Detailed Lesson Plan
In
MATHEMATICS 10
By
DINA A. VILLABUEVA
I. Objectives
At the end of the lesson the students should be able to:
1. Illustrate permutation of objects
2. Solve problems involving permutation
II. Learning Task
1. Subject Matter
PERMUTATION
2. Learning Content
Permutation is the arrangement of all or parts of a set of objects
with proper order.
3. References
MATH 10 Learners Module and Teachers Guide
Pages 286 – 297 (LM), pages 253 – 256 (TG)
4. Materials
QR Codes, TV, Laptop, Cellphone
5. Value Focus
Cooperation
III. Developmental Activity
Teachers Activity
1. Introduction
Siegle, please the prayer
Good Morning Class!
You may take your seats
Who among you can read our
objectives for today?
Yes, Tricia.
Thank you
2. Motivation
At this point, I want you to get your
mobile phones and prepare your
QR Code Reader for a group
Students Activity
Good afternoon Ma’am!
Thank you Ma’am.
1. Illustrate permutation of objects
2. Solve problems involving permutation
activity.
Can you see the codes in different
parts of the classroom?
You are going to discover your task
behind those codes, are you ready?
Yes Ma’am!
Yes Ma’am!
See attached table A
Number
of
objects
(n)
2
2
3
3
3
4
4
4
4
3. Presentation
How do you find our activity?
Those possible combinations are
what we called permutation.
Now let us define what permutation
is
Permutation is the arrangement of
all or parts of a set of objects with
proper order.
We calculate the different
permutations by applying the
formula
𝑛!
P (n,r) = (𝑛−𝑟)! taken r at a time and
P(n,n) = n! taken all at a time
Examples:
1. Ten runners join the race. In how
many possible ways can they be
arranged as first, second and third
Number
of
objects
take at a
time (r)
1
2
1
2
3
1
2
3
4
Exciting and Enjoyable
Number of
possible
arrangements/
Permutations
2
2
3
6
6
4
12
24
24
place?
Who wants to solve?
Yes Jueno!
Using the formula
𝑛!
P (n,r) = (𝑛−𝑟)!
10!
P(10, 3) = (10−3)!
P(10,3) =
10!
7!
P(10,3) =
3,628,800
5040
P(10,3) = 720
2. In how many ways can Aling
Rosing arrange 6 different potted
plants in a row?
4. Activity
I am going to group you into 4
groups and each group will be
given activity sheets.
Group 1
Given the four letter word READ, in
how many ways can we arrange its
letter, 3 at a time?
Group 2
In a school club, there are 5 possible
choices for the president, a
secretary, a treasurer and an
auditor. Assuming that each of them
is qualified for any of these positions,
in how many ways can the 4 officers
be detected?
Group 3
In how many ways can 5 people
arrange themselves in a row for
picture taking?
Group 4
Find the number of permutation in
the word EVEN.
Group 5
Find the number of permutations of
the letters of the word STATISTICS
5. Analysis
Reporting of each group
Questions:
P(6,6) = 6!
720 ways
P (4,4) = 4!
4.3.2.1
24
P(5,4) = 5.4.3.2.1
120 ways
P(5,5)
5.4.3.2.1
120 ways
P=
(4,4)
2!
12 distinguishable permutations
10!
P = 3!3!2!
50 400 permutations
1. How do you solve for the n
permutations taken all at a time?
2. How do you solve for the n
permutations taken r at a time?
6. Application
Answer by group
1. P(6,6)
2. P(10,5)
3. P(8, 3)
4. A teacher wants to assign 4
different tasks to her 4 students, in
how many possible ways can she do
it?
5. How many distinguishable
permutations are possible with all
the letters of the word ELLIPSES?
7. Abstraction
How do you find our lesson today?
Who can give me the summary of
our
lesson?
IV. Evaluation
Answer on a ½ crosswise
1. P(4,2)
2. P (7,7)
3. P(10, 2)
4. How many distinguishable
permutations are possible with all
the
letters of the word MISSION?
5. There are 8 basketball teams
competing for the top 4 standings in
order to move up the semi finals.
Find
the number of possible rankings of
the
four top teams.
VI. Assignment
Answer Activity 7 of your learners
module on page 297
Using the formula P(n,n) = n!
Using the formula P(n, r) =
𝑛!
(𝑛−𝑟)!
1. 720
2. 30240
3.336
4. 24
5. 5040
Easy!
Permutation is the arrangement of all
or parts of a set of objects with proper
order.
We calculate the different
permutations by applying the formula
𝑛!
P (n,r) = (𝑛−𝑟)! taken r at a time and
P(n,n) = n! taken all at a time
Detailed Lesson Plan
In
MATHEMATICS 10
By
DINA A. VILLABUEVA
I. Objectives
At the end of the lesson the students should be able to:
1. Illustrate the DECILE for grouped data
2. Calculate specified measures of position (e.g., 7th DECILE)
3. Cooperate in group activities
II. Learning Task
1. Subject Matter
DECILES FOR GROUPED DATA
2. Learning Content
Deciles are those values that divide the total frequency into 10
equal parts. The kth decile denoted by Dk is composed as
follows:
𝑘𝑁
−𝑐𝑓𝑏
10
Dk = LB +(
𝑓𝐷𝑘
)𝑖
3. References
MATH 10 Learners Module and Teachers Guide
Pages 388-389 (LM), pages
(TG)
4. Materials
Visual Aids, TV, Laptop
5. Value Focus
Cooperation
III. Developmental Activity
Teachers Activity
Good Morning Everyone!
Who wants to lead the prayer?
Before we start our lesson proper let us
first read our objectives for today.
Bonji please read.
Students Activity
Yes Janah.
At the end of the lesson the students
should be able to:
1. Illustrate the DECILE for grouped
data
2. Calculate specified measures of
position (e.g., 7th DECILE)
3. Cooperate in group activities
1. MOTIVATION
Matching type
Match column A with column B
Corresponding numbers will have
corresponding letters that later will reveal
our lesson for today.
2. ACTIVITY
Discussion
Deciles are those values that divide
the total frequency into 10 equal
parts. The kth decile denoted by Dk is
composed as
follows:
𝑘𝑁
−𝑐𝑓𝑏
10
Dk = LB +(
𝑓𝐷𝑘
Matching type
Match column A with column B
Corresponding numbers will have
corresponding letters that later will reveal
our lesson for today.
A
B
1. LB
L - size of class interval
2. N
E - total frequency
3. cfb
D - lower boundary of Dk
4. fDk
E - nth decile,
n=1,2,3,4,5,etc
5. i
C - cumulative frequency
before Dk
6. k
I - frequency of Dk class
)𝑖
I have here table on the board. We
will fill in the table and later on we will
solve for the 7th deciles.
Scores
46-50
41-50
36-40
31-35
26-30
21-25
f
4
8
11
9
12
6
LB
<cf
Group Activity (4 groups)
I have here steps on the board, all
you have to do is follow the steps for
you to come up with our answer.
Step 1: Identify the value of k and N
Step 2: solve for Dk =
𝑘𝑁
10
Since our D7 = 35 this means we need to
find the class interval where the 35th
Scores
46-50
41-50
36-40
31-35
26-30
21-25
K=7
N = 50
7𝑁
D7 = 10
D7 =
7(50)
10
D7 =
350
10
D7 = 35
f
4
8
11
9
12
6
LB
45.5
40.5
35.5
30.5
25.5
20.5
<cf
50
46
38
27
18
6
score is contained. Try to look at our <cf,
where do you think 35th score belongs?
Note that 28th – 38th scores belong to
class interval 36-40, so the 35th score is
also within the class interval.
The D7 class is the class interval 36-40
Step 3 Identify the values of
𝑘𝑁
10
38
𝑘𝑁
, 𝑐𝑓𝑏 , 𝑓𝐷𝑘 , LB, i
Step 4 Solve for the D7 using the formula:
𝑘𝑁
−𝑐𝑓𝑏
10
Dk = LB +(
𝑓𝐷𝑘
10
= 35, 𝑐𝑓𝑏 = 27, 𝑓𝐷𝑘 =11, LB = 35.5, I = 5
Dk = 35.5 +(
)𝑖
35−27
D7 = 39.13
3. ANALYSIS
Choose one reporter to explain their
work in front of the class.
1. What are the things that you will
consider in solving for DECILES for
grouped data?
)
11
1. Values of k, N,
𝑘𝑁
10
, 𝑐𝑓𝑏 , 𝑓𝐷𝑘 , LB, i
2. Position of LB, 𝑐𝑓𝑏 , 𝑓𝐷𝑘
4. APPLICATION
Group Activity (4 groups)
The following is a distribution for the
number of employees in 45 companies
belonging to a certain industry.
Calculate for the 4th and 8th deciles of
the number of employees given the
number of companies.
Number of
Employees
41-45
36-40
31-35
26-30
21-25
16-20
f
LB
<cf
11
6
9
7
8
4
5. ABSTRACTION
Ask student to summarize the topic
today.
Let them watch the video that
summarizes the lesson.
Number of
Employees
41-45
36-40
31-35
26-30
21-25
16-20
f
LB
<cf
11
6
9
7
8
4
40.5
35.5
30.5
25.5
20.5
15.5
45
34
28
19
12
4
IV. EVALUATION
On a 1/2 crosswise pad paper, fill in
the table and solve for the following:
Assume that a researcher wanted to
know the percentage of consultants
who made Php 5, 400.00 or more per
day.
1. D7
2.D4
CONSULTANT
FEES
(in Php)
Number of
LOWER
LESS THAN
Consultants BOUNDARIES CUMMULATIVE
FREQUENCY
(LB)
(<cf)
6400-7599
11
5200-6399
6
4000-5199
9
2800-3999
7
1600-2799
8
V. ASSIGNMENT
Study PERCENTILES OF GROUPED DATA