in finding the
answer.
1. Teacher’s Guide pages
Lesson Guide in Mathematics Grade 6 pp., 332-
336
Century Mathletes, pp. 130-144
Learning Resource
(LR) portal
B. Other Learning
Resources

Ask:
1. What is asked in the problem?
2. What are the given data?
3. how are you going to solve the problem?
Present the table:
Selling
price
Rate of
discoun
t
Discou
nt
Sale
Price
Total
sales
amount
₱1,000.
00
10% ₱100.0
0
₱900.0
0
₱108,0
00
Allow the pupils to analyze the table presented.
Ask:
1. what is 10% of ₱1,000.00?
2. What is the formula in finding the 10% of
₱1000.00?
3. What is the formula in finding the sale price?
If he gets his sandals from his
father’s factory at 650.00
each, how much is Fritz’s total
gain amount if he sells 120
ethnic sandals? How much will
be remitted to BIR for the 12%
vat?
costumer can get a 10%
discount for each pair of ethnic
sandals if he buys 3 pairs.
Each cost ₱1,000.00, each
exclusive of the 12% VAT
(Value Added Tax). For every
pair of sandals that Fritz can
sell,
₱100.00
Multiply ₱1000.00 by 10%
Subtract the amount of
discount form the original price
Lyka waited until after summer to buy a dress. She
found one amounting to ₱2,500.00 and selling at a
discount of 40%. How much did she save by
waiting? How much did she pay for the dress?
Ask:
1. what is asked in the problem?
2. what are the given data?
3. How are you going to solve the problem?
Allow the pupils to solve the problem on the board
Present the formulas in solving discount problems:
a. discount (D) = Discount Rate x Original Price
Reads the problem aloud then
read it silently to analyze on
how to solve the problem
How much did Lyka save by
waiting? How much did she
pay for the dress?
₱2,500.00 original price of the
dress and 40% discount
Multiply 2,500 by 40% then
subtract the answer form the
original price
Take down notes on their
notebooks

b. Original Price = Discount
Discount Rate
c. Discount Rate = Discount x 100%
Original Price
d. Sale Price = Original Price – Discount
e. Sale Price = Original Price x (100% - Discount
Price)
Pair/Share Activity:
Find the missing entries:
Original
Price
Rate of
Discount
Discount Sale Price
₱220.00 10%
₱235.00 ₱47.00
₱930.00 ₱874.20
Original
Price
Rate of
Profit
Profit
Mark up
Price
₱1,050.00 ₱1,470.00
₱6,500.00 25%
₱9,000.00 ₱2,700.00
Present the Problem:
Nancy was offered a house and lot with an original
price of ₱3,500,000.00. the owner of the property
wanted to sell it to raise funds for her daughter’s
education. The data below was the basis for her
decision to buy.
Complete the data on the table to find out how
much discount Nancy will get if the owner of the
offers her 15% discount if he buys the property
Original
Price
Rate of
Discount
Discount
Sale
Price
₱3,500,000 15%

When Nancy reached home, she made a plan to
have a marked-up price attracted to her costumers
as shown below. Complete the table
Original
Price
Rate of
Profit
Profit
Mark up
Price
₱3,500,000 25%
Ask:
1. Who was offered a house and lot?
2. what was the original price of the property?
3. why did the owner of the property want to sell it?
4. how are you going to solve for the discount and
the sale price?
5. how are you going to solve for the profit and the
mark-up price?
Nancy
₱3,500,000.00
To raise funds for her
daughter’s education
Multiply ₱3,500,000.00 by
15% then subtract the product
from the original price to get
the amount of the sale price
25% the add the product to the
original price
How to you solve for percent problems involving
increase/decrease? Discounts? Original price?
Rate of discount? Sale price? Mark up price?
Use the formula
a. discount (D) = Discount
Rate x Original Price
Discount
Rate
c. Discount Rate =
Discount x 100%
Original Price
d. Sale Price = Original Price –
Discount
e. Sale Price = Original Price x
(100% - Discount Price)
Complete the following table:
Selling
Price
Rate of
Discount
Discount Sale Price
₱500.00 20%
₱950.00 35%
25% ₱250.00
12% ₱574.20
₱9,455.00 ₱3,782.00
Original
Price
Mark Up
rate
Mark Up
Price
Selling
Price

300.00 10%
1,055.00 12%
25% ₱275.00
18% ₱1,712.60
11,563.00 ₱1,734.45
V. Remarks:
VI. Reflection:
teacher?
I. OBJECTIVES
The learner is able to demonstrate understanding in solving
word problems involving commission.
problems involving commission.
Objectives
Increase/decrease (discounts, original price, rate of discount,
sale price, marked-up price) commission, sales tax, and
simple interests.
M6NS-IIe-144
Cognitive: Solve word problems involving commission, Rate
of Commission, total sales and total Income
Affective: be financially sufficient to meet one’s needs, show
industry

IV. PROCEDURES:
Drill on finding the rate, base or percentage
Solve the following:
1. 3% of 600 = N
2. 50% of ___ is 45
3. What is 40% of 5?
4. 7% of 400 = N
5. 45 is N% of 50
18
90
2
28
90%
Ask:
What do you call the amount given to the sales
agent after selling an item of the company aside
from having a basic monthly salary? What does
commission mean?
Commission is the money you receive
in selling something
Mr. Baclaya, a real estate agent, receives a 5%
commission on a property he sells. What is his
commission if he sold a lot at ₱1,040,000.00?
Ask:
How are you going to solve for Mr. Baclaya’s
commission?
Pair-Share Activity:
involving commission, Rate of Commission, total sales and
total Income
II. CONTENT Solving Word Problems Involving commission
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages Lesson guide in Elementary Mathematics 6, pp 336-339
Learning Resource
(LR) portal
B. Other Learning
Resources

Bing, a teacher, is also a sales agent of her friend
who owns an appliance store. She sells appliances
with 5% commission. She asked herself the
following questions:
1. if she sells a stand fan at ₱800.00, how much is
her commission?
2. if she sells 5 stand fans, how much is her total
sales and total income?
3. if she sells a tv set at ₱32,000.00 and receives a
commission of ₱3,200, what is the rate of her
commission?
Ask:
1.How are you going to solve for Bing’s
commission in if she were able to sell a stand fan
for ₱800.00?
2. How are you going to solve for Bing’s total sales
and total income if she were able to sell 5 stand
fans?
3. How are you going to solve for Bing’s rate of
commission if she were able to sell a tv set worth
32,000.00 with a commission of 3,200.00?
Guide the pupils on how to solve the problem.
Discuss:
To answer the question on how much is Bing’s
commission in selling a stand fan at ₱800.00 with
5% commission, use the formula:
Total sale x commission rate
Ask:
1. What is Bing’s total sales in selling a stand fan?
2. what is her commission rate?
3. how are we going to find the amount of
commission?
4. How much is Bing’s commission?
Discuss:
To find Bing’s total sales and total income in selling
5 stand fans use the formula:
Commission ÷ commission rate
Ask:
1. How many stand fans did Bing sold?
2. How are you going to solve for Bing’s total sales?
3. How much is her total sales?
4. How are you going to solve for Bing’s total
income?
Reads the problem aloud and
read it silently for the second
time for them to analyze.
Works in pair, discusses
among themselves how to
solve the problem.
₱800.00
5%
₱40.00
5
₱800.00 x 5
₱800.00 x 5 = ₱4,000.00
Bing’s commission in selling a
stand fan for ₱800.00 with a

Discuss:
In finding Bing’s commission rate in selling a tv set
for ₱32,000.00 with a ₱3,200.00 commission, use
the formula:
Commission x 100%
Total sales
Ask:
1. How are you going to solve for Bing’s rate of
commission in selling a tv set?
2. What is Bing’s rate of commission in selling the
tv set?
5% is ₱40.00. Since Bing was
able to sell 5 stand fans, she
would have ₱200.00 income
Divide 3,200 by 32,000 then
multiply the quotient by 100%
10%
Form 5 groups, each group will have to complete the activity
presented below. Give them time to discuss their answers in
front of the class
Sixto works as a sales agent in an appliance center with a
basic monthly salary of 12,000.00. he is given 8% commission
on all items he sells above 50,000.00. At the end of the month,
he needs to know how much money he has. He prepares a
table and solves.
Complete the table:
Total sales
Above
50,000
Rate of
commission
Commission
Total
Income
275,000.00 8%
275,000.00 20,250.00
activity
Discusses among their group
mates on how to solve for
Sixto’s rate of commission,
commission and total sales
Group Activity:
Complete the table:
Total Sales Rate of
Commission
Commission
₱5,000.00 5%
₱12,500.00 8%
14% ₱2,864.12
15% ₱8,350.50
₱112,545.00 ₱28,136.25
Solve the Problem:
1. Mr. Gomez sells used cellphones. His
commission for every cellphone sold is 20%. If his
total sale is ₱33,850.00, how much is his total
commission?
Solves the problem among
their groupmates

2. Mrs. Vargas is a car sales agent who earns
5,850.00 monthly plus 4% commission on all her
sales. During a month, she sold a car worth
₱740,000.00. how much is her total earnings?
3. Jim, a sales agent, has an income of
₱30,000.00 and receives a commission of 5% on
all sales above ₱75,000.00. If his basic salary is
₱13,500.00, what is his total sales?
4. Manuel, a sales agent, has a basic salary of
₱18,000.00 and a commission of 20% on all sales
above
How to you solve for commission? Rate of
commission? Total sales and total income?
Use the formula:
Total sale x commission rate
Commission ÷ commission
rate
Commission x 100%
Total sales
Complete the Table:
Total Sales
Rate of
Commission
Commission
₱5,000.00 5%
₱12,560.00 8%
14% ₱2,864.12
15% ₱8,350.50
₱112,545.00 ₱28,136.25
V. Remarks:
VI. Reflection:
teacher?

IV. PROCEDURES:
I. OBJECTIVES
The learner is able to demonstrate understanding in
solving word problems involving simple interests.
problems involving simple interests.
Objectives
Increase/decrease (discounts, original price, rate of
discount, sale price, marked-up price) commission, sales
tax, and simple interests.
M6NS-IIe-144
Cognitive: Solve word problems involving sales tax and
simple interests.
Affective: be tax conscious, being punctual in paying
one’s tax, be truthful in paying one’s tax
involving simple interest.
II. CONTENT Solving Word Problems Involving Simple Interests
III. LEARNING
RESOURCES
A. References
4. Additional Materials from
Learning Resource
(LR) portal
B. Other Learning
Resources

Who has seen a bank book? What can you see in
it? Does it have an interest? What about the
principal?
Rhoda has a deposit of ₱5,000.00 in a savings
account for 2 years. If the bank pays a simple
interest at the rate of 6%, how much interest will she
receive?
Ask:
1. Who has a savings account in a bank?
2. How much is he deposit?
3. If you were Rhoda will you open a savings
account in the bank? Why?
How will you solve for the interest Rhoda will
receive?
Rhoda
₱5,000.00
Yes, to save money
Jaypee opens a savings account in National
Commercial Bank where the money earns 1.5%
interest per year. If he has ₱7,500.00 in his account,
how much interest will the money earn in one year?
Ask:
1. How much money does Jaypee have in his
savings account?
2. How much is the interest offered by the bank?
3. How will you solve for the interest of Jaypee’s
money in one year?
Discuss:
To find the answer for the problem, present the
formula:
Interest = Principal Amount x Rate x Time
(I = P x R x T)
Ask:
1. How much money does Jaypee have in his
savings account?
Reads the problem aloud
and read it silently to analyze
₱7,500.00
1.5%
₱7,500.00

Say:
₱7, 500.00 is the principal amount, the principal
amount is the money deposited, invested or
borrowed
Ask:
2. How much is the interest offered by the bank?
Say:
1.5% is the rate, rate is the percent added to the
principal amount invested or borrowed, and 1 year
is the length of time the money has been deposited
in the bank.
Present the solution:
I = ₱7,500.00 x 1.5 x 1
I = ₱7,500 x 0.015 x 1
I = ₱112.05
Say:
So Jaypee’s ₱7,500.00 will earn ₱112.50 in one
year
1.5%
Coach Bernard borrowed money from his friend at
8% simple interest. If he paid an interest of ₱480.00
after 18 months, how much money did he borrow?
Ask:
1. How much interest did Coach Bernard paid for
the money he borrowed from his friend?
2. How much was the rate of interest?
3. How will you solve for the principal amount?
Discuss:
To solve for the principal amount, use the formula:
Principal amount = Interest ÷ Rate x Time
Ask:
1. How much interest did Coach Bernard paid for
the money he borrowed from his friend?
Say:
₱480.00 is the interest, it is the amount of money
earned/paid for using another’s money over a
period of time
2. How much was the rate of interest?
Present the Solution:
Reads the problem aloud and read it
silently to analyze
₱480.00
8%
₱480.00
8%

P = ₱480.00 ÷ 8% x 1.5
P = ₱480.00 ÷ 0.12
P = ₱4,000.00
Coach Bernard borrowed ₱4,000.00 from his friend
Group activity:
Give each group strips of paper with a problem,
they have to solve the problems for themselves,
then they will have to present their answers in front
of the class:
1. Nena borrowed ₱75,000.00 from a credit union.
At the end of 2 years she has to pay back 8%
interest. How much is the interest?
2. Ricardo’s father borrows ₱90,000.00 from a
financial institution. At the end of 2 ¾ years he has
to pay an interest rate of 20%. How much will he
pay back the financial institution?
3. Rolando has ₱20,000.00 in his savings account.
If the rate of interest is 4 ½% a year. How much
interest does his money earn? How much money
will he have in all?
4. Yoly paid back the credit union ₱21,000.00. if
she was given 10% interest 4 years ago, how much
did she borrowed?
Actively participates in the activity
Group reporting
Solve the Problem:
1. Sally deposits ₱22,000.00 in her savings
account. If the bank pays 1.5% interest per year,
how much will she receive at the end of the year?
2. Shuyen wanted to save some money. She
deposited ₱300.00 in a bank which pays 0.5%
interest per annum. After nine months, she needed
the money to buy some gifts. How much will she be
able to get if she widraws all her money from the
bank?
How do you solve for the simple interest? Rate of
interest and time?
Use the formula
Interest = Principal Amount x
Rate x Time
(I = P x R x T)

Principal amount = Interest
÷ Rate x Time
Complete the Table:
Principal
Amount
Rate Time
Simple
Interest
₱8,000.00 1% 1 year
₱12,000.00 2% 2 years
₱15,500.00 5% 18 months
₱21,680.00 0.5% 5 years
₱24,742.00 1.25% 9 months
₱4,200.00 4 years ₱252.00
₱6,700.00 6 months ₱73.70
0.25 years ₱120.00
3.5 years ₱15,000.00
₱49,900.00 ₱3,742.50
V. Remarks:
VI. Reflection:
teacher?

IV. PROCEDURES:
(require pupils to bring a sample of sales invoice
from a store e.g. official receipt from Gaisano)
Ask:
Have you been able to buy goods in a store?
What do you receive after buying goods from a
store aside from your change?
Examine the receipt you are holding. What can you
see?
Is there any amount you paid for tax? How much
did you pay for tax?
Yes
Receipt
The amount paid and the individual
amount of each good bought
Yes (the amount of tax paid depends on
how much
I. OBJECTIVES
The learner is able to demonstrate understanding in solving word
problems involving sales tax.
The learner is able to apply knowledge in solving word problems
involving sales tax.
Objectives
Solves Percent problems such as percent of Increase/decrease
(discounts, original price, rate of discount, sale price, marked-up
price) commission, sales tax, and simple interests.
M6NS-IIe-144
Cognitive: Solve word problems involving sales tax and simple
interests.
Affective: be tax conscious, being punctual in paying one’s tax,
be truthful in paying one’s tax
Psychomotor: Write the solutions of word problems on involving
sales tax
II. CONTENT Solving Word problems involving sales tax
III. LEARNING
RESOURCES
A. References
Learning Resource
(LR) portal
B. Other Learning
Resources

A group of Grade 6 pupils ate in a fast food
restaurant. If their orders totaled ₱750.00 plus a
12% VAT, how much is the total amount they paid
to the cashier?
Nena intends to buy a car. She thinks of the tax the
government imposes. She made a table showing
the rate of sales tax imposed as shown:
Item
Selling
Price
Rate
of
Sales
Tax
Sales
tax
Total cost
of the
item
Brand
new car
₱2,500,000 6%
Slightly
Used car
₱1,900,000 ₱2,090,00
Second
hand car
4% ₱20,000
Guide the pupils to solve for the missing entry in
the table shown.
Ask:
1. How are you going to solve for the rate of sales
tax and the total cost of the brand-new car?
Discuss:
In finding the sales tax and the total cost of a brand-
new car, use the formula:
Total amount of product x rate of sales tax
Ask:
1. How much is the cost of a brand-new car?
2. What is the rate of sales tax?
Discuss:
To find the sales tax of the brand-new car, multiply
₱2,500,000.00 by 6%, so you get ₱150,000.00.
Ask:
How much is the sales tax?
To find the total cost of the brand-new car, add the
sales tax to the selling price.
₱2,500,000.00 + ₱150,000.00 = ₱2,650,000.00
Ask:
₱2,500,000.00
6%
₱150,000.00

How much is the total cost of the item?
Ask:
How are you going to solve for the rate of sales tax
and sales tax of a slightly used car?
Discuss:
To find the rate of sales tax and the sales tax use
the formula:
Total cost of the item – Selling price = sales
tax
Sales tax ÷ selling price = rate of sales tax
Ask:
1. how much is the total cost of a slightly used car?
2. how much is the selling price?
3. if we are going to subtract the total cost and the
selling price of the slightly used car? How much is
the sales tax?
4. if we are going to divide the sales tax and the
selling price of the slightly used car, what is the rate
of sales tax?
Ask:
How are you going to solve for the selling price and
total cost of the second hand car?
Discuss:
To find the selling price and the total cost of the
second hand car, use the formula:
Sales tax ÷ rate of sales tax = selling price
Selling price + sales tax = total cost of the item
Ask:
1. How much is the selling price of the second hand
car? If we are going to divide ₱20,000.00 by 4%
what is the answer?
2. how much is the total cost of a second hand car?
₱2,650,000.00
₱2,090,000.00
₱1,900,000.00
₱190,000.00
0.1 or 10%
₱500,000.00
₱520,000.00
Group Activity:
Guide the pupils in completing the table, ask them
to follow the steps discussed on how to solve for
the selling price, sales tax, rate of sales tax and the
total cost of the item. Have each group discuss
their answers in front of the class.
Selling
price
Rate of
sales tax
Sales tax Total cost
₱200.00 3%
₱680.00 ₱34.00 ₱795.00
Actively participates in the activity.
Group reporting

₱750.00 ₱795.00
₱2,500.00 8%
6% ₱300.00
Group Activity:
Solve the problem:
1. Mr. Foronda bought a picture frame for ₱510.00
inclusive for 6% tax. How much is the tax? What is
the selling price of the picture frame?
2. A sales tax for an item is ₱420.00 or 6%. How
much is the total cost and the selling price of the
item?
Solve the problem:
1. A lady’s bag worth ₱1,500.00 has a sales tax of
6%. How much will the buyer pay for the bag?
2. a food item has a sales tax of ₱22.40 or 4%. How
much is the selling price of the item? How much is
the total cost paid by the costumer?
3. The sales tax of an item is ₱125.00. The cost is
₱3,125.00. What is the rate of sales tax? How
much is the selling price?
How do you solve for the sales tax? Rate of sales
tax? And selling price?
Use the formula:
Total amount of product x rate of sales
tax
Total cost of the item – Selling price =
sales tax
Sales tax ÷ selling price = rate of sales
tax
Sales tax ÷ rate of sales tax = selling
price
Selling price + sales tax = total cost of
the item
Fill the data to complete the table:
Selling
Price
Rate of
sales
tax
Sales tax Total Costs

₱1,500.00 3% ₱48.00
₱4,500.00 6% ₱4,770.00
₱900.00 4%
₱9,000.00 ₱720.00
₱600.00 ₱10,600.00
₱18,000.00 ₱540.00
₱80,500.00 2%
4% ₱826.80
₱35,000.00 8%
₱45.00 ₱795.00
V. Remarks:
VI. Reflection:
teacher?

IV.PROCEDURES:
The pupils of Lundagin Elementary School had an
educational trip. One of the places they visited
was Lukban, Quezon. While the group was going
around the place the attention of some pupils was
caught by the signs in one of the stalls. 15% off,
Unsatisfactory Response
I. OBJECTIVES
The learner demonstrates understanding in
rate of discount, sale price, marked up price.
The learner is able to apply knowledge of in
rate of discount, sale price, marked up price
Objectives
Solves percent problems such as percent of
increase/decrease (discounts, original price, rate
of discount, sale price, marked up price)
commission, sales tax, and simple interests.
M6NS-IIe-144
Cognitive: solve word problems involving finding
the increase/decrease on discounts, original price,
rate of discount, sale price and marked up price
Affective: Use money wisely
Psychomotor: write the solution of word
problems on percent of increase/decrease on
discounts, original price, rate of discount, sale
price and marked up price
II. CONTENT
Solving Word problems involving Percent of
Increase/Decrease in discounts, original price,
rate of discount, sale price and Mark up Price
A. References
1. Teacher’s Guide pages
Lesson Guide in Mathematics Grade 6 pp.,
332-336
4. Additional Materials from Learning
Resource
(LR) portal
B. Other Learning Resources

10% off, and 12% off. Can you tell what the signs
mean?
Allow the pupils to read the problem aloud. Then
give them time to read it silently.
Fritz is selling ethnic sandals from his father’s
factory. One day, he decided to rent a stall in a
market to sell his products. A costumer can get a
10% discount for each pair of ethnic sandals if he
buys 3 pairs. Each cost ₱1,000.00, each exclusive
of the 12% VAT (Value Added Tax). For every pair
of sandals that Fritz can sell, he gets 40% of the
profit and the rest will be used for the payment of
other expenses. If he gets his sandals from his
father’s factory at 650.00 each, how much is Fritz’s
total gain amount if he sells 120 ethnic sandals?
How much will be remitted to BIR for the 12% vat?
Reads and analyze the
problem
Group Activity:
Let the pupils discuss the presented problem among their
groupmates, guide them in finding the answer.
Ask:
2. What are the given data?
Present the table:
If he gets his sandals from his
father’s factory at 650.00 each,
how much is Fritz’s total gain
amount if he sells 120 ethnic
sandals? How much will be
remitted to BIR for the 12% vat?
costumer can get a 10% discount
for each pair of ethnic sandals if
he buys 3 pairs. Each cost
₱1,000.00, each exclusive of the
12% VAT (Value Added Tax). For
every pair of sandals that Fritz
can sell,

Selling
price
Rate of
discount
Discount
Sale
Price
Total
sales
amount
₱1,000.00 10% ₱100.00 ₱900.00 ₱108,000
Allow the pupils to analyze the table presented.
Ask:
1. what is 10% of ₱1,000.00?
2. What is the formula in finding the 10% of ₱1000.00?
3. What is the formula in finding the sale price?
₱100.00
Subtract the amount of discount
form the original price
Lyka waited until after summer to buy a dress. She
found one amounting to ₱2,500.00 and selling at a
discount of 40%. How much did she save by
waiting? How much did she pay for the dress?
Ask:
1. what is asked in the problem?
2. what are the given data?
3. How are you going to solve the problem?
Allow the pupils to solve the problem on the board
Present the formulas in solving discount problems:
a. discount (D) = Discount Rate x Original Price
Discount Rate
c. Discount Rate = Discount x 100%
Original Price
e. Sale Price = Original Price x (100% - Discount
Price)
Reads the problem aloud then
read it silently to analyze on
how to solve the problem
How much did Lyka save by
waiting? How much did she
pay for the dress?
₱2,500.00 original price of the
dress and 40% discount
Multiply 2,500 by 40% then
subtract the answer form the
original price
Take down notes on their
notebooks
Pair/Share Activity:
Find the missing entries:
Original
Price
Rate of
Discount
Discount Sale Price
₱220.00 10%
₱235.00 ₱47.00
₱930.00 ₱874.20

Original
Price
Rate of
Profit
Profit
Mark up
Price
₱1,050.00 ₱1,470.00
₱6,500.00 25%
₱9,000.00 ₱2,700.00
Nancy was offered a house and lot with an original
price of ₱3,500,000.00. the owner of the property
wanted to sell it to raise funds for her daughter’s
education. The data below was the basis for her
decision to buy.
Complete the data on the table to find out how
much discount Nancy will get if the owner of the
offers her 15% discount if he buys the property
Original
Price
Rate of
Discount
Discount
Sale
Price
₱3,500,000 15%
When Nancy reached home, she made a plan to
have a marked-up price attracted to her costumers
as shown below. Complete the table
Original
Price
Rate of
Profit
Profit
Mark up
Price
₱3,500,000 25%
Ask:
1. Who was offered a house and lot?
2. what was the original price of the property?
3. why did the owner of the property want to sell it?
4. how are you going to solve for the discount and
the sale price?
5. how are you going to solve for the profit and the
mark-up price?
Nancy
₱3,500,000.00
To raise funds for her
daughter’s education
15% then subtract the product
from the original price to get
the amount of the sale price
25% the add the product to the
original price
How to you solve for percent problems involving
increase/decrease? Discounts? Original price?
Rate of discount? Sale price? Mark up price?
Use the formula
a. discount (D) = Discount Rate x
Original Price

Discount Rate
c. Discount Rate = Discount x
100%
Original Price
e. Sale Price = Original Price x (100% -
Discount Price)
Complete the following table:
Selling
Price
Rate of
Discount
Discount Sale Price
₱500.00 20%
₱950.00 35%
25% ₱250.00
12% ₱574.20
₱9,455.00 ₱3,782.00
V. Remarks:
VI. Reflection:
teacher?

I. OBJECTIVES
A. Content Standards:
The learner is able to demonstrate understanding in creating problems involving percentage with
reasonable answers.
B. Performance Standards:
The learner is able to apply knowledge creating problems involving percentage with reasonable
answers.
C. Learning Competencies/Objectives:
Creates problems involving percent with reasonable answers
M6NS-II-e-144
Cognitive: create word problems involving percent with reasonable answers.
Affective: Use Money Wisely
Psychomotor: solve created word problems involving percent with reasonable answers.
II. CONTENT:
Creating Word Problems (with reasonable answers) involving percent
III. LEARNING RESOURCES:
A. References:
1. Teacher’s Guide Pages:
Lesson guide in Elementary Mathematics
2. Leaner’s Materials Pages:
3. Textbook pages:
21st
4. Materials:
Powerpoint Presentation
Manila Paper
Pentel pen
5. Additional Materials from Learning Resource (LR) portal:
IV. PROCEDURES:

What is your plan/ dream in the future? How do
you plan to achieve it?
Ask: Is it important to make plan before doing any
activity?
Ask: Does making a plan contribute in achieving
one’s goal? Why? Why not?
Lead the pupils to appreciate planning ahead of time
in any activity.
Yes
yes
Present this problem to the class:
Ms. Losinio have 40 pupils. She decided to have a
general cleaning of her room. She assigned 25%
to sweep the floor, 20% to wipe the tables and
blackboards, 40% to fix the books in the cabinet
and 15% to arrange the chairs. How many pupils
were assigned to arrange the chairs?
Guide the pupils in solving the problem. Ask:
2. What are given?
3. What is the operation to be used?
4. What is the number sentence?
5. What is the answer? Does it make sense?
How many pupils were assigned to
arrange the chairs?
40 pupils
25% to sweep the floor
20% to wipe the tables
40% to fix the books
15% to arrange the chairs
Multiplication
Divide the class into 5 groups. The task of the
pupils is to help each other solve the problem.
Give them enough time to perform the task.
After all the groups have finished, ask them to
post their output on the board and let them
discuss their solutions.

Divide the class into four groups. Encourage the
groups to create a problem similar to the one
given.
Create a problem using the given data:
1. 1.5 % interest, ₱4,000.00 money saved
2. a pair of jeans at ₱550.00 with 35% discount
3. 2 books for ₱350.00 each with a sales tax of 6%
Create a problem using the given data:
1. A second hand bag sold for ₱1,500.00 with a
total cost of ₱1,700.00
2. A house and lot with an original price of
₱1,500,000.00 with a 15% discount.
3. A brand-new car with a ₱200,000.00 discount
and a sale price of ₱2,300,000.00
How do you create problems involving percentage
with reasonable answers?
Directions: Create a problem using the given
information.
1. 50 – numbers of pupils in Grade 5 – Jose Rizal
12% - failed in the quarter examination in
Mathematics
V. Remarks:
VI. Reflection:
teacher?

IV. PROCEDURES:
Let the pupils describe the pattern shown.
Let them draw the next picture in the pattern
Ask:
Two
Eight
I. OBJECTIVES
The learner demonstrates understanding of exponent and base
in exponential notations
The learner is able to apply knowledge of exponent and base in
exponential notations
Objectives
Describes the exponent and the base in a number expressed in
exponential notation.
M6NS-IIf-146
Cognitive: Give the meaning of exponent and base
Affective: Appreciate beauty
Be clean and orderly
Psychomotor: Evaluate an expression in solving exponent and
base
II. CONTENT
Identify the exponent and base in a number expressed in
exponential notation
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages Lesson guide in Mathematics Grade 6, pp. 6
Learning Resource
(LR) portal
B. Other Learning
Resources

How many squares are there in the 2nd
figure?
How may squares are there in the 3rd
figure?
What is the rule in finding the number of squares in
the next figure?
How many squares will be in the fifth figure?
Teacher will write 4 x 4 x 4 on the blackboard
Ask:
1. how many times did we multiply 4 by itself?
2. what is the answer if we multiply 4 3 times by
itself?
The teacher will further discuss that this way of
multiplying number by itself is known as
exponential notation.
The teacher will write the equation on the board
4 x 4 x 4 =43
The teacher will further explain that 4 x 4 x 4 can
be written as 43
where 4 is the base and 3 is the
exponent.
3 times
64
Cindy saved ₱2.00 on Monday, ₱4.00 on Tuesday,
₱8.00 on Wednesday, ₱16.00 on Thursday and so
on. If the pattern continues, how much will she save
on Sunday? How much will her total savings be in
a week?
Ask: what do you observe in the pattern?
Pupils will have to read the problem
aloud, and read it silently for the second
time so that they can analyze the
presented problem
Further discuss the problem by asking the following
questions:
a. what is asked in the problem?
b. how will you solve for question number 1?
c. how will you solve for question number 2?
Explain: the pattern shows that Cindy was able to
save twice as much as she saved the previous day.
In this case she will be able to save ₱32.00 on
Friday, ₱64.00 on Saturday, therefore Cindy will
save ₱128.00 on Sunday.
Show the pattern on the board:
Monday: 21
= 2
Tuesday: 22
= 4
How much will Cindy save on Sunday
How much will her total savings be in a
week?
Pupils will have to take down notes

Wednesday: 23
= 8
Thursday: 24
= 16
Friday: 25
= 32
Saturday: 26
= 64
Sunday: 27
= 128
Explain the pattern on how to get the total money
saved on Friday, Saturday, and Sunday. Ask the
pupils how many times did they have to multiply 2
by itself to get the total amount of money saved by
Cindy. Let them identify the exponent and the base
form the equation presented.
Ask the pupils to add up all Cindy’s savings from
Monday to Sunday,
To get the total amount saved on Friday,
we have to multiply 2 by itself 5 times…
Pair-share Activity:
The side of a small cutout square is 7cm. What is
its area?
Ask:
1.Write an expression about the problem.
2. What is the equation?
3. Can you write 7 x 7 in another way? How?
4.What do you call 7 in 72
? 2 in 72
?
Explain:
The Exponent tells how many times the base is
used as a factor to form a product.
The Base is the factor which is to be multiplied by
itself the number of times indicated in the
exponent to obtain the product.
Present the Table:
Exponential
Expression
Read
Meaning &
Value
42
Four to the
second power,
four squared
4 x 4 = 16
23 Two to the third
power, two cubed
2 x 2 x 2 = 8
74 Seven to the
fourth power
7 x 7 x 7 x 7
= 2401
Pupils will analyze the presented
problem…
Exponential notation
Yes… 7 x 7 can also be written as 72
7 is the base, 2 is the exponent
Pupils will have to take down notes

Explain that the table shows some example of
exponential expression, how to read it and its
value
Group Activity:
The pupils will have to complete the table by writing
the base, exponent, meaning, value and the
equation of the given exponential expression.
Expres
sion
Bas
e
Expon
ent
Mean
ing
Value Equation
53
34
63
25
105
93
82
Board Work:
Select pupils to solve and answer the equations
on the board
A. Rewrite each of the following using exponents.
Determine the numerical value.
1. second power of seven
2. fourth power of 5
3. 2 x 2 x 2 x 2 x 2 x 2 =
4. 8 x 8 x 8 =
5. 15 x 15 =
72
54
26
83
152
What is an exponent? base?
The exponent tells how many times the
base is taken as a factor.
The base is the bottom part of anything.
It is the number used as the factor.
A. Evaluate
1.) 6 x 22
+ 7
2.) 3 x 72
+ 5 x 52
3.) 92
- 72
+ 10
4.) 25
x 52
- 32
x 43
5.) (10 + 2)2
- 102

J. Additional activities for applications or remediations
Solve the following problems:
1. Jordan is enlarging a photo on his computer
screen. The photo starts at 4 cm wide. Each time
he enlarges the photo, the width is doubled. Jordan
enlarged the photo 4 times. What is the final width
of the photo on his computer screen?
V. Remarks:
VI. Reflection:
teacher?

I. OBJECTIVES
The learner demonstrates understanding in giving the value of numbers expressed in exponential
notation
The learner is able to apply knowledge in giving the value of numbers expressed in exponential
notation
Gives the value of numbers expressed in exponential notation
M6NS-IIf-147
Cognitive: Evaluate an expression involving exponents
Affective: Show love, care, concern for people with terminal illness
Psychomotor: Write numbers in exponent forms/solve for the value of numbers expressed in
exponential notation
II. CONTENT:
A. References:
Lesson Guide in Mathematics Grade 6
3. Textbook pages
21st
Century Mathematics, pp 174-179
IV. PROCEDURES:
Game:
Can you find a pair of numbers whose sum is equal
to their product?
Example:
2 + 2 = 2 x 2 = 4
Expected answer:
3 + 1.5 = 3 x 1.5 = 4.5
5 + 1.25 = 5 x 1.25 = 6.25
11 + 1.1 = 11 x 1.1 = 12.1
Let us see how well you remember your
multiplication table? Pair the pupils to do the
activity.
Actively participates in finding
the product of the given
equations.

Find the products of the following. See if you can
get them all correctly.
1) 121 x 121
2) 89 x 89
3) 50 x 50 x 50
4) 20 x 20 x 20 x 20
5) 10 x 10 x 10 x 10 x 10
Presents the following equations:
Find the product of each of the following.
1) 100 x 100
2) 35 x 35
3) 9 x 9 x 9
4) 4 x 4 x 4 x 4
5) 2 x 2 x 2 x 2 x 2
Actively participates in finding
the product of the given
equations.
Asks the pupils to look closely at the numbers
used in each expression. Let the pupils answer
the questions orally
.
A. 100 x 100 Are the factors identical?
What are the factors used?
How many times is the number
used as a factor?
What operation is used
repeatedly?
B. 35 x 35: Are the factors identical?
What are the factors used?
How many times is the number
used as a factor?
Are the operations the same?
What operation is used
repeatedly?
C. 9 x 9 x 9: Use the same questions above
to answer letters C to J.
D. 4 x 4 x 4 x 4:
E. 2 x 2 x 2 x 2 x 2:
F. 121 x 121
G. 89 x 89
H. 50 x 50 x 50
I. 20 x 20 x 20 x 20
J. 10 x 10 x 10 x 10 x 10
Yes
100
2 times
Multiplication
Yes
35
2 times
Yes
multiplication

How many times is the number used as a factor?
Are your answers to each of the three questions the
same from Example A to E?
Since all the answers are the same, then we can
rewrite the five examples as equations.
1) 100 x 100 = 1002
We can write the first expression by using
2) 35 x 35 = 352
3) 9 x 9 x 9 = 93
4) 4 x 4 x 4 x 4 = 44
of
5) 2 x 2 x 2 x 2 x 2 = 25
We can write the first expression by using the factor
100 as the base and the exponent (2) which
indicates the number of times the base is used as
a factor.
Are 1002
, 352
, 93
, 44
, and 25
expressions?
What do you observe with these new expressions?
In 1002
, both 100 and 2 are numbers.
How is each one written?
This is known as superscript
Yes, they are expressions
since each one represents a
number.
The number 100 is written in
normal font size, but the
number 2 is written in a smaller
font size and placed above the
right side of 100
You sent an email to 3 of your friends, each of your
3 friends sent the email to 3 more friends. And each
of those friends sent it to 3 other friends, and so on.
Complete the table:
Stage
Email sent as
a power
Value of
power
1 31 3
2 32 9
3 ? ?
4 ? ?
5 ? ?
Guide the pupils in completing the table by asking
the following questions:
1. What is asked?
2. What are the given facts?
activity

Last Monday, Jenny invited 2 friends to her
birthday party. The next day, Tuesday, each of her
2 friends invited 2 other friends. This pattern
continued until Friday. How many friends were
invited on Friday? How many friends were invited
all in all?
Ask:
1. What is asked?
2. what are the given facts?
Guide the pupils in solving the problem.
The total number of friends
invited
Jenny invited 2 friends to her
birthday party. The next day,
Tuesday, each of her 2 friends
invited 2 other friends. This
pattern continued until Friday.
Use multiplication, multiply 2
by itself 5 times
How do we find the value of numbers in an
exponential notation?
Multiply the base by itself the
number of times indicated by
the exponent
A. Complete the following sentences:
1) In 53
, _____ is the base and ______ is the
exponent.
2) 62
is the exponential form of 6 x _____.
3) 144 is the ___ power of 12.
4) 22
means 2 multiplied by _.
5)74
means _____ is multiplied by itself four times.
B. Give the value of the ff:
1)63
=
2)45
=
3)27
=
4)92 =
5)74 =
V. Remarks:
VI. Reflection:

teacher?

I. OBJECTIVES
The learner demonstrates understanding evaluating expression with two different operations with
or without exponents and parenthesis/grouping symbols
The learner is able to apply knowledge evaluating expression with two different operations with
or without exponents and parenthesis/grouping symbols
Interprets and explains the grouping, exponent, multiplication, division, addition, subtraction
(GEMDAS) rule
M6NS-IIf-148
Cognitive: Evaluate an expression with two different operations with or without exponents and
parenthesis/grouping symbols
Affective: be helpful, clean and orderly
Psychomotor: write the solution in evaluating the expression
II. CONTENT:
Order of Operations Involving Integers
A. References:
Lesson Guide in Mathematics Grade 6 pp.
3. Textbook pages
21st
Century Mathletes, pp.180-185
IV. PROCEDURES:
A. Drill
Evaluating the expression
Mechanics:
Form 4 groups of pupils. The teacher flashes the
cards with expressions.
The groups are given 60 seconds to evaluate the
expression. One member of each group
simultaneously goes to the board and writes the
answer. The teacher checks the answer. The group
with the most number of correct answer wins
Sample item:
a.3×4+1 = b.62+3 =
c. (6+3) + 2 = e. (15 + 3) × 2 =
activity

d. (16 ÷ 4) × 3 =
B. Have a review on the divisibility rules. Provide
exercises written on the flash cards.
Richard and Robert are both working on the value
of the expression: 2 + 4 x 3 – 6 ÷ 2. However, they
have different answers. Richard and answered 6
while Robert answered 11. Of the two students,
who answered correctly?
Ask:
If we are going to follow the order of operation in
the expression, what do you think is the answer?
Is there any other way to solve for the answer?
Say:
Today we are going to learn about the order of
operations involving integers.
-Unsatisfactory response
-Analyze the problem and tries
to sole for the correct answer.
Ask:
From the expression presented, what operation
comes first?
Second?
What are we going to do in order to solve for the
right answer for the expression?
What number are we going to multiply?
What operation are we going to perform next after
multiplying 4 and 3?
What number are we going to divide?
Are we going to divide 6 and 2? Yes or no?
Explain:
In a series of operations without grouping symbols,
multiplication ang division are performed first from
left to right, followed by addition and subtraction,
whichever comes first from left to right.
Show the solution on the board:
To solve 2 + 4 x 3 – 6 ÷ 2
Multiplication: 2 + (4 x 3) – 6 ÷ 2
Division: 2 + 12 – (6 ÷ 2)
Addition: (2 + 12) – 3
Subtraction: 14 – 3
Answer: 11
Ask: Who got the correct answer?
What do you observed about the order of operation
that we performed in finding the correct answer for
the expression?
Are you familiar with the GEMDAS rule?
Addition
Multiplication
Perform multiplication first
4 and 3
Division
Yes
Shall take down note in their
notebooks
Robert
We use the MDAS rule

Group Activity:
Divide the class into 6 groups with equal number of
members. Give instructions to the pupils on what
they are going to do to complete the activity
Give the following expression for pupils to read and
analyze. With the use of their paper and pen, they
will have to simplify the different expression, thus
answers the questions corresponding the
expression given. Each group is given time to
discuss their answers in front of the whole class
1. Simplify: 2 + (7 x 3) – 5
What is the grouping symbol in the expression?
How many operations do you have to perform to
get the answer?
What operation are you going to perform first?
How are you able to get the correct answer?
What is the answer?
2. Simplify: 3 x 4 ÷ (7 - 5) – 12 ÷ 4
get the answer?
What is the answer?
3. Simplify: 7 + [ 2 (12 – 5) + 32] – 18 ÷ 3
get the answer?
What is the answer?
4. Simplify: 4 + [ -1 (-2 – 1)]
get the answer?
What is the answer?
5. Simplify: 5 – [4 + 2 x 23
) ÷ 10]
get the answer?
What is the answer?
6. Simplify: 42 – 4 x 32
+ 2(5 − 2)3
Performs the activity with their group mates,
discusses among themselves what is the
correct answer…

get the answer?
What is the answer?
Each group of pupils will be given time to
report/discuss their answers in front of the whole
class. The teacher guides each group. The teacher
helps the pupils on how to simplify the equation. Let
them know what to do in order to arrive for the
correct answer.
Explain about:
How to apply the GEMDAS RULE (grouping
symbols, exponents, multiplication, Division,
addition and subtraction)
group reporting
Perform the Indicated operations.
1. 2 ( -5) + (-3) (-7)
2. 27 ÷ (-9) – (3) (-2)
3. 16 + (42 – 2 x 3) – 34
4. 42 ÷ 7 x [37 ÷ 3 – 8]
5. 32 + 2 [5 x (24 – 6)] – 48 ÷ 24
Solve each Problem:
Klein has 42,500.00 in his bank account. Over the
summer period, he made 3 withdrawals of 8,500.00
each and a deposit of 13,250.00 write an order of
operations to represent this situation
Guide the pupils to give the following
generalizations by asking: What rule would you
follow in order to perform the order of operation?
What does GEMDAS rule mean?
-simplify the operations in grouping
symbols. Start from the innermost
grouping symbol.
-evaluate exponential expressions
-multiply and divide in order they appear
from left to right
Add and subtract in order they appear
from left to right.
Means grouping symbols, exponents,
multiplication, division, addition, and
subtraction.

Using the following values, a = 5, b = 10, and c =
15, perform the indicated operations
1. (a + b) – 5 (c ÷ a)
2. (b x c) ÷ 10 (a x 2)
3. (a – b) + (b ÷ a)
4. (2ab – 45) ÷ a
5. (2bc -5ab) ÷ ab
V. Remarks:
VI. Reflection:
teacher?

I. OBJECTIVES
The learner demonstrates understanding in performing two or more different operations on whole
numbers with exponents and grouping symbols
The learner is able to apply knowledge in performing two or more different operations on whole
numbers with exponents and grouping symbols
Performs two or more different operations on whole numbers with or without exponents and
grouping symbols
M6NS-IIf-149
Cognitive: Evaluate an expression with two different operations with exponents and
Affective: be helpful, be honest
Psychomotor: write the solution in evaluating an expression
II. CONTENT:
Performs two or more different operations on whole numbers with Exponents and
grouping symbols
A. References:
Lesson Guide in Mathematics Grade 6 pp. 17-21
3. Textbook pages
21st
Century Mathletes,
IV. PROCEDURES:
Game
The teacher flashes flash cards with expressions,
the pupils will have to solve for the problem
1. 3 x 4 + 1 =
2. 62 + 3 =
3. (6 + 3) + 2 =
4. (16 ÷ 4) x 3
5. (15 + 3) x 2 =
activity
Ask:

What do you observe when somebody in your
home is sick? Does he take medicine? Is it liquid or
tablets? How are the tablets kept?
Give him/her medicines
In a drugstore, the pharmacist daughter of the
owner helps her mother account the medicines for
fever. She finds specialized squares holders of
tablets. She recorded 4 groups of 10 layers of 10
tablets on each side of the holders and 6 sets of 10
tablets, is she right in reporting that there are
40,060 tablets? Why?
Group Activity: (divides the class into 5 groups with
equal number of members.
Ask:
a. what is the profession of the daughter of the
drugstore owner?
b. what does the pharmacist do?
c. what does she find in the drugstore?
d. if you were the pharmacist? Will you also have a
systematic arrangement of your medicines? Why?
Reads the problem aloud and
read it silently for the second
time to analyze.
Pharmacist
Tablets/medicines
Yes, to easily find the
medicine
Let each group use flats and longs to visualize the
problem
Let them answer the questions:
a. what will you find in the problem?
b. what are the given data?
c. what operations to be used?
Lead the groups to think aloud of a numerical
expression about the problem
(4 x 103
) + (6 x 10)
The total number of tablets
4 groups of 10 layers of 10
tablets and 6 sets of 10 tablets
Multiplication and addition
Group Activity:
Emma helps her mother arrange the items in their
store. Her mother has specialized square tray for
quail eggs. She finds 4 groups of 5 rows with 5 quail
eggs placed in trays and 3 groups with 10 quail
activity

eggs. She informs her mother that they have 1030
quail eggs. Is she right? Why?
Ask each group to answer the following questions:
1. Who helps her mother in the store?
2. What does Emma do to help her mother?
3. What facts are given?
4. how are you going to solve for the answer?
5. ask them to evaluate the numerical expression:
(4 x 52
) + (3 x 10)
(4 x 25) + (3 + 10)
100 + 30
130
Have the pupils analyze which operation should be
performed first, second, next to arrive at the answer
F. Developing Mastery (leads to formative assessment)
Activity 3: Group Activity
Bing asks her son to do his homework and looks
at his notebook. She finds the following:
Evaluate the expressions:
1) 6 + (2 x 7 + 52
)
2) 3 x (4 x 82) – 8
3) 5 x [24  2 x (10 – 8)2  10]
4) (15 – 6) + (4 – 1) x 23
5) 3 x [3 + 2 x (10 – 32)]
Ask each pair of pupils to answer the questions
below, let each group solve the given equations
on the board, allow them to explain their answers
in front of the class.
1) What are the facts given?
2) Which operation should be done first? second?
third? last? Why?
b) Have each pair of pupils evaluate the
expressions.
activity
Group reporting
Think-Pair-Share Activity:
Pupils are given the freedom to choose their
partners for the activity:
Evaluate the ff. expressions:
a) (114 – 4) x (12 ÷ 4)2 + 3
b) 16 + 82 ÷ (4 + 4)
c) (36 – 6) x (3 x 4)2 + 7

d) 122 x 30 + (890 ÷ 2)
e) 62 x 23 + (400 ÷ 2)
How do we evaluate an expression with more
than two operations with exponents and
parenthesis/grouping symbols?
Apply the GEMDAS RULE
1.Evaluate the following expressions:
a) (9 – 2) + (32 x 21)
b) (18 + 14) ÷ (6 + 2)
c) 36 ÷ 22 + 4 x (4 – 2)
d) (36 – 6) + [(3 x 42) + 7]
e) (72 + 15) x 4 –
f) 4 x (15 – 32) + 16
g) (93 + 7) x 6 + 10
h) 12 x 30 + (890 ÷ 10)
i) [(144 ÷ 12)2 x 3] ÷ 3 x 6
j) (16 + 82) ÷ (4 + 4)
2.Evaluate the expression if: a) R = 2
1.[(6R + R x 8) ÷ 13] – 5 + R
2. S = 3 [(7S – S) x 6] + 6S – S x 5
V. Remarks:
VI. Reflection:
teacher?

I. OBJECTIVES
The learner demonstrates understanding in performing two or more different operations on whole
numbers without exponents and grouping symbols
The learner is able to apply knowledge in performing two or more different operations on whole
numbers without exponents and grouping symbols
Performs two or more different operations on whole numbers with or without exponents and
grouping symbols
M6NS-IIf-149
Cognitive: Evaluate an expression with two different operations without exponents and
Affective: be helpful, be honest
Psychomotor: write the solution in evaluating an expression
II. CONTENT:
Order of Operations Involving Integers
A. References:
Lesson Guide in Mathematics Grade 6 pp. 13-16
3. Textbook pages
21st
Century Mathletes,
IV. PROCEDURES:
Form 4 groups:
The teacher flashes numerical expression in a flash
card
One member of the group simultaneously goes to
the board and writes the answer
The teacher checks the answer
The group with the highest number of correct
answer wins
activity

Ask the pupils about the occupation of their
parents. Let them tell how they help their parents
earn a living.
Activity 1 – Use of Role Play in a Sari-Sari Store
Jethro was helping his mother in their store when a
delivery man delivered 20 dozen of eggs at 42 a
dozen. If the delivery man gave him 160, how
much was his money? Was he right in asking for a
change of 260, if his money was 1,000? Why?
Ask the following questions:
Who helped mother in the store?
Who delivered dozens of eggs?
How many dozens of eggs were delivered to them?
If you were Jethro:
will you help your family earn a living? Why?
will you keep the change given by the delivery
man? Why?
Have each pair of pupils act it out using play money
and ask them to answer the following:
What are the given data?
What are the operations to be used?
Jethro
Delivery man
20 dozens
Yes,
No, it’s not good to tell lies
the role play
Lead each pair of pupils to think of an expression
related to the problem.
Let them evaluate the expression they have
formulated.
160 + (20 x P42)
160 + P840
1,000 money of Jethro
Require them to analyze the operations they used
in arriving at the exact change
activity
Group Activity– Learning Stations
Have 3 learning stations. Let the pupils do the
activity in each learning station by group. Once
they have finished an activity, they need to go to
the next station and do the activity indicated there.
Pupils need to do the activity as fast as they can.
Present the Problem first:
the group activity

Tita was absent for a week because she was sick.
When she went to school, she had to take a test.
Few of the items given are shown below.
Ask each group of pupils to answer the following
questions:
What facts are given?
What operations are in each problem? Which
operations come first? Which operation will you
do first?
Guide each pair of pupils to evaluate the
expressions
Group Activity: Evaluate the expression.
a) 8 + 4  2
b) 5 x 8  4
c) 65 – 91  7
d) 72  3 x 8
e) 67 + 33  25
Evaluates the expression
using paper and pen
Group activity:
Write an expression about the problems. Then
evaluate the expression.
1)In a certain eatery, there are 5 glass racks
having 24 glasses and 8 left over. The answer
says there are 130 glasses in all. Is it right?
Why?
2)Use numbers less than 7 once to make the
expression right.
activity
How do we evaluate an expression with two
different operations without exponents and
parenthesis/grouping symbols?
Answers:
Evaluate exponential
expressions
Learning Station 1:
Evaluate:
a) 2 x 3 + 4
b) 7 x 9 – 3
Learning Station 2:
Evaluate:
c) 18 – 12  2
d) 35 – 6 x 3
Learning Station 2:
Evaluate:
e) 3 x 2 + 4
f) 48  12 + 8

Follow the MDAS Rule
Evaluate the following expressions.
1) 4 x 3 + 8
2) 84 ÷ 3 x 4
3) 76 – 8 + 5
4) 53 + 7 – 20
5) 3 x 5 ÷ 25
J. Additional activities for applications or remediations
Assignment:
Write an expression for the problem then, evaluate:
Tickets for children in the carnival cost ₱150.00. A
teacher of a class of 48 pupils gets for the whole
class but only 43 bought tickets. Is it right for the
teacher to say that she ha ₱6,350.00 for the tickets
of the children? Why?
V. Remarks:
VI. Reflection:
teacher?

DETAILED LESSON PLAN
School Grade level VI
Teaching Dates and
Time Week 7 Day 1 & 2
Quarter SECOND
QUARTER
I. OBJECTIVES
 Demonstrates understanding of order of operations, ratio and
proportion, percent, exponents, and integer.
 Apply knowledge of order of operations, ratio and
proportion, percent, exponents, and integers in
mathematical problems and real-life situations.
C. Learning Competencies: Identifies real-life situations that make use
of integers. (M6NS-IIg-150)
Objectives:
Cognitive:
 Identifies real-life situations that make use of integers.
Psychomotor:
 Write an integer to represent each real life situation.
Affective:
 Show teamwork within a group
II. CONTENT: Identifying real-life situations that make use
of integers.
A. References
1. Teacher’s Guide pages: Lesson guide in Elementary Mathematics VI: p 353-356
21st
Century Mathletes: p 47-59
2. Learner’s Materials pages: 21st
Century Mathletes: p 146- 147
3. Textbook pages: 21st
4. Additional Materials from Learning Resource(LR) portal: none
B. Other Learning Resources:
 Activity cards, pictures, room thermometer, Video
presentation about integer.
(https://www.youtube.com/watch?v=uopjGTZdj64) &
Slide deck presentation (Powerpoint)
IV. PROCEDURES
Teachers Activity Student’s/ Pupil’s
Activity
A. Reviewing
previous lesson or
 Call pupils
 do the following actions
walking forward,
 and
volunteers do

presenting the new
lesson
sit down, laugh,
shake head
the opposite
actions
 walking
backward,
stand up, cry,
nod
B. Establishing a
purpose for the
lesson
 Introduce the lesson & set classroom
rules
 present a picture of a child & a ladder/
stairs
 show to the class the movement of going
up and down of the child in the picture
 let the learners describe how many steps
did the child make both in going down and
up.
 Listen to the
teacher
 Listen to the
teacher
 Answers how
many steps
did a child
make in going
up and down.
C. Presenting
examples/instances
of the new lesson.
 Have the learners watch a video about
integers that represent a situation.
 https://www.youtube.com/watch?v=uopjGTZdj64
 Present a number line.
 Describe a number line…
-Tell what is in the number line,
- the numbers in the number line are called
integers.
- define integers
- that a number line has two sides to the
right is the positive integers and to its left are
the negative integers.
 Go back to the picture of a child
 Discuss to the class that if the child made two
steps up that is +2 but if the child goes three
steps down that is -3.
 Watch the
video
 Listen to the
teacher
D. Discussing new
concepts and
#1
 Present another picture to the class of two
Room Thermometer and read the
temperature reflected on the thermometers.
 Compare the readings of the two
thermometers if the temperature reading is 35
degrees above zero we say its +35 and if it is
35 degrees below zero it can be read as -35.
 Listen to the
teacher
E. Discussing new
concepts and
#2
 Present the following situations to the class
a. gain of 5 points
b. 8 steps backward
c. a loss of 100 pesos
 Answers the
situation
given.

F. Developing
mastery (leads to
Formative
Assessment 3)
 Group the learners into 4 groups
 Present an activity
 Write the Integer represented by each
situation.
a. The temperature is 18℃ below 0.
b. The altitude is 75 m below sea level.
c. The corals are 15 m below sea level.
d. He has a weight loss of 5 kg.
e. She spent 375.00 pesos for a dress.
 Group
themselves
into 4 groups
 Answers the
activity given
in groups
using tag/
show me
boards.
applications of
daily living.
- Teacher will present a problem. Let the pupils
solve the problem.
-Yren Walked 7 steps forward, 5 steps backward,
10 steps forward, and 6 steps backward. How
many steps is Yren from where he started?
- Solve the
problem given
H. Making
generalizations and
abstractions about
the lesson
- Teacher will ask the following questions.
What are Integers?
What are its uses?
 Answers the
teachers
question.
I. Evaluating learning  Teacher present a situation.
 Write an Integer from the following situations.
1. loss of 15 kilograms
2. 10 degrees below zero
3. overtime pay of 85.00 pesos
4. 8 hours ago
5. 10 km north
6. gain of 345.00 pesos
7. 230 m below sea level
8. going 4 km downstream
9. 12 years from now
10. spending 50 pesos.
 Answer the
activity
J. Additional
activities for
application or
remediation
 Teacher prepares another set of activity.
 Write an Integer from the following situations.
 1. Water freezes at temperature 0 degrees
centigrade. The temperature was at 20℃
above zero during the day.
 Answer the
activity at
home.
Day 2
B. Establishing a
purpose for the
lesson
 Teacher will prepare some words and class
gives the antonym
Love, good, patience, stubborn
 Teacher will relate the words to the lesson
and use the number line to illustrate.
 Present a number line on the board.
 Have a little review about the negative and
the positive integers.
 Give the
antonym of
the words.

C. Presenting
examples/instances
of the new lesson.
 Teacher prepares a situation card cards
before the lesson.
Let the pupils locate the numbers on the
number line. And give the integers.
a. 5 units to the left
b. 50 meters below the ground
c. 60 degrees above zero.
d. lost 30 points
e. 10 floors up
f. 15 % dropped
D. Discussing new
concepts and
#1
 Teacher discuss to the class the following
words below, above, gained, increased,
decreased, dropped & spent. Relate the
following words to the Number line.
 Example:
230 ft. below sea level,
50 m above the ground
Climb 5 steps up.
 Listen to the
teacher.
E. Discussing new
concepts and
#2
 Present another set of activity.
 Write the Integer represented by each
situation.
1. deposited 15,000.00 pesos
2. 47° above 0
3. gained 15 points
4. grades are increased to 15%
5. enrolment decreased to 115
6. the temperature dropped to 25° C
7. She spent 100.00 pesos from her money.
 Answer the
activity.
F. Developing
mastery (leads to
Formative
Assessment 3)
 Group the class into 3
 Present a situation to the class and each
group will illustrate by drawing, role playing or
acting out.
1. Mang Pepe bought a pair of Polo Shirt
worth 600.00
2. The temperature dropped to 38° C.
3. The highest elevation of the country is
8077 ft.
4. 12 ft. below the ground
5. Yhra makes 5 steps up and 2 steps down
 Perform the
activity
applications of
daily living.
 Prepares an activity (can be grouped or not)
Write an integer described in the situation.
You watched a rocket launching on TV. The
announcer said:
a. blast off 4 seconds
b. 4 seconds after blast off
c. 3 seconds before blast off
 Answer the
activity.

H. Making
generalizations and
abstractions about
the lesson
 How do we represent real life situations?
 Possible answer by using integers
I. Evaluating learning  Write an integer described in the situation.
1. 600 m above the ground
2. lost 15 points
3. gained 30.00 pesos
4. spent 150.00 pesos
5. 150 ft below the ground
6. his grade decreased to 80%
7. 60° above 0
8. dropped to 150
9. 12 steps forward
10. 15 floors up
J. Additional
activities for
application or
remediation
Use a number line to identify the points describe.
1. 6 units to the right
2. 12 units to the left
3. 16 units to -5
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned
80% on the
formative
assessment
B. No. of learners
who require
additional
activities for
remediation
C. Did the
remedial
lessons work?
No. of learners
who have
caught up with
the lesson
D. No. of learners
who continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did these
work?

did I encounter
which my
principal or
supervisor can
help me solve?
G. What
innovation or
localized
materials did I
use/discover
which I wish to
share with other
teachers?

Teaching Dates and
Time Week 7 Day 3
Quarter SECOND
QUARTER
I. OBJECTIVES
 Apply knowledge of order of operations, ratio and proportion, percent,
exponents, and integers in mathematical problems and real-life
situations.
C. Learning Competencies: Describes the set of
integers. (M6NS-IIg-151)
Objectives:
Cognitive:
 Describes the set of integers. (M6NS-IIg-151)
Psychomotor:
 Write an integer from the given number line
Affective:
II. CONTENT: Describing the set of integers.
A. References
21st
 Activity cards, pictures, Number Line, & video
presentation
(https://www.youtube.com/watch?v=5oHJcmYbHvA)
IV. PROCEDURES
Teachers Activity Student’s/ Pupil’s Activity
A. Reviewing
previous lesson or
 Present a puzzle to the class and
group the pupils into 4-5 let the pupils
assemble the puzzle
 Assemble the puzzle

presenting the new
lesson
 Teacher gives awards to the group
who first assemble the puzzle.
 present another number line
 ask the following questions
1. where they can locate the positive
and negative numbers on the number
line.
2. what are the examples of a negative
and positive integers?
 Learner will answer
the questions
B. Establishing a
purpose for the
lesson
 Introduce the lesson to the learners
 Set classroom rules
 Present a video about how to describe
an integer.
(https://www.youtube.com/watch?v=5oH
JcmYbHvA)
 Have a little review on the video
presentation.
 Ask some questions about the video
 Watch the video
 Answer the questions
C. Presenting
examples/instance
s of the new
lesson.
 Present a picture of Mayon Volcano
(http://tiny.cc/rqiz6y)
 Ask the learners what is in the picture.
 Let the learner describe the picture
 Teacher then describe the picture
- Mayon Volcano is 2077 feet above
sea level3
- To write 2077 ft. above sea level as
+2007
 Describe the picture.
D. Discussing new
concepts and
practicing new
skills #1
 Present another problem to the class
(https://www.vigattintourism.com/touris
m/articles/TOP-10-Highest-Mountains-
in-the-Philippines)
Situation: The highest elevation in the
Philippines is Mount Apo between
Davao & Cotabato, is the tallest
mountain in the Philippines, having an
elevation of 2,956 meters. The lowest
elevation Galathea Depth 10,540
metres below sea level.

 above uses the notion of opposites:
Above sea level is the opposite of below
sea level. Here are some more examples
of opposites:
top, bottom | increase, decrease | forward,
backward | positive, negative.
E. Discussing new
concepts and
practicing new
skills #2
 Teacher prepares another set of group
activity or a set of situation this allow
the pupils to find a stair case, prepare
realia like money. Let them present
their activity by group.
 Have them prepare also a number line
basis for their answer.
 Group 1
a. +5 c. 6 d. 15 e. 25
b. -2 f. -8 g. -10 h. -18
Group 2 (uses real objects describes
integers using increase and decrease)
a. +50 stones b. -15 stones c. +18
sticks d. -12 sticks e. +16 papers f. -8
papers.
Group 3 (Uses meter stick or steel
tape; describes integers using top and
bottom)
a. +160cm b. -20cm c. +5 cm
d. -25cm e. 3cm f. -50 cm
 Group themselves into
4 groups
 Answers the activity
given in groups.
(steps forward)
(steps backward)
F. Developing
mastery (leads to
Formative
Assessment 3)
 Prepares pupil activity
 Let each pupil’s answer the following
by describing the integers.
1. +200 m 2. – 500.00 pesos 3. +10
4. -6 5. -100cm
 Answers the activity.
G. Finding
practical
applications of
concepts and skills
in daily living.
 Prepares a problem
Lillia bought 4 pairs of black jeans at
320.00 each. How much money did she
pay the clerk?
- Solve the problem given
H. Making
generalizations
and abstractions
about the lesson
 Ask some questions
 How do we describe the integers?
We can use the following words to
describe integers top, bottom | increase,
decrease | forward, backward | positive,
negative.
 Answers the teachers
question.
I. Evaluating
learning
 Prepares an individual activity.
Describe the following integers using
top, bottom | increase,
 Answer the activity

decrease | forward,
backward | positive, negative.
1. 8 2. 12 3. -17 4. 120 5. -23
J. Additional
activities for
application or
remediation
 A tree post was situated 550 feet
below sea level. If it descends 100
feet, what is its new position?
 Answer the activity at
home.
V. REMARKS
VI. REFLECTION
H. No. of
learners who
earned 80%
on the
formative
assessment
I. No. of
learners who
require
additional
activities for
remediation
J. Did the
remedial
lessons
work? No. of
learners who
have caught
up with the
lesson
K. No. of
learners who
continue to
require
remediation
L. Which of my
teaching
strategies
worked well?
Why did
these work?
M. What
difficulties did
I encounter
which my
principal or
supervisor
can help me
solve?
N. What
innovation or

localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Teaching Dates and
Time Week 7 Day 4
Quarter SECOND
QUARTER
I. OBJECTIVES
situations.
C. Learning Competencies: Compares integers with other numbers such as whole
numbers, fractions, and decimals. (M6NS-IIg-151)
Objectives:
Cognitive:
 Compares integers with other numbers such as whole numbers,
fractions, and decimals. (M6NS-IIg-151)
Psychomotor:
 Write <, >, or = in comparing integers
Affective:
II. CONTENT: Comparing integers with other numbers such as whole numbers,
fractions, and decimals.
A. References
21st
 Activity cards, pictures, Number Line, & video presentation
(https://www.youtube.com/watch?v=Oq2KoAGrY64)
IV. PROCEDURES
A. Reviewing
previous lesson or
 Present a game named Number Line
Assemble to the class and group the
pupils into 2 groups.

presenting the new
lesson
 Teacher distributes number cards from
0 to 9 and a card with a negative sign,
to each group. One pupil one card.
who first assemble the numbers
 The group who assembles first wins
the game
 Discuss the value of teamwork
the questions
B. Establishing a
purpose for the
lesson
 Present a video about how to compare
an integer.
(https://www.youtube.com/watch?v=Oq2
KoAGrY64)
presentation.
 Watch the video
C. Presenting
examples/instance
s of the new
lesson.
 Teacher discuss how to compare
integers using the symbols <, >, or =
 Teacher explains using the number line
- Zero is greater than all negative
integers but smaller than all
positive integers.
- All positive integers are greater
than all negative integers; all
negative integers are less than all
positive integers
- When comparing 2 integers with
the same signs, that one that is
farther to the right on the number
line is the greater integer.
Example:
-4 -8
-8 is greater than - 4 since it is
farther to the right. Use the sign <.
8 -
8
8 is greater than - 8 since it is a
positive number. Use the sign >.
8 >
-8
-4 < -8
13
+13
13 =
+13

D. Discussing new
concepts and
practicing new
skills #1
 Present another individual activity to
the class.
Let the pupils compare integers using
<, >, or =.
a. -4 -8 e. -12 12
b. -10 0 f. -150 -149
c. 8 9
d. -9 -9
 Pupils will answer the
activity
E. Developing
mastery (leads to
Formative
Assessment
activity. This time prepare a number
cards with the following integers.
 Let each group assign a member to
hold the >, <, or =.
 Let them present their activity by
group.
 The group who got the most correct
numbered of pairs win.
-Group 1
a. +5 & 6 b. 15 & 25. 45
c. -2 & -8 d. -10 & -18
-Group 2
a. +50 & -15 b. +18 & -12 .50
c. +16 & -8 d. -28 & -29
Group 3
a. +160 & -20. 75 c. +5 & -25
d. 3 & -50 e. -1 & 1 1/4
4 groups
given in groups.
applications of
concepts and skills
in daily living.
Yren was asked by his teacher to
compare two integers, he chose -5 and
+4. From the two numbers which is
greater and which is lesser?
G. Making
generalizations
and abstractions
about the lesson
 How do we compare integers?
We can use the following symbols to
compare integers using the symbols <, >,
or =.
question.
13 and +13 are the same. Use
= sign.

H. Evaluating
learning
Compare the following integers using
the following symbols <, >, or =. And fill
in the box.
1. 25 -25 2. -16 - 16.45
3. -15 -14 4. 9 - 9
5. 150 149 1/2
I. Additional
activities for
application or
remediation
 Answer page 150 on the 21st
Century
Mathletes.
home.
V. REMARKS
VI. REFLECTION
O. No. of
learners who
earned 80%
on the
formative
assessment
P. No. of
learners who
require
additional
activities for
remediation
Q. Did the
remedial
lessons
work? No. of
learners who
have caught
up with the
lesson
R. No. of
learners who
continue to
require
remediation
S. Which of my
teaching
strategies
worked well?
Why did
these work?
T. What
difficulties did
I encounter
which my

principal or
supervisor
can help me
solve?
U. What
innovation or
localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Teaching Dates and
Time Week 8 Day 1
Quarter SECOND
QUARTER
I. OBJECTIVES
situations.
C. Learning Competencies: Represents integers on the number line. (M6NS-IIh-153)
Objectives:
Cognitive:
 Represents integers on the number line. (M6NS-IIh-153)
Psychomotor:
 Write integers correctly
Affective:
 Appreciate the use of number line.
II. CONTENT: Representing integers on the number line.
A. References
21st
 Activity cards
(https://www.pinterest.ph/pin/573294227556015390/?lp=true),
Number Line, & video presentation
https://www.youtube.com/watch?v=o3kIi8g3mwI) or
(https://www.youtube.com/watch?v=vTfqgqkBges)
(https://www.youtube.com/watch?v=A186iWp5vKQ)
IV. PROCEDURES
Teachers Activity Student’s/ Pupil’s
Activity
A. Reviewing
previous lesson or
 Show a number Line to the class  Listen to the teacher

presenting the new
lesson
 Review on the different parts of the
Number Line
B. Establishing a
purpose for the
lesson
and your objectives.
 Present a video about the number line
https://www.youtube.com/watch?v=o3kIi
8g3mwI) or
(https://www.youtube.com/watch?v=vTfq
gqkBges)
presentation.
 Watch the video
C. Presenting
examples/instance
s of the new
lesson.
 Teacher discuss how represent
integers in the number line
 Teacher explains using the number line
- A whole number is any counting
number. Numbers, like 1/2 or .75,
that you use to describe a part of
something are not whole numbers.
- A positive number is a number
greater than zero. It can be written
with or without a + symbol in front
of it. A gain in something is written
with a positive number. Profit,
increase, and income are all
examples of words that mean
positive.
- A negative number is a number
that is less than zero. It is always
written with a - symbol in front of it.
A loss is written with a negative
number. Decrease, spend, and
decline are examples of words that
mean negative.
- An integer is any positive whole
number or its negative. Zero is also
considered an integer.
-
- Give examples
1. 2 units right of 4

2. 4 units of -2
3. 5 units to the left 0f 1
D. Discussing new
concepts and
practicing new
skills #1
 Present a group activity to the class.
Let the pupils locate the integers using
the Activity card on number line.
1. 3 units to the right of 5
3. 7 units to the left of -2
4. 6 units to the right of zero
5. 5 units to the left of -5
activity
E. Developing
mastery (leads to
Formative
Assessment
 Teacher prepares another set of
individual activity. Use the Number line
activity card.
1. 8 to the right of -8.
2. 2 to the right of 7
3. 5 to the left of -5
4. 6 to the left of -2
5. 8 to the right of -10
given in groups.
applications of
concepts and skills
in daily living.
Kris like to take a walk every day. She
started with a 25 steps forward and add
another 15 steps forward and 16 steps
backward. How many steps did she
make in all?
G. Making
generalizations
and abstractions
about the lesson
 How do we represent integers?
question.
H. Evaluating
learning
 Prepares an individual activity. Use the
number line activity card.
Represent the following integers using
the number line.
1. 3 units to the right of -1
2. 5 units to the right 1
3. 7 units to the left of 2
4. 12 units to the left of 7
I. Additional
activities for
application or
remediation
Represent the following integers using
the number line.
1. 10 units to the right -8
2. 6 units to the right of -10
3. 13 units to right of -6
home.
V. REMARKS
VI. REFLECTION

V. No. of
learners who
earned 80%
on the
formative
assessment
W. No. of
learners who
require
additional
activities for
remediation
X. Did the
remedial
lessons
work? No. of
learners who
have caught
up with the
lesson
Y. No. of
learners who
continue to
require
remediation
Z. Which of my
teaching
strategies
worked well?
Why did
these work?
AA.What
difficulties did
I encounter
which my
principal or
supervisor
can help me
solve?
BB.What
innovation or
localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Activity Cards on Number Line.

Teaching Dates and
Time Week 8 Day 2
Quarter SECOND
QUARTER
I. OBJECTIVES
situations.
C. Learning Competencies: Compares and arranges integers. (M6NS-IIh-154)
Objectives:
Cognitive:
 Compares and arranges integers. (M6NS-IIh-154)
Psychomotor:
 Write integers from greatest to least and vice versa
Affective:
 Appreciate the importance of having order in everyday life.
II. CONTENT: Comparing and arranging integers.
A. References
21st
 Activity cards, pictures, Number Line, & video presentation
(https://www.youtube.com/watch?v=Oq2KoAGrY64)
IV. PROCEDURES
A. Reviewing
previous lesson or
presenting the new
lesson
 Present a game named Arrange Me
game to the class an group the pupils
into 2 groups.
 Teacher distributes number cards from
0 to 20 make sure to include also the
the questions

negative integers, to each group. One
pupil one card.
who first assemble the numbers
 The group who assembles first wins
the game
 Discuss the value of teamwork
B. Establishing a
purpose for the
lesson
and the objectives/ target for learning
 Present a video about how to compare
an integer.
(https://www.youtube.com/watch?v=Oq2
KoAGrY64)
presentation.
 Teacher will review the previous
concepts about comparing numbers
positive integers.
positive integers
 Watch the video
C. Presenting
examples/instance
s of the new
lesson.
 Teacher discuss how to arrange the
integers correctly. From greatest to
least and vice versa.
D. Discussing new
concepts and
practicing new
skills #1
the class.
Let the pupils arrange the integers from
least to greatest & from greatest to
least.
a. -4, -8, -12 , 12, -10
b. -10, 0, -150, -149, 18
c. 8, 9, 15, -18, 20
activity
-4
15
-10
-8
-
13
0
6
9

E. Developing
mastery (leads to
Formative
Assessment
activity. This time prepare a number
cards with the following integers.
 Let each group assign a member to
hold.
-Group 1
+5, 6, 15, 25, 45, -2, -8, -10, -18
-Group 2
+50, -15, +18, -12, 50, 16, -8, 28, -29
Group 3
+160, -20, 75, +5, -25, 3, -50, -1
3 groups
given in groups.
applications of
concepts and skills
in daily living.
Rica was asked by his teacher to
arrange the number blocks on the
shelves she was determined to arrange
the numbers from least to greatest. The
numbers on the blocks are 37, -73, 83,
31, 13, -25, -17, -3, -1.
G. Making
generalizations
and abstractions
about the lesson
 How do we arrange integers?
- By basing it first on the number
line.
positive integers.
positive integers
question.
H. Evaluating
learning
Arrange the following integers from
least to greatest & greatest to least.
- Arrange the following Integers from
least to greatest.
1.) 25, -25, -16, 45, -15
2.) -14 4, 9, - 9, 150
3.) 49, 6, -5, 0, 17
4.) 9 -8 8, -32, -24
5.). 89, 73 17 23

- Arrange the integers from greatest
to least
1.) -3, -6, -4, -1, 5, 12, 10, -18, -45, 31
2. -60, 505, 13, -13, 18, 91, 3, -8, 6, -25
I. Additional
activities for
application or
remediation
 Answer page 150 letter B on the 21st
Century Mathletes.
home.
V. REMARKS
VI. REFLECTION
CC. No. of
learners who
earned 80%
on the
formative
assessment
DD. No. of
learners who
require
additional
activities for
remediation
EE.Did the
remedial
lessons
work? No. of
learners who
have caught
up with the
lesson
FF.No. of
learners who
continue to
require
remediation
GG. Which of
my teaching
strategies
worked well?
Why did
these work?
HH. What
difficulties did
I encounter
which my
principal or
supervisor
can help me
solve?

II. What
innovation or
localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Teaching Dates and
Time Week 8 Day 3
Quarter SECOND
QUARTER
I. OBJECTIVES
situations.
C. Learning Competencies: Describes and interprets the basic operations on integers
using materials such as algebra tiles, counters, chips, and cards. (M6NS-IIh-155)
Objectives:
Cognitive:
 Describes and interprets the basic operations on integers using
materials such as algebra tiles, counters, chips, and cards. (M6NS-IIh-
155)
Psychomotor:
 Add integers using algebra tiles, counters, chips, and cards.
Affective:
II. CONTENT: Describing and interprets the basic operations on integers using
materials such as algebra tiles, counters, chips, and cards.
A. References
21st
 Activity cards, algebra tiles counters, chips, and cards., Number
Line, & video presentation
(https://www.youtube.com/watch?v=eS3_xTshl-4)
(https://www.youtube.com/watch?v=pU2zPf846L4)
IV. PROCEDURES

A. Reviewing
previous lesson or
presenting the new
lesson
 Prepare some activity cards on
addition of numbers and subtraction of
numbers. (http://www.math-
aids.com/Mixed_Problems/)
the activity
B. Establishing a
purpose for the
lesson
 Present a Present a video about how
to add and subtract an integer.
(https://www.youtube.com/watch?v=pU2
zPf846L4
 Watch the video
C. Presenting
examples/instance
s of the new
lesson.
 Teacher discuss how add integers
using counters
- Discuss to the class on how to get
the sum of the two positive integers
and thus by putting together the
counters with the same colors.
- It produces two negative red tiles.
1+ 1=
2
-1 - (-1) = -
1
+2 + (+4) = 6

- Discuss to the class the zero pair
- Zero pair is a process which is to
eliminate the tiles with pair so the
answer is 3 since we pair the 2
negative counters with the 2
positive counters.
D. Discussing new
concepts and
practicing new
skills #1
the class.
Let the pupils add and subtract
integers using counters.
a. -8, + -4= b. -12 ,+ 12, =
c. -10, + 0 - d. 19,+ (-18) =
c. 8, + 9, =
activity
E. Developing
mastery (leads to
Formative
Assessment
activity. This time prepare a different
chips used as counters.
 Let each group draw a counters or
chips to represent the equation.
-Group 1
1.) +5 + 6 = ; 2.) 25 + (-25,) =
, 3.) -45,- -2= ; 4.) -18, + -10=
-Group 2
1.) +50 + (-15), 2.) +18,+ -12=
3.) 50 + 16= 4.) 38, + 29=
Group 3
1.) +16 + (-20) = 2.) -15, + (+5) =
3 groups
given in groups.
+5 + (-2) = +3

3. -5,+ (- 3), 4.) -5 + (-1) =
applications of
concepts and skills
in daily living.
Karen weighs 45 kilograms on April as
she weighs herself 2 weeks after loses
5 kilograms. Compute Karen’s weight
with the use of counters.
G. Making
generalizations
and abstractions
about the lesson
 How do we add integers?
- Observe the signs of the addends
and the sum
- If the addend have the same sign,
the numbers are added and the
common sign is affixed at the sum.
- If the addends have different signs,
the signs are first disregarded and
the difference between the number
is obtained.
- The sign of the greater number is
affixed to the answer.
question.
H. Evaluating
learning
Add the following integers by using the
counter chips provided by the teacher.
I. Additional
activities for
application or
remediation
 Draw a counter chips with the
following integers.
home.
V. REMARKS
(-20) + (+15) =
(-16) + (-1) =
(18) + (-8) =
(11) + (-4) =
(-5) + (-2) =
(35) + (-4) =
(28) + (-12) =

VI. REFLECTION
A. No. of
learners
who earned
80% on the
formative
assessment
B. No. of
learners who
require
additional
activities for
remediation
C. Did the
remedial
lessons
work? No. of
learners who
have caught
up with the
lesson
D. No. of
learners who
continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did
these work?
F. What
difficulties did
I encounter
which my
principal or
supervisor
can help me
solve?
G. What
innovation or
localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Teaching Dates and
Time Week 8 Day 4
Quarter SECOND
QUARTER
I. OBJECTIVES
situations.
Objectives:
Cognitive:
155)
Psychomotor:
 Subtract integers using algebra tiles, counters, chips, and cards.
Affective:
A. References
21st
(https://www.youtube.com/watch?v=eS3_xTshl-4)
(https://www.youtube.com/watch?v=pU2zPf846L4)
IV. PROCEDURES

A. Reviewing
previous lesson or
presenting the new
lesson
addition of integers.
(https://www.mathworksheets4kids.com/
adding-subtracting-integers.php)

( Note: Please see attached copy for
a visible picture)
the activity
B. Establishing a
purpose for the
lesson
to add and subtract an integer.
(https://www.youtube.com/watch?v=pU2
zPf846L4
 Watch the video
C. Presenting
examples/instance
s of the new
lesson.
 Teacher discuss how add integers
using chips
- Discuss to the class on how to get
the difference of the two positive
integers and thus by taking away 1
chips.
+4 –(+1)= +3
(-5) - (-2) = -3

D. Discussing new
concepts and
practicing new
skills #1
the class.
Let the pupils subtract integers using
counters.
a. ( -50,) - ( -14) = b. (-12) ,- (-12)=
c. (-19), - (-8) = d. (-11) - (-18) =
activity
E. Developing
mastery (leads to
Formative
Assessment
activity. This time prepare a different
chips used as counters.
( Note: Please see attached copy)
3 groups
given in groups.
applications of
concepts and skills
in daily living.
Rivera family bought 15 kilograms of
fish. They give away 8 kilograms of fish
to their neighbor. How many kilograms
of fish left for the family? Show your
answer by drawing chips.
G. Making
generalizations
and abstractions
about the lesson
 How do we subtract integers?
-
question.
H. Evaluating
learning
 Subtract the integers using chips as
representation.
I. Additional
activities for
application or
remediation
 Draw a counter chips with the
following integers.
home.

V. REMARKS
VI. REFLECTION
H. No. of
learners who
earned 80%
on the
formative
assessment
I. No. of
learners who
require
additional
activities for
remediation
J. Did the
remedial
lessons
work? No. of
learners who
have caught
up with the
lesson
K. No. of
learners who
continue to
require
remediation
L. Which of my
teaching
strategies
worked well?
Why did
these work?
M. What
difficulties did
I encounter
which my

principal or
supervisor
can help me
solve?
N. What
innovation or
localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Activity Cards on Reviewing previous lessons.

Activity Card on Subtracting Integers
Activity Sheet for Evaluating Learning Outcome
Activity Card 2

References:
Subtracting Integers Activity 1
https://www.google.com/search?tbm=isch&sa=1&ei=aUjmXOrXJIX2hwOo4pgCw
&q=subtraction+of+intergers+worksheet&oq=subtraction+of+intergers+workshee
t&gs_l=img.12...4401232.4410410..4412673...12.0..0.246.4757.0j6j17......1....1..
gws-wiz-img.JEcfFLeYSqQ#imgrc=wU3HxnPpLtxavM:
Subtracting Integers Activity 2

(https://www.google.com/search?tbm=isch&sa=1&ei=aUjmXOrXJIX2hwOo4pgC
w&q=subtraction+of+intergers+worksheet&oq=subtraction+of+intergers+workshe
et&gs_l=img.12...4401232.4410410..4412673...12.0..0.246.4757.0j6j17......1....1.
.gws-wiz-img.JEcfFLeYSqQ#imgrc=H8TFjo-W5Q-x0M:)

Teaching Dates and
Time Week 8 Day 5
Quarter SECOND
QUARTER
I. OBJECTIVES
situations.
Objectives:
Cognitive:
155)
Psychomotor:
 Multiply integers using algebra tiles, counters, chips, and cards.
Affective:
A. References
21st
(https://www.youtube.com/watch?v=RAb2PR4lKvY)
(https://www.youtube.com/watch?v=jcLUewqIRkM&pbjreload=10)
(https://www.youtube.com/watch?v=r9nzpGc8B7s)
IV. PROCEDURES

A. Reviewing
previous lesson or
presenting the new
lesson
subtraction of integers.
(https://www.mathworksheets4kids.com/
adding-subtracting-integers.php)


( Note: Please see attached copy for
a visible picture)
the activity
B. Establishing a
purpose for the
lesson
to multiply an integer.
(https://www.youtube.com/watch?v=RAb
2PR4lKvY)
(https://www.youtube.com/watch?v=jcLU
ewqIRkM&pbjreload=10)
 Watch the video
C. Presenting
examples/instance
s of the new
lesson.
 Teacher discuss how to multiply
integers using tiles
 Use two colors of tiles that represent
the two signs blue for negative and red
for positive.
 Multiplying two positive numbers
- Discuss to the class on how to
multiply the two positive integers
and thus by grouping each tiles.
- Multiplying 2 different signs
(+1) x (+4)= +
4 +3 One Group
only

 Discuss to the class that when you
multiply a positive number to a
negative number the answer will
always have negative sign.
D. Discussing new
concepts and
practicing new
skills #1
the class.
Let the pupils multiply integers using
tiles.
a. ( -5,) x ( -8) = b. (6) x (3)=
c. (-3) x (9) = d. (11) X (-18) =
activity
E. Developing
mastery (leads to
Formative
Assessment
activity using tiles.
3 groups
given in groups.
applications of
concepts and skills
in daily living.
A test has 20 questions. The test
awards 3 points if the answer is correct
and takes away 1 if the answer is
incorrect. Ana answered 5 correctly.
How many points will she received?
G. Making
generalizations
and abstractions
about the lesson
 How do we multiply integers?
-
question.
H. Evaluating
learning
 Multiply the integers using tiles as
representation.
(5) x (-2) = -
10
Five
Groups of
Two only

I. Additional
activities for
application or
remediation
 Draw a tiles with the following
integers.
home.
V. REMARKS
VI. REFLECTION
O. No. of
learners who
earned 80%
on the
formative
assessment
P. No. of
learners who
require
additional
activities for
remediation
Q. Did the
remedial
lessons
work? No. of
learners who
have caught

up with the
lesson
R. No. of
learners who
continue to
require
remediation
S. Which of my
teaching
strategies
worked well?
Why did
these work?
T. What
difficulties did
I encounter
which my
principal or
supervisor
can help me
solve?
U. What
innovation or
localized
materials did I
use/discover
which I wish
to share with
other
teachers?

Activity Cards on Reviewing previous lessons.
https://www.google.com/search?q=sample+activity+cards+on+subtracting+integers&tbm=isch&
source=iu&ictx=1&fir=n4x1jOqho0ui6M%253A%252CpRWpMJ-
fIpSwLM%252C_&vet=1&usg=AI4_-
kRf25DchkyGljuUlg8XT11nrJRoDA&sa=X&ved=2ahUKEwiEx-fE-sXjAhXac94KHT6yD-
AQ9QEwA3oECAkQDw&biw=1242&bih=597#imgrc=n4x1jOqho0ui6M:&vet=1

Activity Card on Multiplying Integers
https://www.k5learning.com/free-math-worksheets/sixth-grade-6/integers/integer-multiplication
Activity Sheet for Evaluating Learning Outcome
https://www.sopexamples.com/multiplying-integers-worksheet/

School Grade Level VI
Teaching Dates
and Time
Week 9, Day 1 Quarter 2ND
I. OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of order of operations, ratio and
proportion, percent, exponents, and integers.
B. Performance
Standards
proportion, percent, exponents, and integers in mathematical problems
C. Learning
Competencies /
Objectives
Performs the basic operations on integers.
(M6NS-IIi-156)
1. Perform addition on integers.
2. Use algebra tiles in adding integers.
II. CONTENT Performing Addition on Integers
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pages
Mathematics CG for Grade 6, p.196
2. Learner’s
Materials pages
21st
Century Mathletes 6, pp 152-157
4. Additional
Materials from
Learning
Resource (LR)
Portal
none
B. Other Learning
Resources
Mathletes 6 textbook, power point presentation, flash cards, answer
sheets, algebra tiles, number line
A. Reviewing
previous lesson
or presenting
the new lesson
Drill:
Flash some cards having pair of
integers.
Ask: Which of the two integers in
each pair has a greater distance
from zero?
1. +5 & -4
2. -2 & -9
3. -10 & -6
4. +7 & -3
5. -12 & + 1
6. +6 & -4
7. -8 & +5
8. -2 & +3
Pupils will give the answer orally.
Possible answers:
1. +5
2. -9
3. -10
4. +7
5. -12
6. +6
7. -8
8. +3

B. Establishing a
purpose for the
lesson
Present the problem.
Aling Maria bought fruits which
cost ₱500 from a wholesaler and
sold them in her fruit stand. On
Monday, her sales was ₱600; and
on Tuesday, ₱300. But on
Wednesday, she lost ₱200
because some of the fruits were
already rotten. Considering the
sales from Monday to Wednesday,
did Aling Maria gain or lose?
Pupils will read and analyze the
problem carefully.
C. Presenting
Examples/
Instances of the
new lesson
Discuss the answer to the problem
by asking comprehension
questions:
Ask:
1. How much was her total sales
from Monday to Wednesday? (ask
a volunteer to solve on the board)
2. How much was her capital?
To know whether Aling Maria
gained or lost, we have to compare
her total sales from Monday to
Wednesday with her capital.
Ask: Did Aling Maria gain or lose?
Pupils will listen attentively to the
discussion and answer the given
questions.
1. (600)+(300)+(-200)=700
2. Her capital was ₱500.
Answer: She gained ₱200.
D. Discussing new
concepts and
practicing new
skills #1
Say: Addition is the same as
“combining”. How do we combine
integers?
Use a number line to help visualize
the addition of integers.
 Add a positive integer by
moving to the right on the
number line.
 Add a negative integer by
moving to the left on the
number line.
Example:
1. 4+3=
Start from 4 and move 3 units to
the right.
Pupils will observe and practice
adding integers using the number
line.

Therefore, 4+3=7
2. (-4)+2=
Start from -4 and move 2 units
to the right.
Thus, (-4)+2=-2
3. (-5)+(-2)=
Start from -5 and move 2 units
to the left.
So, (-5)+(-2)=-7
4. 5+(-7)=
5. (-2)+(-3)
Answer:
4. 5+(-7)= -2
5. (-2)+8= 6
E. Discussing new
concepts and
practicing new
skills #2
Demonstrate adding positive and
negative integers using counters.
Say: We can use positive and
negative counters to model the
addition of integers.
positive negative
What will happen if we put together
1 black tile and another black tile?
Now, how about if we put together
1 white tile and another white tile?
This will produce two black tiles.
=2
This will produce two white tiles
= -2

What will happen if we put together
1 black tile and 1 white tile?
A positive integer paired with a
negative integer form a “zero pair”.
They cancel each other. A zero pair
has a sum of “0”.
Example:
1. Show the sum of +2 and +4
using tiles.
(Let the pupils manipulate the tiles
to show the answer.)
2. Show the sum of +5 and -2 using
tiles.
3. Show the sum of -1 and -3 using
tiles.
4. Show the sum of -4 and +2 using
tiles.
Do you notice a pattern or rule?
- When the signs are the same,
add the numbers together and
keep the sign.
- When the signs are different,
subtract the integers and keep the
sign of the larger digit.
= 0
1.
. = +6
2.
= +3
3
.
= -4
4.
= -2
F. Developing
mastery (Leads
to Formative
Assessment 3)
Group Activity
Divide the class into three groups
and have them add the following
integers:
Members of the group will help
each other in doing the activity.
Group 1 will answer using algebra
tiles.

1) -8 + 8 =
2) -9 + -11 =
3) 13 + (-9) =
4) 7 + 5 =
5) -12 + 10 =
6) -22 + (-16) =
7) 18 + (-5) =
8) -1 + 6 =
9) 0 + (-8) =
10) 4 + 5 =
Group 2 will use the number line in
adding the integers.
Group 3 will add the integers using
the rules.
applications of
concepts and
skills in daily
living
Fish bowl Activity.
The teacher will play a music. As
the music starts, the teacher will
pass a ball to a pupil who will then
pass the ball to the pupil next to
him/her. When the music stops, the
one holding the ball will pick a
paper inside the fish bowl and give
the sum of the integers written on
it.
Pupils will pass the ball to the pupil
next to him. When the music stops,
the one holding the ball will pick a
paper inside the fish bowl and give
the sum of the integers written in it.
H. Making
generalizations
and abstractions
about the lesson
Ask: How do we add integers with
like sign? Unlike sign?
To add integers with like signs, add
the numbers together and keep the
sign.
To add integers with different signs,
subtract the integers and keep the
sign of the larger integer.
I. Evaluating
Learning
The teacher will give a test.
Add the following integers.
1) 8 + 7 =
2) 9 + (-10) =
3) (-3) + (-19) =
4) -2 + 29 =
5) -8 + 3 =
6) -12 + (-30) =
7) -54 + 20 =
8) 6 + (-2) + (-10) =
9) 18 + (-18) =
10) 4 + (-15) =
Pupils will answer individually.
Answers:
1) 8 + 7 = 15
2) 9 + (-10) = -1
3) (-3) + (-19) = -22
4) -2 + 29 = 27
5) -8 + 3 = -5
6) -12 + (-30) = -42
7) 54 + -20 = 34
8) 6+(-2)+(-10) = -6
9) 18 + (-18) = 0
10) 4 + (-15) = -11
J. Additional
activities for
application or
remediation
If the temperature was -7 degrees
(Fahrenheit) at 6 AM, rose 4
degrees by 7 AM and then rose
another 8 degrees by 8 AM, what
was the temperature at 8 AM?
Answer: 5O
F

V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80%
on the formative
assessment
B. No. of learners
who require
additional
activities for
remediation
C. Did the remedial
lessons work?
No. of learners
who have
caught up with
the lesson
D. No. of learners
who continue to
require
remediation
E. Which of my
teaching
strategies
worked well?
Why did these
work?
did I
encountered
which my
principal or
supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover
which I wish to
share with other
teachers?

Teacher
Learning
Area
MATHEMATICS
Teaching Dates
and Time
I. OBJECTIVES
D. Content Standards
The learner demonstrates understanding of order of
operations, ratio and proportion, percent, exponents, and
integers.
E. Performance
Standards
The learner is able to apply knowledge of order of
integers in mathematical problems and real-life situations.
F. Learning
Competencies /
Objectives
(M6NS-IIi-156)
3. Perform subtraction on integers.
4. Use algebra tiles as aid in subtracting integers.
5. Show cooperation in group activity.
II. CONTENT Performing Subtraction on Integers
III. LEARNING
RESOURCES
C. References
pages
Curriculum Guide in Mathematics 6, p.196
6. Learner’s Materials
pages
21st
Century Mathletes 6, pp158-165
8. Additional
Materials from
Learning Resource
(LR) Portal
none
D. Other Learning
Resources
Mathletes 6 textbook, video clip, power point
presentation, answer sheet
K. Reviewing previous
lesson or
presenting the new
lesson
Drill:
Give the opposite of each given
integers.
1. +50
2. +12
3. +42
4. -120
5. -29
Review:
How do we add integers with
like signs? Unlike signs?
Pupils will give the
answer orally.
1. -50
2. -12
3. -42
4. +120
5. +29
To add integers with
like signs, add the
numbers together and
keep the sign.

To add integers with
different signs, subtract
the integers and keep
the sign of the larger
integer.
L. Establishing a
purpose for the
lesson
The teacher will tell a situation.
The temperature in Malaybalay
City is 24O
C in the morning. It
dropped to 19O
C in the
evening. What is the difference
between these temperatures?
Pupils will listen
attentively and will
answer the question
raised by the teacher.
M. Presenting
Examples/Instances
of the new lesson
Discuss the answer to the
problem using the 3 Steps to
subtract integers:
1.Keep
Keep the 1st
number
2.Change
Subtraction sign to Addition
3.Opposite
Write down the opposite of the
2nd
number
-Then add the way you
normally do.
Subtracting integers is adding
the opposite of subtrahend to
the minuend. In this case, the
opposite of +19 is -19. We add
-19 to +24, giving us +5.
Therefore, Malaybalay City’s
temperatures between morning
and evening differ by 5O
C.
Give other examples for pupils
to solve following the above
steps.
Pupils will listen
attentively to the
teacher’s discussion.
N. Discussing new
concepts and
practicing new
skills #1
Show a video clip on how to
subtract integers.
Pupils will watch the
video.
O. Discussing new
concepts and
practicing new
skills #2
Demonstrate another example
of subtraction of integers using
algebra tiles.
Example:
Pupils will perform the
steps in subtracting
integers using algebra
tiles.

1. (+5) – (+2) = ____
Place 5 black tiles on the table.
Take away 2 black tiles.
= +3
Since there are 3 black tiles,
the difference is +3. Thus, (+5)
- (+2) = 3.
2. (-4) – (-3) = ____
Place 4 white tiles on the table.
Take away 3 white tiles.
= -1
Since there is 1 white tile left,
the difference is -1. Thus, (-4) -
(-3) = -1.
3. (-4) – (+1) = ____
Place 4 white tiles on the table.
Take away 1 black tile.
Since we cannot take away 1
black tile from 4 white tiles,
then we must add 1 zero pair.
+
Remove 1 black tile, there
remains 5 white tiles.
Therefore, the difference is -5.
4. +3 – (-5) = ____
Place 3 black tiles on the table.
Take away 5 white tiles.
Since we cannot take away 5
white tiles from 3 black tiles, we
have to add 5 zero pairs
without changing the value of
= 3
= -1
+
= -5

the set. Then, remove 5 white
tiles.
+
The difference is +8.
+3 – (-5) = 8
P. Developing mastery
(Leads to Formative
Assessment 3)
Group Activity:
The teacher will divide the class
into groups of 5 members.
Each group will be given an
activity card to answer. After
five minutes, they are going to
exchange their activity cards for
checking. The group with the
most number of correct
answers will be the winner.
Pupils will answer the
activity by group.
1. (-17)-(-19)-21= -19
2. -13-15-(-18)= -10
3. 45 – (-10) = 55
4. -15 – 6= -21
5. 38 – 9 = 29
Q. Finding practical
applications of
concepts and skills
in daily living
Practice by Pair:
Subtract the following integers.
1. -7 – 15 =
2. 23 – 98 =
3. 48 - 13 =
4. 5 – (- 6) =
5. 17 – 8 =
Each pair will answer
the given activity.
1. -7 – 15 = -22
2. 23 – 98 = -75
3. 48 - 13 = 35
4. 5 – (-6) = 11
5. 17 – 8 = 11
R. Making
generalizations and
abstractions about
the lesson
How do we subtract integers?
(Subtraction of integers
means adding the
minuend and the
opposite of the
subtrahend.) or
Subtract Integers
1.Keep
Keep the 1st
number
2.Change
Subtraction sign to
Addition
3.Opposite
Write down the
opposite of the 2nd
number
-Then add the way we
normally do.
S. Evaluating Learning The teacher will give a test.
Subtract the following integers.
1) 13 - 4 =
Pupils will answer the
test individually.
Answers:

2) -7 - 4 =
3) 12 - (-17) =
4) 12 - 17 =
5) -9 – (-1) =
6) 6 - 9 =
7) -14 - 5 =
8) 6 - 5 – 2 =
9) (-18) - 0 =
10) 13 - 3 =
1) 13 - 4 = 9
2) -7 - 4 = -11
3) 12 - (-17) = 29
4) 12 - 17 = -5
5) -9 – (-1) = -8
6) 6 - 9 = -3
7) -14 - 5 = -19
8) 6 - 5 – 2 = -1
9) (-18) - 0 = -18
10) 13 - 3 = 10
T. Additional activities
for application or
remediation
Answer the following.
1. Subtract 6 from -15.
2. 8 + (-2) – 9 – (-7) = ___.
Answers:
1. -22
2. 4
V. REMARKS
VI. REFLECTION
H. No. of learners who
earned 80% on the
formative
assessment
I. No. of learners who
require additional
activities for
remediation
J. Did the remedial
lessons work? No.
of learners who
have caught up with
the lesson
K. No. of learners who
continue to require
remediation
L. Which of my
teaching strategies
worked well? Why
did these work?
M. What difficulties did
I encountered which
my principal or
supervisor can help
me solve?
N. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?

Teaching Dates
and Time
I. OBJECTIVES
G. Content
Standards
integers.
H. Performance
Standards
The learner is able to apply knowledge of order of
integers in mathematical problems and real-life situations.
I. Learning
Competencies /
Objectives
(M6NS-IIi-156)
1. Perform multiplication on integers.
2. Use algebra tiles in multiplying integers.
3. Show awareness of the importance of reducing
waste in the community.
II. CONTENT Performing Multiplication on Integers
III. LEARNING
RESOURCES
E. References
pages
10. Learner’s
Materials pages
21st
Century Mathletes 6, pp. 166-168
Century Mathletes 6, pp. 166-168
12. Additional
Materials from
Learning
Resource (LR)
Portal
none
F. Other Learning
Resources
Mathletes 6 textbook, video clip, power point presentation,
activity sheets, algebra tiles
U. Reviewing
previous lesson
or presenting the
new lesson
Review: (Board work)
The teacher will call pupils to
write the answer of the
following.
1. 18- 7 = ___
2. -26-12 = ____
3. 35- (-8) = ____
4. 20- (-20) = ____
5. -25-(-25) = ____
Pupils will write the
answer in each number.
1. 18- 7 = 11
2. -26-12 = -38
3. 35- (-8) = 43
4. 20- (-20) = 40
5. -25-(-25) = 0

V. Establishing a
purpose for the
lesson
Present the situation below.
After a campaign on reducing
waste, the amount of garbage
on Jane’s household
decreased by 2 kilograms per
day. By how much will their
garbage decrease after 6
days?
Since Jane’s household had a
decrease of 2 kg in their
garbage, we can represent it
with -2. Such decrease
happened for 6 days, so we
can have:
-2 x 6 = n
Multiplying integers is like
multiplying whole numbers.
We just need to be careful of
the sign we use in the product.
The product of two integers
with different signs is negative.
So, -2 x 6 = -12.
Why is it important to reduce
waste in our community? How
can you help in reducing waste
at home?
Pupils will read and
answer the problem.
Answer:
Jane’s garbage will have
a decrease of 12
kilograms.
W. Presenting
Examples/Instan
ces of the new
lesson
Present the rules in multiplying
integers using power point
presentation.
Say: There are rules that we
need to remember in
multiplying integers:
Rule 1:
Positive x Positive =
POSITIVE
Example:
1. 3 x 6 = 18
2. 5 x 2 = 10
Rule 2:
Negative x Negative =
POSITIVE
Example:
1. -2 x -3 = 6
2. -1 x -25 = 25
Rule 3:
Negative x Positive =
NEGATIVE
Pupils will listen
carefully to the
discussion.

Example:
1. -2 x 6 = -12
2. 3 x -5 = -15
Rule 4:
Any Number x 0 = ZERO
Example:
1. -5 x 0 = 0
2. 0 x 7 = 0
X. Discussing new
concepts and
practicing new
skills #1
Say:
To further understand our
lesson, let us watch a video on
how to multiply integers.
Pupils will watch the
video.
Y. Discussing new
concepts and
practicing new
skills #2
We can also multiply integers
using algebra tiles.
Black tiles represent positive
integers while white tiles
represent the negative
integers.
Example:
1. Find the product of (+3) and
(+4)
Place 4 rows of 3 black tiles
on the table.
Since there are 12 black tiles,
the product is 12. Thus, (+3) x
(+4) = 12.
2. Multiply (+4) by (-3).
Place 3 rows of 4 black tiles
on the table.
Going back to the given, the
other factor is negative, which
means all the tiles in 3 rows
should be flipped over.
Pupils will listen to the
teacher and multiply
tiles.
= 12
= -12

Since there are 12 white tiles,
the product is -12. Thus, (+4) x
(-3) = -12
Z. Developing
mastery (Leads to
Formative
Assessment 3)
Group Activity: Quiz bee
The teacher will divide the
class into 5 groups. Each
group will be given a show-me-
board. Then, they will choose
a leader.
Mechanics:
a. The teacher will flash
integers through power point
slides.
b. Pupils will be given 10
seconds to solve for the
product of the given integers.
c. The leader will write the
product on the show-me-
board.
d. When the time is over, the
teacher will ring the bell and
each group will raise their
show-me-board.
e. The teacher will check the
answers.
f. The group having the most
number of correct answers will
be the winner.
Pupils will go with their
group and choose their
leader.
Answers:
1) 6 x 7 = 42
2) -8 x - 3 = 24
3) 5 x (-3) = -15
4) -12 x 4 = -48
5) -9 x (-2) x (-3) = -54
AA. Finding
practical
applications of
concepts and
skills in daily
living
Pair-share:
Say: Find a pair most
preferably your seatmate.
Then, share your ideas in
finding the product of the
integers.
-2x3=___
-2 x -3 = ___
6x8=___
-7x4=____
7x (-4)=____
2x(-6)=____
Pupils will look for a
pair. They will share
their ideas regarding the
activity given by the
teacher.
-2x3= -6
-2 x -3 = 6
6x8= 48
-7x4= -28
7x (-4)= -28
2x(-6)= -12
BB. Making
generalizations
and abstractions
about the lesson
How do we multiply integers?
 We multiply integers
just like whole
numbers.

 If two integers have
like signs, their
product is positive.
 If two integers have
unlike signs, their
product is negative.
CC. Evaluating
Learning
Multiply the following.
1) (-3) x 8 =
2) -5 x (- 2) =
3) 0 x (-17) =
4) 10 x (-5) =
5) 8 x (-5) x (-2) =
6) (-42) x (-2) =
7) (-9) x (-2) x (-1) =
8) 6 x 2 =
9) (-18) x 1 =
10) -13 x 0 =
Answer:
1) (-3) x 8 = -24
2) -5 x (- 2) = 10
3) 0 x (-17) = 0
4) 10 x (-5) = -50
5) 8 x (-5) x (-2) = 80
6) (-42) x (-2) = 84
7) (-9) x (-2) x (-1) = -18
8) 6 x 2 = 12
9) (-18) x 1 = -18
10) -13 x 0 = 0
DD. Additional
activities for
application or
remediation
Mother went to the market to
buy some fruits and
vegetables. She bought 5
apples at ₱30.00 each and 3
cabbages at ₱10.00 each. She
gave the vendor a 500-peso
bill. How much change did she
get?
Answer: ₱320.00
V. REMARKS
VI. REFLECTION
O. No. of learners
who earned 80%
on the formative
assessment
P. No. of learners
who require
additional
activities for
remediation
Q. Did the remedial
lessons work?
No. of learners
who have caught
up with the
lesson
R. No. of learners
who continue to
require
remediation
S. Which of my
teaching
strategies
worked well?

Why did these
work?
T. What difficulties
did I
encountered
which my
principal or
supervisor can
help me solve?
U. What innovation
or localized
materials did I
use/discover
which I wish to
share with other
teachers?

School
Grade
Level
VI
Teacher
Learning
Area
MATHEMATICS
Teaching Dates
and Time
I. OBJECTIVES
integers.
B. Performance
Standards
The learner is able to apply knowledge of order of operations,
ratio and proportion, percent, exponents, and integers in
C. Competencies /
Objectives
(M6NS-IIi-156)
1. Perform division on integers.
2. Use algebra tiles as aid in division of integers.
II. CONTENT Performing Division on Integers
References
Teacher’s Guide pages Learning Curriculum Guide in Mathematics 6, p.196
Learner’s Materials
pages
21st
Textbook pages 21st
Additional Materials
from Learning Resource (LR)
Portal
none
Other Learning
Resources
Mathletes 6 textbook, power point presentation, algebra tiles,
answer sheets
A. Reviewing previous
lesson or presenting
the new lesson
Have a quick review
on multiplying integers
through flash cards.
1. 5 x (-6)
2. -10 x 9
3. -7 x (-5)
4. -4 x 0
5. -6 x (-6)
Pupils will give the answers orally.
1. 5 x (-6) = -30
2. -10 x 9 = -90
3. -7 x (-5) = 35
4. -4 x 0 = 0
5. -6 x (-6) = 36
B. Establishing a purpose
for the lesson
Present the problem
below.
During summer
vacation, Alfred works
as janitor in a
restaurant. He earns
₱450 per week. If he
works for 5 days every
Answer: Alfred earns ₱90 per day.
450 5 = 90

week, how much does
he earn daily?
C. Presenting
Examples/Instances of
the new lesson
Present the rules in
dividing integers.
Say: Dividing integers
is the same as dividing
whole numbers. We
just need to be careful
of the sign we use in
the quotient.
When dividing
integers, we need to
remember that the
quotient of two
integers with like sign
is always POSITIVE.
Example:
1. (+10) ÷ (+2) = (+5)
2. (-6) ÷ (-3) = (+2)
On the other hand, if
the signs are different
the quotient is a
NEGATIVE integer.
Example:
1. (+10) ÷ (-5) = -2
2. -20 ÷ 4 = -5
Pupils will listen attentively to the
teacher’s discussion.
D. Discussing new concepts
and practicing new skills
#1
Board work:
Give more examples
on dividing integers
using the rules.
Call on pupil
volunteers to solve on
the board and explain
their answer to the
class.
Pupils will solve on the board and
explain their answer.
1. 28 ÷ 2 = 14
The answer is +14 since 28 and 2
have the same sign.
2. -75 ÷ 5 = -15
The quotient is -15 sine 75 and 5
have different signs.
3. 36 ÷ (-3) = -12
The answer is -12 since 36 and
3 have unlike signs.
E. Discussing new concepts
and practicing new skills
#2
Discuss another
method of dividing
tiles.
Example:

1. Divide: (+6) ÷ (+2)
From the 6 black
tiles, make 2 groups
with equal number of
tiles.
There are 3 black
tiles in each group.
Therefore, (+6) ÷ (+2)
= (+3) or simply 3.
2. Divide: (-6) ÷ (+2)
From the 6 white
tiles, make 2 groups
with equal number of
tiles.
There are 3 white
Therefore, (-6) ÷ (+2) =
-3.
3. Divide: (+6) ÷ (-2)
Note: Negative divisor
means take the
opposite of or flip over.
Therefore, from the 6
black tiles, make 2
groups with equal
number of WHITE
tiles.
There are 3 white
Therefore, (+6) ÷ (-2) =
(-3).
4. Divide: (-6) ÷ (-2)
Note: Negative divisor
means take the
opposite of or flip over.
Therefore, from the 6
white tiles, make 2
groups with equal
number of BLACK
tiles.
There are 3 black
Therefore, (-6) ÷ (-2) =
(+3) or simply 3.
Flip over
Flip over
Answer:
1. (-36) ÷ 9 = -4
2. 56 ÷ (-4) = -14

Additional examples:
1. (-36) ÷ 9 =
2. 56 ÷ (-4) =
F. Developing mastery
(Leads to Formative
Assessment 3)
Group Activity:
The class will be
divided into 5 groups.
The teacher will give
each group an activity
card.
Find the quotient of the
following.
1. (-56) ÷ 8 =
2. 120 ÷ (-8) =
3. 144 ÷ 6 =
4. -124÷ 4 =
5. (-48) ÷ (-4) =
Each member of the group will help
each other in answering the activity.
Answer:
1. -7
2. -15
3. 24
4. -31
5. 12
applications of concepts
and skills in daily living
Try this with your
seatmate:
54  6 =
-54  6 =
54  -6 =
-54  -6 =
-12  -4 =
Pupil will answer.
54  6 = 9
-54  6 = -9
54  -6 = -9
-54  -6 = 9
-12  -4 = 3
H. Making generalizations
and abstractions about
the lesson
How do we divide
integers?
 Dividing integers is the same as
dividing whole numbers.
 The quotient of two integers with
like sign is a positive integer.
 The quotient of two integers with
different signs is a negative
integer.
I. Evaluating Learning The teacher will give a
test.
Divide the following.
1. (-28) ÷ (-7) =
2. 45 ÷ (-5) =
3. (-75) ÷ (-5) =
4. -30 ÷ 5 =
5. 250 ÷ (-50) =
Pupils will answer individually.
Answers:
1. (-28) ÷ (-7) = 4
2. 45 ÷ (-5) = -9
3. 75 ÷ 5 = 15
4. -30 ÷ 5 = -6
5. 250 ÷ (-50) = -5
J. Additional activities for
application or remediation
Find the quotient.
1. (-144) ÷ 2 =
2. 56 ÷ (-2) =
Answer:
1. -72
2. -28
V. REMARKS

VI. REFLECTION
A. No. of learners who
earned 80% on the
formative assessment
B. No. of learners who
require additional
activities for remediation
C. Did the remedial lessons
work? No. of learners who
have caught up with the
lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did these work?
F. What difficulties did I
encountered which my
principal or supervisor
can help me solve?
G. What innovation or
localized materials did I
use/discover which I wish
to share with other
teachers?

Teaching Dates
and Time
I. OBJECTIVES
H. Content
Standards
I. Performance
Standards
J. Learning
Competencies /
Objectives
(M6NS-IIi-156)
1. Answer the summative test.
II. CONTENT Answering the Summative Test
III. LEARNING
RESOURCES
G. References
451 Teacher’s
Guide pages
Mathematics CG for Grade 6, p.196
452 Learner’s
Materials pages
21st
453 Textbook
pages
21st
H. Other Learning
Resources
Test paper
K. Reviewing
previous lesson
Have a quick review on the
rules in adding, subtracting,
multiplying and dividing
integers.
Pupils will participate actively in the
review.
L. Setting of
Standards Ask: What are the things
that you need to do in
answering a test.
Possible answers:
1. Follow the directions.
2. Answer silently.
3. Cover your test paper.
4. Don’t talk with seatmates.
5. Don’t cheat.
6. If you’re done, review your answers.
M. Giving of
Instructions and
Distribution of
Test Papers
Read the instructions in
answering the test.
N. Test Proper Supervise the pupils in
answering the summative
test.
Perform the indicated
operation.
Pupils will answer the given test.

1) 9 + (-17) =
2) -2 + 29 + (-16) =
3) (-3) + (-15) =
4) -8 - 5 =
5) 54 - (-20) =
6) -12 x 5 =
7) 6 x (-2) x (-10) =
8) 25 x 12 =
9) 48 ÷ (-3) =
10) -24 ÷ (-2) =
O. Checking of Test
Papers and
Recording of
Scores
answers on the board and
record the scores of pupils.
P. Additional
activities for
remediation
Answer the following:
1) 29 + (-7) =
2) -2 - (-16) =
3) (-3) x (-15) =
4) -48 ÷ 2 =
Answer:
1) 22
2) 14
3) 45
4) -24
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80%
on the formative
assessment
B. No. of learners
who require
additional
activities for
remediation

Teacher
Learning
Area
MATHEMATICS
Teaching Dates and
Time
I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies /
Objectives
Solves routine and non-routine problems involving addition of integers
using appropriate strategies and tools. (M6NS-IIj-157)
II. CONTENT
Solving Routine and Non-routine Problems Involving Addition of
Integers
III. LEARNING
RESOURCES
A. References
Teacher’s Guide
pages
Learner’s
Materials pages
21st
Textbook pages 21st
Additional
Materials from
Learning
Resource (LR)
Portal
none
B. Other Learning
Resources
Mathletes 6 textbook, power point presentation, activity cards
A. Reviewing
previous
lesson or
presenting the
new lesson
Drill: Integers Word Clue!
Teacher will flash cards with a word
which represents either a positive or
negative integer.
When the teacher flashes the
word, pupils will raise the happy
face if the word represents a
positive integer or sad face if it
represents a negative integer.
Answer:
(+) Integers
1. earned
2. saved
3. deposit
4. gained
5. rose
6. increase
7. above
8. ascend
9. profit
10. up
(-) Integers
1. spent
2. cost
3. withdraw
4. lost
5. fell
6. decrease
7. below
8. descend
9. loss
10. down

Call a pupil to perform the indicated
operation.
(+10) + (-9)
(-25) + (+5)
(-80) + (+6)
(-120) + (+20)
(35) + (-20)
(+10) + (-9) = 1
(-25) + (+5) = -20
(-80) + (+6) = -74
(-120)+(+20)= -100
(35) + (-20) = 15
B. Establishing a
purpose for
the lesson
Present the problem to the class.
Problem:
A messenger forgot on what floor in
a building he would deliver his
package. With no one to ask for
directions, he rode the elevator up to
the 10th
floor. Then he went down 5
floors and went up again 4 floors.
Still, he could not find the right floor.
So he went up again 3 floors and
decided to stop for a while. On what
floor did the messenger stop?
Pupils will read the given
problem.
C. Presenting
Examples/Instanc
es of the new
lesson
Use the 4-step plan to solve the
problem.
1. Understand
-What is asked?
-What are given?
2. Plan
-What strategy will you use to
solve the problem?
3. Solve
-Solve the problem using the
strategy.
4. Check
-Check if the answer is correct.
Pupils will analyze and answer
the problem following the steps.
1. a. It asked for the floor where
the messenger stopped.
b. First stop: 10th
floor
down 5 floors
up 4 floors
up 3 floors
2. Use a number line 3. Using
the number line, start at 0 as the
starting point. On the first ride,
the elevator went up to 10th
floor.
So from 10, he went down 5
floors, up again 4 floors, and
went up again 3 floors.
Therefore, the messenger
stopped at 12th
floor
4.Check
10-5+4+3=12
12=12
Thus, the answer is correct.
D. Discussing new
concepts and
Present another problem and guide
the pupils in answering it using the 4-
step plan.
Pupils will answer the problem
using the 4-step plan.

practicing new
skills #1 Problem:
A car is located 40 km north of
Malaybalay City. If it travelled 35km
north then 45 km south, how far from
Malaybalay City was the car at the
end of its travel?
Answer:
40+35-45=30
Thus, the car is located 30 km
north of Malaybalay City.
E. Discussing new
concepts and
practicing new
skills #2
Pair-share:
Answer the problem by pair.
Mrs. Santos lost 3 kg when she was
ill. After recovering, she gained 7 kg.
She went to a fitness center and lost
2 kg. How much did she finally lose
or gain?
Solution:
She lost 3 kg means -3.
She gained 7 kg means +7.
She lost again 2 kg means -2.
Equation:
(-3)+(7)+(-2)=2
Therefore, she gained 2 kg.
F. Developing
mastery (Leads to
Formative
Assessment 3)
Group Activity: Use the 4-step plan
to solve the problem.
1. Divide the class into 4 groups.
2. Give each group an activity card,
marker, and manila paper where
they will write their solution.
3. Pupils are given 10 minutes to do
the activity.
4. When the time is up, each group
will post their output on the board for
checking.
Group 1 and 3
Problem:
In the first half of a trivia game,
Kenneth scored 500 points.
Then, during the second half, he
lost 200 points. What was his
total score?
Solution:
500 + (-200) = 300
Group 2 and 4
Problem:
Simon spent Php1,000 on a
fancy watch and deposited a
Php3,000 paycheck. How much
is the change that Simon had?
Solution:
-
1,000 + 3,000 = 2,000
Simon had Php2,000 more.
applications of
concepts and
skills in daily
living
Use the 4-step plan to solve the
problem.
1. On the first play, the football team
lost 6 yards. On the second play, the
team lost 5 yards. What was their
total change in yards?
Answer:
(-6)+(-5)=(-11)
The team lost 11 yards.
H. Making
generalizations
How do you solve routine and non-
routine problems involving addition of
To solve routine and non-routine
problems involving addition of
integers, we use the 4-step plan:

and abstractions
about the lesson
integers using appropriate strategies
and tools?
1. Understand-Know what is
asked and given.
2. Plan what strategy to use.
3. Solve using the strategy.
4. Check if the answer is
correct.
I. Evaluating
Learning
Solve each problem:
1. Gio walked 5 steps forward, 8
steps backward, 9 steps forward and
3 steps backward. How many steps
is Gio from where he started?
2. A submarine was situated 800 feet
below sea level. If it ascends 250
feet, what is its new position?
Answer:
1.(5)+(-8)+(9)+(-3)=3
Gio is 3 steps from where he
started.
2. (-800)+(250)=-550
The submarine is situated 550
feet below sea level.
J. Additional
activities for
application or
remediation
Give 10 pairs of integers whose
product is greater than zero and
whose sum is less than 50.
Answers may vary.
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned
80% on the
formative
assessment
B. No. of learners
who require
additional
activities for
remediation
C. Did the remedial
lessons work?
No. of learners
who have caught
up with the lesson
D. No. of learners
who continue to
require
remediation
E. Which of my
teaching
strategies worked
well? Why did
these work?
did I encountered

which my
principal or
supervisor can
help me solve?
G. What innovation
or localized
materials did I
use/discover
which I wish to
share with other
teachers?

Teacher
Learning
Area
MATHEMATICS
Teaching Dates
and Time
I. OBJECTIVES
The learner demonstrates understanding of order of operations,
ratio and proportion, percent, exponents, and integers.
and proportion, percent, exponents, and integers in mathematical
C. Learning Competencies
/ Objectives
Solves routine and non-routine problems involving subtraction of
integers using appropriate strategies and tools.
M6NS-IIj-157
II. CONTENT
Solving Routine and Non-routine Problems Involving Subtraction
of Integers
III. LEARNING
RESOURCES
A. References
Teacher’s Guide
pages
Learner’s Materials
pages
21st
Textbook pages 21st
Additional Materials
from Learning Resource
(LR) Portal none
B. Other Learning
Resources
Mathletes 6 textbook, power point presentation
A. Reviewing previous
lesson or
presenting the new
lesson
Drill:
Give the opposite of
each integer.
+25
-57
-100
-82
75
Perform the indicated
operation.
(+20) - (-19)
(-35) - (+5)
(-60) - (-29)
(-45) - (+30)
(55) - (-26)
Answers:
-25
+57
+100
+82
-75
Answer:
+39
-40
-31
-75
+81
B. Establishing a purpose
for the lesson
Present the problem. Pupils will read and analyze the
problem.

The temperature in
Baguio City was 12°
Celsius in the morning.
It dropped to 8° Celsius
in the evening. What is
the difference between
these temperatures?
C. Presenting
Examples/Instances
of the new lesson
Ask the following
questions.
1. What is asked?
2. What is the equation
representing this
situation?
3. What is the difference
between the
temperature of Baguio in
the morning and
evening?
To get the difference
between the two
temperatures, we need
to subtract 8° from 12°.
Answer:
12°- 8° = 4°
D. Discussing new
concepts and
practicing new skills #1
Present another
problem.
During summer, James
weighed 65 kg. When
he came back to school,
he realized that he lost 3
kg. He lost another 2 kg
in December. What was
his weight in December?
1. What is asked?
2. What are given?
3. What is the equation
representing the
situation?
4. What is the final
answer?
Answer:
1. What was his weight in
December?
2. 65 kg, 3kg, 2kg
3. 65-3-2=n
4. 65-3-2=n
=65+(-3)+(-2) [rule in subtracting
integer]
=60kg
E. Discussing new
concepts and
practicing new skills #2
Pair-share:
Answer the problem by
pair.
At sunrise, the outside
temperature was 1°
below zero. By lunch
time, the temperature
rose by 17° and then fell
by 4° by night. What
Pupils will find a partner and answer
the given problem together.
Solution:
The starting temperature is 1° below
zero, or -1°.
Later, the temperature rose, or went
up, by 17°.
Then, the temperature fell, or went
down, by 4°.

was the temperature at
the end of the day? Equation:
-1° + 17° - 4°= -12°
(Leads to Formative
Assessment 3)
Group Activity:
The teacher will divide
the class into 5 groups
and give the activity
card.
Solve the problem.
1. The highest point in
Asia is Mount Everest at
8850 meters. The shore
of the Dead Sea, the
lowest point in Asia, is
about 410 meters below
sea level. What is the
difference between
these elevations?
2. In Fairfield, Montana,
on December 24, 1924,
the air temperature
dropped a record
amount. At noon, the
temperature was 63°F.
Twelve hours later, the
temperature was 21°F.
What was the change in
temperature?
Pupils will answer the problem by
group and report their answer to the
class.
Solution:
Use integers to represent the two
elevations.
Mount Everest: +8850m
Dead Sea: -410 m
Find the difference of 8850 and 410
meters.
8850 -(- 410)
=8850 + 410 [Rule for subtracting
integers]
=9260
ANSWER: The difference between
the elevations is 9260 meters.
2. Solution:
Change in temperature = end
temperature - start temperature
=21 - 63 (Substitute values.)
= 21 + (-63) [Rule for subtracting
integers]
= -42
ANSWER:
The change in temperature was -42,
so the temperature dropped 42°F.
applications of
daily living
Individual Activity
Solve the problem.
1. In the Sahara Desert
one day it was 136°F.
In the Gobi Desert a
temperature of -50°F
was recorded. What is
the difference between
these two
temperatures?
Answer:
136° - (-50°)=n
136° + (50°) = 186°
The difference between the two
temperature is 186°F.
H. Making generalizations
and abstractions about
the lesson
Ask: How do you solve
routine and non-routine
problems involving
subtraction of integers
using appropriate
strategies and tools?
problems involving subtraction of
integers, know what is asked and
given, formulate the equation to
represent the problem, solve the
equation and check your answer.

I. Evaluating Learning The teacher will give a
test.
Solve each problem:
1. RJ was able to save
₱895 from his weekly
allowance. If he wants to
buy a second hand
mobile phone for
₱1,050, how much more
money does he still
need?
2. What is the distance
of an airplane that is 890
m above the sea level
and a submarine that is
102 m below sea level?
Answers:
1. ₱155
2. 992m
J. Additional activities for
application or
remediation
If the temperature was -
7 degrees (Fahrenheit)
at 6 AM, rose 4 degrees
by 7 AM and then rose
another 8 degrees by 8
AM, what was the
temperature at 8 AM?
Answer:
-7 + 4 + 8 = 5 degrees (Fahrenheit)
V. REMARKS
VI. REFLECTION
K. No. of learners who
earned 80% on the
formative assessment
L. No. of learners who
require additional
activities for
remediation
M. Did the remedial
lessons work? No. of
learners who have
caught up with the
lesson
N. No. of learners who
continue to require
remediation
O. Which of my teaching
strategies worked well?
Why did these work?
P. What difficulties did I
encountered which my
principal or supervisor
can help me solve?

Q. What innovation or
localized materials did I
use/discover which I
wish to share with
other teachers?

Teacher
Learning
Area
MATHEMATICS
Teaching Dates
and Time
I. OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of order of operations, ratio
and proportion, percent, exponents, and integers.
B. Performance
Standards
C. Learning
Competencies /
Objectives
The learner solves routine and non-routine problems involving
multiplication and division of integers using appropriate strategies and
tools.
M6NS-IIj-157
II. CONTENT
Solving Routine and Non-routine Problems Involving Multiplication
and Division of Integers
III. LEARNING
RESOURCES
A. References
Teacher’s Guide
pages
Learner’s
Materials pages
21st
Textbook pages 21st
Additional
Materials from
Learning Resource
(LR) Portal
none
B. Other Learning
Resources
Mathletes 6 textbook, video clip, power point presentation
A. Reviewing
previous lesson
or presenting
the new lesson
Drill:
Perform multiplication on
each pair of numbers.
12 & 4
7 & 3
15 & 9
Write positive or negative:
(+) ÷ (+) =
(+) ÷ (−) =
(−) ÷ (+) =
(−) ÷ (−) =
(+) x (+) =
(+) x (−) =
(−) x (+) =
(−) x (−) =
Perform division on each pair
of numbers.
Answers:
48
21
135
(+) ÷ (+) = (+)
(+) ÷ (−) = (−)
(−) ÷ (+) = (−)
(−) ÷ (−) = (+)
(+) x (+) = (+)
(+) x (−) = (−)
(−) x (+) = (−)
(−) x (−) = (+)
9

135 & 15
84 & 6
28 & 7
Review:
Determine if the following
pairs of integers have like
signs or unlike signs.
(+7) & (-12)
(-4) & (-9)
(-5) & (-30)
(+2) & (-11)
(+56) & (-18)
14
4
B. Establishing a
purpose for the
lesson
Present the problem.
After a community campaign
on reducing waste, the
amount of garbage in Rita’s
household decreased by 2
kg. per day. By how much will
their garbage decrease after
6 days? What is the average
reduced waste by each
person in Rita’s household if
there are four of them in the
family?
Pupils will read and analyze the
problem.
C. Presenting
Examples/Instances
of the new lesson
Ask the following questions.
1. What integer will represent
the decrease in garbage in a
day?
2.If such decrease happens
for 6 days, then what
equation will describe the
total decrease of garbage in 6
days?
-Multiplying integers is the
same as multiplying whole
numbers. The product of two
integers with different signs is
negative. On the other hand,
the product of two integers
with same sign is positive.
Solution:
Multiplying 2 and 6 is 12, but
since the signs of the factors
are different, then the product
is -12.
Therefore, after 6 days, Rita’s
household will have a
Answers:
1. -2
2. -2 x 6 = n
3. Divide the total decrease of
garbage by four since they are
four in the family.
4. -12 ÷ 4= n
5. -3kg
Each member of Rita’s
household reduced 3kg in
their garbage.

decrease of 12kg in their
garbage.
3. How are we going to know
the average reduced waste of
each member of Rita’s
household?
-Dividing integers is the same
as dividing whole numbers.
The quotient of two integers
with different signs is
negative. On the other hand,
the quotient of two integers
with the same sign is positive.
4. What will be the equation
representing the average
reduced waste of each
member of Rita’s household?
5. What is the quotient of the
two integers in your
equation?
Solution: 12 ÷ 4 is 3. Since 12
& 4 have different signs, then
the final answer will be -3.
Thus, each of the 4 members
of Rita’s household reduced
3kg in their garbage.
D. Discussing new
concepts and
practicing new
skills #1
Present another problem and
discuss the answer using the
4-step plan.
There were 15 rows of 50
chairs arranged in an
auditorium. Each chair was
rented ₱40. How much was
paid for the rental?
1.Understand
What is asked? Given?
2. Plan
What equation represents
the problem?
3. Solve
4. Check
Pupils will read the problem, listen to
the discussion and answer some
questions raised by the teacher.
Answers:
1. How much was paid for the rental?
Given: 15 rows of 50 chairs, ₱40
each chair
2. 15x50x40=n
3. 15x50x40=₱30, 000

E. Discussing new
concepts and
practicing new
skills #2
Present another problem.
Guide the pupils in answering
the problem.
Alicia owes Php200 to each
of her 4 friends. How much
money does she owe?
Solution: The problem above
can be solved using integers.
Owing Php200 can be
represented by -200. Thus
the problem becomes:
(-200) (+4)
The parentheses indicate that
these integers are being
multiplied. In order to solve
this problem, we need to
know the rules for
multiplication of integers.
We can now use Rule 1 to
solve the problem
arithmetically:(-
200) (+
4) = -
800. So Alicia owes -Php800.
The pupils will read and analyze the
problem.
Rule 1: The product of a positive
integer and a negative integer is a
negative integer.
Rule 2: The product of two
negative integers or two positive
integers is a positive integer.
(Leads to Formative
Assessment 3)
Group Activity:
Divide the class into 5
groups. Give each group an
activity card.
Answer the following
problems. Use the 4-step
plan to solve the problem.
1. A person has a debt of
Php500. Five friends offer to
pay off all of the debt. How
much does each person need
to pay in order to pay off the
debt?
2. Ms. Reyes needed Php250.
She withdrew five times that
amount. How much money did
she withdraw?
3. A sprinkler was -20 feet
below ground level. Mr. Cruz
has a machine that digs -4
Pupils will answer the problem by
group.
Answers:
1. Php100.
2. Php1,250
3. 5 digs

feet at a time. How many digs
does he need to make in order
to reach the sprinkler?
applications of
concepts and skills
in daily living
Present the problem and
have pupils answer it
individually.
Use the 4-step plan to solve
the problem.
1. Four roommates share an
apartment. The balance for
their bills for the month of July
is -Php1600. How much do
they each owe?
2. Yesterday's low
temperature was -2.5. Today's
low temperature is 5 times as
low as yesterday's low
temperature. What is the
temperature today?
Answers:
1. Each of them owes Php400.
2. -12.5
H. Making
generalizations and
abstractions about
the lesson
Ask: How do you solve
routine and non-routine
problems involving
multiplication & division of
integers using appropriate
strategies and tools?
problems involving multiplication &
division of integers, use the 4-step
plan:
1. Understand-what is asked/given
2. Plan-what equation represents the
problem
3.Solve equation
4. Check answer
I. Evaluating Learning The teacher will give a test.
Solve each problem:
1. Mr. Cruz went to market to
buy some fruits and
vegetables. He bought 5
apples at Php30 each and 3
cabbages at Php10 each. He
gave the vendor a 500-peso
bill. How much change did he
get?
2. Mrs. Tan has ₱500 to buy
some groceries. Can she buy
10 can goods that cost ₱40
each? Show your solution.
Answers:
1. Php320
2. Yes
₱500÷₱40=12.5
₱40x10=₱400
Thus, she can buy 10 can
goods worth ₱10 each.

J. Additional activities
for application or
remediation
Math Challenge
1. The sum of two numbers is
96 and one of them is five
times the other. What are the
two numbers?
Answer:
Let x=1st
number
5x=2nd
number
To show the sum:
x + 5x = 96
6x = 96
x = 96 ÷6
x = 16 is the 1st
number.
5x=5(16)=80 is the 2nd
number
Check:
16+80=96
96=96
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80%
on the formative
assessment
require additional
activities for
remediation
C. Did the remedial
lessons work? No.
of learners who
have caught up
with the lesson
D. No. of learners who
continue to require
remediation
E. Which of my
teaching strategies
worked well? Why
did these work?
F. What difficulties did
I encountered
which my principal
or supervisor can
help me solve?
G. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?

DETAILED LESSON PLAN IN MATHEMATICS 6
Teacher
Learning
Area
MATHEMATICS

Teaching Dates
and Time
Week 10, Day 4-5 Quarter 2ND
I. OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of order of operations,
ratio and proportion, percent, exponents, and integers.
B. Performance
Standards
The learner is able to apply knowledge of order of operations,
ratio and proportion, percent, exponents, and integers in
C. Learning
Competencies /
Objectives
Answer the second quarterly test.
II. CONTENT Answering the Second Quarterly Test
III. LEARNING
RESOURCES
A. References
Teacher’s Guide
pages
Mathematics CG for Grade 6, pp.190-196
Learner’s
Materials pages
21st Century Mathletes 6, pp. 82-180
Textbook pages 21st Century Mathletes 6, pp. 82-180
Additional
Materials from
Learning
Resource (LR)
Portal
none
B. Other Learning
Resources
Test paper
A. Setting of
Standards Ask: What are the things
that you need to do in
answering a test.
Possible answers:
1. Follow the directions.
2. Answer silently.
3. Cover your test paper.
4. Don’t talk with seatmates.
5. Don’t cheat.
6. If you’re done, review your
answers.
B. Giving of
Instructions and
Distribution of
Test Papers
Read the instructions in
answering the test.
Distribute the test
papers.
C. Test Proper Supervise the pupils in
answering the second
periodic test.
Pupils will answer the test.

D. Checking of Test
Papers and
Recording of
Scores
answers on the board
and record the scores of
pupils.
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned
80% on the
formative
assessment
B. No. of learners
who require
additional
activities for
remediation
A. Did the remedial
lessons work?
No. of learners
who have
caught up with
the lesson
continue to require
remediation
C. Which of my
teaching strategies
worked well? Why
did these work?
D. What difficulties did
I encountered which
my principal or
supervisor can help
me solve?
E. What innovation or
localized materials
did I use/discover
which I wish to
share with other
teachers?

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