COURSE DESCRIPTION MATHEMATICS

BASIC EDUCATION DEPARTMENT Holy Angel University

Angeles City

LES AND JHS MATHEMATICS DEPARTMENT

WE ARE ALL ABOUT STUDENTS. LAUS DEO SEMPER. 1

BASIC EDUCATION DEPARTMENT

HOLY ANGEL UNIVERSITY

LES AND JHS �

COURSE DESCRIPTION MATHEMATICS


Angeles City



COURSE DESCRIPTION

Mathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic, and reasoning. Mathematics is also a tool of science and a language complete with its own notations and symbols and “grammar” rules, with which concepts and ideas are effectively expressed.

The contents of mathematics include Numbers and Number Sense, Measurement, Geometry, Patterns & Algebra and Statistics and Probability.

Numbers and Number Sense as a strand include concepts of numbers, properties, operations, estimation, and their applications.

Measurement as a strand includes the use of numbers and measures to describe, understand, and compare mathematical and concrete objects. It focuses on attributes such as length, mass and weight, capacity, time, money, and temperature, as well as applications involving perimeter, area, surface area, volume, and angle measure.

Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoning, and geometric modelling and proofs.

Patterns and Algebra as a strand studies patterns, relationships, and changes among shapes and quantities. It includes the use of algebraic notations and symbols, equations, and most importantly, functions, to represent and analyze relationships.

Statistics and Probability as a strand is all about developing skills in collecting and organizing data using charts, tables, and graphs; understanding, analyzing and interpreting data; dealing with uncertainty; and making predictions about outcomes.


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The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it provides necessary concepts and life skills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens of the Philippines.


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LABORATORY ELEMENTARY SCHOOL

The course covers key concepts and skills involving numbers and number sense (whole numbers, number theory, fractions, decimals, ratio and proportion, percent, and integers);measurement (time, length, mass, capacity, speed,

perimeter, circumference and area of plane figures, volume and surface area of solid/space figures, temperature and meter reading); geometry (parallel and perpendicular lines, angles, triangles, quadrilaterals, polygons, circles, and solid

figures); patterns and algebra (continuous and repeating patterns, number sentences, sequences, and simple equations); statistics and probability (data collection and representation in tables, pictographs, bar graphs, line graphs and pie graphs,

simple experiment, and experimental probability) as applied -using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.


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K

The course is designed for kinder students who require skill development on the key concepts and skills involving numbers and number sense (whole numbers up to 20, basic concepts on addition and subtraction); geometry (basic

attributes of objects), patterns and algebra (basic concept of sequence and number pairs); measurement (time, location, non-standard measures of length, mass and capacity); and statistics and probability (data collection and tables) as

applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

• Colors, Shapes, and Patterns

• Sizes of the objects:

Big-Small, Long-Short, Tall-Short, and Heavy-Light)

• Counting Numbers: 0-

20

• Comparing and Ordering Numbers

• Measuring Using

Standard and Non-standard Units

• Days of the Week

and Months of the Year

• Ordinal Numbers from 1st to 20th

• Place Values: Tens and Ones)

• Simple Addition and Picture Addition

• Simple Subtraction and Picture Subtraction

• Money and Addition and Subtraction of Money

• Skip Counting

• Simple Fractions

• Telling Time

• Simple Pictographs


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• Simple Multiplication and Division

GRADE 1

The course covers key concepts and principles of numbers and number sense (whole numbers up to 100, ordinal numbers up to 10th, money up to PhP100, addition and subtraction of whole numbers, and fractions ½ and 1/4);geometry

(2- and 3dimensional objects); patterns and algebra (continuous and repeating patterns and number sentences); measurement (time, non-standard measures of length, mass, and capacity);and statistics and probability (tables,

pictographs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Number Concepts

• Numbers 1-10

• More Than Fewer

Than, and As Many

I. Subtraction of Whole

Numbers

• Subtraction as Taking

Away

I. Fractions

• Equal Parts

• One-Half of a Whole

• One-Half of a Group

I. Time and

Measurement

• Days of the Week

• Months of the Year


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As\

• Comparing and

Ordering Numbers up

to 10

• Numbers 11-100

• Skip Counting by 2s,

5s, and 10s

• Place Value through

Tens

• Ordinal Numbers

II. Addition of Whole

Numbers

• Putting Things

Together

• Fact Families

• Subtraction of One-

Digit Numbers From

Minuends up to 18

• Subtraction Without

Regrouping

• Subtraction With

Regrouping

• Solving Word

Problems Involving

Addition or

Subtraction

II. Money

• Recognizing Money

of Objects

• One-Fourth of a

Whole

• One-Fourth of a

• Group of Objects

II. Shapes and Patterns

• Identifying the Four

Basic Shapes

• Identifying Common

3D Shapes

• Identifying Patterns

• Completing Patterns

• Telling Time

• Heavy or light

• Height and Length

• Capacity

II. Picture Graphs

• Collecting and

Organizing Data

• Reading and

Interpreting Data

• Basic Probability


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• Sums 11up to 18

• Zero in Addition

• Order Property in

Addition

• Addition of Three

One-Digit Numbers

with Sums up to 18

• Addition without

Regrouping

• Addition with

Regrouping

• Mental Addition

• Telling How Much

• Money of Equal Value

• Comparing amounts

• Solving Word

Problems Involving

Addition or

Subtraction of Money

III. Multiplication

• Multiplication as

Repeated Addition

• Properties of

Multiplication

• Multiplication Facts 2



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• Multiplication Facts

10


and 4

IV. Division

• Division by Grouping

• Relationship Between

Multiplication and

Division


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GRADE 2

The course covers concepts and skills involving numbers and number sense (whole numbers up to 1 000, ordinal numbers up to 20th, money up to PhP100, the four fundamental operations of whole numbers, and unit fractions);

geometry (basic shapes, symmetry, and tessellations); patterns and algebra (continuous and repeating patterns and number sentences);measurement (time, length, mass, and capacity); and statistics and probability (tables, pictographs,

and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Whole Numbers

• Numbers to 1 000

• Place Value through 1

000

I. Multiplication of Whole

Numbers

• Meaning of

Multiplication

I. Fractions

• Naming Fractional Part

of Objects

• Identifying Fifths,

I. Measurement

• Measuring Length

Using Nonstandard

Units


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• Comparing and

Ordering Numbers

• Skip Counting by 10s,

50s, and 100s

• Roman Numerals

• Ordinal Numbers

III. Addition of Whole

Numbers

• Properties of Addition

• Addition of Two- to

Three-Digit Numbers

Without Regrouping

• Addition of Two- to

Three-Digit Numbers

With Regrouping

• Problem Solving

• Properties of

Multiplication

• Multiplying by 2, 5, and

10

• Multiplying by 3, 4, and

6

• Multiplication of 2- to 3-

Digit Numbers

• Two- Step Word

Problems Involving

Multiplication and

Addition and

Subtraction

II. Division of Whole

Numbers

• Sharing and Grouping

Sixths, and Eighths

• Fraction as Part of Set

• Comparing Fractions

• Ordering Fractions

• Addition and Subtraction of

Similar

II. Fractions

• Problem Solving

Involving Fractions

III. Money, Calendar, and

Time

• Coins and Paper Bills

• Addition and

Subtraction of Money

• Using Calendar

• Measuring Time

• Measuring Length

Using Meter and

Centimeter

• Measuring Weight

• Finding the Perimeter

• Finding the Area Using

Square Units

II. Statistics and Basic

Probability

• Picture Graphs

• Representation of Data

Using Scales

• Basic Probability


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involving Addition

• Mental Addition

IV. Subtraction of Whole

Numbers

• Subtraction Facts

• Subtraction of Whole

Numbers Without

Regrouping


Numbers With

Regrouping

• Subtraction with Zero

Difficulty

• Mental Subtraction

• Order of Operations

Involving Addition and

of Objects

• Relationship Between

Multiplication and

Division

• Problem Solving

Involving Division

IV. Geometry and

Patterns

• Lines

• 2-D Shapes

• 3-D Shapes

• Identifying Patterns

• Symmetry

• Tessellation


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Subtraction

• Solving Word Problems

Involving Subtraction

• Solving 2-Step Addition

and Subtraction

GRADE 3

The course covers key concepts and skills involving numbers and number sense (whole numbers up to 10 000; ordinal numbers up to 100th; money up to PhP1 000;the four fundamental operations of whole numbers; proper and improper fractions; and similar, dissimilar, and equivalent fractions); geometry (lines, symmetry, and tessellations); patterns and

algebra (continuous and repeating patterns and number sentences); measurement (conversion of time, length, mass and capacity, area of square and rectangle); and statistics and probability (tables, bar graphs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections,

representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Understanding Whole

Numbers

• Counting Whole

I. Multiplication of Whole

Numbers

• Multiplication and Its

I. Fractions

• Concepts of Fractions

• Kinds of Fractions

I. Measurement

• Time

• Converting Time


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Numbers

• Numbers in Standard

Form and Word Form

• Comparing and

Ordering Numbers

• Rounding Off Numbers

• Ordinal Numbers

• Roman Numerals

• Reading and Writing

Money up to 1 000

Pesos

• Comparing Money

Through 1 000 Pesos

II. Addition and

Subtraction of Whole

Properties

• Multiplication Facts of 6,

7, 8, 9, and 10

• Multiplication of Whole

Numbers by 1-Digit

Number With and

Without Regrouping


Numbers by 2-Digit

Numbers With and

Without Regrouping

• Multiplying Numbers By

10, 100, and 1 000

• Estimating Products

• Mental Multiplication

• Solving 2-step Word

• Equivalent Fractions

• Comparing and

Ordering Fractions

• Fractions in The Lowest

Terms

• Addition and

Subtraction of Similar

Fractions

• Addition and

Subtraction of

Dissimilar Fractions

• Fractions of a Number

II. Decimals

• Fractions and Decimals

• Comparing and

Ordering Decimals

Measure

• Length

• Perimeter

• Area

• Mass Measurement

• Capacity Measure

II. Statistics and Basic

Probability

• Pictograph

• Bar Graph

• Line Graph

• Making Simple

Prediction


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Numbers

• Addition Concepts

• Addition of Whole

Numbers Without

Regrouping

• Addition of Whole

Numbers With

Regrouping

• Mental Addition

• Problem Solving

involving Addition


Numbers Without

Regrouping


Numbers With

Problems Involving

Multiplication

• Factors and Multiples

• Prime and Composite

Numbers

• Prime Factorization

• Dividing Whole Numbers

• Division Facts

• Dividing 1-Digit Divisor

Without Remainder

• Dividing 1-Digit Divisor

With Remainder

• Dividing by 2-Digit

Divisors

• Division by Multiples of

10

• Adding Decimals and

Money

• Subtracting Decimals

and Money

• Solve Word Problems

on Addition and

Subtraction of Decimals

II. Geometry

• Lines

• Angles

• Polygons

• Solid Figures

• Lines and Symmetry

• Tessellation

III. Patterns and Algebra


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Regrouping

• Subtraction with Zeroes

in the Minuend

• Mental Subtraction

• Estimating Sums and

Differences


Involving Addition and

Subtraction

• Order of Operation

• Estimating Quotient

• Mental Division

• Solving Multi-step Word

Problems

• Odd and Even Numbers

• Identifying and

Completing Pattern

• Number Patterns

• Finding The Missing

Number in a Number

Sentence


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GRADE 4

The course covers key concepts and skills involving numbers and number sense (whole numbers up to 100 000, multiplication and division of whole numbers, order of operations, factors and multiples, addition and subtraction of fractions, and basic concepts of decimals including money); geometry (lines, angles, triangles, and quadrilaterals);

patterns and algebra (continuous and repeating patterns and number sentences); measurement (time, perimeter, area, and volume); and statistics and probability (tables, bar graphs, and simple experiments) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and

decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Numbers Through

Millions

• Place Value Through

I. Discovering Number

Theory

• Factors

I. Appreciating

Geometry

• Basic Geometric

I. Understanding

Measurement

• Area


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Millions

• Numbers in Standard

Form and Expanded

Notation

• Comparing and

Ordering Whole

Numbers

• Adding and Subtracting

Large Numbers

• Estimating Sum and

Difference

• Mental Addition and

Subtraction

• Problem Solving

II. Multiplication of

Whole Numbers


Numbers

• Factor Trees

• Divisibility Test

• Common Factors and

GCF

• Common Multiples and

LCM

II. Valuing Fractions

• Basic Concepts in

Fractions

• Equivalent Fractions

and Fractions in

Simplest Form

• Improper and Mixed

Form

Figures

• Angles and Lines

• Plane Figures

• Line of Symmetry

• Solid Figures

II. Patterns and Algebra

• Naming Patterns

• Finding Pattern

• Completing Pattern

• Solving Simple

Completion

• Perimeter

• Circle

• Volume

• Linear Measure

• Capacity and Mass

Measure

• Elapsed Time

II. Statistics and Probability

• Organizing and

Interpreting Data in

Tables

• Constructing and

Interpreting Bar Graph

• Favorable Outcomes


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• Basic Facts of

Multiplication


Numbers with One-digit

Multiplier


Numbers with Two to

Three-digit Multiplier

• Multiplying by 10, 100,

and 1000

• Estimation of Product

• Mental Multiplication

• Solving Multi-Step

Problems Involving

Multiplication and

Addition or Subtraction

• Comparing and

Ordering Fractions


with Similar Fractions


with Dissimilar

Fractions

• Multiplication of

Fractions

• Division of Fractions

III. Valuing Decimals and

Money

• Basic Ideas of Decimals

• Compare and Order

Decimals

• Rounding Off Decimal


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III. Division of Whole

Numbers

• Concepts of Division

• Dividing with One- or

Two-Digit Divisors

• Dividing by 10, 100 and

1000

• Estimation of Quotient

• Mental Division



Involving Division and

Any of the Other

Operations

Numbers

• Addition of Decimals

and Money

• Subtraction of Decimals

and Money


Decimals

• Division of Decimals

• Averages


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GRADE 5

The course covers key concepts and skills involving numbers and number sense (whole numbers up to 10 000 000, order of operations, factors and multiples, fractions and decimals including money, ratio and proportion, percent);

geometry (polygons, circles, solid figures); patterns and algebra (sequence and number sentences); measurement (time, circumference, area, volume, and temperature); and statistics and probability (tables, line graphs and experimental

probability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Whole Numbers

• Concepts of Whole

Numbers

• Rounding Off Whole

I. Decimals

• Place Value of

Decimals

• Comparison and Order

I. Percent

• Introduction to Percent

• Conversion of Percent

to Fraction and Decimal

I. Measurement in Our

World

• Perimeter of Simple

Geometric Figures


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Numbers

• Addition and

Subtraction of Whole

Numbers

• Multiplication and

Division of Whole

Numbers


• Average

• Powers and Exponents

II. Introduction of

Number Theory

• Factors and Multiples

• Divisibility Rules

• Prime Factorization

• Greatest Common

of Decimals

• Rounding Off Decimals

• Addition and

Subtraction of Decimals


Fractions


II. Ratio, Rate and

Proportion

• Ratio and Rate

• Proportion

• Direct Proportion

• Inverse Proportion

• Scale Drawing

to Fraction

• Finding the Percentage

of a Number

• Finding the Percentage

• Finding the Base

II. Basic Geometry

• Common Definitions

• Measuring Angles And

Angle Relationship

• Polygons

• Concepts of Circle

• Solid Figures

III. Patterns and Algebra

• Sequences

• Simple Equation

IV. Measurement in Our

• Area of Simple

Geometric Figures

• Circumferences and

Area of Circles

• Volume of Solid Figures


• Bar Graph

• Line Graph

• Circle Graph

• Experimental

Probability


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Factor(GCF)

• Least Common Multiple

(LCM)

III. Fractions

• Basic Concept of

Fractions

• Addition and

Subtraction of Fractions

• Multiplication Involving

Fractions

• Division of Fractions

World

• The Metric System

• Time Around the World

• Measuring Temperature


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GRADE 6

The course covers key concepts and skills involving numbers and number sense (divisibility, order of operations, fractions and decimals including money, ratio and proportion, percent, integers); geometry (plane and solid figures); patterns and

algebra (sequence, expression, and equation); measurement (rate, speed, area, surface area, volume, and meter reading); and statistics and probability (tables, pie graphs, and experimental and theoretical probability) as applied - using

appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Exploring the Number

System

• Concept of Numbers

and Their Properties

I. Ratio, Proportion, and

Percent

• Concept of Ratio

• Concept of Proportion

I. Geometry and

Measurement

• Reviewing of Basic

Geometric Facts

I. Meter Reading

• Electric Meter Reading

• Water Meter Reading



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• Operations Involving

While Numbers


II. Number Theory, Fractions

and Applications

• Divisibility Rules


Numbers and Prime

Factorization

• Greatest Common

Factor (GCF) and Least

Common Multiples

• Concept of Fractions

• Addition and Subtraction

of Fractions


• Kinds of Proportion

• Concept of Percent

• Application of Percent

• More Percent Problems

II. Understanding Integers

• Integers

• Addition of Integers

• Subtraction of Integers


Integers

• Division of Integers

• Classifying, Measuring,

and Drawing Angles

• Polygons

• Congruence

• Perimeter and

Circumference of Plane

Geometric Figures

• Area of Plane Geometric

Figures

• Space Figures and

Surface Areas

• Space Figures and Nets

• Volumes of Space

Figures

• Speed, Distance, and

Time

• Collection and

Presentation of Data

• Line and Bar Graphs

• The Language of

Chance

• Simple Probability

• Theoretical and

Experimental

Probability

• Interpreting Data


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Fractions

• Division of Fractions and

Mixed Numbers

III. Number Theory,

Decimals and Applications

• Visualizing Decimals

• Reading and Writing

Decimals Through Ten

Thousandths

• Decimal Form of a

Fraction

• Comparing and Ordering

Decimals

• Estimating

Sums/Differences of

Whole Numbers and


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Decimals

• Addition and Subtraction

of Decimals


Decimals


• Solving Decimals Using

Mixed Operations


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JUNIOR HIGH SCHOOL

The course is designed for junior high students who require skill development on the key concepts and skills involving numbers and number sense (sets and real numbers); measurement (conversion of units); patterns and algebra (linear

equations and inequalities in one and two variables, linear functions, systems of linear equations, and inequalities in two variables, exponents and radicals, quadratic equations, inequalities, functions, polynomials, and polynomial equations and functions); geometry (polygons, axiomatic structure of geometry, triangle congruence, inequality and similarity, and basic

trigonometry); statistics and probability (data collection and presentation, measures of central tendency, measures of variability, the standard normal distribution, z-scores and measures of skewness; hypothesis testing using z-test, t-test,

simple linear correlation, chi-square test, and regression analysis; combinatorics and probability) as applied - using appropriate technology - in critical thinking, problem solving, communicating, reasoning, making connections,



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GRADE 7

The course is designed for seventh grade students who require skill development on the key concepts and principles of numbers and number sense (sets and real number system); measurement (conversion of units of measurement);patterns and algebra (algebraic expressions and properties of real numbers as applied in linear equations and inequalities in one variable); geometry (sides and angles of polygons); and statistics and probability (data collection and presentation, and

measures of central tendency and variability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Number and Number Sense

• Sets and Subsets • Basic Set Operations

I. Measurements • Historical Development

of Measurement • Measuring Instrument

I. Linear Equations and Inequalities in One Variable

• Concept of Linear

I. Basic Concepts in Geometry

• The Three Elements of


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• Venn Diagram • Solving Problems

Involving Set Operations

II. Real Numbers

• Subsets of Real Numbers

• Properties of Real Numbers

• The Set of Fractions • The Set of Decimals • The Set of Irrational

Numbers III. The Set of Integers

• Addition of Integers • Subtraction of Integers • Multiplication of

Integers • Division of Integers

• Converting Measurement

• Solving for Perimeter • Solving for Area • Solving for Volume

II. Algebraic Expressions

• Terminologies • Simplifying Numerical

Expressions

• Evaluating Algebraic Expressions

• Verbal Phrases and Algebraic Expressions

• The Laws of Exponents • Adding and Subtracting

Polynomials • Multiplying Polynomials • Special Product • Dividing Polynomials

Equations • Difference Between

Equations and Inequalities

• Illustrating Linear Equation and Inequality in One Variable

• Addition Property of Equality

• Multiplication Property of Equality

• More on Solving Linear Equations and Literal Equations

• Solving Linear Equations Involving More Than One Operations

• Solving Equations Involving Fractions

• Solving Equations Involving Decimals

• Linear Equations Involving Absolute Value

• Mathematical Equations and Verbal Sentences

• Solving Real - Life

Geometry • Segments and

their Measurements

• Rules, Betweeness of Points and Segment Addition Postulate.

• Angles and their Measurements

• Use of Protractor

II. Angle Pairs • Congruent Angles • Adjacent Angles • Complementary

Angles • Supplementary

Angles • Linear Pairs • Vertical Angles • Solving Real - Life

Problems Involving Angle Pairs

• Parallel Lines and Transversals

• Use of The Compass and Straightedge


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Problems Involving Linear Equations in One Variable that Include Fractions and Decimals

• Solving Linear Inequalities

• Solving Real - Life Problems Involving Linear Inequalities in One Variable

II. Plane Figures

• Polygons II. Triangles

• Kinds of Triangles • Sum of Angles of a

Triangle • Special Segments

of a Triangle

III. Quadrilaterals • Properties of

Quadrilaterals • Solving Real - Life

Problems Involving Triangles and Quadrilaterals


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GRADE 8

The course is designed for eighth grade students who require skill development on the key concepts and principles of patterns and algebra (factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables); geometry (axiomatic structure of geometry,

triangle congruence, inequalities in a triangle, and parallel and perpendicular lines); and statistics and probability (probability of simple events) as applied - using appropriate technology - in critical thinking, problem solving, reasoning,

communicating, making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Integral Exponents

• Positive Integral Exponents and Laws of Exponents

• Zero and Negative Integral Exponents

II. Polynomials • Idea of Polynomials

I. Rational Algebraic Expressions

• Defining a Rational Expressions

• Simplifying Fractions • Simplifying Rational

Expressions • Multiplication and

I. Linear Equations in Two Variables

• Rectangular Coordinate System

• The Cartesian Plane • Naming a Point • Plotting a Point • Problem Solving

I. Axiomatic Structure of Geometry

• Inductive and Deductive Reasoning

• Illustrates the Properties of Equalities

• Conditional,


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• Understanding Polynomial Addition and Subtraction

• Multiplication of Polynomials

• Synthetic Division III. Special Products

• Multiplying a Polynomial by a monomial

• Multiplying Binomials • Multiplying

Polynomials • Square of Binomial • Product of the Sum

and Difference of Two Terms

• Square of Multinomial • Cube of a binomial • Product of the Form

(x±y)(x2±2xy+y2) • Application of Special

Products IV. Factors of

Polynomials • Common Monomial

Factors • Common Binomial

Factors • Factors of Difference

Division of Rational Expression

• Adding and Subtracting with Similar Rational Algebraic Expressions

• Adding and subtracting with Dissimilar Rational Algebraic Expressions

• Complex Rational Algebraic Expressions

• Solving Rational Equations

• Problem Solving involving Rational Equations

II. Introduction to Linear Function

• Relation and Function • Domain and Range • Dependent and

Independent Variables

• Function Notation and its evaluation

Involving Plotting of Points

• Definition of a Linear Equation in Two Variables

• Graph of a Linear Equation by Point-Plotting

• Graph of a Linear Equation by Intercepts

• Slope of a Line • Graph of a Line using

Slope and a Point on the Line

• Forms of the Equation of a Line

• Equations of Vertical and Horizontal Line

• Solving Problems Involving Linear Equations in Two Variables

II. Systems of Linear Equations in Two Variables

• Identifying different Systems of Linear Equations in Two Variables

Converse, Inverse, Contrapositive and Biconditional Statements

• Drawing Conclusion Based from Definition, Theorems and Postulates

• Proving Angle Pair Relationships

II. Triangle Congruence and Inequalities in a Triangle

• Condition for Triangle Congruence

• CPCTC • Congruence in

Isosceles Triangles • Overlapping Triangles • Right Triangle

Congruence • Bisectors and

Perpendicular Lines • Triangles Inequalities • Parallel and

Penpedicular Lines


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of Two Squares • Perfect Square

Trinomial • Simple Quadratic

Trinomial • Factoring Trinomials

of the Form ax2+bx+c Factoring Sum or Difference of Two Cubes

• Problem Solving involving Factoring

• Solving Systems of Linear Equations by Graphing

• Solving Systems of Linear Equations by Substitution

• Solving Systems of Linear Equations by Elimination

• Solving Systems of Linear Equations by Elimination

• Solving Systems of Linear Equations Using Determinants

• Problems Involving Systems of Linear Equations in Two Variables

• Definition of Linear Inequality in Two Variables

• Graph of Linear Inequality in Two Variables

• Graph of System of Linear Inequalities

• Problem Solving Involving Linear Inequalities in Two


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Variables

GRADE 9

The course is designed for ninth grade students who require skill development on the key concepts and principles of patterns and algebra (quadratic equations and inequalities, quadratic functions, rational algebraic equations, variations,

and radicals) and geometry (parallelograms and triangle similarities and basic concepts of trigonometry) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections,


First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Quadratic Equations

• Solving Quadratic Equation by Extracting Square Roots

• Solving Quadratic Equation by Factoring

• Solving Quadratic Equation by

I. Quadratic Functions • Recognizing

Quadratic Functions • The Standard

form of Quadratic Functions

• The Vertex form of Quadratic Functions

I. Triangle Congruence and Inequalities of Triangle

• Right Triangle Congruence

• Triangle Inequalities • Inequalities in A

single Triangle

I. Six Trigonometric Functions

II. Trigonometric Functions of Special Angles • Trigonometric

Functions of Special Angles of 30, 45 and


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Completing the Square

• Solving Quadratic Equation by Quadratic Formula

• Problems Involving Quadratic Equations

III. Roots of

Quadratic Equations

• Nature of the Roots of Quadratic Equation

• Sum and Product of the Roots of Quadratic Equations

• Equations in Quadratic Form

• Problems involving Roots of Quadratic Equation

III. Quadratic Inequalities

• Properties of Inequality

• The Case-Exploration Method

• The Inspection-of-Signs Method

• The Parabola Method

• Second Difference Test

II. Graphs of Quadratic Functions

• Table of Values • The Parabola • Vertex, Axis of

Symmetry, and Extreme Point of Quadratic Functions

• Problems involving Graphs of Quadratic Function

III. Zeroes of Quadratic Functions

• Finding Zeroes of Quadratic functions by Factoring

• Imaginary Zeroes • Finding Zeroes of

Quadratic functions by Quadratic Formula

• Deriving Quadratic Equations and Functions

• Effects in Changing the Value of a

• Effects in Changing

• Inequalities in Two Triangles

II. Geometric Proportion

• Laws of Proportion • Problems involving

Geometric Proportion • Similar Polygons • Similar Triangles

III. Triangle Similarity

• Similarity Theorems • AAA Similarity

Theorem • AA Similarity

Theorem • SAS Similarity

Theorem • SSS Similarity

Theorem

IV. Right Triangles and Similarities in Right Triangles

• Right Triangle Similarity

• Pythagorean Theorem

• Special Right Triangle

• Problems Involving

60

III. Solutions of Right Triangles

IV. Applications of Angle of Elevation and Angle of Depression

V. Solutions of Oblique Triangles

• Law of Sines • Application of Law of

Sines • Law of Cosines • Applications of Law

of Cosines

VI. Trigonometric Identities

• Simplifying Trigonometric Identities

• Proving Trigonometric Identities


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the value of h and k

IV. Variations • Ratio and Proportion • Direct Variation • Inverse Variation • Joint Variation • Combined Variation • Problems Involving

Variation

V. Rational Exponents and Radicals

• Integral Exponents • Expressions with

Rational Exponents • Roots of a Number • Radical Expressions • Addition and

Subtraction of Radical Expressions

• Multiplication and Division of Radical Expressions

• Radical Equations • Problems Involving

Rational Exponents and Radicals

Triangle Similarity

V. Quadrilaterals • Review of Different

Kinds of Quadrilaterals

• Parallelograms and their Properties

• Special Parallelograms

• Theorems to Prove that Quadrilaterals can be Parallelograms

• Trapezoid • Kites • Problems Involving

Quadrilaterals


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GRADE 9 ENRICHMENT

The course covers key concepts and principles of descriptive statistics (data collection and presentation, measures

of central tendency, measures of variability, the standard normal distribution, z-scores and measures of skewness); and

inferential statistics (hypothesis testing using z-test, t-test, simple linear correlation, chi-square test, and regression

analysis) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating,

making connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Introduction to Statistics

• Origin and Development of

I. The Quantiles

• Computation of Quantiles for Ungrouped Data

I. Hypothesis Testing

• Introduction

• Definition of

I. A Hypothesis Testing Procedure

• Chi-square Goodness-of-fit Test:


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Statistics

• Uses of Statistics

• Fields of Statistics

• Constant and Variables

• Data and information

• Population and Sample

• Sloven’s Formula in Determining the Sample Size

• Census and Sampling techniques

• Random and Non-random Sampling

• Properties of Ramdom Sampling

• Sampling Techniques

II. Organization and presentation of Data Forms of Presentation of Data

• Different Kinds of

• Computation of Quantiles for Grouped Data

II. Measures of Variability, Skewness and Kurtosis

• Introduction

• Measures of Variability

• The Range

• The Average

Deviation

• The Quartile Deviation

• The Standard Deviation

• Skewness and Kurtosis

• Calculating Skewness and Kurtosis

• How Skewness is

Hypothesis

• Definition of Hypothesis Testing

• Two Types of Hypothesis

• Types of Errors

• Definition of Level of Significance

• One tailed and Two tailed Tests

Equal Expected Frequencies

II. Measures of Correlation

• Definition

• The Pearson Product-Moment Correlation Coefficient

• Other Interpretation of Pearson’s r


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Graphs/Charts

III. FREQUENCY DISTRIBUTION

• Definition

• Parts of Frequency Table

• Steps in Constructing a Frequency Distribution Table

• Cumulative Frequency Distribution

• Relative frequency Distribution

• Graphical Representation of the Frequency Distribution

IV. Measures of Central Tendency

Computed

• Interpreting Skewness

• Standard Scores of z-scores


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• Arithmetic Mean

• Characteristics of the Mean

• Uses of the Mean

• Computation of the Mean for Ungrouped Data

• Computing the Mean for Group Data

• The Median

• Characteristics of the Median

• Uses of the Median

• Computation of the Median for Ungrouped Data

• Computing the Median for Group Data

• The Mode

• Characteristics of the


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Mode

• Uses of the Mode

• Computation of the Mode for Ungrouped Data

• Computing the Mode for Group Data


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GRADE 10

The course is designed for tenth grade students who require skill development on the key concepts and principles of patterns and algebra (sequences, series, polynomials, polynomial equations, and polynomial functions); geometry (circles

and coordinate geometry); and statistics and probability (combinatorics and probability, and measures of position) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making

connections, representations, and decisions in real life.

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

I. Probability: • Fundamental

Counting Principles o Tree Diagram

• Permutation o Linear Permutation o Circular Permutation o Distinguishable

Permutation

• Combinations

• Probability of Simple Events

o Odds of an event

I. Polynomial Functions: • Polynomial Functions

and Application o Identifying

polynomial functions

o Synthetic Substitution

• Synthetic Division

o Long Division o Synthetic Division

(binomial divisor) o Synthetic Division

(trinomial divisor)

I. Circles: • Parts of a Circle

o Line Segments related to Circles

o Lines related to Circles

o Angles related to Circles

o Arcs • Central Angles

o The Central Angle-Intercepted Arc Postulate

o The Arc Addition Postulate

o Arc Length

I. Plane Coordinate Geometry:

• The Distance Formula o Distance between

two points

• The Midpoint Formula o Midpoint of two

points

• Placing Figures in the Coordinate o Drawing figures in

the coordinate plane


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• Probability of Compound Events

o Dependent and Independent Events

o Union of two events o Intersection of two

events

II. Sequences and Series: • Number Patterns o Sequence o Series o Summation Notation

• Arithmetic Sequence

o Arithmetic means o Arithmetic series

• Geometric Sequence

o Geometric means o Geometric series

• Other types of

Sequences o Harmonic

sequence o Harmonic means o Fibonacci

sequence

• Remainder Theorem

• Factor Theorem

• Descartes’ Rule of Signs o Variation of Signs o Maximum number

of positive and negative zeros

• Zeros of Polynomial Function o Identifying

Possible Zeros o Rational Zero

Theorem

• Graph of Polynomial Functions o Leading

Coefficient test o End Behavior of

the graph o x – intercepts of

the graph o y – intercept of the

graph o Turning points

• Inscribed Angles o The Inscribed

Angle Theorem

o The Semicircle Theorem

o Inscribed Angles in the same arc Theorem

o Inscribed Quadrilateral Theorem

• Tangents and Secants o The Tangent Line

Theorem o The Tangent –

Diameter Theorem

o The Converse of a Tangent Line Theorem

o The Tangent Segments Theorem

• Angles formed by Secants and Tangents o The Intersecting

Secants – Exterior

o Finding the

missing coordinates of a diagram

• Coordinates in Proofs

o Proving Triangles in a coordinate plane

o Proving Quadrilaterals in a coordinate plane

• Equation of a Circle

o Center – Radius form or Standard Form

o Center at the Origin

o Graphing an Equation or Inequality


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Theorem o The Tangent Point

– Secant Theorem o The Intersecting

Secants – Interior Theorem

• Power Theorems

o The Intersecting Segment of Chords Power Theorem

o The Segment of Secants Power Theorem

o The Tangent Secant Segments Power Theorem

• Circumference and Area of a Circle o The Pi Theorem o Circumference of

a Circle o Area of a Circle o Area of a Sector o Area of a

Segment


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Prepared by:

JENNYLYN E. SAYSON Mathematics Coordinator, LES-JHS

Approved by:

MARIA TERESA N. PUNSALAN Assistant Principal, LES-JHS

Noted by:

LIZABELLE B. GAMBOA Principal, Basic Education Department

Documents

COURSE DESCRIPTION MATHEMATICS