This document outlines a learning plan for a 9th grade mathematics class on patterns and algebra for the first quarter. It includes standards, competencies, lessons, activities and a performance task on solving quadratic equations using different algebraic methods. Students will compare the methods and apply them to design classroom fixtures using measurements and equations. The plan provides instruction, practice and assessments to help students master solving quadratic equations and transfer their knowledge to real-world problems.

1. SANTA IGNACIA ACADEMY, INC.
Santa Ignacia, Tarlac
A.Y. 2023-2024
LEARNING PLAN IN
MATHEMATICS 9
FIRST QUARTER
Subject: MATHEMATICS
Unit Topic: PATTERNS AND ALGEBRA
UNIT STANDARDS AND COMPETENCIES DIAGRAM
PERFORMANCE STANDARD
TRANSFER GOAL PERFORMANCE TASK
ACQUISITION
MAKE MEANING
CONTENT STANDARDS
The learner demonstrates
understanding of key concepts of
quadratic equations, inequalities and
functions, and rational algebraic
equations.
SOLVING QUADRATIC
EQUATIONS
TRANSFER
Grade Level: 9
Quarter: FIRST
The learner on their own and in the
long run will be able to distribute
thoroughly their knowledge and skills
on quadratic equations to solve real
life problems.
Classroom Makeover
The learner is able to investigate
thoroughly mathematical relationships in
various situations, formulate real life
problems involving quadratic equations,
inequalities and functions, and rational
algebraic equations insert them using a
variety of strategies.
The students will know quadratic
equations; how to solve quadratic
equations by: extracting the square
roots; factoring;
EQ: How are the three different
algebraic method of solving quadratic
equations compared?
EU: Students will understand that the
three different algebraic method of
solving quadratic equations are easier
to perform and accurate than the
graphical method.

2. LEARNING PLAN
EXPLORE
This unit is about Patterns and Algebra
Introduction and focus question: The picture of the world famous Mayon Volcano
appears to be an upside down parabolic shape. The Marcelo Fernan Bridge in Cebu
resembles parabola that opens upward these shapes are realistic representations of a
quadratic function.
In this chapter, we graph quadratic functions that determine parabolas; some of which
are narrow, wide and smooth bell shaped curve. As a prerequisite, we need to gain
skills in solving quadratic equations using different methods like extracting square
roots, factoring, completing this clear, and quadratic formula.
Remember to search for the answer to this focus question: How are the three
different algebraic method of solving quadratic equations compared?
Map of Conceptual Change: IRF Chart
Question: How are the three different algebraic method of solving quadratic
equations compared?
Initial Answer:
Revised Answer:
Final Answer:
LEARNING
COMPETENCY FIRM-UP (ACQUISITION)
LC1. Illustrates
quadratic equations;
Learning Targets:
I can identify if the
equation is quadratic or
not.
I can write the
quadratic equation to
general and standard
form
Activity 1
Instruction: Identify of the following equations are quadratic and which are not. If
the equation is not quadratic, explain.
1. 3𝑚 + 8 = 15
2. 𝑥2
− 5𝑥 + 10 = 0
3. 12 − 4𝑥 = 0
4. 2𝑡2
− 7𝑡 = 12
5. 6 − 2𝑥 + 3𝑥2
= 0
6. 25 − 𝑟2
= 4𝑟
7. 3𝑥(𝑥 − 2) = −7
8.
1
2
(ℎ − 6) = 0
9. (𝑥 + 2)2
= 0
10. (𝑤 − 8)(2 + 5) = 14
LC2. Solve quadratic
equation by extracting
the square root and
factoring
Activity 2
Instruction: Identify the very first mistake in the given solution.
1. 7𝑥2
+ 2𝑥 − 5 = 2𝑥 + 23 2. (𝑥 = 1)2
− 3 = 6
7𝑥2
= 28 A 𝑥 + 1) = 9 A

3. Learning Targets:
I can identify if the
roots of a quadratic
equation is real or
and/or unequal
I can recall factoring
polynomials – GCF
and quadratric
trinomials
𝑥2
= 4 B √(𝑥 + 1)2 = ±√9 B
√𝑥2 = √4 C 𝑥 + 1 = ±3 C
𝑥 = ±2 D 𝑥 = 4 𝑎𝑛𝑑 𝑥 = −2 D
No error E No error E
Activity 3
Instruction: Solve the roots of t he following quadratic equation by extracting the
square root.
1. 𝑥2
= 72
2. 2𝑥2
= 242
3. 3𝑥2
− 1 = 26
4. (𝑥 + 1)2
= 25
5. 2(𝑥 − 3)2
+ 1 = 33
Activity 4
Instruction: Supply the missing terms in the given solution below.
1. 3𝑥2
+ 𝑥 = 0
𝑥(3𝑥 + ) = 0
𝑥 = 0 𝑜𝑟 3𝑥+ = 0
𝑥 = 0 𝑜𝑟 𝑥 =
2. 𝑥2
+ 7𝑥 = 8
𝑥2
+ 7𝑥− = 0
(𝑥 − 1)(𝑥 + ) = 0
𝑥 − 1 = 0 𝑜𝑟 𝑥+ = 0
𝑥 = 1 𝑜𝑟 𝑥 =
3. (𝑥 + 3)(𝑥 − 4) = 8
𝑥2
− 4𝑥 + 3𝑥− = 8
𝑥2
− 𝑥 = 0
(𝑥 − )(𝑥 + 4) = 0
𝑥− = 0 𝑜𝑟 𝑥 + 4 = 0
𝑥 = 𝑜𝑟 𝑥 = −4
Activity 5
Instruction: Solve the following quadratic equations by factoring.
1. 2𝑥2
+ 4𝑥 = 0
2. 6𝑥2
− 𝑥 = 15
3. 3𝑥2
+ 𝑥 − 5 = 𝑥 − 4 − 𝑥2
4. 5𝑥(𝑥 + 1) − 2(𝑥 + 1) = 0
5. 2𝑥2
− 11𝑥 = 5𝑥 − 14
Scaffold for TRANSFER 1
Activity 6
Instruction: Do as indicated.
1. Quadrilateral 𝑁𝐼𝐶𝐸 is a square with 𝑁𝐶 = 6𝑥2
− 1 and 𝐼𝐸 = 3 − 3𝑥2
.
Determing the following:
a. x
b. The area of the square
c. The perimeter of the square
N I
C

4. 2. In the figure, the two angles are supplementary.
Determine the following values:
a. x
b. the measure of thee smaller angle
c. the measure of the bigger angle
LEARNING
COMPETENCY DEEPEN (MAKE MEANING)
LC2. Solve quadratic
equation by extracting
the square root and
factoring
Instructions:
GUIDED GENERALIZATION TABLE
Essential Question
How are the three
different algebraic
method of solving
quadratic equations
compared?
Situation 1
What if the number is
not a perfect square?
Situation 2
The quadratic equaitons
entails simple and
special products
Answer:
What is the solution set: is
it real or non-real?
Answer:
What are the patterns that
should be observed?
Supporting Texts:
What part in your solving
solution supports your
answer?
Supporting Texts:
What part in your solving
solution supports your
answer?
Reason:
Why do you say that
solving a solution supports
your answer?
Reason:
Why do you say that
solving a solution supports
your answer?
Common Ideas in Reasons: The three different algebraic method of solving quadratic
equations are easier to perform and accurate than the graphical method
Enduring Understanding/Generalization: Students will understand that the three different
algebraic method of solving quadratic equations are easier to perform and accurate than the
graphical method.
C-E-R Questions:
1. What are your answers to each problem?
2. What concepts did you apply to solve each problem/situation?
3. Why do you say that concept will solve those situations above?
4. How are the three different algebraic method of solving quadratic equations
compared?
Prompt for Generalization:
1. What are the common concepts/ideas you see in each problem?
2. Can you find the roots or solution sets of a given quadratic equation using any of
the two methods??
2𝑥2
+ 17 4𝑥2
+ 67

5. Map of Conceptual Change: IRF Chart
How are the three different algebraic method of solving quadratic equations
compared?
Initial Answer:
Revised Answer:
Final Answer:
Learning Competency TRANSFER
PERFORMANCE
STANDARD:
The learner is able to
investigate thoroughly
mathematical
relationships in various
situations, formulate
real life problems
involving quadratic
equations, inequalities
and functions, and
rational algebraic
equations insert them
using a variety of
strategies.
Transfer Goal: Performance Task
Classroom Makeover
Mr. Gabrelle R. Pagarigan was tasked by his superior to transfer his grade 9
class in a new classroom at the second floor of a new building. The room however
still does not have any fixtures such as teacher’s table and chair, bulletin board,
reading corner, bookshelves or cabinet. To acquire these fixtures he informed the
parents of his students and asked assistances regarding the needs of his room. The
parents decided to donate construction materials such as wood lumbers, plywood,
nails, points and many other needed.
After all the materials have been gathered, he tasked his students to
make the designs of the classroom needs. Grouped his students and each group was
assigned to do the designer of the particular fixture. The designs that the students
will prepare shall be used by the carpenter in constructing the tables, chairs, bulletin
board, reading corner bookshelves or cabinet.
Suppose you are one of the students of Mr. Pagarigan, how will you prepare
the design of one of the fixtures? Make a design of the fixture assigned to your group.
Illustrate every part or portion of the fixture including its measurement. Write
expressions, equations, inequalities that describe the situations and solved.
Formulate problems involving mathematical concepts or principles.
Criteria
CRITERIA
Design
The design is
accurately made
presentable and
appropriate.
The design is
accurately made and
appropriate.
The design is not
accurately made but
appropriate.
The design is made
but not appropriate.
Equations
formulated and
Solved
Equations/Inequaliti
es are properly
formulated and
solved correctly.
Equations/Inequaliti
es are properly
formulated but not
all are solved
correctly.
The design is not
accurately made but
appropriate.
Equations/Inequaliti
es are properly
formulated but are
not solved.
Problems
formulated and
Solved
Poses a complex
problem and finishes
all significant parts
of the solution and
communicate ideas
unmistakably, shows
in depth
comprehension of
the pertinent concept
and processes.
Poses a complex
problem and finishes
most significant
parts of the solution
and communicate
ideas unmistakably,
shows
comprehension of
concept although
neglects or
Poses a problem and
finishes all some
significant parts of
the solution and
communicate ideas
unmistakably but
shows gaps on
theoretical
comprehension.
Poses a problem but
demonstrate minor
comprehension not
being to develop an
approach.

6. CALENDAR OF ACTIVITIES
GRADE 9 - AMETHYST: QUARTER 1 (WEEK 1)
MON TUE WED THU FRI
LEARNING
COMPETENCY
M9AL-Ia-1
M9AL-Ia-b-1
Illustrates quadratic
equations.
Solves quadratic
equations by
extracting the
square root
LESSON
Solving Quadratic
Equation by
Extracting the
Square Roots
REMARKS:
LEARNING
COMPETENCY
M9AL-Ia-b-1
Solves quadratic
equations by
extracting the
square root and
factoring
LESSON
Solving Quadratic
Equation by
Extracting the
Square Roots and
Factoring
REMARKS:
LEARNING
COMPETENCY
M9AL-Ia-b-1
Solves quadratic
equations by
factoring
LESSON
Solving Quadratic
Equation by and
Factoring
REMARKS:
GRADE 9 - DIAMOND: QUARTER 1 (WEEK 1)
MON TUE WED THU FRI
LEARNING
COMPETENCY
M9AL-Ia-1
M9AL-Ia-b-1
Illustrates quadratic
equations.
Solves quadratic
equations by
extracting the
square root
LESSON
Solving Quadratic
Equation by
Extracting the
Square Roots
REMARKS:
LEARNING
COMPETENCY
M9AL-Ia-b-1
Solves quadratic
equations by
extracting the
square root and
factoring
LESSON
Solving Quadratic
Equation by
Extracting the
Square Roots and
Factoring
REMARKS:
LEARNING
COMPETENCY
M9AL-Ia-b-1
Solves quadratic
equations by
factoring
LESSON
Solving Quadratic
Equation by
Factoring
REMARKS:
LEARNING
COMPETENCY
M9AL-Ia-b-1
Solves quadratic
equations by
factoring
LESSON
Solving Quadratic
Equation by
Factoring
REMARKS:
misinterpret less
significant ideas or
details.

7. PREPARED BY:
GABRELLE R. PAGARIGAN
Subject Teacher
APPROVED BY:
MR. FLOR L. SANTOS
Principal
DATE: DATE: