BOW-MATHEMATICS-7-10.docx

BUDGET OF WORKS FOR THE MOST ESSENTIAL LEARNING COMPETENCIES
Grade Level: GRADE 7
Subject: MATHEMATICS
Time Allotment: 60 Minutes for Four (4) Days
QUARTER
Most Essential Learning
Competencies
The learner …
WEEK DAY OBJECTIVES
I
Illustrates well-defined sets,
subsets, universal sets, null set,
cardinality of sets, union and
intersection of sets and the
difference of two sets.
1
1 Defines well-defined sets, universal
sets, null set, and the cardinal number
of sets.
2 Rewrites the set in roster form to set-
builder form and vice versa.
3 Lists the subsets of a set.
4 Illustrates the union of sets,
intersection of sets and the difference
of two sets.
Solves problems involving sets
with the use of Venn Diagram. 2
1 Uses Venn diagrams to represent
union of sets, intersection of sets, and
difference of two sets.
2 Solves problems involving two sets
with the use of Venn Diagram.
3 Solves problems involving three sets
with the use of Venn Diagram.
4 Constructs real-life problems involving
sets and Venn diagrams.
Represents the absolute value of a
number on a number line as the
distance of a number from 0.
3
1 Represents the absolute value of a
number on a number line as the
distance of a number from 0.
Performs fundamental operations
on integers.
2 Adds integers.
3 Subtracts integers.
4 Multiplies and divides integers.
Illustrates the different properties
of operations on the set of
integers.
4
1 Illustrates the different properties of
operations on the set of integers.
2 Changes fractions to decimals.
3 Changes decimals to fractions.

Expresses rational numbers from
fraction form to decimal form and
vice versa.
4 Expresses rational numbers from
fraction form to decimal form and vice
versa.
Performs operations on rational
numbers.
5
1 Adds and subtracts fractions.
2 Multiplies and divides fractions.
3 Adds and subtracts decimals.
4 Multiplies and divides decimals.
Describes principal roots and tells
whether they are rational or
irrational.
6
1 Identifies a perfect square and its
square roots.
2 Identifies an irrational number.
3 Determines whether each square root
is rational or irrational.
Determines between what two
integers the square root of a
number is.
4
Determines two rational numbers
between which a square root lies.
Estimates the square root of a
whole number to the nearest
hundredth.
7
1 Estimates the square root of a whole
number to the nearest hundredth by
using the square root algorithm.
2 Estimates the square root of a whole
number to the nearest hundredth by
using division.
3 Uses a calculator to approximate the
square root of a whole number to the
nearest hundredth.
Plots irrational numbers (up to
square roots) on a number line.
4
Plots irrational numbers (up to square
roots) on a number line.
Illustrates the different subsets of
real numbers.
8
1 Identifies the different subsets of real
numbers.
2 Compares the different subsets of real
numbers.
Arranges real numbers in
increasing or decreasing order and
on a number line.
3 Plots real numbers on the number
line.
4 Arranges real numbers in increasing or
decreasing order.
Writes numbers in scientific
notation and vice versa.
9
1 Writes numbers in scientific notation.
2 Transforms numbers in scientific
notation to decimal form.
Represents real-life situations and
solves problems involving real
numbers.
3 Represents real-life situations which
involve real numbers.

4 Solves problems involving real
numbers.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
II
Approximates the measures of
quantities particularly length,
weight/mass, volume, time, angle
and temperature and rate.
1
1 Approximates the measures of
quantities of length.
quantities of weight/mass.
quantities of volume/capacity.
quantities of angle, time and rate.
Converts measurements from one
unit to another in both Metric and
English systems.
2
1 Converts measurements of length
from one unit to another in both
Metric and English systems.
2 Converts measurements of
weight/mass and volume/capacity
from one unit to another in both
Metric and English systems.
3
Converts Celsius measurements to
Fahrenheit measurements and vice
versa.
Solves problems involving
conversion of units of
measurement.
4 Solves problems involving conversion
of units of measurement.
Translates English phrases to
mathematical phrases and English
sentences to mathematical
sentences and vice versa.
3
1 Translates English phrases to
mathematical phrases and vice versa.
2 Translates English sentences to
mathematical sentences and vice
versa.
Illustrates and differentiates
related terms in algebra:
a. 𝑎𝑛
where n is positive integer
b. constants and variables
c. literal coefficients and numerical
coefficients
d. algebraic expressions, terms
and polynomials
e. number of terms, degree of the
term and degree of the
polynomial.
3
Interprets 𝑎𝑛
where n is positive
integer.
Differentiates between constants and
variables in a given algebraic
expression.
Differentiates literal coefficients and
numerical coefficients.
4 Defines algebraic expressions, terms
and polynomials.

Identifies number of terms, degree of
the term and degree of the
polynomial.
Evaluates algebraic expressions for
given values of the variables.
4
1
Evaluates algebraic expressions for
given values of the variables.
Adds and subtracts polynomials.
2 Adds polynomials.
3 Subtracts polynomials.
4 Adds and subtracts polynomials.
Derives the laws of exponent.
5
1 Applies the Product Rule, Power Rule
and Product-to-a-Power Rule for
exponents.
Multiplies and divides
polynomials.
2 Multiplies polynomials.
3 Applies the Quotient Rule and
Quotient-to-a-Power Rule for
exponents.
4 Divides polynomials.
Uses models and algebraic
methods to find the: (a) product of
two binomials; (b) product of the
sum and difference of two terms;
(c) square of a binomial; (d) cube
of a binomial; (e) product of a
binomial and a trinomial.
6
1 Finds the product of two binomials
and the product of the sum and
difference of two terms.
2 Finds the square of a binomial.
3 Finds the cube of a binomial.
4 Finds the product of a binomial and a
trinomial.
algebraic expressions.
7 to 8
1
Solves problems involving algebraic
expressions.
Differentiates between algebraic
expressions, equations and
inequalities.
2 Creates real-life problems involving
3 Differentiates between algebraic
expressions and equations.
Illustrates linear equation and
inequality in one variable.
4 Illustrates linear equation in one
variable.
5 States the properties of equality.
6 Differentiates between equations and
inequalities.
7 Illustrates linear inequality in one
variable.
8 States the properties of inequalities.
Finds the solution of linear
equation or inequality in one
variable.
9
1
Finds the solution of linear equation
or inequality in one variable.
Solves linear equation or
inequality in one variable involving
2 Solves linear equation in one variable
involving absolute value by: (a)
graphing; and (b) algebraic methods.

absolute value by: (a) graphing;
and (b) algebraic methods.
3 Solves linear inequality in one variable
involving absolute value by: (a)
graphing; and (b) algebraic methods.
equations and inequalities in one
variable.
4
Solves problems involving equations
and inequalities in one variable.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
Represents point, line and plane
using concrete and pictorial
models.
1
1
Represents point, line and plane using
concrete and pictorial models.
Illustrates subsets of a line. 2 Illustrates subsets of a line.
3 Measures angles.
Classifies the different kinds of
angles.
4
Classifies the different kinds of angles.
Derives relationships of geometric
figures using measurements and
by inductive reasoning;
supplementary angles,
complementary angles, congruent
angles, vertical angles, adjacent
angles, linear pairs, perpendicular
lines, and parallel lines.
2
1 Derives relationships of geometric
figures using measurements and by
inductive reasoning; adjacent angles
and complementary angles.
inductive reasoning; supplementary
angles and linear pairs.
inductive reasoning; congruent angles
and vertical angles.
inductive reasoning; perpendicular
lines and parallel lines.
Derives relationships among
angles formed by parallel lines cut
by a transversal using
measurement and by inductive
reasoning.
3
1 Names pairs of angles formed by
parallel lines cut by a transversal;
alternate interior angle, alternate
exterior angles and corresponding
angles.
2 Describes pairs of angles formed by
parallel lines cut by a transversal;
alternate interior angles, alternate
exterior angles, and corresponding
angles.
3 Finds the measure of an angle formed
by parallel lines cut by a transversal.
4 Applies the Parallel – Interior Angles –
Same Side Theorem and Parallel –

Exterior Angles – Same Side Theorem
in finding the measure of an angle.
Uses a compass and straightedge
to bisect line segments and angles
and construct perpendiculars and
parallels.
4
1 Draws a line and an angle.
2 Constructs perpendicular bisector of a
segment and a line perpendicular to a
line from a point on the line.
3 Constructs the bisector of an angle.
4 Constructs parallel lines and
perpendicular lines.
Illustrates polygons: (a) convexity;
(b) angles; and (c) sides.
5
1 Determines a polygon.
2 Differentiates between a convex
polygon and a nonconvex polygon.
3 Determines the number of diagonals
of a polygon.
4 Constructs regular polygons.
derives inductively the
relationship of exterior and
interior angles of a convex
polygon.
6
1 Finds the sum of the measures of the
interior angles of a convex polygon.
2 Finds the measure of each interior
angle of a regular polygon.
3 Finds the measure of each exterior
angle of a regular polygon.
4 Derives inductively the relationship of
exterior and interior angles of a
convex polygon.
Illustrates a circle and the terms
related to it: radius, diameter
chord, center, arc, chord, central
angle, and inscribed angle. 7
1 Defines the terms related to a circle:
radius, diameter chord, center, arc,
chord, central angle and inscribed
angle.
2 Names the radius, diameter chord,
center, arc, chord, central angle and
inscribed angle of a circle.
3 Finds the measure of the radius,
diameter chord, central angle and
4 Illustrates the radius, diameter chord,
center, arc, chord, central angle and
Constructs triangles, squares,
rectangles, regular pentagons, and
regular hexagons.
8
1 Constructs triangles.
2 Constructs squares and rectangles.
3 Constructs regular pentagons.
4 Constructs regular hexagons,
Solves problems involving sides
and angles of a polygon.
9
1 Solves for the number of sides of a
convex polygon given the sum of the
measures of its interior angles.
convex polygon given the measure of
each interior angle.

convex polygon given the measure of
each exterior angle.
4 Solves for the measure of each
interior angle and each exterior angle
given the number of sides.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
Poses problems that can be solved
using Statistics.
1
1 Explains the importance of Statistics.
2 Poses problems that can be solved
using Statistics.
3 Differentiates descriptive statistics
from inferential statistics.
Formulates simple statistical
instruments.
4 Formulates simple statistical
instruments.
Gathers statistical data. 2
1 Gathers data through interview.
2 Gathers data through questionnaire.
3 Gathers data through observation.
4 Identify the sampling technique used
in a given research topic.
Organizes data in a frequency
distribution table. 3
1 Tallies data and counts the frequency.
2 Determines the class boundaries in a
frequency distribution table.
3 Determines the cumulative frequency
in a frequency distribution table.
4 Organizes data in a frequency
distribution table.
Uses appropriate graphs to
represent organized data: pie
chart, bar graph, line graph,
histogram, and ogive.
4 to 5
1 Represents data using a line graph.
2 Represents data using a bar graph
3 Represents data using a pictograph.
4 Represents data in a pie graph.
5 Constructs a pie graph of a given data.
6 Draws a histogram from a frequency
table.
7 Draws an ogive from a frequency table
8 Uses appropriate graphs to represent
organized data: pie chart, bar graph,
line graph, histogram, and ogive.
Illustrates the measures of
central tendency (mean,
median, and mode) of a
statistical data. 6
1 Illustrates the measures of central
tendency (mean, median, and
mode) of a statistical data.
2 Solves for the mean of ungrouped and
grouped data.
3 Solves for the median of ungrouped
and grouped data.

Calculates the measures of
central tendency of ungrouped
and grouped data.
4 Solves for the mode of ungrouped and
grouped data.
Illustrates the measures of
variability (range, average
deviation, variance, standard
deviation) of a statistical data.
Calculates the measures of
variability of grouped and
ungrouped data.
7
1 Calculates the range of ungrouped and
grouped data.
2 Calculates the average deviation of
ungrouped and grouped data.
3 Calculates the variance of ungrouped
and grouped data.
4 Calculates the standard deviation of
ungrouped and grouped data.
Uses appropriate statistical
measures in analyzing and
interpreting statistical data.
Draws conclusions from graphic
and tabular data and measures of
central tendency and variability.
8 to 9
1 Uses appropriate statistical measures
in analyzing and interpreting statistical
data.
2 Draws conclusions from a line graph.
3 Draws conclusions from a bar graph.
4 Draws conclusions from a pie graph.
5 Draws conclusions from the measures
of central tendency.
6 Draws conclusions from the average
mean of a data set.
7 Draws conclusions from the variance
of a data set.
8 Draws conclusions from the standard
deviation of a data set.

QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
I
Factors completely different types
of polynomials (polynomials with
common monomial factor,
difference of two squares, sum and
difference of two cubes, perfect
square trinomials, and general
trinomials).
1 to 2
1 Expresses a polynomial by
extracting its greatest common
monomial factor (GCMF) and its
prime polynomial.
2 Finds the factors of a polynomial by
a difference of two squares (DOTS).
3 Performs factoring a polynomial
using sum and difference of two
cubes (SDTC).
4 Distinguishes a perfect square
trinomial from other types of
polynomials.
5 Applies factoring a polynomial by a
perfect square trinomial (PST).
6 Demonstrates factoring a general
quadratic trinomial (GQT).
7 Determines the most appropriate
method of finding factors of a
polynomial.
Solves problems involving factors of
polynomials.
8 Solves problems involving
polynomials and their factors.
Illustrates rational algebraic
expressions.
Simplifies rational algebraic
expressions.
3
1 Describes and illustrates rational
2 Interprets zero and negative
exponents.
3 Simplifies rational algebraic
expressions.
4 Evaluates procedures on
simplifying rational algebraic
expressions.
Performs operations on rational
1. solves problems involving
rational algebraic
expressions.
Week 4
1 Finds the product and quotient of
two or more rational algebraic
expressions.
2 Performs addition and subtraction
of rational algebraic expressions
with the same denominators.

3
Executes addition and subtraction
of rational algebraic expressions
with different denominators.
4
Creates a new model to solve real
life problems involving rational
Illustrates the rectangular
coordinate system and its uses.
llustrates linear equations in two
variables.
llustrates and finds the slope of a
line given two points, equation, and
graph.
5
1 Defines and illustrates rectangular
coordinate system and its uses.
2 Illustrates linear equations in two
variables using coordinate axes.
3 Finds and interprets the slope of a
line given two points and a graph.
4 Constructs a slope of a line from a
given equation.
Writes the linear equation Ax + By =
C into the form y = mx + b and vice
versa.
Graphs a linear equation given (a)
any two points; (b) the x – and y –
intercepts; (c) the slope and a point
on the line.
Describes the graph of a linear
equation in terms of its intercepts
and slope.
6
1 Writes linear equation Ax + By = C
into the form y =mx+b and vice
versa.
2 Graphs a linear equation given (a)
any two points; and (b) x- and y
intercepts.
3 Constructs the line on a coordinate
axes given a slope and a point.
4
Describes the graph of a linear
equation in terms of its intercepts
and slope.
Finds the equation of a line given
(a) two points; (b) the slope and a
point; (c) the slope and its
intercepts.
7
1 Finds the equation of a line given
(a) any two points and (b) the slope
and a point.
2 Determines equation of a line given
the slope and its intercepts.
Solves problems involving linear
equations in two variables.
3 Solves and evaluates problems
involving linear equations in two
variables.
4 Creates a linear model that solves
real life problems involving linear
Illustrates a system of linear
equations in two variables. 8
1 Describes and illustrates a system
of linear equations in two variables
using practical situations and
mathematical expressions.

Graphs a system of linear equations
in two variables.
Categorizes when a given system of
linear equations in two variables
has graphs that are parallel,
intersecting, and coinciding.
2 Graphs a system of linear
equations in two variables on a
coordinate plane.
3 Categorizes when a given system of
linear equations in two variables
has graphs that are parallel,
intersecting, and coinciding.
4 Distinguishes the kind of systems of
linear equations according to the
number of solutions.
Solves problems involving systems
by (a) graphing; (b) substitution; (c)
elimination.
9
1 Describes and illustrates solutions
to a system of linear equations in
two variables by graphing.
2 Finds solution to problems
involving systems of linear
equations in two variables by
substitution.
3 Solves problems involving systems
by elimination.
4 Distinguishes the most appropriate
method of solving problems in real
life situation (such as age, distance,
motion, investment problems, etc.)
involving systems of linear
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
II
Differentiates linear inequalities in
two variables from linear equations
in two variables.
Illustrates and graphs linear
inequalities in two variables.
Week 1
1 Translates statements from real life
situations to mathematical
equations or inequalities.
2 Differentiates linear inequalities in
two variables from linear equations
in two variables.
3
Illustrates and graphs linear
inequalities in two variables on a
rectangular coordinate plane.
4 Designs model to solve real life
problems involving linear
Solves problems involving systems
of linear inequalities in two
variables.
2
1 Illustrates and interprets real life
situations involving systems of
linear inequalities in two variables.

2 Graphs a system of linear
inequalities in two variables on a
coordinate plane.
3 Solves problems involving systems
of linear inequalities in two
variables.
4
Creates analogy between solutions
to systems of linear equations and
systems of linear inequalities.
Illustrates a relation and a function.
Verifies if a given relation is a
function.
Determines dependent and
independent variables.
3
1 Illustrates a relation and a function
using real life situations.
2 Discusses representations of a
relation.
3 Verifies if a given relation is a
function.
4
Differentiates dependent and
independent variables.
Finds the domain and range of a
function.
Graphs and illustrates a linear
function and its (a) domain; (b)
range; (c) table of values; (d)
intercepts; and (e) slope.
4
1
Describes domain and range of a
function with practical applications.
2 Determine the domain and range
of a function using the different
relation representations.
3 Constructs the graphs of linear
functions through its table of
values.
4
Deconstructs linear functions and
its domain, range, intercept and a
slope through its graph.
functions.
5
1 Translates words phrases in real
life problems involving linear
functions to mathematical
symbols.
2
Transforms verbal sentences into
mathematical equations.
3
Creates a model to solve a real life
problem involving linear function.
4 Evaluates solutions to problems
involving linear functions and
patterns.

Determines the relationship
between the hypothesis and the
conclusion of an if-then statement.
6
1 Defines and illustrates simple
implications.
2 Determines the relationship
between the hypothesis and the
conclusion of an if-then statement.
Transforms a statement into an
equivalent if-then statement.
3 Transforms a statement into an
equivalent if – then statement and
vice-versa.
4 Verifies the truth value of if – then
statements.
Determines the inverse, converse,
and contrapositive of an if-then
statement.
7
1 Illustrates and finds the inverse of
if – then statements.
2 Expresses a simple if-then
statement into its converse.
3 Formulates the contrapositive
statement of a simple implication.
4 Generates the inverse, converse,
and contrapositive of an if-then
statement.
Illustrates the equivalences of: (a)
the statement and its
contrapositive; and (b) the converse
and inverse of a statement.
8
1 Defines logical equivalence of a
statement.
2 Illustrates the equivalence of the
statement and its contrapositive.
3 Illustrates the equivalence of the
converse and inverse of a
statement.
4 Constructs the truth value table of
the statements.
Uses inductive or deductive
reasoning in an argument.
9
1 Illustrates inductive and deductive
reasoning types.
2 Uses inductive or deductive
reasoning in an argument.
Writes a proof (both direct and
indirect).
3 Writes a proof using direct
approach.
4 Shows a proof using indirect
method.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
Describes a mathematical system.
1 Describes a mathematical system.
2 States and illustrates the different
properties of equality.

III
Illustrates the need for an axiomatic
structure of a mathematical system
in general, and in Geometry in
particular: (a) defined terms; (b)
undefined terms; (c) postulates;
and (d) theorems.
1 to 2
3 Uses properties of equality to
justify steps in algebraic solutions.
4 Illustrates the need for an
axiomatic structure of Geometry in
particular: (a) undefined terms;
and (b) defined terms.
5 Constructs diagrams or concept
maps to illustrate the basic terms
in geometry.
6 Illustrates the need for an
axiomatic structure of Geometry in
particular: (c) postulate; and (d)
theorem.
7 Compares and contrasts postulates
and theorems in Geometry through
the application of these
statements.
8 Constructs a design to show the
relationship of the basic structure
in Geometry.
Illustrates triangle congruence.
3 to 4
1 Defines and illustrates congruent
triangles.
2 Determines corresponding parts
between pairs of triangles.
3 Identifies corresponding included
angles and corresponding included
sides between pairs of triangles.
Illustrates the SAS, ASA and SSS
congruence postulates.
4 States and applies SAS Congruence
Postulate to check if pairs of
triangles are congruent.
5 Illustrates and uses ASA
Congruence Postulate to verify if
pairs of triangles are congruent.
6 Investigates if pairs of triangles are
congruent using SSS Congruence
Postulate.
7 Evaluates pairs of triangles
whether congruent or not using
SAS, ASA, and SSS Congruence
Postulates.
8 Solves real life situations applying
congruence postulates.
Solves corresponding parts of
congruent triangles. 5
1 Describes and labels corresponding
parts of congruent triangles.
2 States the relationship between
parts of the given triangles.

3 Finds the measures of the
corresponding parts of congruent
triangles.
4 Solves the unknown quantity in
between parts of congruent
triangles.
Proves two triangles are congruent. 6
1 Describes two – column table and
its related elements.
2 Presents parts and uses of a two –
column proof.
3 Shows that triangles are congruent
using two – column table.
4 Verifies statements on congruent
triangles.
Proves statements on triangle
congruence.
7
1 States and shows the proof of AAS
Congruence Theorem.
2 Applies AAS Congruence Theorem
in proving exercises involving
triangle congruence.
3 Generates LL and LA Congruence
Theorem using the previous
theorems on triangle congruence.
4 Verifies if right triangles are
congruent using HyL and HyA
Congruence Theorems.
Applies triangle congruence to
construct perpendicular lines and
angle bisectors.
8 to 9
1 Defines perpendicular lines and
angle bisectors.
2 Describes and labels the primary
and secondary parts of an isosceles
triangle.
3 Presents and illustrates isosceles
triangle theorem.
4 Formulates and applies the
converse of an isosceles triangle
theorem in solving problems.
5 Generates and proves theorems
about isosceles and
equilateral/equiangular triangles
using two-column table.
6 Verifies the theorem about the
bisector of the vertex angle of an
isosceles triangle using the two-
column proof.
7 Justifies statements using two-
column proof and triangle
congruence theorems.

8 Creates and solves real – life
problems applying triangle
congruence theorems on
constructing perpendicular lines
and angle bisectors.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
IV
Illustrates theorems on triangle
inequalities (Exterior Angle
Inequality Theorem, Triangle
Inequality Theorem, Hinge
Theorem).
1
1 States and illustrates properties of
inequalities both for real numbers
and geometric figures (line
segments and angles).
2 States and illustrates Exterior Angle
Inequality Theorem.
3 Illustrates Triangle Inequality
Theorem and generates its related
theorems.
4 Explains Hinge Theorem and its
converse.
Applies theorems on triangle
inequalities.
2
1 Uses Exterior Angle Inequality
Theorem in solving problems
related to triangle inequalities.
2 Applies Triangle Inequality
Theorem in solving problems
related to triangle inequalities.
3 Solves problems involving triangle
inequalities using Side – Angle and
Angle – Side Inequality theorems.
4 Evaluates problems on triangle
inequalities using Hinge Theorem
and its converse.
Proves inequalities in a triangle. 3
1 Shows proofs of Exterior Angle
inequality and triangle inequality
theorems using a direct proof.
2 Constructs a two – column proof to
verify side – angle and angle – side
inequality theorems.
3 Constructs a two – column table to
prove Hinge Theorem and its
converse.
4 Verifies exercises/problems on
inequalities in a triangle.
Proves properties of parallel lines
cut by a transversal. 4
1 Defines and illustrates parallelism
and a transversal line.
2 Categorizes angle relationships
formed by parallel lines cut by a
transversal.

3 Illustrates properties about
corresponding angles and same
side angles formed by parallel lines
cut by a transversal.
4 Generates the properties about
alternate interior and alternate
exterior angles formed by parallel
lines cut by a transversal.
Determines the conditions under
which lines and segments are
parallel or perpendicular.
5
1 Differentiates parallel and
perpendicular lines
2 Determines the conditions under
which lines and segments are
parallel or perpendicular.
3 Solves the unknown quantity
applying conditions under which
lines and segments are parallel or
perpendicular.
4 Evaluates real life problems
involving parallelism and
perpendicularity.
Illustrates an experiment, outcome,
sample space and event.
6
1 Defines and illustrates simple
probability and its related terms.
2 Differentiates a sample space and
an event.
3 Finds the outcome of probabilistic
experiments.
4 Integrates and evaluates real life
situations involving the concept of
simple probability.
Counts the number of occurrences
of an outcome in an experiment: (a)
table; (b) tree diagram; (c)
systematic listing; and (d)
fundamental counting principle.
7
1 Counts the number of occurrences
of an outcome in an experiment
using table of values.
2 Computes the number of
occurrences of an outcome in an
experiment using a tree diagram.
3 Solves for the number of
occurrences of an outcome in an
experiment using systematic listing.
4 Finds the number of occurrences of
an outcome in an experiment using
Fundamental Principle of Counting
(FPC).
Finds the probability of a simple
event.
8
1 Recognizes the formula in finding
the probability of a simple event
and the different probability rules.

QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
I
Illustrates quadratic equations.
Solves quadratic equations by: (a)
extracting square roots; (b)
factoring; (c) completing the
square; and (d) using the quadratic
formula.
1
1 Illustrates quadratic equation.
Solves quadratic equation by
extracting square roots.
2 Solves quadratic equations by
factoring.
3 Solves quadratic equation applying
completing the square.
4 Applies quadratic formula to solve
quadratic equations.
Characterizes the roots of a
quadratic equation using the
discriminant
2 and 3
1 Characterizes the roots of a
quadratic equation using the
discriminant.
2 Describes the relationship between
the coefficients and the roots of a
quadratic equation
2 Applies fundamental counting
principle in finding the number of
favourable and possible outcomes.
probability of a simple event.
4 Creates a model in solving real life
situations related to simple
probability.
Illustrates an experimental
probability and a theoretical
probability.
probabilities of simple events.
Week 9
1 Defines and illustrates
experimental probability and
theoretical probability.
2 Compares and contrasts
experimental probability from
3 Finds solutions to problems
involving experimental and
4 Creates a design or a concept map
that summarizes all important and
related terms on simple
probability.

Describes the relationship between
the coefficients and the roots of a
quadratic equation.
Solves equations transformable to
quadratic equations (including
rational algebraic equations).
3 Illustrates problems involving the
relationship between the
coefficients and the roots of a
quadratic equation.
4 Solves routine and non-routine
problems involving roots of a
quadratic equation.
5 Solves quadratic equations that are
not written in standard form.
6 llustrates rational algebraic
equations transformable to
7 Determines the roots of rational
algebraic equations transformable
to quadratic equations
8 Solves routine and non – routine
problems involving equations that
are not written in standard form
including rational algebraic
equations.
quadratic equations and rational
algebraic equations.
4
1 Illustrates and applies the steps in
solving problems involving
2 Models and solves problems
related to quadratic equations
3 Illustrates and models problems on
rational algebraic equations.
4 Formulates and solves problems
involving quadratic equations
based on real life situations
including rational algebraic
equations.
Illustrates quadratic inequalities
Solves quadratic inequalities.
quadratic inequalities.
5
1 Illustrates quadratic inequalities.
2 Solves quadratic inequalities.
problems involving quadratic
inequalities.
4 Illustrates and solves problems
involving quadratic inequalities
based on real life situations.
Models real-life situations using
quadratic functions.
6
1 Models and illustrates situations
using quadratic function.

Represents a quadratic function
using: (a) table of values; (b) graph;
and (c) equation.
2
Identifies and represents a
quadratic function given a table of
values.
3
quadratic function given a graph.
4
quadratic function given the
equation.
Transforms the quadratic function
defined by y = ax2
+ bx + c into the
form y = a (x – h)2
+ k.
Graphs a quadratic function: (a)
domain; (b) range; (c) intercepts;
(d) axis of symmetry; (e) vertex; (f)
direction of the opening of the
parabola.
Analyzes the effects of changing
the values of a, h and k in the
equation y = a (x – h)2
+ k of a
quadratic function on its graph.
7 to 8
1 Transforms the quadratic function
defined by y = ax2
+ bx + c into the
form y = a(x – h)2
+ k and vice
versa.
2 Illustrates and describes the graph
of a quadratic function.
3 Determines the following: domain,
range, intercepts of the graph of a
quadratic function.
4 Identifies the axis of symmetry,
vertex and direction of the opening
of the parabola given the quadratic
function.
5 Investigates and analyzes the effect
of changing the value of a of a
quadratic function y= a(x-h)2
+ k on
its graph and make generalizations.
of changing the value of h of a
+ k on
its graph and make generalizations
of changing the value of k of a
+ k on
its graph and make generalizations.
8 Day 8: draws the graph of the given
quadratic function
applying the effects of the values
of a, h, and k in the translation
or movement of its graph.
Determines the equation of a
quadratic function given: (a) a table
of values; (b) graph; (c) zeros.
9
1 Derives the equation of the
quadratic function given the table
of values and its graph.

quadratic functions.
2
Determines the quadratic function
given its zeros.
quadratic function.
involving quadratic function.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
II
Illustrates situations that involve
the following variations: (a) direct;
(b) inverse; (c) joint; (d) combined.
Translates into variation statement
a relationship between two
quantities given by: (a) a table of
values; (b) a mathematical
equation; (c) a graph, and vice
versa.
variation.
1 and 2
1 Illustrates situations that involve
direct variation.
2 Translates into variation statement
a relationship involving direct
variation between two quantities
given by a table of values, a
mathematical equation and a
graph and vice versa.
inverse variation.
a relationship involving inverse
variation between two quantities
given by a table of values, a
mathematical equation and a
graph and vice versa
joint and combined variation
a relationship involving joint and
combined variation between two
quantities given by a mathematical
equation and vice versa.
7
Models and solves problems
involving variation.
involving variation.
Applies the laws involving positive
integral exponents to zero and
negative integral exponents.
3
1 Illustrates expressions with zero
and negative exponents.
2 Applies the laws involving positive
integral exponents to zero and
negative exponents.

3 Simplifies expressions with zero
and negative exponents.
4 Applies the concept of zero and
negative exponents to problems in
real life situations.
Simplifies expressions with rational
exponents.
Writes expressions with rational
exponents as radicals and vice
versa.
4
1 Illustrates expressions with rational
exponents.
2 Applies the laws involving positive
integral exponents to rational
exponents.
3 Simplifies expressions with rational
exponents.
4 Writes expressions with rational
exponents as radicals and vice
versa.
Derives the laws of radicals. 5
1 Illustrates the law of radical ( √𝑎
𝑛
)n
= a, a>0 derived from the laws of
exponents.
2 Illustrates the law of
radical √𝑎𝑏
𝑛
= √𝑎
𝑛
∗ √𝑏
𝑛
, a>0 &
b>0 derived from the laws of
exponents.
3
Illustrates the law of radical √
𝑎
𝑏
𝑛
=
√𝑎
𝑛
√𝑏
𝑛 , 𝑏 > 0
derived from the laws of
exponents.
4 Illustrates the law of
radical √ √𝑎
𝑛
𝑚
= √√𝑎
𝑚𝑛
, a>0
derived from the laws of
exponents.
Simplifies radical expressions using
the laws of radicals.
6
1 Simplifies radical expressions by
removing the perfect nth powers
using the laws of radicals.
reducing the index to the lowest
possible order using the laws of
radicals.
rationalizing the denominator of
the radical using the laws of
radicals.

problems involving simplifying
radical expressions.
Performs operations on radical
expressions. 7
1 Performs addition or subtraction of
radical expressions.
2 Performs multiplication of radicals.
a. radicals of the same
order
b. binomials involving
radicals
c. radicals of different
orders
3 Performs division of radicals.
a. radicals of the same
order
b. radicals of different
order
4
Performs division of radicals with
a denominator consisting of at
least two terms
Solves equations involving radical
expressions.
8
1
Illustrates radical equations.
2 Determines the roots of the radical
equations applying the concepts of
radicals.
 Illustrates extraneous
roots.
3 Solves equations involving radical
expressions.
problems involving radical
equations.
Solves problems involving radicals. 9
1
Illustrates and models real
situations involving radicals.
2 Applies the concept of radical
equations in solving problems
involving radicals.
problems involving radicals.
involving radicals.

QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
III
Determines the conditions that
make a quadrilateral a
parallelogram.
Uses properties to find measures
of angles, sides and other
quantities involving parallelograms.
1
1 Identifies and illustrates
quadrilaterals that are
parallelograms.
2 Determines the conditions that
make a quadrilateral a
parallelogram.
3 Uses properties to find measures
of angles, sides and other
quantities involving parallelograms.
problems involving properties of
parallelogram.
Proves theorems on the different
kinds of parallelogram (rectangle,
rhombus, square).
2
1 Proves theorems that justify a
parallelogram a rectangle.
parallelogram a rhombus.
parallelogram a square.
4 Applies the theorems to find
measures of angles, sides, and
other quantities involving
rectangle, rhombus and square
Proves the Midline Theorem.
Proves theorems on trapezoids and
kites.
3
1 Proves the Midline Theorem.
2 Proves theorems on trapezoids.
3 Applies the theorems to find
other quantities involving
trapezoids.
4 Proves theorems involving kite and
applies these theorems to find
other quantities involving kite.
parallelograms, trapezoids and
kites.
4
1 Illustrates and solves real life
problems involving parallelograms.
2 Models and solves problems based
on real situations involving
trapezoids.
3 Illustrates and models real
situations involving kites.

involving parallelograms,
trapezoids and kites.
Describes a proportion.
Applies the fundamental theorems
of proportionality to solve
problems involving proportions.
5
1 Defines and illustrates a proportion
and its properties.
2 Applies the fundamental rule of
proportion to determine the
unknown quantity in a proportion.
*defines and illustrates a
scale factor
3 Illustrates and applies the Triangle
Proportionality Theorem in solving
4 Illustrates and applies the Triangle
Angle Bisector Theorem in solving
Illustrates similarity of figures.
proves the conditions for similarity
of triangles.
1.1 SAS similarity theorem
1.2 SSS similarity theorem
1.3 AA similarity theorem
1.4 right triangle similarity theorem
1.5 special right triangle theorems
6 to 7
1
Illustrates similarity of figures.
2 Proves the conditions that justify
similarity of triangles by SAS
Similarity Theorem.
similarity of triangles by SSS
Similarity Theorem
4 Proves conditions that two
triangles are similar by AA
Similarity Theorem.
5 Investigates the ratios of
perimeters, areas, volumes of
similar figures (triangles, cubes,
spheres, rectangular prisms).
similarity of triangles by Right
Triangle Similarity Theorem.
7 Illustrates and determines the
special properties of right triangle
when an altitude is drawn to the
hypotenuse.
 Geometric Mean
8 Proves the conditions for right
triangles similarity by the special
right triangle theorems
 45-45-90 Right Triangle
Theorem
 30-60-90 Right Triangle
Theorem

Applies the theorems to show that
given triangles are similar.
Proves the Pythagorean Theorem.
8
1 Illustrates and determines whether
the two given triangles are similar
by applying the similarity
theorems:
*SAS Similarity Theorem
* SSS Similarity Theorem
* AA Similarity Theorem
2 Proves the conditions for a right
triangle by Pythagorean Theorem.
3 Applies Pythagorean Theorem in
finding the missing lengths of the
sides of a right triangle.
4 Classifies the kind of triangle
according to angles by comparing
the squares of the lengths of the
sides of the triangle.
* c2
= a2
+ b2
* c2
> a2
+ b2
* c2
< a2
+ b2
Solves problems that involve
triangle similarity and right
triangles.
9
Day 1: illustrates problems in real
situations that involve triangles
similarity.
Day 2. solves real life problems
applying the concept of similarity
of triangles.
Day 3. formulates and solves real
life problems involving right
triangles especially in finding
heights and distances applying
Pythagorean Theorem.
Day 4: applies the concept of
similarity in dilation; reducing and
enlarging the size of objects and in
scale drawing.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
IV
Illustrates the six trigonometric
ratios: sine, cosine, tangent,
secant, cosecant, and cotangent.
Finds the trigonometric ratios of
special angles.
1 to 2
1 Defines and illustrates the six
trigonometric ratios.
2 Finds the trigonometric ratios of
the given acute angles with the use
of a calculator.
3 Applies trigonometric ratios to
solve right triangle given the length
of the hypotenuse and length of
one leg.

solve right triangle given length of
the hypotenuse and one of the
acute angles.
solve right triangle given the length
of one leg and one of the acute
angles.
solve right triangle
given length of both sides.
7 Determines the trigonometric
ratios involving special angles.
8 Computes and evaluates the exact
numerical values of trigonometric
expressions involving special angles
Illustrates angles of elevation and
angles of depression.
Uses trigonometric ratios to solve
real-life problems
involving right triangles.
3 to 5
1 Defines and illustrates angles of
elevation and depression.
2 Distinguish between angle of
elevation and angle of depression.
3 Solves problems involving angle of
elevation.
4 Solves problems involving angle of
depression.
5 to 6 Formulates and solves problems
involving angle of elevation and
depression.
7 Determines and enumerates some
practical applications of
trigonometry to everyday life and
to the different fields.
8 Solves real – life problems
involving right triangles using
trigonometric ratios. (finding
heights and distances)
9 to 10 Formulates and solves real life
problems involving right triangles
using trigonometric ratios.
11 to 12 Investigates on finding height of
buildings/ mountains, etc. without
actually measuring it.
Illustrates laws of sines and
cosines. 6 to 9
1 Defines and illustrates oblique
triangles.
2 Derives and illustrates the Law of
Sines.

Solves problems involving oblique
triangles.
3 Illustrates the Law of Sines in
solving oblique triangles when
measures of two angles and one
non- included side given. (SAA
Case)
4 Illustrates the law of Sines in
solving oblique triangles given
measures of two angles and the
included side. (ASA Case)
5 Illustrates finding measure of
another angle of the triangle when
measures of two sides and an angle
opposite one of them are given
applying the Law of Sines. (SSA
Case)
6 Determines the missing parts of
oblique triangles applying the Law
of Sines.
7 Applies the Law of Sines to solve
real life problems involving oblique
triangles.
8 Formulates and solves real life
problems involving oblique
triangles applying the Law of Sines.
9 Derives a formula for area of an
oblique triangle using the sine
ratio.
10 Finds the area of an oblique
triangle using the derived formula:
a. A= ½ab Sin C
b. A= ½ bc Sin A
c. A= ½ ac Sin B
11 Illustrates the Law of Cosines
12 Applies the Law of Cosines in
finding the missing parts of an
oblique triangle when measures of
the two sides and the included
angle are given. (SAS Case)
13 Applies the Law of Cosines in
finding the missing parts of the
oblique triangle when measures of
the three sides are given. (SSS
Case)
14 Solves real life problems involving
oblique triangles applying the Law
of Cosines.
 Bearing and Navigation

15 to 16 Formulates and solves real life
problems involving oblique
triangles applying the Law of
Cosines.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
I
Generates patterns.
Illustrates an arithmetic sequence.
Determines arithmetic means, nth
term of an arithmetic sequence and
sum of the terms of a given
arithmetic sequence
Week 1 to
2
1 Generates pattern
2 Derives a mathematical
expression (rule) by searching a
pattern.
3 Illustrates arithmetic sequence.
4 Identifies an arithmetic
sequence.
5 Finds the common difference
and nth
term given the first few
terms of an arithmetic sequence
6 Finds the first term and common
difference or a specified nth
term
given two terms of an arithmetic
sequence
7 Determines the arithmetic
means of an arithmetic
sequence.
8 Finds the sum of the terms of a
given arithmetic sequence.
Illustrates a geometric sequence.
Differentiates a geometric sequence
from an arithmetic sequence.
3
1 Illustrates a geometric
sequence.
2 Generates a rule for geometric
sequence.
3 Distinguishes between
arithmetic and geometric
sequences.
4 Illustrates finite and infinite
geometric sequence.
Determines geometric means, nth
term of a geometric sequence and
Sum of the terms of a given finite or
infinite geometric sequence
4
1 Determines the geometric
means between two terms.
2 Calculates the specified nth
term
given the first few terms of a
geometric sequence.

3 Calculates the sum of the terms
of a finite geometric sequence.
4 Calculates the sum of the terms
of an infinite geometric
sequence.
Solves problems involving sequences. 5
1 Solves real-life problems
involving arithmetic sequence.
2 Solves problems involving the
sum of arithmetic sequence.
3 Solves real-life problems
involving geometric sequence.
geometric means.
Performs division of polynomials
using long division and synthetic
division.
Proves the Remainder Theorem,
Factor Theorem and the Rational
Root Theorem.
6
1 Performs division of polynomials
using long division.
2 Performs division of polynomials
using synthetic division.
3 Proves and applies remainder
theorem and factor theorem.
4 Proves and applies rational root
theorem.
Factors polynomials. 7
1 Factors polynomials by
groupings and by a common
monomial factor.
2 Evaluates polynomials using
substitution method.
3 Determines the factors of the
polynomial using synthetic
division and factor theorem.
4 Determines the factors of the
polynomial using factor
theorem.
Illustrates polynomial equations. 8
1 Illustrates polynomial equations.
2 Solves polynomial equations in
factored form.
3 Determines the solution/root of
the polynomial equation.
4
Creates polynomial equations.
polynomials and polynomial
equations.
9
polynomials.
2 Formulates and solves real - life
problems involving polynomials.
polynomial equations.

4 Formulates and solves real – life
problems involving polynomial
equations.
QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
II
Illustrates polynomial functions.
Understand, describe and interpret
the graphs polynomial functions.
Solves problems involving polynomial
functions.
1 to 2
1 Illustrates polynomial functions.
2 Rewrites the polynomial
function in factored form.
3 Identifies the x and y – intercepts
of a polynomial function.
4 Graphs polynomial functions
using the x and y – intercepts.
5 Identifies end behaviors of the
graph using the leading
coefficient test.
6 Identifies the multiplicity of
root(s)/ zero(es) of polynomial
functions.
7 Describes the graph of
polynomial functions.
polynomial functions.
Derives inductively the relations
among chords, arcs, central angles,
and inscribed angles.
Proves theorems related to chords,
arcs, central angles, and inscribed
angles.
3 to 4
1 Illustrates chords, arcs and
central angles.
2 Derives the relationship
between central angles and their
intercepted arcs.
3 Proves theorems related to
congruent central angles and
their corresponding arcs.
4 Proves theorems related to
congruent chords and their
corresponding arcs.
5 Proves theorem on chord
perpendicular to a diameter (or
radius).
6 Derives the relationship
between inscribed angles and
their intercepted arcs
7 Proves theorems on inscribed
angles.
8 Proves theorems on
quadrilateral inscribed in a
circle.

Illustrates secants, tangents,
segments, and sectors of a circle.
Proves theorems on secants,
tangents, and segments.
Solves problems on circles.
5 to 6
1 Illustrates sector and segment of
a circle.
2 Illustrates secants and tangents
of a circle.
3 Proves theorems on tangent
line.
4 Proves theorems on angles
formed by intersecting secants.
formed by intersecting tangents.
formed by intersecting secant
and tangent.
7 Proves theorems on secant
segment, tangent segments and
external secant segments.
8 Solves problems on circles.
Applies the distance formula to prove
some geometric properties.
7
1 Derives the distance formula.
2 Applies the distance formula in
finding the distance between
two points.
3 Finds the midpoint between two
points.
4 Applies the distance and the
midpoint formula to prove some
geometric properties.
Illustrates the center-radius form of
the equation of a circle.
Determines the center and radius of
a circle given its equation and vice
versa.
8
1 Illustrates the center-radius
form of the equation of a circle.
2 Rewrites the center-radius form
of the equation of a circle into
general form.
3 Rewrites general form of the
equation of a circle into center-
radius form.
4 Determines the center and the
radius of a circle given its
equation and vice versa.
Graphs and solves problems involving
circles and other geometric figures on
the coordinate plane.
9
1 Graphs a circle given the center
and the radius.
2 Graphs a circle defined by the
given equation.
circles.
geometric figures on the
coordinate plane.

QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
III
Illustrates the permutation of
objects.
permutations.
1 to 2
1 Illustrates Fundamental
Counting Principles.
Fundamental Counting
Principles.
3 Illustrates factorial notation.
4 Illustrates permutation of
objects.
5 Finds the permutation of n
objects taken r at a time.
6 Illustrates distinguishable
permutations.
7 Illustrates circular permutations.
permutations.
Illustrates the combination of
objects.
Differentiates permutation from
combination of objects taken at a
time.
3 to 4
1 Illustrates combination of
objects.
2 Derives the formula for finding
the numbers of combinations of
n objects taken r at a time.
3 Determines the combination of
n objects taken r at a time
problems involving
combination.
5 Differentiates permutation from
combination of objects taken at
a time.
6 Identifies the situations that
involve permutation and
combination.
7 Compares the number of
possible arrangements of
permutation and combination of
n objects taken r at a time.
8 Solves problems that involve
both permutation and
combination.
permutations and combinations.
5
1 Illustrates and models problems
involving permutation and
combination.

2 Solves real- world problems
involving permutation.
3 Solves real – life problems
involving combination.
4 Formulates and solves real life
problems involving permutation
and combination.
Illustrates events, and union and
intersection of events.
6
1 Illustrates experiments, sample
space and outcomes.
2 Differentiates simple events and
compound events.
3 Illustrates union of events.
4 Illustrates intersection of events.
Illustrates the probability of a union
of two events.
7
1 Illustrates probability of simple
events.
2 Identifies the samples space
3 Identifies the number of ways
the union of two events can
occur.
4 Illustrates the probability of a
union of two events,
Finds the probability of (𝐴 ∪ 𝐵). 8
1 Finds the probability of the
union of two events.
2 Illustrates probability of
dependent and independent
events.
3 Determines probability of
dependent and independent
events.
4 Solves routine and non routine
problems involving probability
of events.
Illustrates mutually exclusive events.
probability.
9
1 Illustrates mutually and not
mutually exclusive events.
2 Solves real life problems
involving probability of mutually
and not mutually exclusive
events.
Solves real life problems
involving probability of
independent and dependent
events.
Solves real life probability
problems involving permutation
and combination.

QUARTER
Competencies
The learner …
WEEK DAY OBJECTIVES
IV
Illustrates the following measures of
position: quartiles, deciles and
percentiles.
1
1 Illustrates quartiles.
2 Illustrates deciles.
3 Illustrates percentiles.
4 Identifies relationship between
the measures of position.
Calculates a specified measure of
position (e.g. 90th
percentile) of a set
of data.
2
1 Calculates the quartiles of
ungrouped data.
2 Calculates the deciles of
ungrouped data.
3 Calculates percentiles of
ungrouped data.
4 Calculates inter-quartile range
and percentile rank.
Interprets measures of position. 3
1 Interprets quartiles.
2 Interprets deciles.
3 Interprets percentiles.
4 Interprets percentile rank.
Solves problems involving measures
of position.
4 to 5
1 Calculates the quartiles for
grouped data.
2 Calculates the deciles for
grouped data.
3 Calculates percentiles for
grouped data.
4 Calculates inter-quartile range
and percentile rank for grouped
data.
quartiles.
deciles.
percentiles.
percentile rank.
Formulates statistical mini-research. 6 to 7
1 Formulates a simple discussion
on the desired statistical
problem,
2 Creates a question survey that
collects some form of numerical
(quantitative) data.
3 Identifies a sampling method.
4 Conducts a survey.

7 Organizes the data collected.
8 Organizes the data collected.
Uses appropriate measures of
position and other statistical
methods in analyzing and
interpreting research data.
8 to 9
1 Creates a frequency distribution
table.
2 Analyzes the data using an
appropriate measure of
position.
3 Analyzes the data using an
appropriate measure of
position.
4 Writes an interpretation of the
data.
5 Creates a write-up on the mini-
research.
6 Creates a write-up on the mini-
research.
7 Presents the final mini-research
output.
8 Presents the final mini-research
output.

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