Detailed Lesson Plan

School PalawanSU-PCAT Grade Level Grade 9

Teacher Trixy Ann C. Franco Learning Area Algebra
Time & Dates May 14, 2025 (5:00- Quarter First Quarter
5:25)

I. OBJECTIVES
1. Content Standard Students will understand and apply the concept of quadratic
equations and their solutions.
2. Performance Standard Students will be able to solve real-world problems that can be
modeled using quadratic equations.
3. Learning Solve Problems Involving Quadratic Equation M9AL-Ii-j-2
Competencies

Objectives Students will be able to:

a) identify quadratic equations.
b) solve quadratic equations-related problem using various
methods (factoring and quadratic formula).
c) relate quadratic equations to solve real-world problems.
II. CONTENT PROBLEM SOLVING INVOLVING QUADRATIC
EQUATIONS
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
2. Learner’s Materials
pages
3. Textbook pages
4. Additional Materials Mathematics 9 Quarter 1 – Module 3: Solving Problems Involving
from Learning Quadratic Equations and Rational Algebraic Equations
Resources (LR) portal
B. Other Learning Marker, Cartolina
Resources
IV. PROCEDURES
TEACHER’S ACTIVITY STUDENT’S ACTIVITY
PRELIMINARY
ACTIVITIES

Greetings Good Afternoon class! Good Afternoon Ma’am!

How are you today? Are you all

 feeling good? We’re fine, Ma’am!

That’s good to hear.

Class, may I know who is absent

Checking of Attendance today? None, Ma’am!

Good to hear! It is just a

manifestation that all of you are
interested to learn new knowledge
this morning.

Class, are you ready to learn our

new lesson this morning? Yes, Ma’am!

Good! Then, show me that you are

ready. Sit properly and listen
attentively.

A. Reviewing previous Activating prior knowledge

lesson or presenting
the new lesson
Before we proceed to our new Ma’am, our past lesson was all
lesson, let us review our past about solving rational algebraic
lesson. What was our past topic all equation transformable to
about again? quadratic equation.

That’s right. So, again what are the Answer:

steps in solving rational algebraic Steps in Solving Rational
equation transformable to Equation:
quadratic equation?
1. Multiply both sides of the
equation by the LCM or LCD.
2. Write the resulting quadratic
equation in standard form.
3. Solve the equation using any
method in solving quadratic
equation.
4. Check whether the obtained
values of x satisfies the given
equation.
 Good job class! By means of
answering the questions, it means
you truly understood the previous
lesson that we have discussed.
And it’s a sign also that you are
ready for our lesson this afternoon.

B. Establishing a Lesson Objective Setting

purpose for the lesson
To formally start our lesson, let’s
know our lesson objectives. This
will serve as your guide
throughout our discussion for
today’s lesson.
Kindly read.

At the end of the lesson, the (Students will read the learning
learners are expected to: objectives)

a) identify quadratic
equations.
b) solve quadratic equations-
related problem using
various methods (factoring
and quadratic formula).
c) relate quadratic equations
to solve real-world
problems.

After knowing our lesson’s

objectives, I think you are ready to
explore and learn new knowledge Yes, ma’am!
this afternoon. Are you ready
class?

C. Presenting Problem-Based Learning

examples/instances of
the new lesson Before we proceed to our new
lesson, let us have a short activity.

Activity 1: REAL-WORLD
QUADRATICS!
 Problem 1:

A rectangular garden is 3 meters

longer than it is wide. If the area of
the garden is 28 square meters, Answer:
2
what are its dimensions? w + 3 w=28
2
w + 3 w−28=0

( w +7 ) ( w−4 )=0

Therefore, the width (w) is 4

meters.
The length is w + 3 = 4 + 3 = 7
meters.

The dimensions of the

rectangular garden are 4 meters
by 7 meters.

Based on the activity, do you have

any idea what is our new lesson
this afternoon? Solving quadratic equation.

That’s right! Now are you ready to

listen class?
Yes, Ma’am.
D. Discussing new Lecture Method
concepts and
practicing new skill #1
Yesterday, we discussed solving
rational algebraic equation
transformable to quadratic
equation.

This afternoon we will discuss

problem solving involving
quadratic equations.

Now, what is quadratic equations?

Who will read its definition?

Quadratic Equation
Definition: An equation that can
be rearranged in standard form (a student read the definition)
where the variable x represents an
unknown number, and a, b, and c
represent known numbers, where a
≠ 0.

Thank you, ______!

To further understand the

definition of quadratic equation
let’s consider this illustration.

Illustration

The image shows that a quadratic

equation is of the form:
2
a x +bx=0
where:
 a, b, and c are constants
(numbers), and ‘a’ cannot
be zero (a ≠ 0).
 x is the variable
Yes, Ma’am.
Did you understand class?

Alright, let’s have an example.

Area problems
Example 1
Imagine you’re designing a
rectangular flower bed. You want
its length to be 2 meters longer
than its width, and you have
enough soil to cover 15 square
meters. What dimensions should
the flower bed have?

Solution by Factoring:
1. Factoring: Quadratic
equation w 2+ 2 w−15=0
factored into (w+5) (w-3) =
0 leading to w = -5 and w =
3.
2. Discarding the Negative
Solution: Since width
cannot be negative in a
real-world context, the
solution w = -5 is
discarded.
3. Finding the Length: The
length is determined using
the given relationship:
length = w + 2. With w =
3, the length is 5 meters.
4. Verification: 3 meters x 5
meters = 15 square meters,
which matches the given
area in the original
problem.

Alternative Solution by
Quadratic Formula:
1. Applying the Formula:
The quadratic formula,
−b ± √ b2−4 ac
w= is used to
2a
solve w 2+ 2 w−15=0.

−b ± √ b2−4 ac
w=
2a

Where;
a = 1, b = 2, and c = -15 are
substituted into the formula.
 −2 ± √ 22−4(1)(−15)
w=
2(1)

2. Simplifying:

−2 ± √ 64
w=
2

3. Solving for w:

−2 ±8
w=
2

This gives two solutions:

−2 ±8 6
w= = =3
2 2

−2 ±8 −10
w= = =−5
2 2

Again, we discard the negative

solution. Therefore, it leads to a
width of 3 meters and a length of 5
meters.

In summary, this demonstrates two

valid methods for solving a
quadratic equation arising from a
word problem. It highlights the
importance of considering the
context of the problem when
interpreting the solutions and
emphasizes the verification step to
ensure the solution’s accuracy.
The use of both factoring and the
quadratic formula shows a
comprehensive understanding of Yes, Ma’am.
solving quadratic equations.
None, Ma’am.
Did you understand class?

Is there any question or

clarifications?
 I’m glad that you understand.
E. Discussing new To further enrich your learnings
concepts and let’s look at a slightly more
practicing new skill #2 challenging problem. Who wants
to read?

Projectile motion
Example 2
A ball is launched straight up into
the air. Its height (h) in meters, (Student will read)
after t seconds can be modeled by
the equation h=−4.9 t 2+ 19.6 t .
When will the ball hit the ground
again?

Thank you, _______.

Alright class, what can you Ma’am, example 1 and example

observe in our example? 3 are both the same formula
Yes, ______? needed to use.

Yes, that’s right. Class if you

encounter problems like this all
you need to do to find the possible
answer is to use the formula:

−b ± √ b 2−4 ac
t=
2a

In the equation, we can let a = -

4.9, b = 19.6, and c = 0.
Substituting these values:

−19.6 ± √ 19.62 −4 (−4.9)(0)

t=
2(−4.9)

−19.6 ± √ 19.62
t=
−9.8

−19.6 ± √ 19.6
t=
−9.8

−19.6−19.6
t=
−9.8
 t=4

Conclusion:
The ball will hit the ground again
after 4 seconds. Both factoring and
the quadratic formula yield the
same result, but factoring is
simpler in this specific case
because of the zero constant term.
The quadratic formula is a more
general method that works even
the equation doesn’t factor easily.

We followed a similar process of

defining variables, setting up the
equation, solving it, and
interpreting the solution in the
context of the situation. Remember
this is the core of applied
mathematics and crucial when
solving real-world challenges!

Did you get it class?

Yes, Ma’am.
Is there any questions or
clarifications? None, Ma’am.

If none, let’s go on the next part of

our lesson.

F. Developing mastery To test your understanding about

(leads to formative our lesson this afternoon. Let’s
assessment 3) have a short review.

What is stated in Problem Solving Ma’am, problem-solving with

Involving Quadratic Equation? quadratic equations involves
finding the values of the
variable that satisfy a second-
degree polynomial equation
( a x 2 +bx +c=0 ). These
solutions represent the x-
intercepts (roots) of the
corresponding parabola on a
 graph.

Very good!
Any additional answer? Ma’am, it is also satisfy the
equation, typically by factoring,
completing the square, or using
the quadratic formula.

Excellent! That’s right.

G. Finding practical Group Work

applications of
concepts and skills in Activity: Group Activity
daily living
Now, for better understanding of
our lesson this afternoon, I will
group you into 3 groups. Each
group receives 1 problem
scenarios, and all you need to do is
collaborate to complete the
following steps for the given
problem. You will be given 5
minutes to finish your activity.

Did you get it class? Yes, Ma’am.

Alright, you may now proceed to

your assigned groups.

Group 1: Possible answer:

A frog is sitting on a lily pad 1 Group 1:
meter above the surface of a pond. Quadratic Equation
2
He leaps from the lily pad with an h=−4.9 t + 2t +1=1.5
initial upward velocity of 2 meters
per second. The frog’s height (h) this simplifies to
above the water’s surface after t 2
−4.9t +2 t−0.5=0
seconds is given by the equation:
2
h=−4.9 t + 2t +1. where; a = -4.9, b = 2, and c = -
At what time(s) will the frog be 0.5
1.5 meters above the water’s
surface? Solution:
−b ± √ b2−4 ac
w=
2a
 −2 ± √ 22−4(−4.9)(−0.5)
w=
2(−4.9)

−2 ± √−5.8
w=
−9.8

−2−5.8
w=
−9.8

w=0.80 seconds

Group 2:
Group 2: Step 1:
p=2l+2 w=20
A gardener wants to build a
a=lw=2
rectangular vegetable garden with
a perimeter of 20 meters. They
Step 2:
want the area of the garden to be
l+w=10
21 square meters.
l=10−w
What are the dimensions of the
rectangular garden?
( 10−w ) w=21
2
w −10 w+ 21=0
( w−3 )( w−7 )=0

Step 3:
If w=3, then l=10-3=7
If w=7, then l=10-7=3

The dimensions of the

rectangular garden are 3 meters
by 7 meters

Group 3:
Solution:
Group 3:
A basketball player shoots a free Equation
2
throw. The path of the ball can be −0.2 x + x +2=3
modeled by the equation
2
h=−0.2 x + x +2, where ‘h’ is the Simplifies to
2
height of the ball in meters and ‘x’ −0.2 x + x −1=0
is the horizontal distance from the
free-throw line in meters. The Where; a = 1, b = -5, and c = 5
hoop is 3 meters high.
Will the ball go through the hoop? −b ± √ b2−4 ac
x=
2a

−−5 ± √−52 −4 (1)( 5)

x=
2(1)

−5 ± √−45
x=
2

−5 ±6.71
x=
2

−5−6.71
x=
2

This gives two solutions:

−5 ±−6.71 −11.71
x= =
2 2

¿ 5.86

−5 ±6.71 1.71
x= =
2 2

¿ 0.86

The ball will be at the height of

the hoop (3 meters) at
approximately 5.86 meters and
0.86 meters from the free-throw
line.

Please be guided by our rubric.

Rubric for Evaluation:

Excellent Proficient Developin Needs

Criteria
(4) (3) g (2) Improve
ment (1)
 Accuratel
Identifies
y
most Identifies
identifies Fails to
relevant some
all identify
Underst informatio relevant
relevant relevant
anding n; minor informatio
informatio informati
omissions n but with
n and on.
in variable omissions.
defines
definition.
variables.

Sets up Sets up
Fails to
Correctly the the
set up a
Equatio sets up the equation equation
correct
n Setup quadratic with with
quadratic
equation. minor significant
equation.
errors errors.

Does not
Correctly Solves the
attempt
solve the equation Attempts
to solve
quadratic with to solve
Solution or uses
equation, minor but with
Method an
showing errors; significant
inapprop
all steps most steps errors.
riate
clearly. shown.
method.

Correctly
interprets Interprets Interprets
Fails to
the the the
Solution interpret
solution(s) solution(s) solution(s)
Interpre the
in context, with with
tation solution(
discarding minor significant
s).
irrelevant errors. errors.
solutions.

H. Making Let me see if you truly listen and

generalizations and understand out discussion this
abstractions about the afternoon.
lesson
1. What is our lesson all Problem Solving involving
about? Quadratic Equation

2. Without looking at An equation that can be

your notes. In your own rearranged in standard form
understanding, what is where the variable x represents
the Problem Solving an unknown number.
involving Quadratic
Equation all about?

3. Who can give the factoring, quadratic formula,

various methods in completing the square
solving quadratic
equation?
 4. How about the formula −b ± √ b2−4 ac
finding the length? w=
2a

5. How can we relate this Quadratic equations help solve

lesson in real-life real-life problems involving
situation? optimization, such as
determining the maximum
profit or minimum cost of a
product, or calculating the
trajectory of a projectile.

Excellent class! I’m glad that you

truly understand our lesson this
afternoon. Please give yourselves
5 claps.

I. Evaluating Learning Summative Assessment

But before we proceed to your

short quiz, do you have any
question or clarifications regarding
on our lesson? None, Ma’am.

If none, let’s have a quiz. I will be

giving you 3 minutes to finish
your worksheet.

ASSESSMENT (Multiple Choice)

Directions: Read and understand
each item carefully. Encircle your
answer in your worksheet.

1. Which of the following is NOT a Answer Key:

method for solving quadratic 1. D
equations?
a) Factoring
b) Quadratic Formula
c) Completing the Square
d) Guess and Check

2. A quadratic equation is an 2. C
equation of the form
2
a x +bx +c=0 , where a, b, and c
are constants and a ≠ 0. What does
 the ‘a’ represent?
a) The y-intercept
b) The x-intercept
c) The coefficient of the x 2
term
d) The constant term

3. What is the discriminant of a 3. A

quadratic equation, and what does
it tell us?
a) b 2−4 ac ; it determines the
number and type of
solutions
b) a 2+ b2 +c 2; it determines the
sum of the solutions
c) b−4 ac ; it determines the
product of the solutions
d) b 2+ 4 ac ; determines the
nature of the roots

4. The quadratic equation

2 4. A
x −5 x+ 6=0 is solved by
factoring. What are the solutions?
a) x = 2 and x = 3
b) x = -2 and x = -3
c) x = 2 and x = -3
d) x = -2 and x = 3

5. A ball is thrown upward and its

5. B
height (h) in meters after t seconds
is given by the equation
2
h=−5 t +20 t+ 5. At what time
does the ball reach its maximum
height?
a) 1 second
b) 2 seconds
c) 3 seconds
d) 4 seconds

Are you done class?

Yes, Ma’am!
Alright class, please pass your
(students will pass their paper)
paper.

J. Additional activities For your assignment, please do

for application or advance reading on your materials
remediation about “Problem Solving Involving
Rational Algebraic”.

Understood class? Yes, ma’am!

Okay, that’s all for today. Have a Goodbye, ma’am!

nice day ahead and goodbye, class!

V. REMARKS
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
lesson work? No. of
learners who have
caught up with the
lesson
D. No. of learners who
continue to require
remediation
E. Which of my
teaching strategies work
well 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:
TRIXY ANN C. FRANCO
 Student

Prepared to:
JASON L. TORIO MAEM
College Supervisor, BSEd-Mathematics