education

1. Annex 2B.1 to DepEdOrderNo.42 ,s. 2016
Time : 11:00 – 12:00 ARROYO Monday
I. OBJECTIVES
A. ContentStandard The learnerdemonstratesunderstandingof keyconceptsof quadratic
equations.
B. Performance standard The learnerisable to investigatethoroughlymathematical
relationships invarioussituations,formulate real-lifeproblems
involvingquadraticequations.
C. LearningCompetencies
Write the LC Code for each
The learner characterizes the roots of a quadratic equation using the
discriminant.
M9AL-Ic-1
II. CONTENT The Nature of the Roots of a Quadratic Equation
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide pages
2. Learner’s materialspages pp. 56-65
3. Textbook pages
4. Additional Materialsfrom
Learning Resource (LR) portal
B. Other Learning Resources PowerPoint Presentation, Student Activity Sheet and Black cartolina
IV. PROCEDURES TEACHER ACTIVITY STUDENT ACTIVITY
A. Reviewingpreviouslessonor
presentingthe new lesson.
Good MorningClass!
House Rule:
1. Enter tolearn
2. Behave
3. Be responsible
Do youunderstand?
VeryGood!
Our lessonfortodayisabout The
Nature of the Rootsof Quadratic
Equation.Butbefore we goon, let
us have a short review.
Rememberthatthe quadratic
formulais,
𝑥 =
−𝑏±√𝑏2−4𝑎𝑐
2𝑎
Andb2
– 4ac isthe discriminantof
the equationax2
+ bx + c = 0.
Good morningsir!It’snice to
see you!
Yes sir!
Smiling
Listening
DAILY LESSON
LOG
School
PRESIDENT QUIRINO
NATIONAL HIGH SCHOOL
Grade Level GRADE 9
Teacher JOHN L. PADASAN Learning Areas MATHEMATICS
Teaching
Day
JULY 08, 2019 (Day26) Quarter FIRST

2. B. Establishinga purpose for the
lesson.
(Lecture Method)
Thisvalue can be describedthe
nature of the rootsof quadratic
equation.Itcan be,
1. Real numberandare equal if the
discriminantisequal tozero.
2. Rational numberbutnotequal if
the discriminantisgreaterthan
zeroand a perfectsquare.
3. Irrational numbers andnotequal
if the discriminantisgreaterthan
zerobut not a perfectsquare.
4. Noreal roots if the discriminant
islessthan zero.
Like forexample,
Listening
C. Presentingexamples/instancesof
the lesson.
(Demonstrationand Socratic
Method)
1. Describe the rootsof
x2
– 4x + 4 = 0
a = 1, b = -4 , c = 4
b2
– 4ac = (-4)2
– 4 (1)(4)
= 16 – 16
= 0
Since the value is0, thenthe roots
are real and are equal.
Another problemand letthe
studentto answerit on the board.
2. Determine the nature of the
roots of x2
+ 7x + 10 = 0.
Since the value isgreaterthan0
and perfectsquare then whatisthe
nature of the roots?
3. Describe the rootsof x2
+ 6x + 3
= 0
Since the value isgreaterthan0
and nota perfectsquare thenthe
roots is?
4. Determine the nature of the
roots of x2
+ 2x + 5 = 0
Since the value islessthan0 then
the equationhas?....
Understand?
Is there anyquestion?
VeryGood! Not yet. Now,proceed
to yourgroup and do the following
activities.
Listeningandasksany
clarification
Givenproblemansweredbythe
studenton the board.
x2
+ 7x + 10 = 0.
a = 1, b = 7 , c = 10
b2
– 4ac = (7)2
– 4 (1)(10)
= 49 – 40
= 9
Rational numberbutnotequal.
Givenproblemansweredbythe
studentonthe board.
x2
+ 6x + 3 = 0
a = 1, b = 6 , c = 3
b2
– 4ac = (6)2
– 4 (1)(3)
= 36 – 12
= 24
Irrational numberandnot
equal.
Givenproblemansweredbythe
studentonthe board.
x2
+ 2x + 5 = 0
a = 1, b = 2 , c = 5
b2
– 4ac = (2)2
– 4 (1)(5)
= 4 – 20
= - 16
No real roots.
Yes,sir!
None sir! Quiz!Quiz!Quiz!
Ugh…
Proceedtotheirrespective
groupand do the activities.
D. Discussing newconcepts and
practicing new skills#1
(ActivityMethod)
(Concept)
Activity5: Place Me on the Table!
Do the activity by group

3. E .Discussing newconcepts and
practicing new skills#2
(Process)
Activity7: What IsMy Nature?
Do the activity by group
F. Developingmastery
( Leadsto Formative Assessment3)
(Reflect)
Activity9: How Well DidI
Understand the Lesson?
Do the activity by group
G.FindingPractical applications of
concepts and skillsin dailyliving
(Transfer)
Activity10: Will Itor Will ItNot?
Do the activity by group
H. Presentationof Activity
(Socratic Method)
Askthe studentsto presentto
presenttheirwork. Present the work done.
I. Making generalizationsand
abstractions about the lesson
The lessonprovidedyouwith
opportunitiestodescribe the
nature of the rootsof quadratic
equationusingthe discriminant
evenwithoutsolvingthe equation.
Most importantly,youwere able to
findouthow the discriminantof a
quadraticequationisillustratedin
real-lifesituation.
Listening
J. Evaluating learning Formative Answerthe formative exam
K. Additional activities for
application or remediation.
Assignment Note the assignment
V. REMARKS Achieved
VI. REFLECTION
A. No. of learnerswho earned
(80%) in the evaluation
60
(Note: 80% in 0=60 transmutation formula is 1/2 of the highest possible score)
B. No. of learnerswho require
additional activitiesfor remediation.
5
C. Did the remedial lessonswork?
No. Of learnerswho have caught up
with the lesson.
5
D. No. of learnerswho continue to
require remediation.
0
E. Whichof my teachingstrategies
worked well?Whydidthese work?
Lecture method, Demonstration method, Activity Method and
Socratic method.
F. What difficultiesdidIencounter
which my principal or supervisorcan
helpme solve?
None
G. Whatinnovation or localized
materialsdid I use/discoverwhich I
wish to share with otherteachers?
Used of black cartolina and chalk as student/group work sheet for
presentation.
Preparedby:
JOHN L. PADASAN
Math Teacher
Checkedby:
NIEVA B. COSTALES, MT-I
Math DepartmentHead

4. ACTIVITY SHEET
July 08, 2019
Rule: Work in group. After doing the following activities the group leader will pick a number
from which of the following activities will be presented by the group. The leader shall also
assign rate to the members from 1-5 based on participation. The fraction hereof is multiplied to
the group score by the teacher for individual score in performance tasks.
Name of Group: ____________________
Leader: ___________________________
Members: Rate:
1. _________________________ __________
2. _________________________ __________
3. _________________________ __________
4. _________________________ __________
5. _________________________ __________
A. Activity 5: Place Me on the Table!
Answer the following.
1. Complete the table.
Equation b2- 4ac Roots
1. x2 + 5x = 4
2. -4 x2 = 8x - 3
3. 10x - 1 = 4x2
4. 15 + 8x - 3x2
5. 3x(x – 14) = 12
2. Which quadratic equation has roots that are….
a) Real numbers and equal? __________________________
b) Rational numbers? _______________________________
c) Irrational numbers? _______________________________
d) Not real numbers? ________________________________
B. Activity 7: What Is My Nature?
Determine the nature of the roots of the following quadratic equations using the discriminant.
1. x2 + 6x + 9 = 0 discriminant:__________ nature of the roots: __________
2. 2x2 - 10x + 8 = 0 discriminant:__________ nature of the roots: __________
3. x2 + 5x + 10 = 0 discriminant:__________ nature of the roots: __________
4. 3x2 - 2x - 5 = 0 discriminant:__________ nature of the roots: __________
5. 9x2 - 6x = -9 discriminant:__________ nature of the roots: __________
a. How didyoudetermine the nature of the rootsof each quadraticequation?
_____________________________________________________________________________________
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b. Whendo yousay that the rootsof a quadraticequation isreal or not real numbers?Rational or
irrational numbers?Equal ornotequal?
_____________________________________________________________________________________
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c. How doesthe knowledgeof the discriminanthelpyouindeterminingthe nature of the rootsof any
quadraticequation?
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5. _____________________________________________________________________________________
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C. Activity 9: How Well Did I Understand the Lesson?
Answer the following questions.
1. Describe the roots of the quadratic equation when the discriminant is
a. Zero. ____________________________________________________________
b. Positive perfect square. _________________________________________________
c. positive but not perfect square. ___________________________________________
d. negative. _____________________________________________________________
2. Danica says that the quadratic equation 2x2 + 5x - 4 = 0 has two possible solutions
because the value of its discriminant is positive. Do you agree with Danica? Justify your
answer.
________________________________________________________________________
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D. Activity 10: Will It or Will It Not?
Answer the following.
1. When a basketball player shoots a ball his hand at an initial height of 2 m with an initial
upward velocity of 10 meters per second, the height of the ball can be modeled by the
quadratic expression -4.9t2 + 10t + 2 after t seconds.
a. What will be the height of the ball after 2 seconds?
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b. How long will it take the ball to reach the height of 4.5m? How long will it take to touch
the ground?
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c. Do you think the ball can reach the height of 12 m? Why?
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d. Will the ball hit the ring if the ring is 3 m high?
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