math cg_grade 8

8/11/2019 Math CG_Grade 8

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Republic of the PhilippinesDepartment of Education

DepEd Complex, Meralco AvenuePasig City

September !, "#

K to 12 Curriculum Guide

MATHEMATICS$%rades &'#"(


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K TO 12 MATHEMATICS

CONCEPTUAL FRAMEWORK

Mathematics is one sub)ect that pervades life at any age, in any circumstance* +hus, its value goes beyond the classroom and the

school* Mathematics as a school sub)ect, therefore, must be learned comprehensively and ith much depth*

+he tin goals of mathematics in the basic education levels, -'#" are Critical +hin.ing and Problem Solving* /e adopt the definition of critical

thin.ing by Scriven and Paul $#01&(2

Critical thin.ing is the intellectually disciplined process of actively and s.illfully conceptuali3ing, applying, analy3ing, synthesi3ing, and4orevaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and

action*

5n the other hand, e define Problem Solving in mathematics using Polya6s $#078 9 #0!( definition2

Mathematical problem solving is finding a ay around a difficulty, around an obstacle, and finding a solution to a problem that is un.non*

+hese to goals are to be achieved ith an organi3ed and rigorous curriculum content, a ell'defined set of high'level s.ills and processes,desirable values and attitudes, and appropriate tools, recogni3ing as ell the different contexts of :ilipino learners*

+here are five content areas in the curriculum, as adopted from the frameor. prepared by MA+;+ED 9 SE< $"#"(2 =umbers and =umberSense, Measurement, %eometry, Patterns and Algebra, and Probability and Statistics*

+he specific s.ills and processes to be developed are2 -noing and >nderstanding? Estimating, Computing and Solving? @isuali3ing andModelling? Representing and Communicating? Con)ecturing, Reasoning, Proving and Decision'ma.ing, and2 Applying and Connecting*

+he folloing values and attitudes are to be honed as ell2 Accuracy, Creativity, 5b)ectivity, Perseverance, and Productivity*

/e recogni3e that the use of appropriate tools is needed in teaching mathematics* +hese include2 manipulative ob)ects, measuring

devices, calculators and computers, Smartphones and tablet PCs, and the


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+he frameor. is supported by the folloing underlying learning principles and theories2 Experiential and Situated earning, Reflective

earning, Constructivism, Cooperative earning and Discovery and


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K TO 12 MATHEMATICS

BRIEF COURSE DESCRIPTION

Mathematics from -'#" is a s.ills sub)ect* y itself, it is all about Buantities, shapes and figures, functions, logic and reasoning* Mathematics isalso a tool of science and a language complete ith its on notations and symbols and grammarF rules, ith hich concepts and ideas are effectivelyexpressed*

+he contents of mathematics include =umbers and =umber Sense, Measurement, %eometry, Patterns 9 Algebra and Statistics and Probability*=umbers and =umber Sense as a strand includes 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 concreteob)ects*


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K TO 12 MATHEMATICS

LEARNING AREA STANDARD2 +he learner demonstrates understanding and appreciation of .ey concepts and principles of mathematicsas applied, using appropriate technology, in problem solving, critical thin.ing, communicating, reasoning, ma.ing connections, representations,and decisions in real life*

KEY STAGE STANDARDS:

- G H 7 G ! & G #"

At the end of %rade H, the learnerdemonstrates understanding and appreciationof .ey concepts and s.ills involving numbersand number sense, measurement, geometry,patterns and algebra, statistics and probability

as applied, using appropriate technology, incritical thin.ing, problem solving, reasoning,communicating, ma.ing connections,representations and decisions in real life*

At the end of %rade !, the learnerdemonstrates understanding and appreciationof .ey concepts and s.ills involving numbersand number sense, measurement, geometry,patterns and algebra, statistics and probability

as applied, using appropriate technology, incritical thin.ing, problem solving, reasoning,communicating, ma.ing connections,representations and decisions in real life*

At the end of grade #", the learnerdemonstrates understanding and appreciationof .ey concepts and s.ills involving numbersand number sense, measurement, patterns andalgebra, geometry, probability and statistics,

and trigonometry as applied, using appropriatetechnology, in critical thin.ing, problem solving,communicating, reasoning, ma.ingconnections, representations, and decisions inreal life*

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K TO 12 MATHEMATICS

GRADE LEVEL STANDARDS:

GRADE LEVEL %RADE E@E S+A=DARDS

K

+he learner demonstrates understanding and appreciation of .ey concepts and s.ills involving hole numbers up to ", spaceand measurement, simple geometric figures, pre'algebra concepts and data collection as applied, using appropriatetechnology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections, representations anddecisions in real life*

GRADE 1

+he learner demonstrates understanding and appreciation of .ey concepts and s.ills involving hole numbers up to #"",fractions, measurement, simple geometric figures, pre'algebra concepts, data collection and representation as applied, usingappropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections, representationsand decisions in real life*

GRADE 2

+he learner demonstrates understanding and appreciation of .ey concepts and s.ills involving hole numbers up to # """,fractions, measurement and geometric figures, pre'algebra concepts, data collection, representation and analysis as applied,using appropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections,

representations and decisions in real life*

GRADE 3

+he learner demonstrates understanding and appreciation of .ey concepts and s.ills involving hole numbers up to #" """,fractions, measurement, geometric figures, pre'algebra concepts, data collection, representation and analysis as applied,using appropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections,representations and decisions in real life*

GRADE 4

+he learner demonstrates understanding and appreciation of .ey concepts and s.ills involving hole numbers up to #"" """,fractions, decimals including money, ratio, angles, plane figures li.e sBuare, rectangle, and triangle, measurement $perimeter,area of triangle, parallelogram and trape3oids, volume of cubes and rectangular prisms, pre'algebra concepts, data collection,representation and analysis as applied, using appropriate technology, in critical thin.ing, problem solving, reasoning,communicating, ma.ing connections, representations and decisions in real life*

GRADE 5

+he learner demonstrates understanding and appreciation of .ey concepts and s.ills involving hole numbers up to #" """""", fractions, decimals including money, ratio, percent, geometry $circles and five or more'sided polygons(, measurement$circumference, area of circle, volume of cubes and rectangular prisms, temperature( ,pre'algebra concepts, data collection,representation and analysis as applied, using appropriate technology, in critical thin.ing, problem solving, reasoning,communicating, ma.ing connections, representations and decisions in real life*

GRADE 6 +he learner? demonstrates understanding and appreciation of .ey concepts and s.ills involving fractions, decimals includingmoney, ratio and proportion, percent, rate, integers, geometry $spatial figures(, measurement $surface area, volume, meter

reading(, pre'algebra concepts, data collection, representation and analysis, probability, expressions and eBuations as

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applied, using appropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections,representations and decisions in real life*

GRADE 7+he learner demonstrates understanding of .ey concepts and principles of number sense, measurement, algebra, geometry,probability and statistics as applied, using appropriate technology, in critical thin.ing, problem solving, reasoning,communicating, ma.ing connections, representations and decisions in real life*

GRADE

+he learner demonstrates understanding of .ey concepts and principles of algebra, geometry, probability and statistics asapplied, using appropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections,

representations, and decisions in real life*

GRADE !+he learner demonstrates understanding of .ey concepts and principles of algebra, geometry, and trigonometry as applied,using appropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ing connections,representations and decisions in real life*

GRADE 1"

+he learner demonstrates understanding of .ey concepts and principles of number sense, algebra, geometry, probability and

statistics as applied, using appropriate technology, in critical thin.ing, problem solving, reasoning, communicating, ma.ingconnections, representations and decisions in real life*

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K TO 12 MATHEMATICS

GRADE 8

CONTENT CONTENT STANDARDS PERFORMANCE STANDARDS LEARNING COMPETENCIES

Ale!r" +he learner demonstratesunderstanding of .eyconcepts of special productsand factors of polynomials,rational algebraicexpressions, algebraicexpressions ith integralexponents, linear functions,and systems of lineareBuations and ineBualities in

to variables*

+he learner is able to formulatereal'life problems involvingspecial products and factors,rational algebraic expressions,algebraic expressions ithintegral exponents, linearfunctions, and systems of lineareBuations and ineBualities in tovariables and solve these ithutmost accuracy using a variety of

strategies*

T#e le"r$er%

o identifies polynomials hich are special

products2 polynomials ith common monomialfactors, trinomials that are product of tobinomials, trinomials that are product of sBuaresof a binomial, and products of sum and differenceof to terms*III

o finds special products and factors of certain

polynomials2 product of to binomials, product of

sum and difference of to terms, sBuare of abinomial, cube of a binomial, and product ofspecial case of multiplying a binomial ith atrinomial*

o factors completely different types of polynomials

$polynomials ith common monomial factors, adifference of to sBuares, sum and difference ofto cubes, perfect sBuare trinomials, generaltrinomials( using special formulas, grouping andother techniBues*

o solves problems involving polynomials and their

products and factors*

o describes and illustrates rational algebraic

expressions*

o simplifies rational algebraic expressions

o performs operations on rational algebraic

expressions*

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o simplifies complex fractions*

o solves problems involving rational algebraic

expressions*

o interprets 3ero and negative exponents

o evaluates and simplifies algebraic expressions

involving integral exponents*

o describes and illustrates the rectangularcoordinate system and its uses*III

o describes and plots positions on the coordinate

plane using coordinate axes* III

o


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$b( the slope and a point? $c( the slope and itsintercepts*

o solves problems involving linear functions and

linear patterns*

o differentiates beteen mathematical expressions

and mathematical eBuations*

o differentiates beteen mathematical eBuations

and ineBualities*

o illustrates linear ineBualities in to variables*

o graphs linear ineBualities in to variables on the

coordinate plane*

o describes systems of linear eBuations and

ineBualities using practical situations andmathematical expressions*

o identifies hich given systems of linear

eBuations have graphs that are parallel, intersectand coincide*

o graphs systems of linear eBuations in to

variables*III

o solves systems of linear eBuations by $a(

graphing? $b( elimination? $c( substitution*III

o graphs system of linear ineBualities in to

variables*III

o solves a system of linear ineBualities in to

variables by graphing*III

o solves problems involving systems of linear

eBuations and ineBualities in to variables*

G#$%#&'( +he learner demonstratesunderstanding of .eyconcepts of axiomaticdevelopment of geometry,triangle congruence,

+he learner is able tocommunicate mathematicalthin.ing ith coherence andclarity in formulating,investigating, analy3ing, and

+he learner **

o identifies the hypothesis and conclusions of if'

then and other types of statements*

o formulates the inverse, converse and

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ineBualities in triangles andparallel and perpendicularlines*

solving real'life problemsinvolving parallelism andperpendicularity of lines andcongruent triangles usingappropriate and accuraterepresentations

contrapositive of an implication*

o distinguishes beteen inductive and deductive

reasoning*

o provides formal arguments that explain results

of a phenomenon or a situation*

o rites formal arguments as a series ofstatements that ma.e up a proof $both directand indirect(*

o illustrates the undefined terms in geometry*

o explains the need for defined terms previously

introduced*

o differentiates beteen postulate and theory and

give the importance of each*

o i


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prove results involving triangle ineBualities*

o illustrates parallel and perpendicular lines*III

o illustrates and proves properties of parallel lines

cut by a transversal*III

o names the different .inds of Buadrilaterals and

identify those that are parallelograms*

o determines the conditions that ma.e a

Buadrilateral a parallelogram,

o determines and proves the conditions under

hich lines and segments are parallel orperpendicular*

o uses properties to find measures of angles,

sides, and other Buantities involvingparallelograms*

S&)&*+&*,+ )-. P'$/)/*0*&( +he learner demonstrates

understanding of .eyconcepts of measures ofcentral tendency andmeasures of variability of dataand basic concepts ofprobability

*

+he learner is able to **

o compute accurately

measures of central tendencyand measures of variabilityand apply these appropriatelyto data analysis andinterpretation in fields such asresearch, business,education, science,technology, economics, etc*

+he learner J

o finds the mean, median and mode of statistical

data

o describes and illustrates the mean, median and

mode of ungrouped and grouped data*

o discusses the meaning of variability*

o calculates the different measures of variability of

a given set of data2 $a( range? $b( averagedeviation? $c( variance? $d( standard deviation*III

o describes a set of data using measures of

central tendency and measures of variability*o use precisely counting

techniBues and probability insolving problems related todifferent fields of endeavor*

o describes an experiment, outcome, sample

space and event*III

o explains and interprets the probability of an

event*

o differentiates beteen an experimental

probability and a theoretical probability*

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o counts the number of occurrences of an

outcome in an experiment and organi3e themusing a table, tree diagram, systematic listingand the fundamental counting principle*III

o solves simple problems involving probabilities of

events*

S#+&*$- $' ICT #-)-,#. 0#++$- #- ))*0)/0# )-. #'# )88'$8'*)

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math cg_grade 8

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