School Mati National Comprehensive High School Grade Level 10

DAILY
Teacher Nonito P. Adalid Jr. Learning Area MATHEMATICS
LESSON LOG
Teaching Dates February 19-23, 2024 Quarter THIRD

Session
Session 1 Session 2 Session 3 Session 4
5

I. OBJECTIVES

Content Standards The learner demonstrates understanding of the key concepts of combination and probability.

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

Learning Competencies The learner illustrates the The learner illustrates the The learner solves problems The learner solves problems CATCH
permutation of objects. permutation of objects. involving permutations. involving permutations. UP
M10SP - IIIb – 1 M10SP - IIIb – 1 FRIDAY
(M10SP-IIIa-1) (M10SP-IIIa-1)
a. Solve problems involving a. Solve problems involving
Objectives circular permutations and linear permutations and
State and explain permutation a. Formulate the number of permutations with permutations taken r at a time
of objects. permutations of n objects repetitions.
b. Analyze each word problem
taken r at a time. b. Analyze each word to identify the given
List the possible ways a certain
task or activity can be done. b. Find the number of problem to identify the given information
permutations of n objects information
Solve the possible number taken at a time.
ways using Fundamental
 Counting Principle.

II. CONTENT Illustration of Permutation Permutation of n objects taken at r Problem Solving Involving Problem Solving Involving
time Permutation Permutation

III. LEARNING RESOURCES

References

Teacher’s Guide pp. 248-252 252-255 256 – 257 256 – 257

Learner’s Materials pp. 283-285 286-290 283 – 300 283 – 300

Textbook

Basic Probability and Statistics, Basic Probability and Statistics, pp.

pp. 120-121 Elementary 120-121 Elementary Statistics: A Step
Statistics: A Step by Step Approach, by Step Approach,
pp. 221-223
pp. 221-223

Additional Materials from https://onlinecourses.scie Worksheets and power point

Learning Resources (LR) nce.psu.edu/stat414/nod e/29
portal http://www.analyzemath. Worksheets and power point Worksheets and power point
com/statistics/counting.ht ml presentation presentation

Other Learning Resources Activity Sheets/Worksheets

and PowerPoint presentation
http://www.mathsisfun.com

/data/basic-counting-
principle.html http://www.math-
play.com/Permutations/per
mutations%20millionaire.ht ml
IV. PROCEDURES

A. Reviewing previous ELICIT: Think-Pair-Share The class will be divided into 4 Drill See
lesson or presenting the with uneven number of Attache
new lesson There won't be a review of the Answer the following with your members. Each group will be Compute the permutations of the d
prior lesson because the seatmate: asked to arrange themselves in following mentally. Individu
subject is unfamiliar to the a circle. In how many ways can this al
students. Instead, the lesson You have 3 shirts and 4 pants. How P (4,2)
many possible outfits can you be possible? Workpla
will start with a few warm-up P (5,2) n for
questions. have?
Catching
P (6,1)
(The teacher will call students Up
to answer the questions.) P (3,3) Friday!

1. Observe the picture below, P (7,4)

what did you observe?
2. There
are 6 flavors
of ice- cream, and 3
different
cones in a grocery
store. How many orders of ice
cream can you make?

2. What do you understand by

the term "arrangement”?

3. Can you think of examples

where the order matters?

4. For personal password in a

computer account, did you
know why a shorter password
 is “weak” while the longer
password is “strong”?

B. Establishing a purpose ENGAGE Answer the following with Give real-life situations were Mr. Calix lost his ATM card which
for the lesson your seatmate. circular permutations and can be opened with a 4-digit
Note: Let the student read the permutations with repeated password.
scenario synchronously. Then Your task in this activity is to elements.
call students to answer the think on how many ways the
question that follows. following objects can be
arranged. Should he be worried overnight
Activating Prior Knowledge without reporting the loss of his
card to the bank?
Erna invited her close friends
Chona, Mary Grace and Emilie
for a picture taking at The
LOKAL. She prepared a special
place with chairs placed in a
row to be occupied by her
three friends.

List all the possible seating

arrangements.

How many ways they can be

seated in a row? Show
another way/s of finding the
 answer in item 1.

C. Presenting READ AND ANALYZE The different arrangements Your mother made pickles, gelatin, One of the schools in the province
examples/Instances of the which can be made out of a leche plan, ube jam, sapin-sapin of Davao Oriental will conduct a
new lesson Let the student read the text given number of things by taking and graham. beauty pageant “Search for
synchronously some or all at a time are called Binibining Kalikasan”. For this year,
permutation. You are to arrange the side dishes 10 students join on the said event.
In combinatorics, a field of and desserts in a round table.
mathematics that deals with In how many ways can second
Let r and n be the positive Find the circular permutation that runner up, first runner up and the
the counting, organizing, and integers such that 1  r  n. Then you can make.
choosing of items. title holder be selected?
the numbers of all permutations
An arrangement of of n things taken at a time is
items in a particular order is
denoted by P(n,r) or nPr.
called a permutation. It
describes the quantity of Let 1  r  n. Then the
possible configurations for a
set of things. Different number of all permutations of n
configurations of the same set different things taken r at a time
of objects are regarded as is given by
unique permutations because
P (n,r)=n!
the order of the items in a
permutation matters. (n-r)! Solution:

The number of permutations of Given: n = 10 students

n things taken r at a time is the
same as the number of different r = 3 winners
It can be determined by ways in which r
10!
listing, using table, tree
place in a row can be filled with n
diagramming, and by using the (10,3) =
different things. (10 − 3)!

The first place can be filled up 10!

by any one of these n things. So.
Tthere are n ways of filling up the =
 Fundamental Counting first place. 7!
Principle. FCP is used to
calculate the total number of We are left with (n-1) things. So, = 720
permutations in a given there are (n-1) ways of filling the
situation. The principle may second place.
not tell what exactly those There are 720 ways to select top
permutations are, but it gives three winners
the exact number of Now, we are left with n-2 things.
permutations there should be. So there are n-
The FCP tells that you can
2 ways of filling up the third
multiply the number of ways
place.
each event can occur.
By the fundamental principle of
counting, the number of ways of
filling up the first three places is

n(n-1)(n-2).
Given: n = 6 Solution: P = (n – 1)!
Continuing this manner,
= (6 – 1)!
the rth place can be filled up
with any of these n-(r-1) things. = 5!
So there are n-r+1 ways of filling
= 120
up the rth place.
There are 120 ways to arrange
Thus, the total number of ways is the side dishes and desserts in a
round table.
P(n,r) = n(n-1)(n-2)…(n-r+1)

=n(n-1)(n-2)…(n-r+1)((nr)…..3.2.1

(n-r)(n-r-1)….3.2.1

= n! (n-r)!

D. Discussing new EXPLORE Do you want to be a THINK-PAIR-SHARE THINK-PAIR-SHARE

concepts and practicing Identify each given situation Millionaire? Let’s Play! How many arrangements can be
new skills # 1 illustrates a permutation or Permutation Millionaire! made from the word TAGAYTAY?
not and explain. Analyze the given problem.
You have to answer every Solution:
In explaining student are free question for 10 seconds. Every
to use the native tongue to correct answer has a let T equals n1. A equals n2 G equals
n3 Y equals n4 In how many ways can a coach assign
express themselves clearly. corresponding point. The highest the starting positions in a basketball
score a student can earn will be n= n1 = n2 = game to nine equally qualified
1. Arranging Letters in a Word: an additional point to become a n3 = n4 = men?
When creating different millionaire.
arrangements of the letters in 1. In how many ways can three

𝑃=
𝑛!
a word, such as rearranging runners line up on the starting
the letters in "CAT" to form line?
"ACT," "ATC," "TAC," "TCA,"
𝑛1!2!𝑛3!𝑛4!
and so on. A. three B. Nine

𝑃=
2. Choosing an Office Position: C. Six D. Five
!
=
Selecting a president, vice- 2. In how many ways can 4 books
president, and secretary from be arranged in a shelf? ! ! ! !
a group of candidates, where
the order in which they are A. 24 B. 12
selected matters C. 8 D. 4
3. Race Finishing Order: 3. In how many ways can a scoop The word TAGAYTAY can be
Determining the different of chocolate, a scoop of vanilla arranged into ways.
orders in which participants and one of strawberry be arranged
can finish a race, where the on an ice cream cone?
position of each participant A. Six B. Nine
matters.
C. Ten D. Three
4. Matching Outfits:

Selecting clothing items to

wear for the day, where the 4. A class has 10 students. How
 specific order in which the many choices for a president
items are worn does not and a vice- president are
impact the overall outfit. possible?

5. Selecting Books from a A. 90 B. 1000

Shelf:
C. 100 D. 10,000
Choosing books to read from a
shelf, where the order in 5. A couch can hold five people.
which the books are selected In how many ways can five people
does not affect the reading sit on a couch?
experience A. 120 B.125

C. 150 D.100

E. Discussing new concepts Discuss the following Using the numbered heads How did you find the activity? How did you find the activity?
and practicing new skills # examples: together answer the following.
2 What concepts of permutations What concepts of permutations did
Illustrative Example 1: did you use to solve the problem? you use to solve the problem?

Let's say you use a Find the number of permutations How did you apply the principles
combination lock to lock your of the letters in the word PAPAYA of permutation in solving the
bike. You subsequently forgot . problem? How did you apply the principles of
the four-digit code. All you can permutation in solving the problem?
recall about the code is that it Can you cite other real-life problems
that can be solved using Can you cite other real- life problems
has the numbers 1, 3, and 4,
permutation? that can be solved using
as well as 7.
permutation?
List all possible codes out of
the given digits.

How many possible codes are

there?

Possible Answer:

a. Possible codes containing

the four digits 7, 4, 3, 1:

(The list must be made

systematically to ensure
completeness.)

1347 3147 4137 7134

1374 3174 4173 7143

1437 3417 4317 7314

1473 3471 4371 7341

1734 3714 4713 7413

1743 3741 4731 7431

b. There are 24 possible

outcomes.

Illustrative Example 2:

In how many ways can Aling

Rosa arrange 6 potted plants
in a row?

Using the Fundamental

Counting Principle

Let N = number of
possible arrangements of the
plants

N = (6) (5) (4) (3) (2) (1)

N = 720 ways
because there are 6 choices
 for the 1st position, 5 choices
left for the 2nd position, 4
choices for the 3rd, and so on.

F. Developing mastery EXPLAIN Answer the problem individually. Solve the following problems Solve the following problems.
(leads to Formative
Assessment 3) Solve the following problems How many permutations does Two raffle tickets are drawn from
by group. each word have? 20 tickets for the first and second
In how many ways can 5 prizes. Find the number of sample
In how many ways can 5 KURBADA different plants be planted in a points in the sample spaces.
people arrange themselves in circle?
a row for picture taking? Give PALIKO
3 possible ways. There are 4 copies of
TUWID Mathematics book, 5 copies of A teacher wants to assign 4
An apartment has 7 different English book and 3 copies of different tasks to her 4 students. In
units. There are seven tenants Science book. In how many ways how many ways can she do it?
waiting to be assigned. In how can they be arranged on a shelf?
many ways can they be
assigned to the different
units? Give 3 possible ways?

Students will work by group to

solve the problems see to it
that their cultural, socio
economic, religious and
linguistic backgrounds are
being considered. (Indicator 7
and 8)

Present their output/answer

in the class. Teacher must
consider to provide a timely,
accurate, and constructive
feedback to students to
improve their learnings.
(Indicator 9) Then the group
 will choose one presenter for
their output. In explaining
student are free to use the
native tongue to express
themselves clearly.

Adapted and used culturally

appropriate teaching
strategies to address the
needs of learners from
indigenous group

Adapted and used culturally

appropriate teaching
strategies to address the
needs of learners from
indigenous group

G. Finding practical ELABORATE: Call student to Group activity: In a worksheet try (The students will be working in (The students will be working in
application of concepts answer the following to answer the following using groups and will be presenting their groups and will be presenting their
and skills in daily living questions strips of paper. output in class.) output in class.)

1. How did you determine the Directions: Find the number of Solve the following problems. Solve the following problems.
different possibilities asked for permutations. Use the formula
in the given situations? and concepts you learn from this 1. In how many ways can 4 students 1. How many different ways can a
lesson. be seated at around table? president and a vice-president be
2. What mathematics concept selected for classroom officers if
or principle did you use to 1. MALAYA 2. How many arrangements can there are 30 students in a class?
determine the exact number be made from the word
of ways asked in each activity? 2. MAMAYA CALCULATOR? 2. How many ways can 10 students
line up in a food counter?
3. Can you give another 3. MAMA
example that illustrates 3. In how many different ways can 5
3. Find the number of different bicycles be parked if there are 7
permutation? ways that a family of 6 can be available parking spaces?
seated around a circular table with
 6 chairs. 4. In how many different ways can
12 people occupy the 12 seats in a
4. How many distinguishable front row of a mini- theater?
permutations are possible with all
the letters of the word ELLIPSES?

H. Making generalizations Remember: Permutation is an Permutation with Repeated Permutation is an arrangement of

and abstractions about the arrangement, listing, of objects in Elements. The number of n objects taken in a specific order.
lesson which the order is important. distinct permutation of n objects Linear Permutation. The number of
of which n1 are one of a kind, n2 of permutations of n distinct of
In general, when we are given a
second kind, nk of a kth kind is distinct objects is n!
problem involving permutations,
𝑛!
𝑃 =
where we are choosing r Factorial Notation. n! is the product
members from a set with n of the first n consecutive natural
𝑛 𝑛1!2!𝑛3!….
members and the order is numbers.
important, the number of
permutations is given by the Permutation of n elements taken r
where n1+ n2+ n3+…. = n at a time
expression
𝑃(𝑛, 𝑟) = 𝑛𝑃𝑟 =
Circular Permutation. When
P =n · (n - 1) · (n - 2) · …
n r
things are arranged in places along
𝑛!
·(n - r + 2) · (n - r + 1). a closed curve or circle, in which where 0

(𝑛−𝑟)!
any place may be regarded as the
The first factor indicates we can first or last place, they form a
choose the first member in n circular permutation. Thus with n ≤r≤n
ways, the second factor indicates distinguishable objects we have
we can choose the second (n-1)!
member in n - 1 ways once the first
member has been chosen, and so Arrangements. In symbol,

𝑃𝑐 = (𝑛 − 1)!
on.

I. Evaluating learning Call student to give a Quiz Solve the following problems. Solve the following problems.
generalization on the concept
discuss. Answer each permutation problem 1. A man flips ten coins among 1. A store manager wishes to
completely. his ten children. The coins are two display 8 different brands of
A permutation is an one-centavo coins, three five- shampoo in a row. How many ways
 arrangement of all or part of a 1. In how many ways can 10 people centavo coins, and five twenty- can this be done?
set of objects with proper line up at a ticket window of a five centavo coins. If each item is
regard to order. cinema hall? to get one coin, in how many 2. Mar, Marlon, Marvin, Martin and
ways can the children share the Marco decided to go to SM
We determine the different 2. Seven students are contesting coins? Dasmarinas. Each of them has their
permutations by listing. We election for the president of the own motorcycle. Upon arriving at
also use table, tree diagram student union. In how many ways 2. A bracelet needs 10 chains of the parking lot, there are 7
and as well as the can their names be listed on the different colors. In how many available parking spaces. In how
Fundamental Counting ballot paper? ways can the chains be arranged many different ways can their
Principle. or joined to form a bracelet? motorcycle be parked?
3. There are 3 blue balls, 4 red
balls and 5 green balls. In how
many ways can they be arranged
in a row?

J. Additional activities for EVALUATE: (Indicator 9) Follow-up. Follow-up Follow-up

application or remediation
Find the permutation of the It is in international summits In how many ways can a jack, a
following. that major world decisions queen and a king be chosen from a
Consider the following happen. Suppose that you were deck of 52 cards?
scenarios. Identify which PACKAGE the overall in charge of the
situations demonstrate seating in an international Study : Circular Permutation and
permutation if it is, then MOUNTAIN Permutation with Repetition
convention wherein 12 country-
provide an example of a SCOUT representatives were invited.
possible arrangement, as well Give the formula for circular
They are the prime permutation and permutation with
as the overall number of ministers/presidents of the
arrangements. repetition.
B. Study permutation with countries of Canada, China, France,
repetition. Germany, India, Japan, Libya, Give real-life situations where
Malaysia, Philippines, South circular permutation and
Determining the top three Korea, USA, and United Kingdom. permutation with repetition can be
winners in a Mathematics Quiz applied.
Bee. If the seating arrangement is to
be circular, how many seating
Choosing five group mates for arrangements are possible?
your Mathematics project.
 Three people posing for a Study : Combination
picture.
a. Differentiate combination from
4. Assigning 4 practice permutation
teachers to 4 different grade
levels. c. Give real-life situations where
combination can be applied
5. Picking 5 questions to
answer from a bowl.

V. REMARKS EXTEND

Follow-up: How many

numbers consisting of 3 digits
can be made from 1, 2, 3, 4, 5,
and 6 if

Repetition is allowed

Repetition is not allowed

Study permutation of n
objects taken r at a time.

VI. REFLECTION

A. No. of learners who

earned 80% in the evaluation

B. No. of learners who

require additional activities
for remediation who scored
below 80%

C. Did the remedial lessons

work? No. of learners who
have caught up with the
lesson

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: Checked by:

Nonito P. Adalid Jr. Marilou M. Mapa Nestor A. Baldoz

Secondary School Teacher I Master Teacher I Secondary School Head

Teacher III