SYLLABUS IN MATHEMATICS 9
FIRST QUARTER
PROGRAM STANDARD
GRADE LEVEL STANDARD
CONTENT STANDARD
PERFORMANCE STANDARD
The learner demonstrates understanding and appreciation of key concepts and
principles of mathematics as applied - using appropriate technology - in problem
solving, critical thinking, communicating, reasoning, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts and principles of patterns
and algebra (quadratic equations, quadratic functions, rational algebraic equations,
variations, and radicals) and geometry (parallelograms and triangle similarities and
basic concepts of trigonometry) as applied - using appropriate technology - in critical
thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts of quadratic equations
and functions.
The learner is able to investigate thoroughly mathematical relationships in various
situations, formulate real-life problems involving quadratic equations and functions and
solve them using a variety of strategies.
TIME
FRAME
TOPICS
Week 1
CLASSROOM ORIENTATION
LEARNING COMPETENCIES
The learner…

Orientation on Policies Relating to 
Scholastic Work and Policies
Relating to Standards of Conduct
on Campus

Orientation of the Subject Matter:

ASSESSMENT
Formative:
 Getting-to-Know
Me!
recognizes the do’s and don’ts of
 Let Me Try!
the school, and of the behavior
 Story Making Using Math
that is/are expected from them.
Words
 Recitations
identifies
the
scope
and
sequence, grading system, and
Scope and Sequence, Grading
System, and Requirements
requirements for Math 9.
Values on Focus:
- Sense of Responsibility
- Commitment
- Respect
Week 2
PATTERNS AND ALGEBRA

Quadratic Equations
Values on Focus:
-
Weeks 3
Week 4

Perseverance
Courteousness
Collaboration
The learner ….
 M9AL-Ia-1: illustrates quadratic
equations.

expresses quadratic equations in
standard form : ax2 + bx + c = 0.
Summative:
 Learning Log
 Reaction Paper
Formative:
 Perfect Shots of Man’s
Ingenuity
 Frayer
Model
(Graphic
organizer) – Group Activity
 Quadratic or Not Quadratic
and Set Me To Your
Standard (Triad)
Summative:
 Quiz
Formative:
Solving Quadratic Equations by The learner ….
Extracting Square Roots and  M9AL-Ia-b-1: solves quadratic  Find My Roots (Recitation)
Factoring
equations by: (a) extracting  Extract Me!!! (Think-Pairsquare roots; and, (b) factoring;
Share Activity)
Values on Focus:
 Factor Then Solve!
- Critical Thinking
- Self – Reliance
- Accuracy
Formative:
 Solving Quadratic Equations by The learner ….
Completing the Square and the  M9AL-Ia-b-1: solves quadratic  Make It Perfect!!!
use of Quadratic Formula
equations by: (c) completing the  Lead Me to the Formula!
square; and (d) by using the
(Group Work)
Values on Focus:
quadratic formula.
 Is the Formula Effective?
-
Critical Thinking
Self – Reliance
Accuracy
Summative:
 Quiz Bee Game
1ST MID – QUARTER EXAMINATION
Week 5
Week 6

Nature of the Roots of Quadratic The learner ….
Equations
 M9AL-Ic-1: characterizes the
- Discriminant
roots of a quadratic equation
- Sum and Product of Roots
using discriminants.
 M9AL-Ic-1:
describes
the
Values on Focus:
relationship
between
the
- Enthusiasm
coefficients and the roots of a
- Appreciation
quadratic equation.
Formative:
 Math in A, B, C? (Review)
 What is My Nature?
Summative:
Quiz
Week 7

Equations Transformable
Quadratic Equations

Applications
Equations
Formative:
 Let Me Try!
 Triad
Summative:
 Quiz
of
Values on Focus:
Week 8

to The learner ….
 M9AL-Ic-d-1: solves equations
transformable
to
quadratic
equations
(including
rational
Quadratic
algebraic equations).
 M9AL-Ie-1: solves problems
involving quadratic equations.
Determination
Carefulness
Quadratic Functions
Values on Focus:
-
Respect and Tolerance
Zest
The learner ….
 M9AL-Ig-2:
situations
functions.

models
real-life
using
quadratic
recognizes and differentiates
quadratic functions and quadratic
equations.
Formative:
 Identify Me!
 Where Do You Belong?
 The Hidden Message (Group
Work)
Summative:
 Quiz
Performance Task #1

Week 9

Graphs of Quadratic Functions
Values on Focus:
-
Patience
Neatness and Cleanliness
M9AL-Ih-1:
transforms
the
quadratic function defined by y =
ax2 + bx + c into the form y = a(x
– h)2 + k.
The learner ….
 M9AL-Ig-h-i-1:
graphs
a
quadratic function: (a) domain;
(b) range; (c) intercepts; (d) axis
of symmetry; (e) vertex; (f)
direction of the opening of the
parabola.

Week 10
M9AL-Ij-1:
determines
the
equation of a quadratic function
given: (a) a table of values; (b)
graph; (c) zeros.
ST
1 QUARTER EXAMINATION
Formative:
 Describe My Paths
 Draw and Describe Me
Summative:
 Quiz
SYLLABUS IN MATHEMATICS 9
SECOND QUARTER – GRADE 9
PROGRAM STANDARD
GRADE LEVEL STANDARD
CONTENT STANDARD
PERFORMANCE STANDARD
TIME FRAME
The learner demonstrates understanding and appreciation of key concepts and
principles of mathematics as applied - using appropriate technology - in problem
solving, critical thinking, communicating, reasoning, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts and principles of patterns
and algebra (quadratic equations, quadratic functions, rational algebraic equations,
variations, and radicals) and geometry (parallelograms and triangle similarities and
basic concepts of trigonometry) as applied - using appropriate technology - in critical
thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts of variation and radicals.
The learner is able to formulate and solve accurately problems involving radicals.
TOPICS
PATTERNS AND ALGEBRA
LEARNING COMPETENCIES
The learner…..

Reviewing the Concepts of 
Ratio and Proportion

Introduction to Variations
Week 1
Values :
ASSESSMENT

Formative :
 Pre-Assessment:
“Before
Lesson
reviews the basic concepts and skills
in ratio and proportion.
Response
identifies the relationships between Summative :
two quantities.
 Who Am I?
-
Punctuality
Cooperation
The learner ….

Variations
-
Week 2

Direct Variations
Values :
- Self – Reliance
- Critical Thinking


Formative :
recognizes relationships between  Inter active Lecture
the two quantities that involve direct  Large
Group
variations.
Discussion
Summative :
M9AL-IIa-1: identifies situations that  Solve Please!
involve quantities that vary directly.
 It’s Your Turn!
 Quiz
M9AL-IIb-c-1:solves
problems
involving direct variations.
The learner ….
-
Inverse Variations

Week 3
Values :
- Perseverance
- Collaboration
- Critical Thinking

Formative:
 Minute Paper
M9AL-IIa-1: recognizes relationships  Brainstorming
between the two quantities that Summative :
involve inverse variations.
 Observe and
M9AL-IIb-c-1: identifies situations
Compare!
that involve inverse variations.
 Think Deeper!
 Quiz
The learner ….
-
Week 4
Joint and Combined
Variations
Values :
- Perseverance
- Collaboration
- Critical Thinking


Formative :
 Think Pair Share
M9AL-IIa-1: recognizes relationships
between three or more quantities Summative :
that involve joint variations or  What is Joint
combined variations.
Together?
M9AL-IIb-1: translates statements  Think-Pair-Share
that involve joint or combined
Activity: Who is
variations
to
mathematical
This Filipino
equations.


Inventor?
DV and IV
Combined!
Wrap it Up!
Performance Task
#2
2nd MID- QUARTER EXAMINATION
Week 5
The learner ….
Formative :
 AnticipationReaction Guide
M9AL-IId-1: applies the laws
involving positive integral exponents  Inter active Lecture
to zero and negative integral
exponents.
Summative :
 Remember Me this
Way!
 Express It!

Week 6
Week 7
Reviewing the Concepts of
Exponents

- Laws of Exponents
- Zero
Exponents
&
Negative
Integral
Exponents
Values :
- Patience
- Perseverance
The learner ….
 Rational
Exponents
and
Radicals
 M9AL-IId-2: illustrates and simplifies
expressions with rational exponents.
Values :
- Critical Thinking
 M9AL-IIf-1: writes an expression
- Determination
with rational exponents as radicals
and vice versa.
The learner ….

Radicals
Week 8
Values :
- Obedience

Formative :
 Brainstorming
Summative :
 Make Me Simple!
 I Challenge You!
 Quiz
Formative :
 Drill Activity
M9AL-IIf-2: derives the laws of  Exposition
radicals.
 Recitation
Summative :
-
Neatness

M9AL-IIg-1:
expressions
radicals.
simplifies
radical 
using the laws of 

Fill-Me-In
Who Am I?
Quiz
The learner ….

Week 9
Week 10
Application of Radicals
Values :
- Obedience
- Simplicity
- Critical Thinking


Formative :
 Inter active Lecture
M9AL-IIh-1: performs operations on  Active Review
radical expressions.
Sessions
M9AL-Iii-1:
solves
equations
involving radical expressions.
Summative :
 What’s the
Message?
 A Noisy Game!
 Quiz Bee Game
(By Group)
2nd QUARTER EXAMINATION
SYLLABUS IN MATHEMATICS 9
THIRD QUARTER – GRADE 9
PROGRAM STANDARD
GRADE LEVEL STANDARD
CONTENT STANDARD
PERFORMANCE STANDARD
TIME FRAME
The learner demonstrates understanding and appreciation of key concepts and
principles of mathematics as applied - using appropriate technology - in problem
solving, critical thinking, communicating, reasoning, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts and principles of patterns
and algebra (quadratic equations, quadratic functions, rational algebraic equations,
variations, and radicals) and geometry (parallelograms and triangle similarities and
basic concepts of trigonometry) as applied - using appropriate technology - in critical
thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts of ratio and proportion
and Similarity.
The learner is able to investigate, analyze and solve problems involving ratio and
proportion similarity through appropriate and accurate representation.
TOPICS
LEARNING COMPETENCIES
ASSESSMENT
The learner…
Week 1
 Ratio and Proportion
 Laws of Proportion
Values:
- Perseverance
- Resourcefulness



M9GE-IIIf-1: identifies and find
simple ration
M9GE-IIIf-1:
describes
and
illustrate the basic properties of
ratio and proportion
M9GE-IIIf-1:
solves
problems
involving ratio and proportions.
Formative:
 Discussion
 Let’s
be
fairproportion please!
 Follow-Up Practice
Summative:
 Quiz
Week 2
 Basic Proportionality
Theorems
 Congruent Triangles
Values:
- Orderliness
- Determination
The learner ….
Formative:
 M9GE-IIIf-1: defines proportional  Minute Paper
segments.
 Group Sharing
 M9GE-IIIf-1: proves and apply the
basic proportionality theorems
Summative:
 M9GE-IIIg-1:
identifies
and
 Quiz
illustrates
similar
polygon/
triangles.
The learner ….

Week 3
Proportional Segments in a
Triangle
 Similarity Postulates
Values:
- Honesty
- Logical Thinking


Formative:
 Peer Discussion
M9GE-IIIg-1: illustrates, explains,  Mind Strainer
and proves the conditions for  Group Evaluations
similarity of triangles
Summative:
M9GE-IIIj-1: applies the similarity  Show me the Proof!
postulates / theorems
The learner ….


Week 4
Week 5
Right Triangles
Right Triangles Similarity
Theorems
 Geometric Mean Theorem
 Pythagorean Theorem and
Special Right Triangles
Values:
- Gratitude
- Systematic


M9GE-IIIi-1 : identifies the parts of
a right triangle
M9GE-IIIi-2 : proves and apply
the pythagorean theorem
3RD MID- QUARTER EXAMINATION
Formative:
 Minute Paper
 Brainstorming
 Group Activity
Summative:
 Are we similar or
proportional
 Quiz
Performance Task #3
Week 6
 Quadrilaterals
Values:
- Enthusiasm
- Accuracy

Week 7
Week 8
Week 9
Week 10
Properties of
Parallelograms
 Theorems to Prove that
quadrilaterals can be
Parallelograms
Values:
- Collaboration
- Critical Thinking
 Special Parallelograms
Values:
- Creativity
- Self - Reliance
 Trapezoids
Values:
- Patience
- Curiosity and Willingness
The learner ….
 M9GE-IIIa-1:identifies
quadrilaterals
that
parallelograms
Formative:
 Inter active Lecture
are  Brainstorming
Summative:
 Quiz
The learner ….
Formative:
 Think
Pair
Share
 M9GE-IIIa-2:
determines
the  Simulations
properties that guarantee a Summative:
quadrilateral a parallelogram
 Quiz
 M9GE-IIIc-1: proves theorems on
the different kinds of parallelogram
The learner ….
 M9GE-IIIc-2: differentiates
kinds of parallelograms
and
Formative:
the  Minute Paper
 Group Sharing
Board work
Summative:
 Quiz
The learner ….
Formative:
 M9GE-IIId-2: proves theorems on  Discussion / Review
trapezoids and kites
 Group activity
 M9GE-IIIe-1: solves problems Summative:
involving trapezoids
 Quiz
3RD QUARTER EXAMINATION
SYLLABUS IN MATHEMATICS 9
FOURTH QUARTER – GRADE 9
PROGRAM STANDARD
GRADE LEVEL STANDARD
CONTENT STANDARD
PERFORMANCE STANDARD
TIME
FRAME
Week 1
The learner demonstrates understanding and appreciation of key concepts and
principles of mathematics as applied - using appropriate technology - in problem
solving, critical thinking, communicating, reasoning, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts and principles of patterns
and algebra (quadratic equations, quadratic functions, rational algebraic equations,
variations, and radicals) and geometry (parallelograms and triangle similarities and
basic concepts of trigonometry) as applied - using appropriate technology - in critical
thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of key concepts of trigonometry and
triangle trigonometry.
The learner is able to investigate, analyze and solve problems involving
quadrilaterals and trigonometry through appropriate and accurate representation.
TOPICS

Six Trigonometric Ratios
Values
LEARNING COMPETENCIES
The learner…
 M9GE-Iva-1: defines the six
trigonometric ratios
 M9GE-IVb-1: finds the six
trigonometric of an acute angle of a
ASSESSMENT
Formative:
 Discovery Approach
 Think Pair and Share
Summative:
 Quiz-
Find
my
-
Recognize the importance
of
Technology
and 
importance of humanity.

Week 2
Values
Show neatness and
orderliness in presenting
solution to a problem.
-

Week 3
Week 4
Solving right triangles
right triangle.
M9GEIVb-c-1: finds the values of
the six trigonometric ratios for each
angle given.
The learner ….

M9GE-IVe-1:
solves
involving right triangles.
Formative:
 Inter active Lecture
problems  Brainstorming
Summative:
 Quiz -How Special
Right Triangle is?
-
Values
Patience
Creativity
The learner ….
 M9GE-IVd-1: illustrates angle of
depression and elevation.
 M9GE-IVe-1:
solves
problems
involving angle of elevation and
depression.

Solving Oblique Triangles

Values
Show strength when
facing/ solving problems.

-
Angle of Depression and
Angle of Elevation
M9GE-IVf-1: defines an
triangle.
M9GE-IVh-j-1:
solves
triangles.
SOHCAHTOA!
Formative:
 Self - assessment

Group Sharing
Summative:
 Quiz - What is my angle
of elevation and angle of
depression?
oblique Formative:
 Minute Paper
oblique  Group Evaluations
Summative:
 Quiz
Performance Task #4
Week 5
4th MID –QUARTER EXAMINATION
a

Trigonometric Identities
The Eight Fundamental
Identities
Week 6
The learner ….

Values
- Show neat and orderly
proof.
 Simplifying Trigonometric
Identities
discusses the eight fundamental
identities.
.
Summative:
 Quiz
The learner ….

simplifies trigonometric identities
Values
- Patience
- Exercise orderliness in
answering the problem.
Week 7
Formative:
 Inter active Lecture
 Think Pair and Share
Formative:
 Minute Paper
 Brainstorming
Summative:
 Quiz
The learner ….
Week 8
 Proving Trigonometric
Identities
Values
- Cooperation
- Patience
 Trigonometric Equations
Week 9
-
Values
Build self – confidence
Patience

proves trigonometric identities
.
Formative:
 Inter active Lecture
 Minute Paper
 Brainstorming
Summative:
 Quiz
The learner ….

solves trigonometric equations.
Formative:
 Inter active Lecture
 Brainstorming
Summative:
 Quiz
Week 10
FINAL EXAMINATION