Grade 9
Grade 9
I. OBJECTIVES
A. Content Standard                           Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                   The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
                                                                                                                                                                                                     FACTORING QUADRATIC
II. CONTENT                                     ORIENTATION              INTRODUCTION TO FACTORING                               FACTORING                           SPECIAL PRODUCTS                     EQUATIONS
III. LEARNING RESOURCES
A. References
1. Teacher's Guide pages
2. Learner's Materials pages
3. Textbook pages
4. Additional Materials from
Learning Resource (LR) portal
B. Other Learning Resources                                                 Math 8 Learner's Material                   Math 8 Learner's Material                 Math 8 Learner's Material        Math 8 Learner's Material
IV. PROCEDURES
A. Reviewing previous lesson or                                                                                      Let the students answer the question:      Using flash cards to facilate an
                                                                          Brainstorming: What are the various
                                                                                                                    What have you learned from yesterday's
presenting the new lesson                                                        methods of factoring?                            discussion?                          engaging review
C. Presenting examples/Instances of the                                   Demonstrate the "factoring using the       Demonstrate the "factoring using
new lesson                                                                   common monomial factor"                   difference of two squares"
                                                                                                 Using a random recitation, instruct
D. Discussing new concepts and                    Allow students to answer the exercises
                                                                                                 students to answer the 5 problems Ask a volunteer to show his/her solution
practicing new skills # 1                         entitled as " Check your understanding"
                                                                                                        written on the board
                                                                                                                                                on the board
                                                                                                                                                                              Summative Quiz
I. Evaluating learning
J. Additional activities for application or                                                                 Assignment
remediation
                                            The students will know the                                             The students will know the                   The students will be able to
                                          characteristics and definition of             No Classes                standard form of a quadratic                                                      No Classes
                                                                                                                                                               identify Quadratic Equations
                                                Quadratic Equation                                                          equation
I. OBJECTIVES
D. Discussing new concepts and                  Give the definition of Quadratic       Share to the class the Standard Form
practicing new skills # 1                                  Equation                          of a Quadratic Equation.
                                                 Complete the statement: Today I've     Complete the statement: Today I've learned
H. Making generalizations and                         learned ____________                           ____________
abstractions about the lesson
                                                           Drill/Exercise                              Seatwork                                Summative Quiz
I. Evaluating learning
J. Additional activities for application or
remediation
A. Content Standard                                       Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                                   The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each
F. Developing mastery (leads to                 Conduct a Boardwork about the                                                            Answer Activity 4 on page 31 of
Formative Assessment 3)                                     topic                                                                               LM (items 1-5)
G. Finding Practical applications of concepts    What value/s in life have you            What are the things that have positive and What practical application can we associate to
and skills in daily living.                       learned from the topic?                       negative effects in our lives?                our disccusion for today?
                                                  Ask the students to Complete the          Ask the students to Complete the             Ask the students to Complete the statement :
H. Making generalizations and                     statement : Today, I've learned…          statement : Today, I've learned…                         Today, I've learned…
abstractions about the lesson
                                                                                           Answer Activity 6 on page 23 of               Answer Activity 4 on page 31 of LM
                                                 Conduct the "Ticket to leave" activity                                                                                                          Group Activity
I. Evaluating learning                                                                         the Learner's Module                                 (items 6-10)
J. Additional activities for application or
remediation
                                                    MONDAY
                                           The students   will know             TUESDAY                       WEDNESDAY                        THURSDAY                         FRIDAY
                                                                                                                                      The students will know the
                                                                       The students will know the     The students will know the                                       The students will know
                                            the method on how to                                                                       steps in solving Quadratic
                                                                      method on how to find for the  method on how to find for the                                        the procedures in
I. OBJECTIVES                                find for the roots by          roots by factoring             roots by factoring        Equations   by completing the
                                          The students   will be able The students will be able to The students will be able to solve The students                     completing   the square
                                                   factoring                                                                                     square
                                                                                                                                                     will be able to  The students will be able to
                                              to solve quadratic     solve quadratic equations using   quadratic equations using         analyze the procedure in    apply the steps in completing
                                          equations using factoring             factoring                      factoring                  completing  the  square             the squares
A. Content Standard                                    Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
                                             The students in the long run and on their own will be able to investigate thoroughly mathematical relationships in various situations, formulate reallife problems involving
B. Performance Standard                                             quadratic equations, inequalities and functions, and rational algebraic equations and solve them using a variety of strategies.
                                                                                  Seatwork about solving perfect square Give additional exercises from other Conduct a recitation about the steps in                   Answer "Make it Perfect"
F. Developing mastery (leads to                                                          trinomials by factoring                       books                        Completing the square
Formative Assessment 3)                                                                                                                                                                                                    Activity (6-10)
G. Finding Practical applications of concepts                                        What does Perfect Square Trinomial         Do the practical Task entitled "Meet my                                                 Ask students to perform
and skills in daily living.                                                                   revealed to us?                     demands" on page 34 of the L.M.             Why do we need to be aware of the best           Activity 8
                                                                                                                                                                                method on how to solve problem?
                                                     MONDAY
                                          The students    will know the                   TUESDAY                             WEDNESDAY                             THURSDAY                               FRIDAY
                                            application of Quadratic          The students will know the The students will know the
                                                     Formula                    application of Quadratic              application of Quadratic
I. OBJECTIVES                                                                             Formula                               Formula                   Long Quiz for Quadratic
                                          The students will be able to The students will be able to The students will be able to                                                                         Quiz Bee
                                                                                                                                                                    Equations
                                           solve Quadratic Equations           solve Quadratic Equations             solve Quadratic Equations
                                            using Quadratic Formula             using Quadratic Formula               using Quadratic Formula
A. Content Standard                                    Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
                                              The students in the long run and on their own will be able to investigate thoroughly mathematical relationships in various situations, formulate reallife problems involving
                                                                     quadratic equations, inequalities and functions, and rational algebraic equations and solve them using a variety of strategies.
B. Performance Standard
C. Learning Competency/Objectives Write
the LC code for each                         solves quadratic equations by          solves quadratic equations by        solves quadratic equations by Quadratic solves quadratic equations by Quadratic solves quadratic equations by Quadratic
                                            Quadratic Formula (M9AL-Ia-b-1)        Quadratic Formula (M9AL-Ia-b-1)               Formula (M9AL-Ia-b-1)                   Formula (M9AL-Ia-b-1)                   Formula (M9AL-Ia-b-1)
II. CONTENT Quadratic Formula Quadratic Formula Quadratic Formula Quadratic Formula Quadratic Formula
A. Reviewing previous lesson or            Answer the activity:It's good to be     What is the Quadratic Formula?        What have you learned about Quadratic
presenting the new lesson                               simple                                                                         Formula?
G. Finding Practical applications of concepts What do you think is the formula to have a   What do you think is the formula to have a   What do you think is the formula to have a
and skills in daily living.                                better society?                              better society?                              better society?
I. OBJECTIVES
A. Content Standard                           Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                   The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each
                                                                                                         solves equations transformable to quadratic equations (including rational algebraic equations)      . (M9AL-Ic-d-1)
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
A. Content Standard                                    Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                              The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each                                                            Describes the relationship between the coefficients and the roots of a quadratic equation. M9AL-Ic-2
A. Reviewing previous lesson or            Review the different methods in                                                                                     Recall the previous lesson by asking
                                           solving the roots of a quadratic                                        Recall the formula for quadratic equaion.
presenting the new lesson                             equation.
                                                                                                                                                                          some students
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
A. Content Standard                                    Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                              The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each
                                                                                Describes the relationship between the coefficients and the roots of a quadratic equation. M9AL-Ic-2
II. CONTENT                                                                                                              Patterns and Algebra
A. Reviewing previous lesson or            Review the different methods in                                                                                      Recall the previous lesson by
                                           solving the roots of a quadratic                                        Recall the formula for quadratic equaion.
presenting the new lesson                             equation.                                                                                                    asking some students
E. Discussing new concepts and                                                                                                                                                              Let the students, solve the problems
practicing new skills # 2                                                                                                                                                                                  given.
                                                   Use the quadratic equations below to                                                       Let the students derive the formula for the
F. Developing mastery (leads to                      answer the questions that follow.                                                         sum and product of quadratic equations.
                                                                                                                                                                                            Use songs in choosing students
Formative Assessment 3)                                You may work in groups of 4.                                                                                                                  to answer.
G. Finding Practical applications of concepts                                                  Solving finding the side of a land given the
and skills in daily living.                                                                                area and perimeter.
                                                                                                                                                                                            Knowing the importance of valuing things
H. Making generalizations and                                                                  Use exit Card to know if the students have     Ask some students to summarize what they
abstractions about the lesson                                                                              learned something                               have learned.                                                                      Think-pair-share
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
A. Content Standard                                   Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                              The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each                      Solves equations transformable to quadratic equations (including
                                                     rational algebraic equations). M9AL-Ic-d-1
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
II. CONTENT
A. Reviewing previous lesson or            Answer the activity:It's good to be      What is the Quadratic Formula?      What have you learned about Quadratic
presenting the new lesson                               simple                                                                        Formula?
D. Discussing new concepts and                      Discuss: Transforming into the   Apply the Quadratic Formula in the given       Review the technique of using
practicing new skills # 1                                   standard form                      Quadratic Equation                        Quadratic Formula
                                                                                                                                                               Solve the sum and product of      Solve the sum and product of
I. OBJECTIVES                              No Classes Due to Habagat               No Classes Due to Habagat         No Classes Due to Habagat                                                       quadratic equations
                                                                                                                                                                   quadratic equations
A. Content Standard                                    Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                              The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each                                                            Describes the relationship between the coefficients and the roots of a quadratic equation. M9AL-Ic-2
II. CONTENT
A. Reviewing previous lesson or            Review the different methods in                                                                                     Recall the previous lesson by
                                           solving the roots of a quadratic                                       Recall the formula for quadratic equaion.
presenting the new lesson                             equation.                                                                                                   asking some students
E. Discussing new concepts and                                                                                                                                             Let the students, solve the problems
practicing new skills # 2                                                                                                                                                                 given.
H. Making generalizations and                                                    Use exit Card to know if the students have     Ask some students to summarize what they                                               Directions: Use the values of a,
abstractions about the lesson                                                                learned something                               have learned.                                                            b, and cThink-pair-share
                                                                                                                                                                                                                               of each of the following
                                                                                                                                                                                                                             quadratic equations
                                                                                                                                                                                                                      in determining the sum and the
                                                                                                                                                                                                                       product of its roots. Verify your
                                                                                                                                                                                                                                   answers
                                                                                   Find the roots of each of the                                                                                                        by obtaining the roots of the
                                                                                  following quadratic equations                                                                                                       equation. Answer the questions
                                                                                              using
                                                                                    Explain the     any of deriving the formula to find the sum and product of quadratic equation
                                                                                                 process                                                                                                                         that follow.
                                                                                 method. Answer the questions                                                                                                              1. x2 + 4x + 3 = 0 Sum:
                                                                                             that follow.                                                                                                                _____Product: _____ Roots:
                                                                                 1. x² + 3x + 2 = 0 3. 15h² – 7h –                                                                                                             _____________
                                                                                                2=0                                                                                                                   2. 6x2 + 12x – 18 = 0 Sum: _____
                                                                                                                                                                                                                            Product: _____ Roots:
                                                                                 2. s² – 5s + 6 = 0 4. 12s² – 5s – 3                                                                                                           _____________
I. Evaluating learning                                                                           =0                                                                                                                    3. x2 + 4x – 21 = 0 Sum: _____
J. Additional activities for application or                                                                                                                                                                                 Product: _____ Roots:
remediation                                                                                                                                                                                                                    _____________
V. REMARKS
VI. REFLECTION
A. Content Standard                                   Demonstrates understanding of the key concepts of quadratic equations and solve problems involving Quadratic equations using a variety of strategies.
B. Performance Standard                                           The students in the long run and on their own will be able to select the best way to find the unknown in their lives
C. Learning Competency/Objectives Write
the LC code for each
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES                                                      Rechecking and Review of the                                               Solve problems involving direct   Solve problems involving
                                          National Heroes Day                                                Define variations
                                                                       First Periodic Exam                                                              variations                  direct variations
A. Content Standard                                                          The learner demonstrates understanding of key concepts of variation and radicals.
B. Performance Standard                                                   The learner is able to formulate and solve accurately problems involving radicals.
C. Learning Competency/Objectives Write
the LC code for each                                                                                                                                                            IIllustrates situations that
                                                                                                    IIllustrates situations that involve IIllustrates situations that involve       involve the following
                                                                                                        the following variations: (a)        the following variations: (a)       variations: (a) direct; (b)
                                                                                                      direct; (b) inverse; (c) joint; (d) direct; (b) inverse; (c) joint; (d)        inverse; (c) joint; (d)
                                                                                                           combined. M9AL-IIa-1                 combined. M9AL-IIa-1              combined. M9AL-IIa-1
II. CONTENT
E. Discussing new concepts and                         Explain the importane of           Explain on how to solve direct variation
practicing new skills # 2                              variation in everyday life                       problems
I. OBJECTIVES
A. Content Standard                                                         The learner demonstrates understanding of key concepts of variation and radicals.
B. Performance Standard                                                  The learner is able to formulate and solve accurately problems involving radicals.
C. Learning Competency/Objectives Write
the LC code for each
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                         The learner demonstrates understanding of key concepts of variation and radicals.
B. Performance Standard                                                  The learner is able to formulate and solve accurately problems involving radicals.
C. Learning Competency/Objectives Write
the LC code for each
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                         The learner demonstrates understanding of key concepts of variation and radicals.
B. Performance Standard                                                  The learner is able to formulate and solve accurately problems involving radicals.
C. Learning Competency/Objectives Write
the LC code for each
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                         The learner demonstrates understanding of key concepts of variation and radicals.
B. Performance Standard                                                  The learner is able to formulate and solve accurately problems involving radicals.
C. Learning Competency/Objectives Write
the LC code for each
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                                 The learner demonstrates understanding of key concepts of parallelograms and triangle similarity.
B. Performance Standard                            The learner is able to investigate, analyze, and solve problems involving parallelograms and triangle similarity through appropriate and accurate representation.
C. Learning Competency/Objectives Write
the LC code for each                                                                                                                                                                             Uses properties to find
                                                                                                                                                                                              measures of angles, sides and
                                          Uses properties to find measures of angles, sides and other quantities involving parallelograms. M9GE-IIIb-1                                         other quantities involving
                                                                                                                                                                                              parallelograms. M9GE-IIIb-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                             The learner demonstrates understanding of key concepts of parallelograms and triangle similarity.
B. Performance Standard                        The learner is able to investigate, analyze, and solve problems involving parallelograms and triangle similarity through appropriate and accurate representation.
C. Learning Competency/Objectives Write
the LC code for each                                                                                                                                                                         Proves theorems on the
                                          Proves theorems on the different kinds of parallelogram (rectangle, rhombus, square).                                                          different kinds of parallelogram
                                                                              M9GE-IIIc-1                                                                                                 (rectangle, rhombus, square).
                                                                                                                                                                                                    M9GE-IIIc-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                         The learner demonstrates understanding of key concepts of parallelograms and triangle similarity.
B. Performance Standard                    The learner is able to investigate, analyze, and solve problems involving parallelograms and triangle similarity through appropriate and accurate representation.
C. Learning Competency/Objectives Write
the LC code for each                                                                                                                                                                     Proves theorems on the
                                                                                                                                                                                     different kinds of parallelogram
                                                                                                                                                                                      (rectangle, rhombus, square).
                                                                                                                                                                                                M9GE-IIIc-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
A. Content Standard                                                                  The learner demonstrates understanding of key concepts of parallelograms and triangle similarity.
B. Performance Standard                             The learner is able to investigate, analyze, and solve problems involving parallelograms and triangle similarity through appropriate and accurate representation.
C. Learning Competency/Objectives Write
the LC code for each                                                                                                                                                                               Proves theorems on the
                                                                                    Proves the conditions for
                                          Illustrates similarity of figures.                                                      Proves the Pythagorean                                       different kinds of parallelogram
                                                                                    similarity of triangles. (SAS, SSS,
                                          M9GE-IIIg-1                                                                              Theorem. M9GE-IIIi-2                                         (rectangle, rhombus, square).
                                                                                    AA) M9GE- IIIg-h-1                                                                                                    M9GE-IIIc-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                                       The learner demonstrates understanding of the basic concepts of trigonometry.
B. Performance Standard                                       The learner is able to apply the concepts of trigonometric ratios to formulate and solve real-life problems with precision and accuracy.
C. Learning Competency/Objectives Write
the LC code for each
                                          Illustrates the six trigonometric ratios: sine, cosine, tangent, secant, Finds the trigonometric ratios of                                         Finds the trigonometric ratios of
                                                           cosecant, and cotangent. M9GE-IVa-1                      special angles. M9GE -IVb-c-1                                             special angles. M9GE -IVb-c-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                                   The learner demonstrates understanding of the basic concepts of trigonometry.
B. Performance Standard                                   The learner is able to apply the concepts of trigonometric ratios to formulate and solve real-life problems with precision and accuracy.
C. Learning Competency/Objectives Write
the LC code for each
                                                                                                                     illustrates angles of elevation and                                  illustrates angles of elevation
                                          finds the trigonometric ratios of special angles. M9GE -IVb-c-1            angles of depression. M9GE-IVd-                                         and angles of depression.
                                                                                                                                      1                                                             M9GE-IVd-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                                      The learner demonstrates understanding of the basic concepts of trigonometry.
B. Performance Standard                                      The learner is able to apply the concepts of trigonometric ratios to formulate and solve real-life problems with precision and accuracy.
C. Learning Competency/Objectives Write
the LC code for each
                                          illustrates angles of elevation and angles of depression. M9GE-IVd- finds the trigonometric ratios of                                             Finds the trigonometric ratios of
                                                                             1                                  special angles. M9GE -IVb-c-1                                                special angles. M9GE -IVb-c-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                                      The learner demonstrates understanding of the basic concepts of trigonometry.
B. Performance Standard                                      The learner is able to apply the concepts of trigonometric ratios to formulate and solve real-life problems with precision and accuracy.
C. Learning Competency/Objectives Write
the LC code for each
                                          illustrates angles of elevation and angles of depression. M9GE-IVd- finds the trigonometric ratios of                                             Finds the trigonometric ratios of
                                                                             1                                  special angles. M9GE -IVb-c-1                                                special angles. M9GE -IVb-c-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                                    The learner demonstrates understanding of the basic concepts of trigonometry.
B. Performance Standard                                    The learner is able to apply the concepts of trigonometric ratios to formulate and solve real-life problems with precision and accuracy.
C. Learning Competency/Objectives Write
the LC code for each
                                                                                                                      Illustrates angles of elevation and                                  Illustrates angles of elevation
                                          Finds the trigonometric ratios of special angles. M9GE -IVb-c-1              angles of depression. M9GE-IVd-                                        and angles of depression.
                                                                                                                                       1                                                             M9GE-IVd-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION
I. OBJECTIVES
A. Content Standard                                                             The learner demonstrates understanding of the basic concepts of trigonometry.
B. Performance Standard                             The learner is able to apply the concepts of trigonometric ratios to formulate and solve real-life problems with precision and accuracy.
C. Learning Competency/Objectives Write
the LC code for each
                                                                                                                   Solves problems involving                                          Solves problems involving
                                          llustrates laws of sines and cosines. M9GE-IVf-g-1                    oblique triangles. M9GE-IVh-j-1                                    oblique triangles. M9GE-IVh-j-1
II. CONTENT
I. Evaluating learning
J. Additional activities for application or
remediation
V. REMARKS
VI. REFLECTION