Notre Dame of Midsayap College

Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School AGRICULTURE HIGH SCHOOL Grade Level Grade 10
Grade 10 Teacher LORIC GAY P. CALLOS Learning MATHEMATICS
Area
Daily Lesson
Plan
Teaching Quarter 3rd
Date

Illustrates the permutation of objects.

I. OBJECTIVES
Demonstrates understanding of key concepts of combination and
A. Content Standard probability.

The learner is able to use precise counting technique and probability in

B. Performance
Standard formulating conclusions and making decisions.

C. Learning
Competency/Objec
tive M10SP-IIIa-1
(Write the LC
code for each)

II. CONTENT PERMUTATION OF OBJECTS

III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide PP. 288-294
pages
2. Learner’s Mathematics Learner's Grade 10 PP. 388-330
Materials pages
3. Textbook pages
4. Additional Internet
Materials from
Learning
Resource (LR)
portal
B. Other Learning Manila paper, marker, Book, Laptop, Visual Aids, TV, cards
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to lead One student will lead the
A. Prayer our prayer. prayer in his/her own words

B. Greetings Good morning, class! Good morning, sir!

Before we are going to start our class today, Yes, sir.

let us first check your attendance. Kindly say
"present" if your name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and throw

it in a garbage bin.
 Always arrange you chairs properly.
 Sit accordingly to your proper sitting
arrangement.
 Be on time.
C. Setting of
 Listen if somebody is talking.
rules/guidelines and
 Be cooperative and participative.
Checking of
 Be respectful.
Attendance

Is everything clear?

Yes, sir.

D. Review of the Who can still recall your previous topic? What (One student will raise his
previous topic was your previous topic all about? hand)

Our last topic was all about

equation of a circle.
To check the students learning on the
previous topic, the teacher will review the
topic through an activity.
 Answers:
1.
a. (0, 0)
Find the following: b. r= 4
c. (x-0)² + (y-0)² = 16
a. Center
b. Radius
c. Equation of a Circle

2.
a. (-3, 3)
Find the following: b. r= 6
c. (x+3)² + (y-3)² = 36
a. Center
b. Radius
c. Equation of a Circle

E. Motivation/ Before we are going to start, let us have first

an activity. This activity is what we called
Priming/Establishing
“ARRANGE THEM TO HAVE ME!”
a purpose
Students will group into four equal groups
and jumbled words will be given in each
 group.

1. RODER

correct answer: ORDER

2. AGERNMANERT

correct answer: ARRANGEMENT

3. SOSLBEPI

correct answer: POSSIBLE

4. ELCTONESI

correct answer: SELECTION

5. JTOBCE

correct answer: OBJECT

F. Presenting The teacher will present a scenario then

examples/instances students will answer the questions.
of the new lesson
Suppose you secured your bike using a
combination lock. Later, you realized that you
forgot the 4-digit code. You only remembered
that the code contains the digit 1, 3, 4, and 7.

Students’ answer
1. List all the possible codes out of the
1374 3471 4731 7134
given digits.
1347 3417 4713 7143

1437 3714 4137 7413

 1473 3741 4173 7431

1734 3147 4317 7341

1743 3174 4371 7314

2. How many possible codes are there?

24 ways

3. What can you say about the list you

made?
(Students’ answers may
vary)

G. Discussing new The teacher explains the topic. Students listen attentively
concepts and to the teacher’s discussion.
practicing new skills PERMUTATION – refers to any one of all
possible arrangements of the elements of the
given set.

Basically permutation is an arrangement of

objects in a particular way or order. Thus,
permutation focuses on the selection as well
as arrangement. In short, ordering is very
much essential in permutations. In other
words, the permutation is considered as an
ordered combination.

Example 1: Write down the possible ways to

rearrange the word ‘WAY’ and determine the
total number of arrangements.
Six possible ways.
Possible ways:

WAY WYA

AYW AWF
Is it 120 sir?
YWA YAW

How about the word ‘ORDER’? How many

possible ways are there?

Example 2: If there are 7 seedlings to be

planted in how many possible ways it can be
arrange?

In mathematics, there’s one notation or

symbol you should familiar with which is
helpful in solving permutation.

Have you encountered this already?

Not yet, sir.
So, this one is a symbol for factorial.

So here’s the thing. Factorial is very useful for

when we are trying to count on how many
different orders there are for things or how
many different ways we can combine things.

7! = 7∙ (7-1) ∙ (7-2) ∙ (7-3) ∙ 3 ∙ 2 ∙ 1

7! = 7∙6∙5∙4∙3∙2∙1

7! = 5,040
 Another example,

Linda has 10 books in her mini library, in how

many ways she can arrange the books?

10! = 10∙(9-1)∙(9-2)∙(9-3)∙(9-4)∙(9-
5)∙3∙2∙1

10! = 10∙9∙8∙7∙6∙5∙4∙3∙2∙1

10! = 3,628,800 ways

Let’s have a game and it is called,

“MASTER, SOLVE ME FASTER”

Activity Situation: Students will group into 4

equal groups. The teacher will pick a
prepared questions on the box and read it
twice. The first group to raise their hand and
utter the correct answer will gain a one star
which is equivalent to 5 points. The first
group to gain 5 stars will declare as winner.
Answers:
Questions:

H. Developing How many possible ways to arrange the:

5,040
Mastery
 7 students in a row
40,320
 8 plants in a balcony
39,916,800
 11 glass on a table
24
 Letters R-E-A-D
5,040
 Numbers 1-7
120
 Even number in the numbers 1-10
3628,800
 Odd numbers in the numbers 6-25
1
 1!

I. Finding practical The teacher will ask the questions and

application of students will answer the following questions.
concepts and skills in
daily living 1. What other real life situations that we can
 use permutation? Students answer may vary.

2. How useful is the permutation in your daily

living?

How do you find our topic for today? Can you Permutation refers to any
give me the summary of our lesson today? one of all possible
What does permutation means? arrangements of the
elements of the given set.
We also discussed about
factorial notation and its
J. Making importance.
generalizations and What symbol we can use in solving the
abstraction
permutation of objects?

Is there any clarification regarding our topic Factorial notation po sir.

today?

Let’s give 10 claps for ourselves. There’s none so far, sir.

K. Evaluating Learning Direction: Illustrate permutation of objects by

answering the following questions. Write
your complete answer in a ½ sheet of paper. Answers:

1. What are the possible arrangement of the STEP TEPS EPTS PSTE
letters S-T-E-P?. STPE TESP EPST PSET

SEPT TSPE ESTP PEST

SETP TSEP ESPT PETS

SPET TPES ETPS PTES

SPTE TPSE ETSP PTSE

2. How many possible ways to arrange the 7

books. 7! = 7∙ (7-1) ∙ (7-2) ∙ (7-3)
∙3∙2∙1

7! = 7∙6∙5∙4∙3∙2∙1

7! = 5,040

3. Find the possible way to arrange the vowel

5! = 7∙ (5-1) ∙ (5-2) ∙ 2 ∙ 1
letters in the alphabet?
 5! = 5∙4∙3∙2∙1

5! = 120

4. Find the possible order to arrange a half 6! = 6 ∙ (6-1) ∙ (6-

2)∙3∙2∙1
dozen of egg in a tray.
6! = 6∙5∙4∙3∙2∙1

6! = 720

8! = 8∙ (8-1) ∙ (8-2) ∙ (8-3)

5. How many ways to arrange 8 person in a ∙ (8-4) ∙ 3 ∙ 2 ∙ 1
row?
8! = 8∙7∙6∙5∙4∙3∙2∙1

8! = 40,320

Assignment

Direction: On a 1 whole sheet of paper,

determine the possible arrangement in
each item using LISTING METHOD and
FACTORIAL NOTATION. Show your
complete answer.
L. Additional activities
for application or 1. L-O-V-E
remediation
2. D-A-I-S-Y

3. E-V-E-N

4. I-S-S-U-E

5. O-R-D-ER

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
lesson 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?
 Notre Dame of Midsayap College
Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School AGRICULTURE HIGH SCHOOL Grade Level Grade 10
Grade 10 Teacher LORIC GAY P. CALLOS Learning MATHEMATICS
Area
Daily Lesson
Plan
Teaching Quarter 3rd
Date

solve permutations using the formula for finding the n objects taken r at a
time;
IV. OBJECTIVES
Simplify circular permutation and permutation with repetition.

Demonstrates understanding of key concepts of combination and

D. Content Standard probability.

E. Performance The learner is able to use precise counting technique and probability in
Standard
 formulating conclusions and making decisions.

F. Learning
Competency/Objec
tive M10SP-IIIa-1
(Write the LC
code for each)

V. CONTENT PERMUTATION OF OBJECTS

VI. LEARNING
RESOURCES
C. References
5. Teacher’s Guide PP. 288-294
pages
6. Learner’s Mathematics Learner's Grade 10 PP. 388-330
Materials pages
7. Textbook pages
8. Additional Internet
Materials from
Learning
Resource (LR)
portal
D. Other Learning Manila paper, marker, Book, Laptop, Visual Aids, TV, cards
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to lead One student will lead the
A. Prayer our prayer. prayer in his/her own words

B. Greetings Good morning, class! Good morning, sir.

C. Setting of Before we are going to start our class today, Yes, sir
rules/guidelines and let us first check your attendance. Kindly say
Checking of "present" if your name is called.
Attendance
In my class, you already know the rules.

 Pick up pieces of garbage and throw

it in a garbage bin.
 Always arrange you chairs properly.
 Sit accordingly to your proper sitting
arrangement.
 Be on time.
 Listen if somebody is talking.
 Be cooperative and participative.
 Be respectful.
 Is everything clear?

Yes, sir.

Who can still recall your previous topic? What (One student will raise his
was your previous topic all about? hand)

Our last topic was all about

Permutations sir.
To check the students learning on the
previous topic, the teacher will review the
topic through an activity.

What is Permutation? PERMUTATION – refers to

any one of all possible
arrangements of the
elements of the given set.
Very Good!
D. Review of the
previous topic 1. If there are 7 seedlings to be planted in
how many possible ways it can be arrange? 120 ways sir.

Very good!

What Symbol is this (!)?

Precisely! Factorial sir.

Since you already understand our last topic

last meeting, let’s have another topic for
today.

E. Motivation/ Before we proceed to our next topic last, let’s

have an activity. This activity is called
Priming/Establishing
“Arrange Me”.
a purpose
Group yourselves into two groups.
1,2,1,2,1….

I have here deck of cards. In your group,

 arrange the cards according to their suits in
ascending order from ace to king.
Yes, sir.
Am I clear?
Yes, sir.
Are all the groups done?
There are 4 types sir.
How many types or suits in a deck of cards
class? Heart, diamond, spade
and club.
That’s right!

What are those 4 types?

Exactly!

Now class what did you observed?

F. Presenting The teacher will present the learning

examples/instances objectives that students expected to meet.
of the new lesson

solve
permutatio
ns using Objectives:

the solve permutations using

the formula for finding

formula
the n objects taken r at a
time simplify circular
permutation and

for permutation
repetition.
with

finding the
n objects
 taken r at
a time;
b. simplify
circular
permutatio
n and
permutatio
n with
repetition;
Objectives:

solve permutations using the formula

for finding the n objects taken r at a time

simplify circular permutation and

permutation with repetition.

Kindly Read.

G. Discussing new The teacher will present the main lesson.

concepts and
practicing new skills Kindly Read. Permutation is a set of
objects in an ordered
arrangement of the objects.
N

Permutation Formula:

The number of
 permutations of n distinct
objects taking r (r ≤ n) at a
time without repetition is
given by the formula:

nPr = n!/(n-r)!

Factorial Notation: Let n ≥

1 be an integer. The
factorial notation nis
defined as (!).
Class there are 2 kinds of Permutations.
Circular Permutation:

The number of
permutations of n distinct
objects arranged in a circle
is given by: P = (n – 1)!

Permutation with
Repetition: The number of
permutations of n objects
wheren1 are alike n2 are
Example 1: What kind of expression is our alike , and nk are alike is
example number 1? (3!) given by: where; n = n1+n2+
…+nk
Thant’s right! Who can Evaluate the
expression? Factorial Notation

Correct! So, what would be the answer? 3! = 3x2x1

Very good! Now, are there questions? 6

Okay, so let’s proceed to another example. None, sir.

2. There are 7 pupils who entered a bus with

only 5 empty seats. In how many ways can
these pupils be seated?

What formula can we use in example 2?

Permutation formula
Exactly! Why is it so?
Based on the problem, the
number of ways that 7
pupils can be seated in a
That’s right! Now how can we solve the row of 5 seats is the number
problem? of permutations of 7 objects
taken 5 at a time?
Who can evaluate the expression based on
the given formula of permutations? The given are: n = 7 and r =
5.
Very good! Who would be the next?
nPr = n!/(n-r)!
That’s right! Who will do next?
7P5 = 7!/(7-5)!
Correct! And what would be the answer?
7P5= 7!/(2)!

7P5= 7x6x5x4x3x2x1/2x1
Perfect! So, what would be the conclusion?
7P5=2,520
Excellent! Now, are there any question?
Therefore, the pupils can be
Let’s proceed to another example. seated in 2,520 ways.
3. In how many ways can a group of 8 None, sir.
persons arrange themselves around a circular
table?

What formula are we going to use?

Exactly! Now, what is the value of n? Circular Permutation

Precisely!
N=8

P=(n-1)!

Who can P=(8-1)!

P=7!

evaluate P=7x6x5x4x3x2x1

the
P=5,040

Therefore, there are 5,040

expression
ways can a group of 8
persons arrange themselves
around a circular table.

based on
 the given Yes, sir!

formula of
circular
permutatio
ns?
Precisely! Who can evaluate the expression
based on the given formula of circular
permutations?

What would be the next?

Very good! What would be the next?

That’s right! And what would be the answer?

Correct! So, what is the conclusion?

Excellent! Now class, do you have any

question or clarification?

Permutation is very important to our daily

lives. We take time to wonder. Without
wondering, life is merely an existence. The
many ways a thing can happen will make your
horizon broader.

Is that clear class?

H. Developing
Mastery
 The teacher will call someone and ask them
what is/are the formula of different
Permutations. To make it for exciting the
teacher will let the students to raise their
hand as quick as they can to make them
stand and answer the question with price if
their answer is right.

The teacher will ask the questions and

students will answer the following questions.
I. Finding practical
1. What other real life situations that we can
application of Students answer may vary.
concepts and skills in use permutation?
daily living
2. How useful is the permutation in your daily
living?

J. Making In your respective groups, your activity is

generalizations and called “Maze Me Finish”
abstraction
In this activity, each group will be given
amaze to solve in each problem and start
solving in the starting point. Use the answers
as a guide until the end of the maze.
Mechanics:
Now class, kindly read the mechanics and
also the directions of this activity. There are 2 groups involved
in this activity. You will be
given a maze and solve each
problem in the starting
point. Use the answers as a
guide until the end of the
maze. After that, post your
work in the board. This
activity is good for
5minutes.
 Directions:

Solve each expression and

problem in permutations
and then highlight the path
you take until you reach
the finish point. Show
Take note, the group who finished the activity your solutions in a given
with correct answer and posted their activity manila paper.
first will be declared as winner.

Am I clear class?

(The teacher will distribute the bond paper

and the highlighter in each group). Yes, sir!

Let’s begin!

(After the activity)

The winner will be announced. Let’s give

them a round of applause please.

Directions: Solve the following permutations.

Show your solutions.

1. (nPr) given: n=12, r=5

2. In how many ways can 9 people be seated

around a circular table?
K. Evaluating Learning
3. What is Permutations?

4. What are the two (2) kinds of

Permutations?

5. What Permutations with this formula

(P=(n-1)!)?

Assignment
L. Additional activities
for application or Read your notes to make sure that the
remediation lesson will be remain.

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
lesson 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?

Notre Dame of Midsayap College

Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

Grade 10 School AGRICULTURE HIGH SCHOOL Grade Level Grade 10

Daily Lesson Teacher LORIC GAY P. CALLOS Learning MATHEMATICS

 Area

Teaching Quarter 3rd

Plan
Date

Illustrate the combination of objects.

VII. OBJECTIVES Derive the formula for finding the number of combinations of n objects taken r at a
time.

Demonstrates understanding of key concepts of combination and

G. Content Standard probability.

The learner is able to use precise counting technique and probability in

H. Performance
Standard formulating conclusions and making decisions.

I. Learning
Competency/Objec
tive M10SP-IIIc-1 & M10SP-IIId-1
(Write the LC
code for each)

VIII.CONTENT COMBINATIONS
IX. LEARNING
RESOURCES
E. References
9. Teacher’s Guide PP. 288-294
pages
10. Learner’s Mathematics Learner's Grade 10 PP. 301-309
Materials pages
11. Textbook pages Mathematics Learner's Grade 10 PP. 301-309
12. Additional Internet
Materials from
Learning
Resource (LR)
portal
F. Other Learning Book, Power Point Presentation, and (work sheets).
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to lead One student will lead the
A. Prayer our prayer. prayer in his/her own words

B. Greetings Good morning, class! Good morning, sir!

 Before we are going to start our class today, Yes, sir.
let us first check your attendance. Kindly say
"present" if your name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and throw

it in a garbage bin.
 Always arrange you chairs properly.
 Sit accordingly to your proper sitting
arrangement.
 Be on time.
C. Setting of
 Listen if somebody is talking.
rules/guidelines and
 Be cooperative and participative.
Checking of
 Be respectful.
Attendance

Is everything clear?

Yes, sir.

D. Review of the “Okay, before we proceed to our lesson Our lesson last time was
previous topic today, what was our lesson last time?” (The about permutation.
teacher will call a student answer.)
Permutation refers to the
number of arrangements of
“Very, good. We talked about permutation.
objects where order is
So, what do you mean by permutation?” important.
“Excellent, take note that permutation is an Linear permutation
arrangement of objects where order is
important. We also discussed different types
of permutation. Can you give me one type?”

“Very good, what else?” Circular permutation

“Ok very good, anything else?” Permutation with repetition

or distinguishable
permutation

“Excellent. So those are the types of

permutation. We also solve several problems
 involving those types of permutation.”

Activity: Put Some Order Here

Study the tasks or activities below, write

“arrangement is important” if it is
important and “not important” if the
arrangement is not important.
1. not important
1. Choosing 5 questions to answer out of
2. arrangement is
10 questions in a test.
important
2. Opening a combination lock.
3. arrangement is
3. Winning in a contest. important
4. Selecting 7 people to form a Student 4. not important
Affairs Committee.
5. not important
5. Forming triangles from 6 distinct points
in which no 3 points are collinear. 6. arrangement is
E. Motivation/ important
6. Assigning seats to guests at dinner.
Priming/Establishing 7. not important
a purpose 7. Drawing a set of 6 numbers in a lottery
containing numbers 1 to 45. 8. arrangement is
important
8. Entering the PIN (Personal
Identification Number) of your ATM card. 9. not important
9. Selecting 3 posters to hang out of 6 10. not important
different posters.

10. Listing the elements of subsets of a

given set.

Any question? Clarification? None?

None, sir!
 What is Combination?

A combination is an arrangement of n objects

with no repetition and the order is not
important.

The number of combinations of n objects

F. Presenting
n
examples/instances taken r at a time is denoted by C (n, r), C r , or
of the new lesson
(nr).
The formula for combinations is C (n, r)=
n!
.
r ! ( n−r ) !

G. Discussing new Complete the table below.

concepts and
practicing new skills Number of Number of Number of
Objects (n) Objects Taken Possible
Answer may vary.
at a Time (r) Selections

2 1

2 2

3 1

3 2

3 3

4 1

4 2

4 3

4 4

5 1

5 2

5 3

5 4
 5 5

In the results above, can you find the pattern

in the results?
Yes, sir.

Solve the following:

6. C (9, 3) Answer may vary.

7. C (10, 6)
H. Developing
Mastery
3. C (12, 10)

4. C (13, 7)

5. C (8, 4)

I. Finding practical Combinations are everywhere.

application of
concepts and skills in Below are the examples that can be found in
daily living real life.
 Remember:

A combination is an arrangement of n objects

J. Making
with no repetition and the order is not
generalizations and
abstraction important.

1
In a sheet of paper, provide what is ask
2
below.

1. C (8, 3)

2. C (10, 5) Answer may Vary.

K. Evaluating Learning

3. C (12, 10)

4. C (11, 9)

5. C (7, 4)

L. Additional activities
for application or
remediation
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
lesson 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?
 Notre Dame of Midsayap College
Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching Quarter 3rd
Date

X. OBJECTIVES
Demonstrates understanding of key concepts of combination and
J. Content Standard probability.

The learner is able to use precise counting technique and probability in

K. Performance
Standard formulating conclusions and making decisions.

L. Learning List the possible ways a certain task or activity can be done
Competency/Objec
tive Appreciate permutations as vital part of one’s life.
(Write the LC
code for each) M10SP-IIIa-1

XI. CONTENT PERMUTATION OF OBJECTS

XII. LEARNING
RESOURCES
G. References
13. Teacher’s Guide PP. 248-252
pages
14. Learner’s Mathematics Learner's Module 10 PP. 283-285
Materials pages
15. Textbook pages
16. Additional Internet
Materials from
Learning
Resource (LR)
portal
H. Other Learning Work sheets and power point presentation
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to lead One student will lead the
A. Prayer our prayer. prayer in his/her own words

B. Greetings Good morning, class! Good morning, sir.

Before we are going to start our class today, Yes, sir

let us first check your attendance. Kindly say
"present" if your name is called.

In my class, you already know the rules.

 Pick up pieces of garbage and throw

it in a garbage bin.
 Always arrange you chairs properly.
 Sit accordingly to your proper sitting
arrangement.
 Be on time.
C. Setting of
 Listen if somebody is talking.
rules/guidelines and
 Be cooperative and participative.
Checking of
 Be respectful.
Attendance

Is everything clear?

Yes, sir.

D. Review of the Who can still recall your previous topic? What (One student will raise his
previous topic was your previous topic all about? hand)

Our last topic was all about

Combinations sir.
To check the students learning on the
previous topic, the teacher will review the
topic through an activity.

What is Combinations? COMBINATIONS – A

combination is a
mathematical technique
that determines the number
 of possible arrangements in
a collection of items where
the order of the selection
does not matter.

Very good! n!
C (n, r)=
r ! ( n−r ) !
What is the formula for Combination?

Exactly!

Now is there any question, clarification

None, sir!
before we proceed to our topic today?

E. Motivation/ Before we proceed to our next topic last, let’s

have an activity. This activity is called “You
Priming/Establishing
are invited”.
a purpose
Go back to your groups.

Ema invited you with Chona, Mary Grace

and Emilie to her 18th birthday. She prepared
a special table with chairs placed in a row to
be occupied by you and her three friends.

1. List all the possible seating arrangements.

Answers may vary.
2. How many ways they can be seated in a
row?

3. Show another way/s of finding the answer

in item 1.

Drill

Compute the permutations of the following

12
mentally.

1. P (4,2) 20

2. P (5, 2) 6

3. P (6, 1) 6
 4. P (3, 3) 840

5. P (7, 4)

For personal password in a computer account Answers may vary.

(Facebook), did you know why a shorter
password is “weak” while the longer
password is “strong”?

One of the schools in the province of

Cotabato will conduct a beauty pageant
“Search for Binibining Kalikasan”. For this
year, 10 students join on the said event. In
how many ways can second runner up, first
runner up and the title holder be selected?

Answer may vary.

F. Presenting
examples/instances
of the new lesson

Solution:

Given: n=10 students

r= 3 winners

P (10,3)= 10!/(10-3)!

= 10!/ 7!

There are 720 ways to select top three

winners.

G. Discussing new Do you want to be a Millionaire? Let’s Play!

concepts and
practicing new skills Permutation Millionaire!

You have to answer every question for 10

seconds. Every correct answer has a
corresponding point. The highest score a
student can earn will be an additional point
to become a millionaire.

1. In how many ways can three runners line

up on the starting line?

A. Three B. Nine

C. Six D. Five

2. In how many ways can 4 books be Winner/s may vary.

arranged in a shelf?

A. 24 B. 12

C. 8 D. 4

3. In how many ways can a scoop of

chocolate, a scoop of vanilla and one of
strawberry be arranged on an ice cream
cone?

A. Six B. Nine

C. Ten D. Three

4. A class has 10 students. How many choices

for a president and a vice-president are
possible?

A. 90 B. 1000

C. 100 D. 10,000

5. A couch can hold five people. In how many

ways can five people sit on a couch?

A. 150 B. 125

C. 120 D. 100
 Solve the following problems individually.

1. In how many ways can you place 9

different books on a shelf if there is enough
space only for five books? Give 3 possible
ways?

2. In how many ways can 5 people arrange

themselves in a row for picture taking? Give 3
H. Developing
Mastery possible ways? Answer may vary.

3. An apartment has 7 different units. There

are seven tenants waiting to be assigned. In
how many ways can they be assigned to
different units? Give 3 possible ways?

Solve the following problems

1. In how many ways can 5 different

plants be planted in a circle?
2. There are 4 copies of Mathematics
book, 5 copies of English book and 3 Answer may vary.
I. Finding practical copies of science book. In how many
application of
possible ways can they be arranged
concepts and skills in
on a shelf?
daily living
3. An apartment has 7 different units.
There are seven tenants waiting to be
assigned. In how many ways can they
be assigned to different units? Give 3
possible ways?

J. Making Remember: Permutation is an arrangement,

generalizations and listing, of objects in which the order is
abstraction important.

In general, when we are given a problem

involving permutations, where we are
choosing r members from a set with n
members and the order is important, the
 number of permutations is given by the
expression

nPr=n (n-1) (n-2)…. (n-r+2) (n-r+1).

Quiz

Answer each permutation problem

completely.

1. In how many ways can 10 people line

up at a ticket window of a cinema
hall?
2. Seven students are contesting Answer may vary.
K. Evaluating Learning election for the president of the
student union. In how many ways can
their names be listed in the ballot
paper?
3. There are 3 blue ball, 4 red balls, and
5 green balls. In how many ways can
they be arranged in a row?

Follow up

 In how many ways can a jack, a

queen, and a king be chosen from
a deck of 52 cards?
L. Additional activities
for application or
 Give real-life situations where
remediation circular permutation and
permutation with repetition can be
applied.

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
lesson 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?

Checked & observed by:

Norie J. Baya

Cooperating Teacher
 Notre Dame of Midsayap College
Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching Quarter 3rd
Date

XIII. OBJECTIVES

M. Content Standard Demonstrates understanding of key concepts of combination and probability.

The learner is able to use precise counting technique and probability in

N. Performance
Standard formulating conclusions and making decisions.

O. Learning Solving combination with real life situation;

Competency/Obj
ective Applying the Fundamental Counting Principle of combination, and
(Write the LC
 Derive the formula for finding the number of combinations of n objects
code for each) taken r at a time.
M10SP-IIIc-1 & M10SP-IIId-1

XIV.CONTENT COMBINATIONS
XV. LEARNING
RESOURCES
I. References
17. Teacher’s PP. 288-294
Guide pages
18. Learner’s Mathematics Learner's Module 10 PP. 301-309
Materials
pages
19. Textbook Mathematics Learner's Module 10 PP. 301-309
pages
20. Additional Internet
Materials
from Learning
Resource (LR)
portal
J. Other Learning Book, Power Point Presentation, and (work sheets).
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

C. Setting of Before we are going to start our class Yes, sir.

rules/guidelines and today, let us first check your attendance.
Checking of Kindly say "present" if your name is called.
Attendance
In my class, I have rules and these are:

 Pick up pieces of garbage and

throw it in a garbage bin.
 Always arrange you chairs
properly.
 Sit accordingly to your proper
sitting arrangement.
 Be on time.
 Listen if somebody is talking.
 Be cooperative and participative.
 Be respectful.
 Is everything clear?

Yes, sir.

The teacher will ask what was the activity Students will answer.
last meeting.

The teacher will ask if there is an

Students will answer.
assignment.

D. Review of the The teacher will ask the students if there is

previous topic a question, clarification before proceeding
to the next topic.

The teacher will recall the formula of

combination before presenting the FCP
or the Fundamental Counting Principle.

What was the formula for the n!

C (n, r)=
combination? r ! ( n−r ) !
E. Motivation/
That’s correct!
Priming/Establishing None, sir!
Now, is there any question before we
a purpose
discuss our next topic?

Alright!

Always remember that in combination Noted, sir!

the “Order is not Important”.

F. Presenting Pre-assessment
examples/instances
of the new lesson Open your books on page 303, and answer
numbers 1-3.
 Students answer may vary.

G. Discussing new Solve the following:

concepts and
practicing new skills 1. If each Automated Teller Machine card 10x9x8x7=5,040 passcodes
of a certain bank has to have 4 different
digits in its passcode, how many different
possible passcodes can there be?

2. On a circle there are 9 points selected.

How many triangles with edges in these
points exist?
 3. In how many ways you can choose 8 of
32 playing cards not considering their
order?

Solve the following:

1. In how many ways you can

select 5 basketball players out
of 10 team members for
different positions?

H. Developing Answer may vary.

Mastery 2. In how many ways you can
pick 6 balls from a basket of 12
balls?

3. In how many ways you can

choose 6 questions to answer
out of 10 questions in a test?
 Combinations are everywhere.

Below are the examples that can be found

in real life.

I. Finding practical
application of
concepts and skills in
daily living

Remember:

A combination is an arrangement of n
objects with no repetition and the order is
not important.

Fundamental Counting Principle (FCP), is

J. Making used when the given problem has no
generalizations and restrictions or there are to item to be
abstraction selected or be chosen.

The formula of the combination will be use

if the given problem has n object/s taken r
at a time.

K. Evaluating 1
In a sheet of paper, provide what is ask
Learning 2
below.

1. In how many ways can 5 English books

and 4 Mathematics books be placed on a
 shelf if books of the same subject are to be Answer may Vary.
together?

2. If each ATM card of a certain bank has

to have 4 different digits in its passcode,
how many different possible passcodes can
there be?

3. On a circle there are 12 points selected.

How many triangles with edges in these
points exist?

L. Additional
activities for
application or
remediation
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
lesson 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?

Notre Dame of Midsayap College

Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching Quarter 3rd
Date
XVI. OBJECTIVES
Demonstrates understanding of key concepts of combination and
P. Content Standard probability.

The learner is able to use precise counting technique and probability in

Q. Performance
Standard formulating conclusions and making decisions.

Illustrate combination of object in real life situation;

R. Learning
Competency/Objec Determine the number of ways a combination may occur, and
tive
(Write the LC Value the presence of combinations in our daily life.
code for each)
M10SP-IIIc-1

XVII. CONTENT COMBINATIONS

XVIII. LEARNING
RESOURCES
K. References
21. Teacher’s Guide PP. 259-270
pages
22. Learner’s Mathematics Learner's Module 10 PP. 301-318
Materials pages
23. Textbook pages Mathematics Learner's Module 10 PP. 301-318
24. Additional Laptop, Power Point Presentation, Worksheet
Materials from
Learning
Resource (LR)
portal
L. Other Learning Book, Power Point Presentation, and (work sheets).
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

C. Setting of Before we are going to start our class Yes, sir.

rules/guidelines and today, let us first check your
Checking of attendance. Kindly say "present" if your
Attendance name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and

 throw it in a garbage bin.
 Always arrange you chairs
properly.
 Sit accordingly to your proper
sitting arrangement.
 Be on time.
 Listen if somebody is talking.
 Be cooperative and
participative.
 Be respectful.

Is everything clear?

Yes, sir.

The teacher will ask if there are any None, sir!

question or clarification about the last
topic.

The teacher will ask:

Your mother asked you to withdraw

Php5000 from her Landbank account in
Midsayap and gave you, her PIN.
Unfortunately, you forgot the correct
D. Review of the order of numbers. You only remember 3!= 6
previous topic
that the PIN contains 7,3, 5, 4 and the
last digit is 4.

How many possible combinations are

there?

That’s right!

The teacher will explain to the students

why is it the answer is 6 and not 24.

Group activity
E. Motivation/
Perform the activity as a group.
Priming/Establishing
a purpose Follow all the instructions and write
all your answers on a clean sheet of
 paper. Then, answer the questions
that follow.

Consider the fruits below.

a. 6 kinds

b. (f1,f2,f3), (f1,f3,f2),
1. a. Select one fruit at a time. (f2,f1,f3), (f2,f3,f1,) (f3,f1,f2),
Do all possible selections. (f3,f2,f1).
b. Illustrate or describe each c. 3 kinds
selection you made.
c. Count the number of
different selections you made
when using 1 object at a time a. 1 kind
from the 3 given fruits. b. (f1,f2,f3)
2. a. Select 3 fruits at a time. c. 3 kinds
b. Illustrate or describe each
selection you made.
c. Count the number of
different selections you made
when using 1 object at a time
from the 3 given fruits.

F. Presenting A group of students from manila wants

examples/instances to visit Tagaytay as part of their Lakbay
of the new lesson Aral. A tourist guide suggested some
nice places to visit, namely, Taal Vista
(Tv), Puzzle Mansion (Pm), Sky Ranch
(Sr), Residence Inn (Ri), and Picnic Grove
(Pg), to name a few. How many ways
5C3= 5!/(5-3)! 3!
can a student select three out of the
 mentioned places? =5x4x3x2x1/2x1x3x2x1

=10

1. If you are one of the students, what

three places will you suggest?

G. Discussing new 2. How many combinations are there?

concepts and Answer may vary.
practicing new skills 3. Is there another way to get the
correct answer asige from listing
method? Explain briefly your answer.

H. Developing Do the following with a partner!

Mastery
Aside from the beautiful places,
Tagaytay is also known for its
pasalubong items. Rowena’s Pasalubong
Shop offers different tarts: (Buko, Ube,
Pineapple, Yema, and Mango). A box of
tart contains 9 pieces and you are
allowed to have a maximum of three
Answer may vary.
different flavors per box, how many
possible combinations are there?

a. There is only one flavor

Solution:
How many flavors are there? 5
_________________________________
____

b. There are two flavors

Solution:
4
How many different flavors can you pair
with buko?
_________________________________
____
4
How many different flavors can you pair
with
Ube?
_________________________________
____ 5

c. There are three flavors

 Solution:
How many different flavors can you pair
with Ube? 3
_________________________________
____

How many different flavors can you pair

with Ube and Mango?
_________________________________
____
Combinations are everywhere.

Supposed you are the owner of a sari-

sari store and you have 8 pieces of
different canned goods (Ligo, 555,
Mega, Young’s town, Master, Saba, Blue
Bay, and Century) and you are only
allowed to display 7 canned goods on
the shelf, list down all the possible
combinations.

8C7=8

I. Finding practical
application of
concepts and skills in
daily living
 Combination- the number of ways of
J. Making
selecting from a set when the order is
generalizations and
abstraction not important.

Solve the following problems.

1. Mrs. Dela Cruz selected 8 students in

the entire Grade 10 to represent in
Math culminating activity. List down the
ways Mrs. Dela Cruz can select 2 10C2=45
K. Evaluating Learning students to work in the activity.

2. In a 10-item Mathematics problem-

solving test, how many ways can you
select 5 problems to solve?
10C5=252

Answer the following problems

L. Additional activities completely.
for application or
Give 3 examples of the situations in
remediation
real life that illustrates combination.

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
lesson 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?
 Notre Dame of Midsayap College
Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching Quarter 3rd
Date

 OBJECTIVES
Demonstrates understanding of key concepts of combination and
a. Content Standard probability.

The learner is able to use precise counting technique and probability in

b. Performance
Standard formulating conclusions and making decisions.

c. Learning
Competency/Objec Answering questions related to permutation and combination.
tive
(Write the LC M10SP-IIId-e-1
code for each)

 CONTENT COMBINATIONS
 LEARNING
RESOURCES
d. References
S. Teacher’s Guide PP. 259-270
pages
T. Learner’s Mathematics Learner's Module 10 PP. 301-318
Materials pages
U. Textbook pages Mathematics Learner's Module 10 PP. 301-318
V. Additional Laptop, Power Point Presentation, Worksheet
Materials from
 Learning
Resource (LR)
portal
e. Other Learning Book, Power Point Presentation, and (work sheets).
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

Before we are going to start our class Yes, sir.

today, let us first check your
attendance. Kindly say "present" if your
name is called.

In my class, I have rules and these are:

1. Pick up pieces of garbage and

throw it in a garbage bin.
2. Always arrange you chairs
properly.
3. Sit accordingly to your proper
C. Setting of
sitting arrangement.
rules/guidelines and
4. Be on time.
Checking of
5. Listen if somebody is talking.
Attendance
6. Be cooperative and
participative.
7. Be respectful.

Is everything clear?

Yes, sir.

The teacher will review the topic

involving permutations and
combinations.
D. Review of the
previous topic Permutation: Order is important

Combination: Order is not important.

E. Motivation/ The teacher will give 5 minutes to

the students to get their notebooks
 and let them study the formulas. Students are
Priming/Establishing
studying/scanning their
a purpose
notebooks.

ORDER

Permutation Matters

Combination Does not matter

It is very important to make the

distinction between permutations and
combinations. In permutations, order
matters and in combinations order does
not matter. The important information
can be summarized by:

F. Presenting
examples/instances Examples:
of the new lesson
The principal of DNHS has to select 3
students from a group of 5 candidates
( Anna, Bernard, Carlo, Darna, and
Efren) to attend the leadership training
as president, vice president and
secretary to be held at Bulacan P(5, 3)= 5!/(5-3)! = 60 distinct
International Convention Center. How ways to pick these officers.
many different ways can this be done if:
C (5, 3)= 5!/(5-3)! 3! = 10
1. The students are distinct? combinations

2. The students are not distinct?

G. Discussing new Study the following situations. Then

concepts and answer the questions that follow.
practicing new skills
1. Choosing 2 household chores to do
before dinner Combination

2. Arrangement of 5 basketball players Permutation

out of 10 team members for the
different positions
Combination
3. Choosing three of your classmates to
attend your party
 4. Picking 6 balls from a basket of 12 Combination
balls

5. Forming a committee of 5 members

from 20 people Combination

Questions:

a. In the items above, identify which

situations illustrate permutation and
which illustrate combination.

b. How did you differentiate the

situations that involve permutation
from those that involve combination?

Who am I?

Identify which situations illustrate

permutation and which illustrate
combination then solve.

a. Determine the top five winners from P(6, 5)= 720

6 contestants (1,2,3,4,5,6) in a
mathematics quiz bee.
C(4,2)= 6
H. Developing b. Choosing 2 household chores to do
Mastery before dinner from 4 different chores
(cooking, washing, marketing,
P(5,4)=
scrubbing).
P(5,4)= 120
c. Forming a committee of 4 members
from 5 people (Alma, Brando, Charlie,
Dhana, Ella).
nPn=4! = 24
d. Four people (Ivy, Cheska, Neil, Max)
posting picture in a row.

I. Finding practical Think, Pair and Share!

application of
concepts and skills in 1. Let us say there are three flavors of nPr=n!/(n-r)!
daily living ice cream: cheese, chocolate, and
vanilla. =3!/(3-2)!

We can have two scoops. How many =3x2x1/1!

 variations will there be? =6

nPn=n!
2. In how many ways can 6 students be
seated in a row of 6 seats if 2 of the = 5!2!
students insist on sitting beside each =240
other?

Combination is the number of ways of

selecting from a set when the order is
not important.

Permutation refers to the different

possible arrangements of sets of
J. Making
objects.
generalizations and
abstraction
The basic difference between a
combination and a permutation is that
while former is just a way of selecting
something, the latter is a way of
selecting as well as arranging it.

K. Evaluating Learning Choose the letter that you think best

answers the question.

1. What do you call the different

arrangements of the objects of a group?

A. selection

C. permutation

B. differentiation

D. combination

2. Which situation illustrates

permutation?

A. forming a committee of councilors

B. selecting 10 questions to answer out

of 15 questions in a test

C. choosing 2 literature books to buy

from a variety of choices

D. assigning rooms to conference

participants

3. It is the selection of objects from a

set.

C. permutation

A. combination

D. distinction

B. differentiation

4. Which of the following situations

illustrates combination?

A. arranging books in a shelf

B. drawing names from a box containing

200 names

C. forming different numbers from 5

given digits

D. forming plate numbers of vehicles

5. Which of the following situations

does NOT illustrate combination?

A. selecting fruits to make a salad

B. assigning telephone numbers to

homes

C. choosing household chores to do

after classes

D. selecting posters to hang in the walls

of your room

6. Which of the following expressions

represents the number of
distinguishable permutations of the
letters of the word CONCLUSIONS?

A. 11!

C.11!/2! 2! 2!

B. 11!/ 81

D. 11!/2! 2! 2! 2!

7. A certain restaurant allows you to

assemble your own vegetable salad. If
there are 8 kinds of vegetables
available, how many variations of the
salad can you make containing at least 5
vegetables?

A. 56

B. 84

C 93

D. 96

8 Calculate P(12, 4).

A. 40 320

B 11 880

C 090

D 495

9. How many different 3-digit numbers

can be formed from the digits 1, 3, 4, 6.
7, 9 if repetition of digits is not allowed?

A 840

B. 720

C. 360

D. 120

10. Miss Cruz plotted some points on

the board, no three of which are
colinear When she asked her student to
draw all the possible lines through the
points, he came up with 45 lines. How
many points were on the board?

A 10

B. 9

C8

11. If P(9. r) 504, what is r?

A.7

B. 6

C5

D.3

12. If P(n, 4)17 160, then n =

A. 9

B. 11

C. 13

D. 7

13. If =P(7,4), y=P(8,4 ), and z = P(9,3) ,

arrange x, y, and z from smallest to
greatest

A. x, y, z

B. z,x,y

C. y,x,z

D.xzy

14. Calculate \frac{7!}{3!\cdot2!}.

A. 420^{\wedge}

B. 840

C. 1680

15. Which of the following can be a

value of r n C(15, r)=1365?

A. 6
B. 5

16. If C(n,5)=252 , then n =

A. 7

B.8

C. 4

D.3

17. Calculate: C(20, 5)

A. 6840

B. 15 504

C. 116 280

D. 2310

18. Let a=C(7,4) , b=C(7,5) , c=C(7,6) and

d=C(7,7) . If there are 7 points on the
plane, no three of which are collinear,
what represents the total number of
polygons that can be formed with at
least 5 sides?

A. a+b

B. c+d

C. a+b+c

D. b+c+c

19. Find C(18, 4).

A. 2400

B. 3060

C. 4896

D 73 440

20. Evaluate: C(25, 4) + C(30, 3) +

C(35,2)

A. 17 900

B. 17 305
C 16 710

D. 4655

21. In how many different ways can 7

potted plants be arranged in a row?

A. 5040

B. 2520

C. 720

D.10

22. In how many different ways can 10

different-colored horses be positioned
in a carousel?

A. 504

B. 4032

C. 362 880

D. 3 628 800

C. 720

23. In how many possible ways can Juan

answer a 10-item matching type quiz if
there are also 10 choices and he
answers by mere guessing?

A. 3 628 800

B. 40 320

C. 5040

D. 720

24. Khristelle was able to calculate the

total number of 3-digit numbers that
can be formed from a given set of non
zero digits, without repetition. If there
were 60 numbers in all, how many digits
were actually given?

A. 8

B. 7
C6

D. 5

25. How many different rays can be

formed from 8 distinct points on a
plane, no three of which lie on the same
line?

A. 56

B. 28

C. 26

D. 4

26. If a committee of 8 members is to be

formed from 8 sophomores and 5
freshmen such that there must be 5
sophomores in the committee, which of
the following is/are true?

1. The 8 committee members can be

selected in 1 287 ways. be selected in 56
ways.

II. The 5 sophomores can III. The 3

freshmen can be selected in 10 ways

A. I only

B. I and II

C. II and III

D. I, II, and III

27. In a gathering, each of the guests

shook hands with everybody else. If a
total of 378 handshakes were made,
how many guests were there?

A. 30

B. 28

C. 25

D. 23

28. If 4 marbles are picked randomly

 from a jar containing 8 red marbles and
7 blue marbles, in how many possible
ways can at least 2 of the marbles
picked are red?

A. 1638

B. 1568

C. 1176

D. 1050

L. Additional activities
for application or
remediation
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
lesson 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?
Prepared by: IVAN GUI DOMINIC C. PANCHO

Pre-service Teacher

Checked & observed by:

NORIE J. BAYA

Cooperating Teacher

Notre Dame of Midsayap College

Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching Quarter 3rd
Date
XIX. OBJECTIVES
Demonstrates understanding of key concepts of combination and
W. Content Standard probability.

The learner is able to use precise counting technique and probability in

X. Performance
Standard formulating conclusions and making decisions.

Y. Learning
Competency/Objec Illustrate events, and union intersection of events
tive
(Write the LC M10SP-IIIf-1
code for each)

XX. CONTENT COMBINATIONS

XXI.LEARNING
RESOURCES
M. References
25. Teacher’s Guide PP. 259-270
pages
26. Learner’s Mathematics Learner's Module 10 PP. 319-326
Materials pages
27. Textbook pages Mathematics Learner's Module 10 PP. 319-326
28. Additional Laptop, Power Point Presentation, Worksheet
Materials from
Learning
Resource (LR)
portal
N. Other Learning Book, Power Point Presentation, and (work sheets).
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

C. Setting of Before we are going to start our class Yes, sir.

rules/guidelines and today, let us first check your
Checking of attendance. Kindly say "present" if your
Attendance name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and

throw it in a garbage bin.
 Always arrange you chairs
 properly.
 Sit accordingly to your proper
sitting arrangement.
 Be on time.
 Listen if somebody is talking.
 Be cooperative and
participative.
 Be respectful.

Is everything clear?

Yes, sir.

The teacher will ask if there are any

questions, clarification about the last
None, sir!
D. Review of the topic.
previous topic
The teacher will make sure that the
students will retain the previous topic.

Pre-assessment

The teacher will let the students

answer the pre-assessment on their
books page (321-325). The students will scan their
books and will answer the
E. Motivation/ given pre-assessment.
Priming/Establishing You can answer the pre-assessment
a purpose in your notebooks.
None, sir!
Any questions?

Okay, answer silently.

F. Presenting Example
examples/instances
of the new lesson Flipping a coin twice, it is a compound
event since there are composition of
two or more simple events.
 Flipping a coin twice

S= { (H,H), (H,T), (T,H), (T,T) }

= 2x2= 4 outcomes.
Yes, sir!
What is the probability of getting two
tails in flipping the coin twice?

S= { (H,H), (H,T), (T,H), (T,T) }

P (two tails) = ¼ or ½ x ½ = ¼

Understand class?

G. Discussing new Compound event: is defined as a

concepts and composition of two or more simple
practicing new skills events.

The teacher will give examples;

Like flipping two coins and rolling two

dice.

Now what is the event that composed Simple event sir!

only one event?

The teacher will call someone to

answer.

Yes, that’s right!

When we are flipping one coin, it is

considered or categorized as simple
event.

You should also take note that in

 compound event, there are two or more
elements in the outcomes.

Answer the following:

1. What is the probability of getting two S= { (H,H), (H,T), (T,H), (T,T) }

heads in flipping a coin twice?
P(two heads)= ½ x ½ = ¼
H. Developing
Mastery
2. What is the probability of getting a 5
and 1 in rolling two dice? Outcomes= {(1,5), (5,1) }

P (getting a 5 and 1)= 2/36 = 1/18

I. Finding practical Example 1: There are 40 girls and 30 If a student is selected it can only
application of boys in a class. 10 girls and 20 boys like be a girl or a boy. Thus, the
concepts and skills in tennis while the rest like swimming. If a probability that the selected
daily living
student is selected at random then what student will be a girl or a boy is 1.
is the probability that it will be a boy or
a girl. Answer: P(Boy or Girl) = 1

Example 2: If a dice is rolled then find

the compound probability that either a Solution: P(2) = 1 / 6
2 or 3 will be obtained.
P(3) = 1 / 6
Solution: P(2) = 1 / 6
P(A or B) = P(A) + P(B)
P(3) = 1 / 6
P(2 or 3) = (1 / 6) + (1 / 6)

=2/6
As this is an example of a mutually
exclusive event thus, the compound =1/3
probability formula used is
Answer: P(2 or 3) = 1 / 3
P(A or B) = P(A) + P(B)

P(2 or 3) = (1 / 6) + (1 / 6)

=2/6

=1/3
 Answer: P(2 or 3) = 1 / 3

Compound event- is the probability of

two or more independent events
occurring together.

Compound probability can be calculated

J. Making
for two types of compound events,
generalizations and
abstraction namely, mutually exclusive and
mutually inclusive compound events.

Simple event- is the probability of

independent event occurring.

Pair me

Solve the following problems

completely. (Choose a partner)
Outcomes= {(3,4), (3,4) }
 What is the probability of
getting a 4 and 3 in rolling two P (getting a 3 and 4)= 2/36 = 1/18
dice?

S= { (H,H), (H,T), (T,H), (T,T) }

 What is the probability of
P(two tails)= ½ x ½ = ¼
K. Evaluating Learning getting two tails in flipping a
coin twice? P(A or B) = P(A) + P(B)

P(2 or 3) = (1 / 6) + (1 / 6)
 If a dice is rolled then find the
=2/6
compound probability that
either a 6 or 3 will be obtained. =1/3

Answer: P(2 or 3) = 1 / 3

L. Additional activities
for application or
remediation
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
lesson 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?

Checked & observed by:

NORIE J. BAYA

Cooperating Teacher

Notre Dame of Midsayap College

Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

Grade 10 School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Daily Lesson
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
 Area

Teaching Quarter 3rd

Plan
Date

XXII. OBJECTIVES
Demonstrates understanding of key concepts of combination and
Z. Content Standard probability.

The learner is able to use precise counting technique and probability in

AA. Performance
Standard formulating conclusions and making decisions.

BB. Learning Illustrates events, and union intersection of events

Competency/Objec
tive Illustrates the probability of a union of two events.
(Write the LC
code for each) M10SP-IIIf-1

XXIII. CONTENT PROBABILITY OF COMPOUND EVENTS

XXIV. LEARNING
RESOURCES
O. References
29. Teacher’s Guide PP. 259-270
pages
30. Learner’s Mathematics Learner's Module 10 PP. 319-326
Materials pages
31. Textbook pages Mathematics Learner's Module 10 PP. 319-326
32. Additional Laptop, Power Point Presentation, Worksheet
Materials from
Learning
Resource (LR)
portal
P. Other Learning Book, Power Point Presentation, and Deck of cards.
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

C. Setting of Before we are going to start our class Yes, sir.

rules/guidelines and today, let us first check your
Checking of attendance. Kindly say "present" if your
 name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and

throw it in a garbage bin.
 Always arrange you chairs
properly.
 Sit accordingly to your proper
sitting arrangement.
 Be on time.
 Listen if somebody is talking.
Attendance  Be cooperative and
participative.
 Be respectful.

Is everything clear?

Yes, sir.

What is a compound event? Compound event is a composition

of two or more events.
Very good!

How about a simple event?

Simple event is a single event
D. Review of the Yes, that’s right! occurring.
previous topic
Do you have any questions,
clarifications before we proceed to our None, sir!
topic today?

Okay, let’s proceed!

E. Motivation/ Word Puzzle ( Arrange the word)

Priming/Establishing 1. Ocoundmp vente Compound event
a purpose
Answer: Compound event

2. Inpendendte vente Simple event

Answer: Independent event

 3. Tumuayll Sivecluxe vente Mutually Exclusive event

Answer: Mutually Exclusive event

4. Tumuayll Siveluinc vente Mutually Inclusive event

Answer: Mutually Inclusive event

5. Tendenped vente

Answer: Dependent event

F. Presenting Examples
examples/instances
of the new lesson 1.You draw a marble from a bag that
has 4 red, 2 blue, and 3 green, you also
flip a coin. What is the probability you
will draw a blue marble and flip a head?

Solution: (4+2+3) = 9 marbles

P(Blue Marble)= 2/9

P(Head)= ½

P(Blue marbles and Head)= 2/9 x ½ =

2/18= 1/9

2. In a standard deck of 52 cards, what

is the probability of getting either a face
card or a spade?

P( Face Card)= 12/52

P( Spade)= 13/52

P( Face of Spade) =3/52

P(Face or Spade= P(F) + P(S)- P(Face of

Spade)

= 12/52 + 13/ 52 – 3/52

= 25/52 – 3/52
 = 22/52

P( Face or Spade)= 22/52 = 11/26

3. When a die is rolled, what is the

probability of getting a prime number or
4?

P ( Prime)= 3/6

P ( 4) = 1/6

P ( Prime or 4) = 3/6 + 1/6

= 4/6

P( Prime or 4) = 2/3

Let A and B be two events

P(A and B)= P(A) x P(B) “Independent

Events”

(The outcome isn’t affeted by the

another event)

P( A and B)= P(A) x P(BIA) “Dependent

G. Discussing new
Events”
concepts and
practicing new skills
(The outcome is affected by the another
event)

P(A or B)= P(A) + P(B) “Mutually

Exclusive”

P(A or B)= P(A) + P(B) – P(A and B)

“Muttually Inclusive”

H. Developing Solve the following

Mastery
1. Let X and Y be the two events. If P(X P(X or Y)=P(X) + P(Y) – P(X and Y)
or Y) =0.75, P(X)= 0.43, and P(X and Y)=
0.27, find P(Y). 0.75= 0.43 + P(Y) – (0.27)

0.75=0.16 + P(Y)
 0.75-0.16= P(Y)

P(Y)=0.59

2. There are 60 fruits in a basket: 18

papayas, 22 bananas, and 20 guavas.
What is the probability that a fruit is P(Papaya) 18/60
either a papaya or a guava? P(Guava)= 20/60

P(Papaya or Guava)= 18/60 +

20/60

P(Papaya or Guava)=38/60
=19/30

I. Finding practical Example 1: There are 40 girls and 30 If a student is selected it can only
application of boys in a class. 10 girls and 20 boys like be a girl or a boy. Thus, the
concepts and skills in tennis while the rest like swimming. If a probability that the selected
daily living
student is selected at random then what student will be a girl or a boy is 1.
is the probability that it will be a boy or
a girl. Answer: P(Boy or Girl) = 1

Example 2: If a dice is rolled then find

the compound probability that either a Solution: P(2) = 1 / 6
2 or 3 will be obtained.
P(3) = 1 / 6
Solution: P(2) = 1 / 6
P(A or B) = P(A) + P(B)
P(3) = 1 / 6
P(2 or 3) = (1 / 6) + (1 / 6)

=2/6
As this is an example of a mutually
exclusive event thus, the compound =1/3
probability formula used is
Answer: P(2 or 3) = 1 / 3
P(A or B) = P(A) + P(B)

P(2 or 3) = (1 / 6) + (1 / 6)

=2/6

=1/3
 Answer: P(2 or 3) = 1 / 3

The formula to be used in different

events are

INDEPENDENT EVENT- is an event in

which the outcome isn't affected by
another event.

P(A and B)= P(A) x P(B)

DEPENDENT EVENT- A dependent event

is affected by the outcome of a second
event.
J. Making
generalizations and P( A and B)= P(A) x P(BIA)
abstraction
MUTUALLY EXCLUSIVE EVENT- is an
event that can’t happen at the same
time.

P(A or B)= P(A) + P(B)

MUTUALLY INCLUSIVE EVENT- is an

event that can happen at the same
time.

P(A or B)= P(A) + P(B) – P(A and B)

K. Evaluating Learning QUIZ

1. In a standard deck of 52 cards, what P( Face Card)= 12/52

is the probability of getting either a face
card or a heart? P( Heart)= 13/52

P( Face of Heart) =3/52

P(Face or Heart= P(F) + P(S)-

P(Face of Heart)

= 12/52 + 13/ 52 –
3/52

= 25/52 – 3/52
 = 22/52

P(Face of Heart)=11/26

2. A coin and a number cube with the

numbers 1 through 6 are tossed. What
is the probability of the coin showing P(Tail)= ½
tails and the number cube showing the P(Number 3)= 1/6
number 3?
P(Tail and Number 3)= ½ x 1/6 =
3. A weather newscaster reported that 1/12
the probability that it will rain tomorrow
is 50%, the probability of lightning is P(Rain)= 50%
40% and the probability that both can
P(Lightning)= 40%
happen is 20%. What is the probability
that an outdoor event will be cancelled P(Both can happen)= 20%
due to rain or lightning?
P(Rain or Lightning)= P(Rain) +
P(Lightning) – P(Both can happen)

P(Rain or Lightning= 50% + 40% -

20%

= 90% - 20%

P(Rain or Lightning)=70% or .70

L. Additional activities
for application or
remediation
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
lesson 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?
 Notre Dame of Midsayap College
Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching Quarter 3rd
Date

XXV. OBJECTIVES
Demonstrates understanding of key concepts of combination and
CC.Content Standard probability.

The learner is able to use precise counting technique and probability in

DD. Performance
Standard formulating conclusions and making decisions.

EE. Learning Illustrates the probability of Mutually Exclusive Events

Competency/Objec
tive Solve problem involving events that cannot happen at the same time.
(Write the LC
code for each) M10SP-IIIf-1

XXVI. CONTENT PROBABILITY OF COMPOUND EVENTS

XXVII. LEARNING
RESOURCES
Q. References
33. Teacher’s Guide PP. 259-270
pages
34. Learner’s Mathematics Learner's Module 10 PP. 319-326
Materials pages
35. Textbook pages Mathematics Learner's Module 10 PP. 319-326
 36. Additional Laptop, Power Point Presentation, Worksheet
Materials from
Learning
Resource (LR)
portal
R. Other Learning Book, Power Point Presentation, and Deck of cards.
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

Before we are going to start our class Yes, sir.

today, let us first check your
attendance. Kindly say "present" if your
name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and

throw it in a garbage bin.
 Always arrange you chairs
properly.
 Sit accordingly to your proper
C. Setting of
sitting arrangement.
rules/guidelines and
 Be on time.
Checking of
 Listen if somebody is talking.
Attendance
 Be cooperative and
participative.
 Be respectful.

Is everything clear?

Yes, sir.

When can we used the formula for When the outcome of first event
“Independent Event”? will not be affected by another
event.
What is the formula for the
D. Review of the P(A and)= P(A) x P(B)
previous topic independent event?

Is there any question, clarification about

to our previous topic? None, sir!
 Mutually Exclusive or not?

1. Mario has 45 red chips, 12 blue Mutually Exclusive

chips, and 24 white chips. What is
the probability that Mario randomly
selects a red chip or a white chip?

2. Drawing a 5 or 8 from a standard

deck of cards.
Mutually Exclusive
E. Motivation/

Priming/Establishing 3. Getting a grade of 90 in Math and

a purpose a grade of 90 in English. Not
4. In a standard deck of 52 cards,
what is the probability of getting
either a face card or a spade? Not

5. You draw a marble from a bag

that has 4 red, 2 blue, and 3 green,
Mutually Exclusive
you also flip a coin. What is the
probability you will draw a blue
marble and flip a head?

Examples:

1. When a die is rolled, what is the P ( Prime)= 3/6

probability of getting a prime number or
4? P ( 4) = 1/6

P ( Prime)= 3/6 P ( Prime or 4) = 3/6 + 1/6

P ( 4) = 1/6 = 4/6

F. Presenting P ( Prime or 4) = 3/6 + 1/6 P( Prime or 4) = 2/3

examples/instances
of the new lesson = 4/6

P( Prime or 4) = 2/3

2. A six-sided die, numbered 1 to 6 is P(3)= 1/6

rolled. What is the probability of the die P(EVEN)=3/6
landing on a 3 or an even number?
P(3 or Even)=1/6 + 3/6

P(3 or Even)= 4/6 = 2/3

 Let A and B be two events

P(A or B)= P(A) + P(B) “Mutually

Exclusive”

(The events cannot happen at the same

time)

We can only used the formula for

Mutually Exclusive events when the
events can’t happen at the same time.
These events has no common elements. P(7)= 1/15

Example: P(15)= 1/15

1. A bowl contains 15 chips numbered 1 P(7 or 15)= 1/15 + 1/15

to 15. If a chip is drawn randomly from
= 2/15
G. Discussing new the bowl, what is the probability that it
concepts and is a 7 or 15?
practicing new skills
P(Purple)= 4/10 or 2/5

P(Number greater than 4)= 2/10

or 1/5
2. A bag contains six yellow jerseys
numbered 1 to 6. The bag also contains P(Purple or Number greater that
four purple jerseys numbered 1 to 4. 4)= ½ + 1/5
You randomly pick a jersey. Find the
probability that you will pick a purple = 2/5 + 1/5
jersey or a jersey that has a number
= 3/5
greater than four.

H. Developing Solve the following

Mastery
1. A basket contains three apples, three P(Apple)= 3/10
peaches, and four pears. You randomly
select a piece of fruit. Find the P(Peach)= 3/10
probability that it is an apple or peach. P(Apple or Peach)= 3/10 + 3/10

= 6/10 or 3/5
 2. There are 80 fruits in a basket: 18 P(Papaya) 18/80
papayas, 22 bananas, and 40 Mangos.
What is the probability that a fruit is P(Banana)= 20/80
either a papaya or a banana? P(Papaya or Banana)= 18/80 +
20/80

P(Papaya or Banana)=38/80
=19/40

I. Finding practical Example 1: There are 40 girls and 30 If a student is selected it can only
application of boys in a class. 10 girls and 20 boys like be a girl or a boy. Thus, the
concepts and skills in tennis while the rest like swimming. If a probability that the selected
daily living
student is selected at random then what student will be a girl or a boy is 1.
is the probability that it will be a boy or
a girl. P(Boy)= 30/70

P(Girl)=40/70

P(Boy or Girl)= 30/70 + 40/70

= 70/70

P(Boy or Girl)= 1

Example 2: If a dice is rolled then find Solution: P(2) = 1 / 6

the compound probability that either a P(3) = 1 / 6
2 or 3 will be obtained.
P(A or B) = P(A) + P(B)
Solution: P(2) = 1 / 6
P(2 or 3) = (1 / 6) + (1 / 6)
P(3) = 1 / 6
=2/6

=1/3
As this is an example of a mutually
exclusive event thus, the compound Answer: P(2 or 3) = 1 /3
probability formula used is

P(A or B) = P(A) + P(B)

 P(2 or 3) = (1 / 6) + (1 / 6)

=2/6

=1/3

Answer: P(2 or 3) = 1/3

MUTUALLY EXCLUSIVE EVENT- is an

event that cannot happen at the same
time.

J. Making And the formula for Mutually Exclusive

generalizations and events is defined as:
abstraction
P(A or B)= P(A) + P(B)

These events has no common elemets.

K. Evaluating Learning Solve the following

1. A six-sided die, numbered 1 to 6 is P(5)= 1/6

rolled. What is the probability of the die
landing on a 5 or an even number? P(Even)=3/6

P(5 or Even)= 1/6 + 3/6

P(5 or Even)= 4/6 = 2/3

2. There are 3 red balls, 7 blue balls and P(Red)=3/15

5 green balls in a bag. One ball is picked P(Blue)=7/15
from the bag. Calculate the probability
of a red or a blue ball being picked. P(Red or Blue)= 3/15 + 7/15

P(Red or Blue)=10/15 = 2/3

3. In a bag there are 5 yellow balls, 6 P(Yellow)=5/26

blue balls, 7 red balls and 8 green balls.
P(Red)=7/26
One ball is picked. What is the
probability that a yellow or red ball is P(Yellow or Red)=5/26 + 7/26
picked?
P(Yellow or Red)= 12/26 =6/13

P(Odd)= 3/6
4. Barry rolls a 6-sided die. What is the
probability Barry rolls an odd number or P(6)=1/6
a 6?
 P(Odd or 6)=3/6 + 1/6

P(Odd or 6)= 4/6 = 2/3

L. Additional activities Assignment

for application or
Study Mutually Inclusive Events
remediation

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
lesson 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?

Prepared by: IVAN GUI DOMINIC C. PANCHO

Pre-service Teacher
 Notre Dame of Midsayap College
Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching February 28, 2024 Quarter 3rd
Date

XXVIII. OBJECTIVES
Demonstrates understanding of key concepts of combination and
FF. Content Standard probability.

The learner is able to use precise counting technique and probability in

GG. Performance
Standard formulating conclusions and making decisions.

Define the probability of a union of two events,

HH. Learning
Competency/Objec
Illustrates the probability of Mutually Inclusive Events; and
tive
Show the importance of solving problem involving events that can
(Write the LC
code for each) happen at the same time.
M10SP-IIIg-1

XXIX. CONTENT PROBABILITY OF COMPOUND EVENTS

XXX. LEARNING
RESOURCES
S. References
37. Teacher’s Guide PP. 259-270
pages
38. Learner’s Mathematics Learner's Module 10 PP. 319-326
Materials pages
39. Textbook pages Mathematics Learner's Module 10 PP. 319-326
40. Additional Laptop, Power Point Presentation, Worksheet
Materials from
Learning
Resource (LR)
portal
T. Other Learning Book, Power Point Presentation, and Deck of cards.
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

Before we are going to start our class Yes, sir.

today, let us first check your
attendance. Kindly say "present" if your
name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and

throw it in a garbage bin.
 Always arrange you chairs
properly.
 Sit accordingly to your proper
C. Setting of
sitting arrangement.
rules/guidelines and
 Be on time.
Checking of
 Listen if somebody is talking.
Attendance
 Be cooperative and
participative.
 Be respectful.

Is everything clear?

Yes, sir.

D. Review of the When can we used the formula for

 “Mutually Exclusive event”?

What is the formula for the Mutually

Exclusive event?
previous topic
Is there any question, clarification about
to our previous topic?

Mutually Inclusive or not?

1. You choose a card from a standard

deck of cards, what is the probability
of getting a queen or a heart? Mutually Inclusive

2. One card is drawn from a standard

deck of cards, what is the probability Not
of drawing a 2 or an Ace?
E. Motivation/ 3. A bag contains 4 green, 6 yellow,
Priming/Establishing and 8 blue marbles. What is the
a purpose probability of picking a green or a
yellow? Not

4. In a standard deck of 52 cards,

what is the probability of getting
Mutually Inclusive
either a queen or a diamond?

5. What is the probability of drawing

a queen or a king in a standard deck Not
of card?

F. Presenting Examples:
examples/instances
of the new lesson 1. You choose a card from a P(Queen)= 4/52
standard deck of cards, what is the
P(Heart)= 13/52
probability of getting a queen or a
heart? P(Queen or Heart)= 4/52 + 13/52-
1/52

= 16/52 = 4/13

2. In a standard deck of 52 cards,

what is the probability of getting P(5)= 4/52
either a 5 or a diamond?
 P(Diamond)= 13/52

P(5 or Diamond)= 4/52 + 13/52-

1/52

= 16/52 = 4/13

Let A and B be two events

P(A or B)= P(A) + P(B) – P(A and B)

“Mutually Inclusive”

(The events can happen at the same

time)

The events has common elements.

We can only used the formula for

Mutually Inclusive events when the
G. Discussing new events can happen at the same time.
concepts and These events has common elements.
practicing new skills
Example: P(5)= 4/52

1. If you draw one card from a P(Diamond)= 13/52

standard deck, what is the
probability of drawing a 5 or a P(5 or Diamond)= 4/52 + 13/52 –
diamond? Are the events 1/52
inclusive or mutually exclusive?
= 16/52

= 4/13

H. Developing Solve the probability of two events

Mastery
1. A card is drawn at random from a
deck of 52 playing cards. Find the
probability that the card is:

a) A jack or a heart a) P(Jack)= 4/52

P(Heart)= 13/52

P(Jack or Heart)= 4/52 +13/52 –

1/52
 = 16/52 = 4/13

b) A diamond or a king b) P(Diamond)= 13/52

P(King)= 4/52

P(Diamond or King)= 13/52 +

4/52 –

1/52

=16/52 =
c) A spade or a 7 4/13

c) P(Spade)= 13/52

P(7)= 4/52

P(Spade or 7)= 13/52 + 4/52 –

1/52

= 16/52 = 4/13

Example 1: A die is rolled, what is the P(Prime)= 3/6

probability that you can get a prime or a
2? P(2)=1/6

P(Prime or 2)= 3/6 + 1/6 – 1/6

= 3/6 = ½

I. Finding practical
application of
Example 2: What is the probability of P(King)= 4/52
concepts and skills in
daily living getting a king or a heart in a standard P(Heart)= 13/52
deck of cards?
P(King or Heart)= 4/52 + 13/52 –
1/52

= 16/52 = 4/13

J. Making MUTUALLY INCLUSIVE EVENT- is an

generalizations and event that can happen at the same
abstraction
 time.

And the formula for Mutually Inclusive

events is defined as:

P(A or B)= P(A) + P(B) – P(A and B)

These events has common elemets.

K. Evaluating Learning Solve the following

1. A six-sided die, numbered 1 to 6 is

rolled. What is the probability of the die
landing on a 4 or an even number?
P(4)= 1/6

P(Even)=3/6

P(4 or Even)= 1/6 + 3/6 – 1/6

2. What is the probability of choosing a P(4 or Even)= 3/6 = ½

card from a deck of cards that is club or
a ten?
P(Club)= 13/52

P(Ten)= 4/52

P(Club or Ten)= 13/52 + 4/52 –

1/52

= 16/52 = 4/13
3. What is the probability of choosing a
number from 1 to 10 that is less than 5
or odd?

P(<5)= 4/10
 P(Odd)= 5/10

P(<5 or Odd)= 4/10 +5/10 – 2/10

4. Roy rolls a 6-sided die. What is the = 7/10

probability Barry rolls an odd number or
a 3?
P(Odd)= 3/6

P(3)= 1/6

P(Odd or 3)= 3/6 + 1/6 – 1/6

= 3/6 = ½

L. Additional activities Assignment

for application or
Study Dependent Events
remediation

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
lesson 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?

Prepared by: IVAN GUI DOMINIC C. PANCHO

Pre-service Teacher

Checked & observed by:

NORIE J. BAYA

Cooperating Teacher

Notre Dame of Midsayap College

Poblacion 5, Midsayap, Cotabato

COLLEGE OF EDUCATION

DAILY LESSON PLAN IN MATHEMATICS 10

School LIBUNGAN NATIONAL HIGH Grade Level Grade 10
SCHOOL
Grade 10
Teacher IVAN GUI DOMINIC C. PANCHO Learning MATHEMATICS
Daily Lesson Area
Plan
Teaching February 28, 2024 Quarter 3rd
Date

XXXI. OBJECTIVES
 Demonstrates understanding of key concepts of combination and
II. Content Standard probability.

The learner is able to use precise counting technique and probability in

JJ. Performance
Standard formulating conclusions and making decisions.

Define the probability of a union of two events,

KK. Learning
Competency/Objec
Illustrates the probability of Mutually Inclusive Events; and
tive
Show the importance in solving problem involving events that can
(Write the LC
code for each) happen at the same time.
M10SP-IIIg-1

XXXII. CONTENT PROBABILITY OF MUTUALLY INCLUSIVE EVENTS

XXXIII. LEARNING
RESOURCES
U. References
41. Teacher’s Guide PP. 259-270
pages
42. Learner’s Mathematics Learner's Module 10 PP. 319-326
Materials pages
43. Textbook pages Mathematics Learner's Module 10 PP. 319-326
44. Additional Laptop, Power Point Presentation, Worksheet
Materials from
Learning
Resource (LR)
portal
V. Other Learning Book, Power Point Presentation, and Deck of cards.
Resources
IV. PROCEDURES
Let us pray first, may I ask a volunteer to One student will lead the prayer
A. Prayer lead our prayer. in his/her own words

B. Greetings Good morning, class! Good morning, sir!

C. Setting of Before we are going to start our class Yes, sir.

rules/guidelines and today, let us first check your
Checking of attendance. Kindly say "present" if your
Attendance name is called.

In my class, I have rules and these are:

 Pick up pieces of garbage and

throw it in a garbage bin.
 Always arrange you chairs
properly.
  Sit accordingly to your proper
sitting arrangement.
 Be on time.
 Listen if somebody is talking.
 Be cooperative and
participative.
 Be respectful.

Is everything clear?

Yes, sir.

When can we used the formula for When the two events cannot
“Mutually Exclusive event”? happen at the same time.

Very good!
P(A or B)= P(A) + P(B) – P(A and B)
What is the formula for the Mutually
D. Review of the Exclusive event?
previous topic

Exactly!

Is there any question, clarification about None, sir!

to our previous topic?

E. Motivation/ In 1/8 sheet of paper write a

situation or example that shows
Priming/Establishing Answer may vary.
“mutually inclusive events”
a purpose

F. Presenting Examples:
examples/instances
of the new lesson 1. Suppose you are playing with the
spinner in the image below. What is
the theoretical probability that the
spinner would randomly land on
either a top quadrant or a red
P(Red)= 2/4
quadrant?
P(Top)= 2/4
 P(Red and Top)= ¼

P(Red or Top)= 2/4 + 2/4 – ¼

=3/4 or 75%

P(5)= 4/52

P(Diamond)= 13/52

P(5 or Diamond)= 4/52 + 13/52-

1/52

= 16/52 = 4/13

2. In a standard deck of 52 cards,

what is the probability of getting
either a 5 or a diamond?

G. Discussing new Let A and B be two events

concepts and
practicing new skills P(A or B)= P(A) + P(B) – P(A and B)
“Mutually Inclusive”

(The events can happen at the same

time)

The events has common elements.

We can only used the formula for

Mutually Inclusive events when the
events can happen at the same time.
These events has common elements.

Example: P(5)= 4/52

1. If you draw one card from a P(Diamond)= 13/52

standard deck, what is the
probability of drawing a 5 or a P(5 or Diamond)= 4/52 + 13/52 –
diamond? Are the events 1/52
inclusive or mutually exclusive?
= 16/52
 = 4/13

Groupings

Group yourselves into four groups. 1,2,3,4,1,2…..

H. Developing
Mastery
Go to your group silently.

Example 1: A die is rolled, what is the P(Prime)= 3/6

probability that you can get a prime or a
2? P(2)=1/6

P(Prime or 2)= 3/6 + 1/6 – 1/6

= 3/6 = ½

I. Finding practical
application of
Example 2: What is the probability of P(King)= 4/52
concepts and skills in
daily living getting a king or a heart in a standard P(Heart)= 13/52
deck of cards?
P(King or Heart)= 4/52 + 13/52 –
1/52

= 16/52 = 4/13

J. Making MUTUALLY INCLUSIVE EVENT- is an

generalizations and event that can happen at the same
abstraction time.

And the formula for Mutually Inclusive

events is defined as:

P(A or B)= P(A) + P(B) – P(A and B)

 These events has common elemets.

Answer the following P(<7)= 6/10

1. What is the probability of choosing a P(Even)= 5/10

number from 1 to 10 that is less than 7
or even? P(<7 or Even)= 6/10 +5/10 – 3/10

= 8/10 = 4/5

2. What compound events that can Mutually Inclusive Event

happen at the same time?

3. What is the formula of “Mutually P(A or B)=P(A) +P(B) – P(A and B)

Inclusive events”?

P(Even Numbered)=5/52
4. What is the probability of randomly
K. Evaluating Learning pulling either an even numbered card or P(Black)= 26/52
a black card from a standard deck?
P(Even or Black)= 10/52

P(A or B)= 5/52 + 26/52 – 10/52

= 21/52
5. What is the probability that the
P(Prime)= 5/12
outcome of one roll of a 12-sided die
will be either prime or odd? P(Odd)= 7/12

P(Prime and Odd)= 5/12

= 5/12 + 7/12- 5/
12

= 7/12

L. Additional activities Assignment

for application or
Study Dependent Events
remediation
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
lesson 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?

Prepared by: IVAN GUI DOMINIC C. PANCHO

Pre-service Teacher

Checked & observed by:

NORIE J. BAYA

Cooperating Teacher