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.

practicing new skills
#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.
Distribute the test papers.
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.
The teacher will post the
answer on the board and
record pupils score.
Pupils will check the test papers.
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
Teacher Learning Area MATHEMATICS
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
solving word problems involving
increase/decrease on discounts, original price,
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
Multiply ₱3,500,000.00 by
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
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)
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%
Multiply ₱800.00 by 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
4. Additional Materials from
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?

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