Northeastern College, Inc.
Santiago City
College of Education
A Detailed Lesson Plan
In Mathematics 10
LEARNING AREA:
SCHOOL:
NAME OF TEACHER:
I. OBJECTIVES
A.
CONTENT
STANDARD:
B.
PERFORMANCE
STANDARD:
Mathematics 10
Northeastern College
Myckhaell Jhon Xyrille C. Agcanas
4th QUARTER
WEEK 1 DAY 1
DATE/TIME:
The learner demonstrates an understanding of key concepts of measures
of Position.
The Learner is able to investigate thoroughly the mathematical relationship
in situations, formulate real-life problems involving measures of position,
and solve them using a variety of strategies.
C.
LEARNING Illustrates the following measures of position: quartiles, deciles, and
COMPETENCIES:
percentiles.
LEARNING CODE:
M10SP-IVa-1
UNPACKED
 Identify the quartiles for ungrouped data as measures of position.
COMPETENCY
 Calculate the lower and upper quartiles using the formula.
/LEARNING OBJECTIVE:
 Illustrate the quartile value of ungrouped data.
 Appreciate the concept of measures of position in real-life situations.
II. CONTENT
Illustrating Measures of Position: Quartiles, Deciles, and Percentiles
III. LEARNING RESOURCES
A. References:
1. Teacher’s Guide
Mathematics 10 Teacher’s Guide p. 328-332
2.
Learner’s Mathematics 10 Learner’s Materials p. 373-377
Materials Pages
3. Textbook pages
4.
Additional Projector, Smartphone, Laptop, Powerpoint Presentation, Interactive
Materials from Learning Online Apps, and Game-based assessment apps
Resource (LR)
CO_Q4_Mathematics 10_ Module 33
B. Other Learning
Resources
IV. LEARNING
PROCEDURE:
A. Reviewing the
previous lesson or
presenting the new
lesson
TEACHER’S ACTIVITY
STUDENTS’
ACTIVITY
Prayer, Greetings, and Checking of Attendance.
Since everyone here is amazing, may I invite you to
listen and follow these mathematical steps that will be
presented through an AVP.
https://www.youtube.com/watch?v=95Ac9ZxyOp4
What do you think is our lesson for today?
Student A: Measures
of Position (Quartiles,
Deciles, and
Percentiles)
Northeastern College, Inc.
Santiago City
College of Education
B. Establishing a
purpose for the
lesson
Very good, thank you for sharing your ideas.
For us to be guided on what we expect, here are our
objectives, anyone please read.
At the end of the
lesson, students will
be able to:
a) Identify the
quartiles for
ungrouped
data as
measures of
position.
b) Calculate the
lower and
upper quartiles
using the
formula.
c) Illustrate the
quartile value
of ungrouped
data.
d) Appreciate the
concept of
measures of
position in
real-life
situations.
C. Presenting
Use of Games Activity 1: “Decode me!”
examples/instances Direction: The students are required to open their mobile
of the new lesson
phone and join in the game. (classpoint.app)
1. MEASURE
2. POSITION
3. QUARTER
4. ARRANGE
D. Discussing new
Based on our activity, what are the words you are able to
concepts and
decode from the pictures?
practicing new skills
#1
Very good!
Student A: Measure,
position, quarter, and
arrange.
Northeastern College, Inc.
Santiago City
College of Education
So, we have the measure and position, quarter, and
arrange.
What do you feel with the activity?
Student B: Exciting
sir.
Do these words connected to each other?
Student C: Some of
the words are
connected to each
other like quarter and
arrange.
Okay, those words are connected to each other because
it is part of our lesson this morning.
E. Discussing new
A measure of position determines the position of a
concepts and
single value in relation to other values in a sample data
practicing new skills set. It gives us a way to see where a certain data point
#2
or value falls in a sample or distribution. This measure
will tell us whether a value is about the average, or
whether it's unusually high or low.
Quartiles are the 3 score points that divide the data or
distribution into four equal parts. These are the first
quartile (Q1), the second quartile (Q2), and the third
quartile (Q3).
Take note:
a) 25 % of the data has a
value ≤ Q1 or Lower
Quartile
b) 50 % of the data has a
value ≤ Q2 or Median
c) 75 % of the data has a value ≤ Q3 or Upper
Quartile
The difference between the upper quartile (Q3) and the
lower quartile (Q1) is called Interquartile Range (IQR). In
the above-given values, the IQR is equal to Q3 – Q1 or 15
–6=9
Remember:
Northeastern College, Inc.
Santiago City
College of Education
FINDING THE VALUE OF QUARTILES OF
UNGROUPED DATA
STEPS IN SOLVING QUARTILES USING THE
MENDENHALL AND SINCICH METHOD
Step 1. Arrange the data values in increasing
(Smallest to biggest) order.
Step 2. Use the following formulas/rules to compute the
positions/values of Q1 and Q3.
a) Lower Quartile (L) =
Position of Q1 = (where is the number of elements
in a data. If L (Position of Q1) is a decimal number,
round up (e.g. 3.25 becomes 4 and 7.5 becomes
8).The Lth element is the lower quartile value (Q1).
b) Upper Quartile (U) =
Position of Q3 = (where is the number of elements
in a data. If U (Position of Q3) is a decimal number,
round down (e.g. 3.25 becomes 3 and 7.5
becomes 7). The Uth element is the upper quartile
value (Q3).
1. Lower QuArtile (Q1):
Step1: Arrange the data elements in increasing order.
Step 2: Apply the given formulas/rules to compute the
position of Q1.
Step 3. Locate the element in the arranged data set that
corresponds to the computed position.
The 3rd element from the arranged data set is 7.
Therefore, the value of the Lower Quartile (Q1) = 7.
Northeastern College, Inc.
Santiago City
College of Education
2. MediAn (Q2):
a) If the number of elements (n) in a data is odd, there
is only one middle number, and this is the median.
b) If the number of elements (n) in a data is even, there
are two middle numbers, and you have to compute
their average to get the median.
3. Upper QuArtile (Q3)
(Follow the same steps in solving Lower Quartile.)
Remember:
Rounding Up is only used in finding the position of
the Lower Quartile (Q1) Rounding Down is only
used for the Upper Quartile (Q3) if and only if L or U
is non-integral.
4. InterquArtile RAnge (IQR) is the difference
between the values of the upper and the lower quartiles.
LINEAR INTERPOLATION
Another method of solving the value of Q1 and Q3 is
by using Linear Interpolation. Interpolation is used
when the computed value of the position is decimal or
non-integral.
Example:
Compute the value of the upper quartile (Q3) using
linear interpolation. Use the same set of data.
Northeastern College, Inc.
Santiago City
College of Education
F. Developing
mastery (Leads to
formative
assessment 3)
Since 8.25 is a decimal number, we need to interpolate.
Take note: the 8.25th position lies between the 8th
and 9th elements of the given data.
Use of Games Activity 2: “Let’s Master!”
Direction: Answer the given questions. Show your
solutions on your answer sheet. (Wheel of Names to
answer on the board)
1. Consider the score distribution of 15 students given
below and perform the tasks as instructed.
25, 16, 23, 18, 20, 21, 19, 21, 24, 15, 26, 17, 10,
22, 23
For the guide questions:
1. Arrange the data elements in increasing order.
2. Find the value of Q1 or Lower Quartile.
3. Calculate the median or Q2.
4. Find the value of Q3 or Upper Quartile.
5. Compute the interquartile range (IQR).
I will give you 5 minutes to do the activity. Am I
Understood?
Yes, sir!
Solution:
1. 10, 15, 16, 17, 18,
19, 20, 21, 21, 22,
23, 23, 24, 25, 26.
1
2. Q1 = 4 (15 + 1)
1
Q1 = 4 (16)
Q1 = 4th
Q1 = 17
3. Q2 = 21
3
4. Q3 = 4 (15 + 1)
3
Q3 = 4 (16)
Q3 = 12th
Q3 = 23
Northeastern College, Inc.
Santiago City
College of Education
5. IQR = 23 – 17
IQR = 6
G. Finding practical
applications of
concepts and skills
in daily living
Activity 3: “Let’s Identify!”
Let me group you into two, Arrange the data elements in
increasing order, and determine the Lower Quartile (Q1),
and the Median (Q2) and Upper Quartile (Q3) of the given
data set. Please be guided by the rubrics below.
Solution:
Group 1
1) 9, 10, 15, 16,
17, 18, 19, 20,
21, 21, 22, 23,
9, 25, 16, 23, 18, 20, 21, 19, 26, 21, 24, 15, 26,
23, 24, 25, 26,
17, 10, 22, 23
26
2. A group of farmers harvested the following: 14 kilos of
1
2) Q1 = 4 (17 + 1)
corn, 16 kilos of watermelon, 19 kilos of tomatoes 15
1
kilos of pumpkin, 10 kilos of cabbage, 20 kilos of
Q1 = 4 (18)
strawberry, 14 kilos of cucumber, 19 kilos of eggplant,
Q1 = 4.5
25 kilos of mulberry, 15 kilos of carrots, and 16 kilos of
Q1 = 5th
potatoes.
position
Q1 = 17
Group 2
3) Q2 = 21
1. Consider the allowance distribution per day of 17 grade
3
4) Q3 = 4 (17 + 1)
7
Group 1
1. Consider the score distribution of 17 students given
below and perform the tasks as instructed.
Students given below and perform the tasks as
instructed.
20, 50, 60, 70, 80, 90, 90, 100, 30, 20, 40, 30, 40, 80,
50
2. Given the ages of the farmers who voted in precinct
no.
232B: 39, 42, 32, 30, 50, 32, 21, 21and 50.
3
Q3 = 4 (18)
Q3 = 13.5
Q3 = 13th
position
Q3 = 23
Northeastern College, Inc.
Santiago City
College of Education
Group 2
1) 20, 20, 30, 30,
40, 40, 50, 50,
60, 70, 80, 80,
90, 90, 100.
1
2) Q1 = 4 (15 + 1)
1
Q1 = 4 (16)
Q1 = 4th
position
Q1 = 30
3) Q2 = 50
3
4) Q3 = 4 (15 + 1)
3
Q3 = 4 (16)
Q3 = 12th
position
Q3 = 80
H. Making
generalizations and
abstractions about
the lesson
(Ask the students to state the concept they have
learned.)
Again, what is the first step to do in our data?
Arrange the data
values in increasing
order.
Yes, very good!
So, after we arrange the data values , what formula or
rules are we going to use to find the values of Lower (Q1)
‘
By simply using the
formula
1
Q1 = 4 (𝑛 + 1)
Where n = to the
number of elements in
the data.
How about the Upper Quartile (Q3)?
3
Q3 = 4 (𝑛 + 1)
Where n = to the
number of elements in
the data.
I. Evaluating
learning
Very good!
Use of ICT (Google Form)
Assessment:
Directions: Choose the letter of the correct answer.
1. When a distribution is divided into 4 equal
parts, each score point that describes the
Answers:
1. D.
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Santiago City
College of Education
distribution is called.
A. median
B. percentile
C. decile
D.
quartile
2. If the 25% of the data has a value of lesser
than
or equal to 15, it means that
.
A. Q1= 15
B. Q2= 15
C. Q3= 15
D. Q4=
15
3. Given the scores 7, 9, 10, 13, 15, 16, 20, what
is \
the value of lower quartile?
A. 7
B. 9
C. 10
D. 13
4. In the quartile, the median to be measured must be in
.
A. first quartile
B. second quartile
C. third quartile
D. fourth quartile
5. The IQR of a certain data is 5.5. If the
value of Q1= 3.25, what is the value of Q3?
A. 2.30
B. 2.35
C. 8.75
D. 8.80
6. Find the value of Q2 using the following data:
11, 14, 10, 27, 23, 23, 48, 15
A. 18
B. 19
C. 20
D. 21
For Question 7-10
. A group of students of JNHS obtained the following
scores
in their Statistics quiz: 32, 39, 27, 23, 42, 35, 42, 29, 46,
37, 42.
7. Find the Lower Quartile.
A. 32
B. 23
8. Find the Median or the Q2.
A. 42
B. 46
9. Find the Upper Quartile.
A. 42
B. 23
10. Find the IQR.
A. 13
B. 15
J. Additional
activities for
application or
remediation
C. 46
D. 29
C. 23
D. 37
C. 27
D. 32
C. 18
D. 21
Assignment/ Additional Activity: (Kahoot.it) Joining code
will be posted on our gc to submit your answers
1. You are going to know what the quartiles of the scores
in your mathematics class of your 5 friends including
yours. The scores are 3, 5, 6, 8, 8, 10. Find the Q1, Q2,
and Q3.
2. You have a big problem in your assignment about
getting the quartiles of the given distribution. Now, find a
2. A.
3. B.
4. B.
5. C.
6. B.
7. D.
8. D.
9. A.
10. A.
Northeastern College, Inc.
Santiago City
College of Education
way that you can get the values of the quartiles of the
ages of malnourished children in JNHS. 7, 9, 9, 10, 11,
12, 13, 15, 15, 16, 16
Write something about your learning for today’s lesson
and the instances you find hard.
V. REMARKS
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
_________________________________________________________________
VI. REFLECTION
1.
2.
3.
4.
5.
6.
7.
No.of learners who earned 80%
on the formative assessment
No.of learners who require
additional activities for
remediation.
Did the remedial lessons work?
No .of learners who have
caught up with the lesson.
No.of learners who continue to
require remediation
Which of my teaching strategies
worked well? Why did this
work?
What difficulties did I encounter
that my principal or supervisor
can help me solve?
What innovation or localized
materials did I use/discover that
I wish to share with other
teachers?
Prepared by:
Myckhaell Jhon Xyrille C. Agcanas
Demo Teacher
Checked By:
Rina A. Guingab, LPT
Teacher Observer