Instructional Planning
(The process of systematically planning, developing, evaluating and managing the
instructional process by using principles of teaching and learning - D.O. 42, s. 2016)
Detailed Lesson Plan (DLP)
DLP No.:
Learning Area:
1
Mathematics
Learning Competency/ies:
(Taken from the Curriculum Guide)
Key Concepts / Understandings to be
Developed
Grade Level:
10
Quarter:
4
Illustrates the following measures of
position: quartiles,
deciles and percentiles.
Knowledge
The fact or condition of knowing
something with familiarity gained
through experience or association
Skills
The ability and capacity acquired
through deliberate, systematic, and
sustained effort to smoothly and
adaptively carryout complex
activities or the ability, coming from
one's knowledge, practice,
aptitude, etc., to do something
Values
2. Content
3. Learning Resources
4. Procedures
4.1 Introductory Activity
3
minutes
4.2 Activity
4
4.4 Abstraction
M10SP - IVb - 1
OBJECTIVES:
Understanding
Determine the quartiles of an ungrouped data;
Applying
Solve quartile value of an ungrouped data;
Analyzing
Evaluating
●
●
Appreciate the concept of measures of position in real life situations;
Display teamwork and collaboration with others during the discussion.
Measures of Position (Quartile)
Grade 10 Mathematics Learner’s Materials (pp. 168-174), Internet Sources
Opening Prayer
Checking of Attendance
ACTIVITY 1: Find your Center…
minutes
4.3 Analysis
3
Code:
Remembering
Creating
Responding to
Phenomena
Valuing
Attitude
Date:
April 27, 2023
Pythagorean Theorem: In a right triangle, the square of the hypotenuse (c)
is equal to the sum of the squares of the legs (a and b).
In symbols; 𝑐 2 = 𝑎2 + 𝑏 2
Converse of the Pythagorean Theorem: If the square of the length of the
longest side of a triangle is equal to the sum of the squares of the lengths of
the other two sides, then the triangle is a right triangle.
Adapted
Cognitive
Process Dimensions
(D.O. No. 8, s. 2015)
Domain
Duration:
60 minutes
The midpoint between two numbers x and y on the real number line is
𝑥+𝑥
2
1) How do you feel about the activity?
minutes
2) Why do you think these concepts are necessary?
The quartile for ungrouped data
The quartiles are the score–points which divide a distribution into four equal parts. Twenty-five percent
(25%) of the distribution are below the first quartile, fifty percent (50%) are below the second quartile,
and seventy–five percent (75%) are below the third quartile. Q1 is called the lower quartile and Q3 is
the upper quartile. Q1 < Q2 < Q3 , where Q2 is the median. The difference between Q3 and Q1 is
the interquartile range.
Since the second quartile is equal to the median, the steps in finding the median are the same as the
steps in finding the Q1 and the Q3.
20
minutes
a. 25% 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 ℎ𝑎𝑠 𝑎 𝑣𝑎𝑙𝑢𝑒 ≤ 𝑄1
b. 50% 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 ℎ𝑎𝑠 𝑎 𝑣𝑎𝑙𝑢𝑒 ≤ 𝑀𝑑 𝑜𝑟 𝑄2
c. 75% 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 ℎ𝑎𝑠 𝑎 𝑣𝑎𝑙𝑢𝑒 ≤ 𝑄3
Example 1: The owner of a coffee shop recorded the number of customers who came into his café
each hour in a day. The results were 14, 10, 12, 9, 17, 5, 8, 9, 14, 10, and 11. Find the lower quartile
and upper quartile of the data.
Solution:
● The ascending order of the data is 5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17
● The least value in the data is 5 and the greatest value in the data is 17.
● The middle value in the data is 10.
● The lower quartile is the value that is between the middle value and the least value in the
data set.
● So, the lower quartile is 14.
Example 2: Find the average of the lower quartile and the upper quartile of the following data.
Component
Quantity
hard disk
290
monitors
370
keyboards
260
mouse
180
speakers
430
Solution:
●
The increasing order of the data is 180, 260, 290, 370, 430.
●
The least value of the data is 180 and the greatest value of the data is 430.
●
The middle value of the data is 290.
●
The lower quartile is the value that is between the least value and the middle value.
●
So, the lower quartile is 260.
●
The upper quartile is the value that is between the greatest value and the middle value.
●
So, the upper quartile is 370.
●
The average of the lower quartile and the upper quartile is equal to 315.
Example 3: The lower quartile of a data set is the 8th data value. How many data values are there in
the data set?
Solution:
●
The lower quartile is the median data value of the lower half of the data set.
●
So, there are 7 data values before and after the lower quartile.
●
So, the number of data values in the lower half is equal to 7 + 7 + 1. The number of values
in the data set is equal to lower half + upper half + 1.
●
The number of values in the lower and upper halves are equal.
●
Formula: 15 + 15 + 1 = 31.
●
So, the data set contains 31 data values.
Another solution:
1
𝑛+1=8
4
𝑛 + 1 = 32
𝑛 = 31
Example 4: Mendenhall and Sincich Method. Using Statistics for Engineering and the Sciences,
define a different method of finding quartile values. To apply their method on a data set with n
elements, first calculate:
1
Lower Quartile (𝑄1 ) = Position of 𝑄1 = (𝑛 + 1)
4
and round to the nearest integer. If L falls halfway between two integers, round up. The Lth element
is the lower quartile value of (𝑄1 ).
Next calculate:
3
Upper Quartile (𝑄3 ) = Position of 𝑄3 = (𝑛 + 1)
4
and round to the nearest integer. If U falls halfway between two integers, round down. The Uth
element is the upper quartile value of (𝑄3 ).
Example:
{1, 3, 7, 7, 16, 21, 27, 30, 31} and 𝑛 = 9.
1
To find 𝑄1 , locate its position using the formula 4 (𝑛 + 1) and round off to the nearest integer.
1
1
1
Position of 𝑄1 = (𝑛 + 1) = (9 + 1) = (10) = 𝟐. 𝟓
4
4
4
The computed value 2.5 becomes 3 rounding up. The lower quartile value (𝑄1 ) is the 3rd data
element, so 𝑄1 = 7. Similarly:
3
3
3
Position of 𝑄3 = (𝑛 + 1) = (9 + 1) = (10) = 𝟕. 𝟓
4
4
4
The computed value 7.5 becomes 7 rounding down. The upper quartile value (𝑄3 ) is the 7th data
element, so 𝑄3 = 27.
Try It?
Using this method, the upper quartile (𝑄3 ) and lower quartile (𝑄1 ) values are always two of
the data elements.
Find the first quartile (𝑄1 ), second quartile (𝑄2 ), and the third quartile (𝑄3 ), given the scores of 10
students in their Mathematics activity using Mendenhall and Sincich Method.
4
9
7
14
10
8
12
15
6
11
Answer key Q1 = 6 Q2 = 8.5 Q3 = 11
Example 5:
Find the first quartile (𝑄1 ), second quartile (𝑄2 ), and the third quartile (𝑄3 ), given the scores of 9
students in their Mathematics activity using Linear Interpolation.
1
27
16
7
31
7
30
3
21
Solution:
a. First, arrange the scores in ascending order.
1
3
7
7
16
21
27
30
31
b. Second, locate the position of the score in the distribution.
1
1
1
Position of 𝑄1 = (𝑛 + 1) = (9 + 1) = (10) = 𝟐. 𝟓
4
4
4
Since the result is a decimal number, interpolation is needed.
c. Third, interpolate the value to obtain the 1st quartile.
Steps of Interpolation
Step 1: Subtract the 2nd data from the 3rd data.
7−3=4
Step 2: Multiply the result by the decimal part obtained in the second step (Position of 𝑄1 ).
4 (0.5) = 2
Step 3: Add the result in step 2, to the 2nd or smallest number.
3+2=5
Therefore, the value of 𝑸𝟏 = 𝟓.
Solution:
a. First, arrange the scores in ascending order.
1
3
7
7
16
21
27
30
31
b. Second, locate the position of the score in the distribution.
3
3
3
Position of 𝑄3 = (𝑛 + 1) = (9 + 1) = (10) = 𝟐. 𝟓
4
4
4
Since the result is a decimal number, interpolation is needed.
c. Third, interpolate the value to obtain the 1st quartile.
Steps of Interpolation
Step 1: Subtract the 2nd data from the 3rd data.
30 − 27 = 3
Step 2: Multiply the result by the decimal part obtained in the second step (Position of 𝑄3 ).
3(0.5) = 1.5
Step 3: Add the result in step 2, to the 2nd or smallest number.
27 + 1.5 = 28.8
Therefore, the value of 𝑸𝟑 = 𝟐𝟖. 𝟓
Note: As we can see, these methods sometimes (but not always) produce the same results.
4.5 Application
Activity: Find Me
Find the first quartile (𝑄1 ), second quartile (𝑄2 ), and the third quartile (𝑄3 ), given the scores of 9
10
minutes
students in their Mathematics activity using Mendenhall and Sincich Method and Linear
Interpolation.
4
8
9
12
7
15
14
6
10
11
Answer Key:
4.6 Assessment
A. For each triangle find the missing length. Round your answer to the nearest
Quiz
tenth.
B. Use the Pythagorean Theorem to find the unknown side of the given right
triangle if the lengths of its two sides are given.
5. a = 12 ; b = 5; c = _____________
6. a = 8 ; b =____________ ; c = 10
7. a = 15 ; b =____________ ; c = 17
8. a = ____________ ; b = 40 ; c =50
9. a = ____________ ; b = 2 ; c = 4
10. a = 6 ; b = 8 ; c = ___________
15
ANSWER KEY!
1) 6√2 ≈ 8.5
2) 13.9
3) 17.3
4) 14.9
5) 13
minutes
6)
7)
8)
9)
10)
6
8
30
2√3 ≈ 3.46
10
4.7 Assignment
A. Given a set of three numbers, show that these represent a Pythagorean
3
triple.
minutes
1) 3, 4, 5
2) 6, 8, 10
3) 7, 24, 25
4) 6, 15, 18
5) 7, 9, 12
B. Use the Pythagorean theorem to find the unknown side of the given right
triangle if the lengths of its two sides are given.
Enhancing /
improving the
day’s lesson
Right Triangle
A
B
C
D
E
Shorter leg (a)
3
5
8
9
Longer leg (b)
12
24
15
Hypotenuse (c)
5
25
41
C. Calculate the missing side measurement using 𝑎2 + 𝑏 2 = 𝑐 2 .
ANSWER KEY!
A.
1) 25 = 25
2) 100 = 100
3) 625 = 625
4) 261 ≠ 324
Pythagorean triple
Pythagorean triple
Pythagorean triple
Not a Pythagorean triple
Not a Pythagorean triple
5) 130 ≠ 144
B.
A. 4
B. 13
C. 7
D. 17
E. 40
C.
1) 𝑎 = √𝑐 2 − 𝑏 2 = √24.012 − 20.52 = 12.5 𝑚𝑖
2) 𝑏 = √𝑐 2 − 𝑎2 = √12.652 − 82 = 9.8 𝑚
3) 𝑐 2 = √𝑎2 + 𝑏 2 = √16.42 + 12.42 = 20.56 𝑦𝑑
4.8 Concluding Activity
2
minutes
Output: Fill Me!
To check if you understood the lesson, fill the table below to check your understanding of the lesson
about the Pythagorean theorem.
Draw a Right Triangle and label the
three sides.
Describe the sides:
Legs:
Hypotenuse:
Pythagorean
Theorem
Write the theorem
The formula:
5. Remarks
6. Reflections
A. No. of learners who earned 80% in the
evaluation.
C. Did the remedial lessons work? No. of learners who have
caught up with the lesson.
B. No. of learners who require additional
activities for remediation.
D. No. of learners who continue to require remediation.
E. Which of my learning 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:
Name:
Regine Marie L. Leguro
School:
Tubod National High School
Position/
Designation
:
Contact
Number:
Student Teacher
Division:
Cebu Province
+639605060509
Email address:
reginemarie.leguro@ctu.edu.ph