k to 12 mathematics curriculum guide

7/28/2019 K to 12 Mathematics Curriculum Guide

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Republic of the PhilippinesDepartment of Education

DepEd Complex, Meralco AvenuePasig City

May 21, 2011

K to 12CURRICULUM GUIDE

MATHEMATICS


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I.

Philippine Education Mathematics Framework


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Philippine Education Mathematics Framework

This framework directs the teaching, learning and assessment of mathematics in the K to 10 curriculum. It shows the components of an effectivemathematics program from Kindergarten up to Grade 10.

Problem solving is at the heart of mathematics learning. Hence, the primary goal of the mathematics program is the development of a mathematicalproblem solver. To be a mathematical problem solver requires mastery of a wide range of concepts and skills, the acquisition of certain processes, and thedevelopment of metacognitive ability and attitudes that support mathematical thinking.

The five components that support the development of a mathematical problem solver are concepts, skills, processes, attitudes and metacognition.

The mathematical concepts covered are numerical, geometrical, statistical, analytical, and probabilistic concepts. Various learner-centered strategiesshould be used to allow students to explore the concepts in depth, to discover relationships on their own, and to see the connections among the differentideas. Along with providing students experiences in practical work and outdoor activities, technological aids and manipulatives should be used to enhancetheir learning experiences in mathematics and make mathematics learning relevant and meaningful in their lives. Mathematical concepts are organized in aspiral manner, with the concepts presented in each grade level building on the concepts presented in the previous levels.

Mathematical skills include arithmetic and algebraic computation, estimation, mental computation, measurement, use of technological tools, dataanalysis, visual thinking, and spatial sense. The development of skills is an essential component in mathematics learning. Students should have well-developed procedural skills for numerical calculation, algebraic manipulation, spatial visualization, data analysis, estimation and use of mathematical andtechnological tools. However, these skills should be developed alongside the development of concepts and processes. Students must understand theunderlying mathematical principles of each procedure. Overemphasizing procedural skills must be avoided.

Mathematical processes refer to the knowledge skills involved in the process of acquiring and applying mathematical knowledge. These includemathematical reasoning, communicating mathematically, making connections and representations, modeling, and decision making. Each of these processesmust be developed alongside the development of mathematical skills through a variety of strategies and activities. Making connections means showing howall concepts in mathematics are interrelated and that mathematics is an integrated whole. It also means seeing how mathematics is related to other disciplinesand areas in real-life.

Metacognition refers to the ability to control ones thinking processes, in particular, the selection and use of problem -solving strategies. It includesmonitoring ones own thinking and self -regulation of learning. To promote metacognition, students should be encouraged to think aloud, to discuss their thinking and choice of strategies in problem solving, and to seek alternative ways of solving problems.

Attitude and values refer to the affective aspects of mathematics learning such as beliefs about mathematics and its usefulness; interest andenjoyment in learning mathematics; appreciation of the beauty and power of mathematics; confidence in using mathematics; and perseverance in solving aproblem.


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Students attitudes determine to a great extent their performance in mathematics. Since students attitudes towards mathematics are often the resultof their classroom experiences, mathematics teachers should take great effort in promoting a fun and exciting classroom environment. Activities should beprovided to build students confidence in and appreciation of mathematics.

Assessment is inherent in all the components of the framework. Assessment is not independent of the learning process; rather, it is interdependentwith teaching and learning. To assess all facets of mathematics learning, teachers should use balanced assessment, which combines traditional pen-and-paper tests and authentic forms such as performance and portfolio assessment.


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K to 12 Curriculum: Overall Goal, Desired Outcomes, Content and Standards

MATHEMATICSOverall Goal: Functionally Literate and Holistically Developed Filipino

II. Desired Outcomes: A learner who:1. Possesses a healthy mind and body.2. Has solid moral and spiritual grounding.3. Has essential knowledge, skills, values and attitudes to continuously develop himself/herself to the fullest.4. Engages in critical thinking and creative problem solving.5. Contributes to the development of a progressive, just, and humane society.6. Is proud to be a Filipino.7. Appreciates the beauty of the world around him/her and cares for the environment.

III. Key Stage Outcomes:

At the end of Grade 3, theFilipino learner is able to.. Grade 6 ... ... Grade 10 ... ... Grade 12 ...

Communicationand literacies

1. understand the value of and enjoy the learning anduses of language andliteracy in discoveringknowledge through thelanguages of the home andthe school

1. develop language andliteracy competenciesnecessary to understand,process, and evaluatevaried types of texts and beable to express ideas andfeelings effectively

1. employ suitable languageand literacy abilities inmaking sense of variedinputs and processes toefficiently and creativelycarry out different real-lifetasks and functions

1. use correct, appropriate,and elegant language toaccomplish a wide range of meaningful communicationpurposes

Critical thinkingand problemsolving

1. demonstrate curiosity andlogical thinking inunderstanding the self andthe immediate environment

1. understand causalrelationships and able topose questions about theenvironment andinvestigate the environment

1. able to grasp issues andmake logical inferences todeepen understanding of the environment

1. apply abstraction andlogical reasoning inproposing solutions toproblems in variouscontexts


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Creativity andinnovation

1. know the importance of andappreciate the learning of the arts and humanities

1. use his/her imagination,knowledge and skills in artsand humanities inexpressing his/her ideasand experiences

1. combine technological andartistic skills, andknowledge in generatingnew ideas and creatingoriginal products

1. recognize and analyzeproblems in daily life, andwork with others to inventor refine tangible productsto solve them

Ethical, moraland spiritualvalues

1. define age-appropriateethical, moral and spiritualvalues and concepts andcivic virtues

2. exhibit open-mindedness inanalyzing situations inhis/her immediateenvironment

1. analyze thoroughly ethical,moral and spiritual values/concepts and civic virtues

2. use reasoning andevaluation skills inresolving age-appropriateethical, moral and spiritualissues/problems/predicaments andlocal/national community

concerns3. develop and employrational criteria for evaluating moral integrityand trustworthiness

1. use with discipline andrelative ease highlydeveloped analytic,reasoning, argument andevaluation skills inresolving age-appropriateethical, moral and spiritualissues/problems/predicaments and local/nationalcommunity concerns

2. develop and employrational criteria whenascertaining someonesmoral integrity andtrustworthiness

3. evaluate ones ownreasoning in ethical, moral ,spiritual or civic matters;state possible objections toones own arguments, andmake a rebuttal to fully

justify ones position 4. tell from experience with

distinct clarity theimportance of being inpossession of shared

1. use with ease highlydeveloped analytic,reasoning, and argumentevaluation skills inresolving age-appropriateethical, moral and spiritualissues/problems/predicaments and local/nationalcommunity concerns

2. give critical evaluation of

the ethical, moral , spiritualand civic situation in thePhilippines

3. employ rational criteriawhen ascertainingsomeones moral status or integrity andtrustworthiness

4. offer viable solutions to realand difficult ethical, moral ,spiritual and civic problems

5. participate in moral or civicdiscourse at the regional or national level

6. know right from wrong


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ethical, moral and spiritualvalues and civic virtues of Filipinos

Life and career competencies

1. recognize the contributionof persons to communities

2. value ones own rules in

the home or community

1. recognize and appreciatethe value of work andexhibit appropriate

behavior when working in ateam

1. demonstrate appropriatework habits and behavior (e.g. sustainable use of

resources, productivity &accountability, flexibility &adaptability)

1. know and exploreoccupational possibilities

2. demonstrate with

confidence prerequisiteskills for their chosencareer path

3. demonstrate life skill suchas: (a) communication andinterpersonal skills; (b)decision-making and criticalthinking skills; (c) copingand self-management skills

Development of self and senseof community

1. appreciate personalidentity and values andones abilities

2. appreciate local culture(visual and performingarts)

3. know his/her rights andduties as a child

4. understand personalhistory and simplehistorical events

1. able to use ones abilitiesto think and expressoneself

2. appreciate what it is to bea Filipino.

3. have care and concern for others

4. develop narrativeunderstanding of history.

1. use abilities to help thecommunity and other people

2. take pride in his/her Filipino heritage

3. have a sound sense of social responsibility

4. understand the complexityof the past

1. strive for personalexcellence

2. work with others topreserve Filipino culture

3. exercise civicresponsibilities

4. able to use lessons fromthe past to make informeddecisions as responsiblecitizens

National andglobalorientedness

1. know, appreciate anddemonstrate pride in onesidentity as an individualand as a member of his/her family, community,

1. recognize, appreciate andrespect differences inPhilippine society and theworld at large, such asage, gender, religion,

1. analyze culturalcomplexities; understandfactors contributing tosocietal and globalconflicts and articulate a

1. appreciate his/her role asa global citizen; thinksystematically aboutpersonal, national, andglobal decisions,


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and the Filipino people,while being aware of basichuman differences

social class, language,ethnicity, ability, sexualorientation; know andrespect human rights asreflected in his/her fair relationships with people.

stand on local and globalissues

interactions andconsequences, guided bypr ide in ones Filipinoidentity and respect for diversity and human rights

IV. Core Learning Area Standard: (for the entire K to 12)

The learner demonstrates understanding and appreciation of key concepts and principles of mathematics as applied, using appropriatetechnology, in problem solving, communicating, reasoning, making connections, representations, and decisions in real life.

V. Key Stage Standards: (Standard for the Core Learning Area for K-3, 4-6, 7-10, and 11-12)

K

3 4

6 7

10 11

12 At the end of Grade 3, the learner demonstrates understanding andappreciation of key concepts andskills involving whole numbers up toten thousand, fractions,measurement, simple geometricfigures, pre-algebra concepts anddata representation and analysis asapplied, using appropriatetechnology, in problem solving,reasoning, communicating, makingconnections, representations anddecisions in real life.

At the end of Grade 6, the learner demonstrates understanding andappreciation of key concepts andskills involving rational numbers,measurement, geometric figures,pre-algebra concepts, simpleprobability and data analysis asapplied, using appropriatetechnology, in problem solving,reasoning, communicating, makingconnections, representations anddecisions in real life.

At the end of grade 10, the learner demonstrates understanding andappreciation of key concepts andskills involving number sense,measurement, algebra, geometry,probability and statistics, andtrigonometry as applied, usingappropriate technology, in problemsolving, communicating, reasoning,making connections,representations, and decisions inreal life.

At the end of grade 12, the learner demonstrates understanding andappreciation of key concepts andskills involving personal financialmanagement, linear programming,logic, probability and statistics,analytic geometry and calculus, asapplied, using appropriatetechnology, in problem solving,communicating, reasoning, makingconnections, representations, and

decisions in real life.


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VI. Grade Level Standards:

Grade Level Grade Level Standards

K

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10, space andmeasurement, simple geometric figures, pre-algebra concepts and data collection as applied, using appropriate technology, inproblem solving, reasoning, communicating, making connections, representations and decision in real life.

Grade 1

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 100, fractions,measurement, simple geometric figures, pre-algebra concepts, data collection and representation as applied, using appropriatetechnology, in problem solving, reasoning, communicating, making connections, representations and decision in real life.

Grade 2

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 1 000, fractions,measurement and geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriatetechnology, in problem solving, reasoning, communicating, making connections, representations and decision in real life.

Grade 3

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10 000, fractions,

measurement, geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriatetechnology, in problem solving, reasoning, communicating, making connections, representations and decision in real life.

Grade 4

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 100 000,fractions, decimals including money, ratio, percent, angles, plane figures like square, rectangle, and triangle, measurement(perimeter, area of triangle and parallelogram, volume of cubes and rectangular prisms, pre-algebra concepts, data collection,representation and analysis as applied, using appropriate technology, in problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.

Grade 5

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10 000 000,fractions, decimals including money, ratio, percent, geometry (circles and five or more-sided polygons), measurement (circumference,area of trapezoid and circle, volume of cubes and rectangular prisms, temperature) , pre-algebra concepts, data collection,representation and analysis as applied, using appropriate technology, in problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.


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Grade Level Grade Level Standards

Grade 6

The learner is expected to have mastered the concepts and operations on whole numbers; demonstrates understanding andappreciation of the key concepts and skills involving fractions, decimals including money, ratio and proportion, percent, integers,geometry (spatial figures), measurement (surface area, volume, meter reading), pre-algebra concepts, data collection, representationand analysis, analysis and probability, expressions and equations as applied, using appropriate technology, in problem solving,reasoning, communicating, making connections, representations and decisions in real life.

Grade 7 The learner demonstrates understanding of key concepts and principles of number sense, measurement , algebra, geometry,probability and statistics as applied, using appropriate technology, in problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.

Grade 8The learner demonstrates understanding of key concepts and principles of algebra, geometry, probability and statistics as applied,using appropriate technology, in problem solving, reasoning, communicating, making connections, representations and decisions inreal life.

Grade 9 The learner demonstrates understanding of key concepts and principles of algebra, geometry, and trigonometry as applied, usingappropriate technology, in problem solving, reasoning, communicating, making connections, representations and decisions in real life.

Grade10The learner demonstrates understanding of key concepts and principles of number sense, algebra, geometry, probability andstatistics as applied, using appropriate technology, in problem solving, reasoning, communicating, making connections,representations and decisions in real life.

Grade 11The learner demonstrates understanding of key concepts and principles of number sense as applied in consumer mathematics,trigonometry, statistics, linear algebra and plane coordinate geometry using appropriate technology, in problem solving, reasoning,communicating, making connections, representations and decisions in real life.

Grade 12The learner demonstrates understanding of key concepts and principles of number sense as applied in consumer mathematics,trigonometry, statistics, linear algebra and plane coordinate geometry using appropriate technology, in problem solving, reasoning,communicating, making connections, representations and decisions in real life.


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Grade Level Kindergarten Grade 1Content:

Domain/Strand

Content Standard Performance Standards Content Standards Performance Standards

The learner demonstratesunderstanding of the keyconcepts of

1. Whole Numbers2. Operations of Whole

Numbers3. Fractions4. Measurement5. Probability and Statistics6. Geometry7. Pre-Algebra

The learner creates, analyzesand solves mathematicalsituations involving wholenumbers, operations of wholenumbers, fractions,measurement, probability andstatistics, geometry and pre-algebra through appropriateand accurate representations.



Numbers3. Fractions4. Measurement5. Probability and Statistics6. Geometry7. Pre-Algebra

The learner creates, analyzesand solves mathematicalsituations involving wholenumbers, operations of wholenumbers, fractions,measurement, probability andstatistics, geometry and pre-algebra through appropriateand accurate representations.

Whole

Numbers

The learner demonstrates

understanding of therelationship between numbersand quantities up to 10.

The learner is expected to:

1. recognize sets of objectsup to 10 using concreteobjects;

2. compare two or moresets of objects up to 10;

3. recognize, represent,match, name, read,count, and write wholenumbers up to 10;

4. compare and order

whole numbers up to 10;and5. apply these skills in

solving problems.


understanding of number notation and place value,cardinal and ordinal numbers,and comparing and orderingnumbers up to 100.


1. Represent equivalentforms of the samenumber through the useof physical models,diagrams, and number expressions;

2. Count and group objectsin ones and tens;

3. Count, read and writewhole numbers up to

100;4. Compare and order whole numbers up to 100by using symbols; and

5. Identify ordinal numbersfrom 1 st-10 th.


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Domain/Strand


WholeNumbers

The learner demonstratesunderstanding of simpleaddition and subtraction withsums or differences through10.

The learner is expected to:1. use manipulatives to

explore the concepts of addition and subtractionwith sums or differencesthrough 10;

2. use the words puttogether, add to, andplus to understand theconcept of additionthrough 10;

3. use the words takeaway and minus to

understand the conceptof subtraction; and

4. use concrete objects todetermine answers toaddition and subtractionproblems.

Number Senseof Fractions

The learner demonstratesunderstanding of the conceptof dividing wholes into equalparts.

The learner is expected to dividea whole into two or four equalparts.

Operations of Whole

Numbers

The learner demonstratesunderstanding of the meaningof addition and its propertiesand subtraction of wholenumbers up to 100.

The learner is expected to:1. use addition and

subtraction to solveproblems using pictorialrepresentation.


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Domain/Strand


The learner demonstratesunderstanding of the conceptof multiplication of wholenumbers using concretematerials and pictorialrepresentations.

The learner demonstratesunderstanding of the conceptof division.

The learner is expected to:1. show the relationship of

multiplication to additionwith quantities up to 40.

The learner is expected to:1. show division as a

grouping or partitioningprocess with quantity notgreater than 20.

Fractions The learner demonstrates

understanding of the conceptsof halves and fourths andapplies them in dividing awhole or set equally.


1. visualize halves andfourths;

2. identify and names a part(1/2, ); and

3. divide a whole or set inhalves and fourths.

Measurement The learner demonstratesunderstanding of the conceptsof time, length, mass, andcapacity using non-standard

units of measure.

The learner is expected to:1. observe sunrise and

sunset to tell the time of the day (morning,

noontime, evening);2. tell the number of days in

a week and the number of months in a year; and

3. measure and comparethe length, mass, and

The learner extends his/her concept of time and measuresand compares objects usingdirect comparison and non-

standard units of length, massand capacity.

The learner is expected to:1. identify the days in a

week and months in ayear and hour and half

hour; and2. measure, compare and

estimate length, massand capacity using non-standard units.


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Domain/Strand


capacity of familiar objects using non-standard units.

Probability andStatistics

The learner demonstratesunderstanding of pictograph.

The learner is expected to:1. participate actively in

gathering informationabout objects or eventsin their environment;

2. make a pictograph basedon the informationgathered; and

3. answer questions aboutthe pictograph.

The learner demonstratesunderstanding of organizing,representing and comparingdata using pictographs.

The learner is expected to:1. collect, organize, read,

construct and interpretpictographs.

Geometry The learner demonstratesunderstanding of shapes,sizes, and positions of common two- to three-dimensional objects in theenvironment.

The learner is expected to:1. explore the environment

to observe, identify,describe, and two- tothree-dimensionalobjects;

2. compare shapes, sizes,and positions of two- tothree-dimensional

objects; and3. use manipulative to

create two- to three-dimensional objects.

The learner demonstratesunderstanding of 2-D and 3-Dshapes through identifying,classifying and creating figuresusing cut-outs and concretemodels.

The learner is expected to:1. identify, name and

describe square,rectangle, triangle andcircle in 2-D and 3-Dobjects and classifiesthem by commonattributes.


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Domain/Strand


Pre-Algebra The learner demonstratesunderstanding of pre-algebraconcepts.

The learner is expected to:1. extend patterns of

shapes, colors, numbers;

2. sort and classify objectsby attributes; and

3. identify objects that donot belong in a particular group.

The learner demonstratesunderstanding of simplepatterns.

The learner is expected to:1. recognize simple

patterns of objects and

numbers.


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Grade Level Grade 2 Grade 3Content:

Domain/Strand




Numbers3. Measurement4. Probability and Statistics5. Fractions6. Geometry7. Pre-Algebra

The learner creates, analyzesand solves mathematicalsituations involving whole

numbers, operations of wholenumbers, measurement,probability and statistics,fractions, geometry and pre-algebra through appropriateand accurate representations.



Numbers3. Measurement4. Probability and Statistics5. Fractions6. Geometry7. Pre-Algebra


numbers, operations of wholenumbers, measurement,probability and statistics,fractions, geometry and pre-algebra through appropriateand accurate representations.

WholeNumbers


understanding of therelationships betweennumbers, and place value of whole numbers up to 1000.


1. compare and order whole numbers up to1000; and

2. read and write money incompound units usingdecimal notation.

The learner demonstratesunderstanding of the conceptsof whole numbers, place valueup to 10 000 and Romannumerals up to M, and odd andeven numbers.


1. read and write wholenumbers up to 10000and identifies the placevalue for each digit;

2. compare, order andround whole numbers upto 10000;

3. round off tens andhundreds;

4. identify and expressRoman numerals inHindu-Arabic; and

5. develop and apply oddand even numbers.

Operations of Whole

Numbers

The learner demonstratesunderstanding of the conceptof the four operations of wholenumbers and the identity and

The learner is expected to:1. add and subtract

numbers up to 1000;2. multiply and divide

The learner demonstratesunderstanding of the four operations of whole numbersand of the concept of identity,commutative, associative and

The learner is expected to:1. add 4-digit numbers with

or without regrouping(sum up to 19 998);


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Domain/Strand


zero properties of multiplication.

numbers within themultiplications tables of 2, 3, 4, 5 and 10;

3. show the relationshipbetween multiplicationand division;

4. model and solve simpleproblems involvingmultiplication anddivision; and

5. apply identity and zeroproperties of multiplication.

distributive properties of addition and multiplication.

2. subtract 3 to 4-digitnumbers from 4-digitnumbers with or without

regrouping;3. add and subtractmentally;

4. multiply and dividenumbers within themultiplications tables upto 10 by 10;

5. multiply and divide 2 to3-digit by 1-digitnumbers; 10, 100;

6. apply commutative,associative and

distributive properties of multiplication; and

7. estimate, calculate andsolve word problemsinvolving addition,subtraction, multiplicationand division of wholenumbers up to 10000.

Measurement The learner demonstratesunderstanding of the conceptand application of time and

using standard units inmeasuring length, mass, areaand capacity

The learner is expected to:1. measure time in minutes

including a.m. and p.m.

and length, mass andcapacity using standardunits;

2. measure time in minuteand length, mass andcapacity using standard

The learner extends his/her understanding of the conceptand application of time (inminutes), length, mass, areaand capacity.

The learner is expected to:1. recognize and use

common conversion of units; hour to minute, mto cm, kg to g, L to ml;

2. solve the area of squares and rectangles;

3. measure capacity usingthe standard units of measure; and


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Domain/Strand


units;3. find the duration of time

in hours;

4. find the area of squaresand rectangles usingsquare units; and

5. solve word problemsinvolving time, length,mass, area and capacity.

4. solve word problemsinvolving time, area andcapacity.


The learner demonstratesunderstanding of pictographswith scale representations.

The learner is expected to:1. collect, read, organize

and interpret pictograph2. make pictographs using

a scale representation.

The learner demonstratesunderstanding of tables andbar graphs.

The learner is expected to:1. read, organize, interpret

and construct tables andbar graphs.

Fractions The learner demonstratesunderstanding of unit fractionsand proper and similar fractions.

The learner is expected to:1. visualize, model, identify,

read and write unitfractions, other fractionsless than one, andsimilar fractions(denominator less than10)

2. compare unit fractions

and similar fractions

The learner demonstratesunderstanding of the basickinds of fractions and knowshow to simplify, order andrelate them to whole numbersand objects in the environment.

The learner is expected to:1. identify, read, write,

compare and order proper, improper, andmixed numbers; and

2. understand and use theconcept of equivalentfractions.

Geometry The learner demonstratesunderstanding of the basicproperties of geometricshapes, simple tessellationand symmetry.

The learner is expected to:1. identify, classify, describe

and draw semicircle andquarter circle;

2. construct squares,

The learner demonstratesunderstanding of the basicelements of angles, lines andrays.

The learner is expected to:1. visualize and identify

point, line, line segment,ray, perpendicular,parallel, and intersecting


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Domain/Strand


rectangles, triangles andcircles using cut-outs andsquare grids;

3. identify tessellation andsymmetry; and

4. identify straight lines andcurves, flat and curvedsurfaces of a 3-D object.

lines in bothmathematical andeveryday setting.

Pre-Algebra The learner demonstratesunderstanding of patterns onnumbers and geometricobjects.

The learner is expected to:1. create, identify,

describe, and findpatterns on numbersand geometric objects.

The demonstratesunderstanding of patterns of numbers, operations,geometric objects andrelationships.

The learner is expected to:1. create, describe,

explain patterns onnumbers, operations,geometric objects andrelationships.


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Domain/Strand




Numbers3. Fractions4. Decimals5. Ratio, Proportion and

Percent6. Probability and Statistics7. Measurement8. Geometry


numbers, operations of wholenumbers, fractions, decimals,ratio, proportion and percent,probability and statistics,measurement, geometrythrough appropriate andaccurate representations.



Numbers3. Fractions4. Decimals5. Ratio, Proportion and

Percent6. Probability and Statistics7. Measurement8. Geometry


numbers, operations of wholenumbers, fractions, decimals,ratio, proportion and percent,probability and statistics,measurement, geometrythrough appropriate andaccurate representations.

Whole Number The learner demonstratesunderstanding of number notation and place value of numbers up to 100000, and of factors and multiples up to100.

The learner is expected to:1. read, write, compare,

order numbers up to100000 and recognizethe place value;

2. round off number to thenearest ten thousand;

3. identify factors, GCF andmultiple of a number upto 100;

The learner demonstratesunderstanding of number notation and place value of numbers up to 10 million andof some number theoryconcepts.

The learner is expected to:1. read and write numbers

up to 10 million;2. differentiate prime from

composite numbers;3. express composite

numbers as products of prime factors;

4. find GCF and LCM of twonumbers; and

5. apply appropriatenumber theory concepts(primes, factors,multiples and divisibilityrules for 2, 3, 4, 5, 6, 8,9, 10, 11) to various real-life situations.


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Domain/Strand


to mixed forms and viceversa.

Decimals The learner demonstratesunderstanding of the conceptdecimals, addition andsubtraction of decimals up tohundredths.

The learner is expected to:1. use models/pictures to

illustrate the relationshipof fractions anddecimals;

2. read, write, round,compare and order decimals up tohundredths;

3. add and subtract

decimals throughhundredths; and

4. solve word problemsinvolving decimals.

The learner demonstratesunderstanding of decimals upto ten thousandths.

The learner is expected to:1. understand decimal

digits in the context of place value;

2. read, write, compare andorder decimals;

3. perform the four fundamental operationson decimals; and

4. solve word problemsinvolving decimals.

Ratio,Proportion and

Percent

The learner demonstratesunderstanding of the meaningof ratios.

The learner is expected to:1. recognize and describe a

ratio when comparingtwo quantities.

The learner demonstratesunderstanding on the use of ratio and proportion.

The learner is expected to:1. review ratios when

comparing quantities;2. express one value as a

fraction of another giventheir ratio and vice versa;

3. find how many times one

value is as large asanother given their ratioand vice versa;

4. recognize that twoquantities are in directproportion; and

5. solve word problems on


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Domain/Strand


ratio and directproportion.

Probability and

Statistics


understanding of tables andbar graphs.


1. collect data and presentthe data in a table form;

2. read and interpret tablesand bar graphs andconstruct bar graphs;and

3. solve problems usingdata presented in bar graphs and tables.

The learner records, arranges,

presents, and interprets datausing tables and line graphs.


1. create, read and interpretline graph and itsassociated table of data

2. calculate the average of a set of data

Measurement The learner demonstrates

understanding of units of measure of area and perimeter of a square, a rectangle andtheir related figures, andvolume of a cube and liquid.


1. find the area andperimeter of a figuremade up of squares andrectangles;

2. use formula in finding thevolume of a rectangular prism and liquid in arectangular container including conversionsbetween liter, millilitreand cubic meter; and

3. solve word problemsinvolving area andperimeter of squares andrectangles and volume of solids and liquids.


understanding onmeasurement in metric units toapproximate measure andcompute circumference, area,volume and temperature.


1. use and describemeasures of circumference, area of atrapezoid/circle, volumeof cube/rectangular prism, body and weather temperature;

2. estimate, make and usemeasurement to describeand comparephenomena includingconversion of units of

measure in the metricsystem;

3. select and useappropriatemeasurement units andtools for consistency andto the degree of


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Domain/Strand


accuracy; and4. solve word problems

involving circumference,area, volume andtemperature.

Geometry The learner demonstratesunderstanding of parallel andperpendicular lines, measuresof angles, symmetry, planefigures up to 4 sides, and 2-Drepresentation of a 3-D solid.

The learner is expected to:1. draw perpendicular and

parallel lines using ruler and set squares;

2. estimate size of anglesand measures angles indegrees using aprotractor;

3. draw a given angle using

a protractor including90 , 180 and 270 ;

4. identify and visualizesymmetry in theenvironment and indesigns;

5. complete a symmetricfigure with respect to agiven line of symmetry;

6. name and describe

various plane figures upto 4 sides; and

7. visualize and drawfigures made by unitcubes.

The learner demonstratesunderstanding of polygons upto 10 sides, congruence andsimilarities of polygons, circleand its parts.

The learner is expected to:1. name and describe

polygons up to 10 sides;2. draw and describe

similar and congruentpolygons; and

3. describe and identify theparts of a circle.


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Domain/Strand


Pre-Algebra The learner demonstratesunderstanding of therelationships among whole

numbers

The learner is expected to:1. solve the unknown in

simple equations

involving one or moreoperations of wholenumbers.

The learner demonstratesunderstanding of therelationship among whole

numbers and fractions.

The learner is expected to:1. solve the unknown in

simple equations

involving one or moreoperations of wholenumbers and fractions.


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Domain/Strand

Content Standard Performance Standards


1. Number Sense2. Geometry3. Measurement4. Probability and Statistics5. Algebra

The learner creates, analyzesand solves mathematicalsituations involving number

sense, geometry,measurement, probability andstatistics, algebra, throughappropriate and accuraterepresentations.

Number Sense The learner demonstratesmastery of the operations of fractions and decimals.

The learner demonstratesunderstanding of ratio, directproportion and percentage.

The learner is expected to:1. compare, order and

estimate fractions anddecimals; and

2. perform operations andsolves problemsinvolving fractions anddecimals.

The learner is expected to:1. use ratios, proportions

and percent in a varietyof ways; and

2. develop, apply andexplain methods for solving problemsinvolving proportions(direct, partitive andinverse) and percents(percent


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The learner demonstratesunderstanding of the conceptof integers, exponents, baseand scientific notation.

increase/decrease,discounts and mark-ups,commission, simple

interest and sales tax).

The learner is expected to:1. use real-life experiences,

physical materials andtechnology to constructmeaning for integers;

2. compare and order positive and negativeintegers;

3. use the notation andcomputation of positivewhole number powers;

4. perform series of operations includinggrouping symbols andexponents (PEMDAS);and

5. write very big or verysmall numbers asscientific notation.

Geometry The learner demonstratesunderstanding of angles ingeometric figures using variousproperties, 2-D representationof a 3-D solid and identification

The learner is expected to:1. find the unknown angles

in geometric figuresusing the properties of angles in a straight line,


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of nets of cube, prism andpyramid.

angles at a point,vertically oppositeangles, and square,

rectangle, parallelogram,rhombus, trapezium, andtriangle; and

2. visualize a prism and apyramid from drawings;

3. identify nets of a cube, aprism and a pyramid.

Measurement The learner demonstratesunderstanding of area andcircumference of a circle, area

and perimeter of figuresrelated to square, rectangle,triangle and circle, surfacearea and volume of rectangular prisms and capacity, andelectric and water consumption.

The learner is expected to:1. identify the parts of a

circle and use the

formula to findcircumference and areaof a circle, semicircle andquadrant including areasof composite figures;

2. find the area andperimeter of a figurerelated to these shapes:rectangle, square andtriangle;

3. find the surface area of cubes and rectangular prisms;

4. find the volume of a solidmade up of cubes andvolume of liquid; and

G d L l G d 6


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The learner demonstratesunderstanding of 24-hour clockand duration of time andspeed.

5. solve word problemsinvolving area andperimeter of the plane

figures, surface area andvolume of rectangular prisms and volume of liquid, and electric andwater consumption.

The learner is expected to:1. interpret 24-hour clock,

including conversionbetween 12-hour clock

and 24-hour clock;2. find duration of time;3. calculate time in different

time zones.4. calculate speed, distance

and time; and5. solve word problems

involving average, rateand speed.


The learner records, arranges,presents and interprets datausing tables and circle graphsand understands the meaningof probability.

The learner is expected to:1. create, read and interpret

circle graphs and itsassociated table of data;

2. solve 1-step problemsusing informationpresented in pie charts

G d L l G d 6


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(exclude use of degreesfor calculation);

3. generate and analyze

data obtained fromspinners and dice; and4. make simple predictions

based on experimentalprobability.

Algebra The learner demonstratesunderstanding of constants,variables and algebraicexpressions in one variable.

The learner is expected to:1. use a letter to represent

an unknown number andwrite a simple algebraic

expression in onevariable for a givensituation;

2. simplify algebraicexpressions (excludeexpressions involvingbrackets);

3. evaluate simple algebraicexpressions bysubstitution; and

4. solve word problemsinvolving algebraicexpressions.

Grade Level Grade 7 Grade 8


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Domain/Strand



1. Number Sense2. Measurement3. Algebra4. Geometry5. Probability and Statistics

The learner creates, analyzesand solves mathematicalsituations involving number

sense, measurement, algebra,geometry, probability andstatistics through appropriateand accurate representations.


1. Algebra2. Geometry3. Probability and Statistics

The learner creates, analyzesand solves mathematicalsituations involving, algebra,

geometry, probability andstatistics through appropriateand accurate representations.

Number Sense The learner demonstrates theknowledge and understandingof the real number system:natural numbers, wholenumbers, integers, rationalnumbers, irrational numbers,real numbers.

The learner is expected to:1. describe and represent

the real number bydiagram;

2. relate the differentsubsets of realnumbers;

3. visualize the absolutevalue of a number on anumber line as distancefrom the origin;

4. solve simple absolutevalue equations usingthe number line;

5. perform fundamental

operations on integers:addition, subtraction,multiplication, division;

6. state and illustrate thedifferent properties



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(commutative,associative, distributive,identity, inverse);

7. visualize rationalnumbers and their order on a number line;

8. translate rationalnumbers (bothterminating andrepeating / non-terminating) fromfraction form to decimalform and vice versa;

9. perform operations onrational numbers andillustrate the differentproperties;

10. represent real-lifesituations which involvesquare roots of arational number;

11. identify square rootswhich are rational andwhich are not rational(irrational);

12. visualize irrationalnumbers (square roots)and their order on anumber line;



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13. estimate/approximatethe square roots withand without technology;

14. arrange real numbersin increasing or decreasing order;

15. solve problemsinvolving real numbers,precision/accuracy,rounding numbers,significant digits,estimation; and

16. write a very large or avery small number inscientific notation.

Measurement The learner demonstratesknowledge and understandingof measurement and the use of measuring devices and skill inapplying this knowledge insolving real life situations.

The learner is expected to:1. appreciate the

development of measurement from theprimitive to the presentinternational system of units;

2. use instrument tomeasure length,weight/mass, volume,time, angle,temperature;

3. convert measurementsfrom one unit to



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another usingproportional reasoning;

4. calculate to obtain

measurementsinvolving ratios andrates; and

5. solve real-life problemsinvolvingmeasurements (e.g.water meter reading,electric meter reading,speed, etc.).

Algebra The learner demonstratesunderstanding and skills

1. related to simplifyingand performingoperations onpolynomials; and

2. in transforming andsolving mathematicalsentences with onevariable.

The learner is expected to:1. identify constants,

variables from a givenalgebraic expression;

2. translate verbalphrases tomathematical phrasesand vice versa;

3. evaluate algebraicexpression for givenvalues of the variablesinvolved, numericalexpressions (includingthose with wholenumber exponents);

4. give examples of polynomials (monomial,

The learner demonstratesunderstanding and skills

1. in multiplying anddividing polynomials;

2. in finding specialproducts and factors of certain polynomials;

The learner is expected to

1. give the meaning of x

a where x is a positiveinteger;

2. multiply and dividepolynomials using thelaws of exponents;

3. use the shortcutmethods to obtainproducts3.1. product and

difference of twosquares

3.2. square of abinomial

3.3. cube of a binomial



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binomial, trinomial,multinomial);

5. identify the base,

coefficient andexponent in amonomial;

6. add and subtractpolynomials;

7. differentiate:7.1 mathematical

expressions frommathematicalequations

7.2 equations frominequalities;

8. translate verbalsentences, patternsand pictorialrepresentations toequations andinequalities and viceversa;

9. find the solution of anequation or inequalityinvolving one variable(including absolutevalue equation /inequalities)9.1. from a given

3.4. special case of multiplying abinomial and

trinomial3.5. product of twobinomials;

4. identify polynomialswhich are specialproducts4.1. polynomials

whose terms havea commonmonomial factor

4.2. trinomials whichare products of two binomials

4.3. trinomials whichare squares of abinomial

4.4. products of thesum anddifference of twoquantities

2 2

( x y ,3 3 x y ,3 3 ) x y ;

5. factor completely a



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replacement9.2. intuitively by

guess and check

9.3. by algebraicprocedures(applying theproperties of equality /inequalities)

9.4. by geometricprocedures (usingintervals or rayson a number line);and

10. apply knowledge andskills with equationsand inequalities tosolve problems.

3. related to rationalexpressions;

4. related to rectangular coordinate system;

given polynomial usingone or more of thefollowing procedures

5.1. factoringpolynomialswhose terms havea commonmonomial factor

5.2. factoring adifference of twosquares

5.3. factoring sum anddifference of twocubes

5.4. factoring a perfectsquare trinomial

5.5. factoring bygrouping

5.6. factoring generaltrinomials;

6. solve problemsinvolving polynomialsand their products andfactors;

7. perform fundamentaloperations on rationalexpressions;

8. describe positions on aplane;



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5. related to functions ingeneral and linear functions in particular;and

9. identify whether a givenrelation is a functiongiven9.1. table of ordered

pairs9.2. graphs9.3. equations;

10. rewrite a linear equation Ax By C

in the form y mx b and vice versa;

11. graph a linear function y mx b given

11.1. any two points11.2. the intercepts11.3. the slope and a

given point;12. characterize the graph

of a linear function inthe terms of 12.1. intercepts12.2. slope;

13. obtain the equation of a

line given13.1. two points13.2. slope and one

point13.3. slope and y-

Grade Level Grade 7 Grade 8C


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6. in finding solutions tosystems of linear equations andinequalities in twovariables.

intercept;14. graph linear inequality

in two variables;15. solve problems

involving linear relationship;

16. identify which givenlinear equations havegraphs which areparallel, which intersectand which coincide;

17. solve systems of linear equations17.1. by graphing17.2. by substitution17.3. by elimination;

18. solve problemsinvolving systems of linear equations; and

19. solve systems of linear inequalities bygraphing.

Geometry The learner demonstratesknowledge and understandingof certain concepts used todescribe shapes of trianglesand quadrilaterals.

The learner is expected to:1. describe a point, line

and plane;2. define, identify and

name the subsets of aline;

3. illustrate, name, identify

The learner demonstrates theability

1. to prove deductivelycertain properties andrelationships of geometric figures;

2. to analyze, verify and

The learner is expected to:1. apply deductive

reasoning skills toprove certainproperties/relationshipsof geometric figures;

2. state and illustrate the



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and define differentkinds of angles;

4. apply measurementand inductive reasoningto derive certainproperties of geometricfigures4.1. supplementary

angles4.2. complementary

angles4.3. congruent angles4.4. adjacent angles4.5. linear pairs4.6. perpendicular lines4.7. parallel lines;

5. apply measurementand inductive reasoningto derive relationship5.1. between vertical

angles5.2. among angles

formed by parallellines cut by atransversal;

6. illustrate name andidentify different kindsof triangle, convexquadrilateral and their

prove trianglecongruence; and

3. construct geometricalfigures.

conditions on trianglecongruence;

3. prove inductively anddeductively thetheorems on trianglecongruence;

4. apply the theorems to4.1. prove certain

relationshipsrelated to trianglecongruence

4.2. solve problemsinvolving trianglecongruence; and

5. use compass andstraightedge toconstruct geometricalfigures.



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parts;7. classify triangles

according to their angles and accordingto their sides;

8. apply measurementand inductive reasoningskills to deriverelationships amongsides and angles of atriangle;

9. illustrate, name andidentify the differentkinds of quadrilaterals;

10. apply measurementand inductive reasoningskills to derive therelationship of angles of quadrilaterals; and

11. apply measurementand inductive reasoningskills to derive therelationship of angles(exterior/interior) of anyconvex polygon.


The learner demonstratesunderstanding and skills in theeffective use of tables andgraphs and averages in

The learner is expected to:1. collect statistical data

and average or organize in a table

The learner demonstratesknowledge and understanding

1. related to variability of given set data; and

The learner is expected to:1. calculate the different

measures of variabilityrelated to the given set



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analyzing and interpreting datafor problem solving.

according to somesystematicconsiderations;

2. use appropriate graphto represent organizeddata2.1. pictograph2.2. bar graph2.3. pie graph2.4. line graphwhichever isappropriate;

3. analyze, interpretaccurately and drawconclusions fromgraphic and tabular presentations of statistical data;

4. find the mean, medianand mode of ungrouped statisticaldata; and

5. state somecharacteristics of the

collection of data, giventhe mode, median or mean.

2. of the probability of events and outcomes.

of data;2. describe a given data

using a measure of central tendency and ameasure of variability;

3. differentiate anexperimental probabilityfrom theoreticalprobability;

4. use simulation to modelreal world situations;and

5. solve simple problemsin probability.



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Content: Domain/Strand Content: Domain/Strand Quarter 11. Number Sense

1.1. Basic Idea of Sets

1.2. Real Number System1.2.1 Subsets of Real Numbers1.2.2 Integers1.2.3 Rational Numbers1.2.4 Irrational Numbers

1.3. Estimation / Approximation1.3.1 Square Roots

1.4. Scientific Notation

2. Measurement2.1. Standard and Non Standard Units of Measure2.2. SI and Customary2.3. Metric System2.4. Conversion of Units2.5. Perimeter 2.6. Volume2.7. Ratio, Rate and Speed

Quarter 23. Algebra

3.1. Number Sequence and Pattern Finding3.2. Algebraic Expressions

3.2.1 Constants and Variables3.2.2 Mathematical Phrases3.2.3 Evaluation of Algebraic Expressions3.2.4 Polynomials3.2.5 Addition and Subtraction of Polynomials

3.3. Linear Equations and Inequalities in One Variable3.3.1 Linear Equations (including Absolute Value)

Quarter 11. Algebra

1.1. Multiplication of Polynomials1.1.1 Laws of Exponents1.1.2 Multiplication of Monomials1.1.3 Multiplication of Monomial by Polynomial1.1.4 Multiplication of Polynomials

1.2. Division of Polynomials1.2.1 Division of Monomials1.2.2 Division of Polynomial by Monomial1.2.3 Division of Polynomials

1.3. Special Products1.3.1 Product of Sum and Difference of Two Terms1.3.2 Square of a Binomial1.3.3 Cube of a Binomial1.3.4 Special Case of Multiplying a Binomial and

Trinomial1.3.5 Product of Two Binomials

1.4. Factoring1.4.1 Greatest Common Monomial Factor 1.4.2 Difference of Two Squares1.4.3 Sum and Difference of Two Cubes1.4.4 Perfect Square Trinomial

1.4.5 Factoring by Grouping1.4.6 Factoring General Trinomials

1.5. Application of Special Products and Factoring



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3.3.2 Applications of Linear Equations3.3.3 Linear Inequalities (including Absolute Value

Inequality)3.3.4 Applications of Linear Inequalities

Quarter 34. Geometry

4.1. Introduction to Geometry4.1.1 Undefined Terms4.1.2 Angles4.1.3 Angle Pairs4.1.4 Parallel4.1.5 Transversal

4.2. Polygons4.2.1 Kinds of Polygons4.2.2 Triangles (including Triangle Inequality)4.2.3 Quadrilaterals4.2.4 Interior/Exterior Angles of Convex Polygons

Quarter 45. Probability and Statistics

5.1. Introduction to Statistics5.1.1 Definition of Terms5.1.2 Uses and Importance of Statistics5.1.3 Data Gathering / Collection

5.2. Data Representation5.2.1 Frequency Table

5.3. Graphical Representation5.3.1 Pictograph5.3.2 Bar Graph5.3.3 Pie Graph5.3.4 Line Graph

5.4 Measures of Central Tendency Ungrouped Data

Quarter 21.6. Rational Expressions

1.6.1 Simplifying Rational Expressions1.6.2 Multiplication and Division of Rational Expressions1.6.3 Addition and Subtraction of Rational Expressions1.6.4 Complex Fractions

1.7. Linear Functions and Inequalities1.7.1 Rectangular Coordinate System1.7.2 Basic Ideas on Functions1.7.3 Graphs of Linear Equations in Two Variables

1.7.3.1 Using Table of Values1.7.3.2 Using Intercepts1.7.3.3 Using Slope-Intercept

1.7.4 Obtaining the Equation of a Line1.7.5 Graphs of Linear Inequalities in Two Variables1.7.6 Solve problems involving linear relationship

Quarter 31.8 Systems of Linear Equations and Inequalities

1.8.1 Kinds of Systems of Linear Equations1.8.2 Solving Systems of Linear Equations

1.8.2.1 By Graphical Method1.8.2.2 By Elimination Method1.8.2.3 By Substitution Method

1.8.3 Application of Systems of Linear Equations1.8.4 Systems of Linear Inequalities

2. Probability and Statistics2.1. Measures of Variability (Ungrouped Data)



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5.4.1 Mean5.4.2 Median5.4.3 Mode

2.1.1 Range2.1.2 Average Deviation2.1.3 Standard Deviation

2.2. Simple Probability2.2.1 Sample Space2.2.2 Probability of Events


3.1. If-Then Statements3.2. Writing Proofs

3.2.1 Prove deductively relationship derived inductively inGrade 7

3.3. Triangle Congruence3.3.1 SAS3.3.2 ASA3.3.3 SSS3.3.4 HyL3.3.5 LL3.3.6 HyA

3.4. Pythagorean Theorem3.5. Geometrical Constructions

3.5.1 Using Compass and Straightedge3.5.2 Bisecting Line Segments

3.5.3 Bisecting Angles



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1. Algebra2. Geometry3. Trigonometry

The learner creates, analyzesand solves mathematicalsituations involving algebra,geometry, and trigonometrythrough appropriate andaccurate representations.


1. Algebra2. Geometry3. Probability and Statistics

The learner creates, analyzesand solves mathematicalsituations involving algebra,geometry, probability and

statistics through appropriateand accurate representations.

Algebra The learner demonstratesknowledge and understanding

1. related to quadraticfunctions and equations;

The learner is expected to:1. recognize a quadratic

function and aquadratic equation inone variable;

2. graph quadraticfunction and determinefrom its graph the2.1. intercepts2.2. zeros2.3. axis of symmetry2.4. highest/lowest

point2.5. direction of

concavity;3. transform quadratic

function2 y ax bx c to

2 y a x h k ;4. analyze the effects on

The learner demonstratesunderstanding and skills

1. related to sequencesand series; and

2. related to polynomial

The learner is expected to1. generalize and observe

patterns;2. give examples of

arithmetic sequenceand geometricsequence;

3. describe an arithmetic,geometric and other sequences by3.1 giving few terms3.2 giving the formula

for the nth term3.3 drawing the graph;

4. find the sum of a givenarithmetic or geometric

sequence;5. solve problems

involving sequencesand series;

6. recognize polynomial



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2. related to rational

the graph of changes ina , h and k in aquadratic function;

5. formulate the quadraticfunction given5.1 table of values5.2 graph;

6. solve quadraticequations by6.1 factoring6.2 completing the

square6.3 quadratic formula;

7. determine the nature of the roots of quadraticequations;

8. formulate the quadraticequation given its rootsor relationship of itsroots;

9. relate zeros of quadratic functions androots of quadraticequation;

10. solve problemsinvolving quadraticfunction and quadraticequation;

11. solve problems

functions. functions;7. use synthetic division,

remainder theorem andfactor theorem to findthe factors of thepolynomials;

8. find the zeros of polynomial functions;and

9. solve problemsinvolving polynomialfunctions.



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equations;

3. of the relationship amongvariables in a variation;

4. related to expressionhaving rationalexponents; and

involving rationalequations;

12. recognize relationshipsbetween two quantitiesin real life that obey12.1. direct12.2. inverse12.3. joint12.4. combined,

variations;13. translate statements

that involve variationstatement to a table of values, a mathematicalequation or a graphand vice versa;

14. solve problemsinvolving variation;

15. extend their knowledgeon the laws of exponents (positiveintegral) to15.1. zero to negative

exponents

15.2. fractionalexponents;

16. simplify expressionswith rational exponents;

17. apply scientific notation



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5. related to radicalexpressions.

in performingoperations involvingvery small or very largenumbers;

18. solve problemsinvolving expressionswith rational exponents;

19. recognize radicalexpressions;

20. relate expressions withfractional exponents toradical expressions;

21. simplify radicalexpressions;

22. perform fundamentaloperations on radicalexpressions; and

23. solve problemsinvolving radicalexpressions.

Geometry The learner demonstrates theability

1. to analyze, verify andprove triangle similarity;

and

The learner is expected to:1. state and illustrate the

conditions on trianglesimilarity;

2. prove inductively anddeductively thetheorems on trianglesimilarity;

3. relate triangle similarity

The learner demonstrates1. understanding and skills

related to circles;

The learner is expected to:1. derive inductively and

deductively therelations among arcs,

central angles andinscribed angles1.1. theorems related to

circles;2. solve problems related



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2. knowledge andunderstanding relatedto transformation andsymmetry.

to triangle congruence;4. apply the theorems to

4.1 prove certainrelationship relatedto triangle similarity

4.2 solve problemsinvolving trianglesimilarity;

5. apply triangle similarityon5.1 enlargement and

reduction5.2 scale drawings5.3 similar figures;

6. explain why certainshapes tessellate;

7. identify the symmetry7.1 with respect to a

line7.2 with respect to a

point; and8. can draw the

translations, reflectionsand rotations of an

object.

2. the ability to provedeductively when is aquadrilateral aparallelogram;

3. understanding and skillsin working with geometricfigures in a coordinateplane; and

to circles;3. prove deductively when

is a quadrilateral aparallelogram;

4. solve problemsinvolving cyclicquadrilaterals;

5. derive the distanceformula between twopoints on the plane5.1 when one point is

the origin5.2 when neither point

is the origin;

6. apply the distanceformula to derive/proveother geometricproperties;

7. find the equation of aline given7.1 two points7.2 slope and one

point7.3 slope and y-

intercept;8. derive/state the

standard form of theequation of a circle withradius r and center at



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4. knowledge andunderstanding related to

transformation andsymmetry.

0,0 or ,h k ;9. find the center and

radius of the circle

given its equation andvice versa; and10. solve problems

involving geometricfigures in thecoordinate plane.

Trigonometry The learner demonstratesunderstanding and skillsrelated to sine, cosine andtangent related to triangles.

The learner is expected to:1. state and illustrate the

trigonometric ratios,sine law and cosine

law; and2. apply the trigonometricratios, sine law andcosine law in solvingproblems includingareas of triangles andbearing.


The learner demonstrates the1. understanding and

skills related tomeasure of position(quantiles);

The learner is expected to:1. calculate specified

percentiles of a setoff ungrouped data (e.g.deciles, quartiles, 50 th percentile);

2. use percentile to infer



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2. ability in countingnumber of combinations of eventsor number of subsets ina set; and

3. ability to solveproblems involvingprobability of compound events.

information from a setof ungrouped data;

3. apply knowledge of percentile to solveproblems;

4. count the number of occurrences of eventsusing grid table, treediagram, systematiclisting and thefundamental countingprinciple;

5. count the number of arrangements

(permutation) of r objects at a time from aset of n objects;

6. count the number of ways objects can beselected out of a set of n objects(combinations);

7. solve problemsinvolving permutations

and combinations;8. find the probability of

compound events

8.1 P A or B


C S d d P f S d d C S d d P f S d d


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8.2 P A and B ; and9. solve problems

involving compound

events.Content: Domain/Strand Content: Domain/Strand Quarter 11. Algebra

1.1. Quadratic Functions and Equations1.1.1 Definition of a Quadratic Function1.1.2 Graph of Quadratic Function1.1.3 Quadratic Function in Different Forms

1.1.3.1 2 y ax bx c

1.1.3.2 2 y a x h k 1.1.4 Effects on the graph of changes in a , h , k in a

quadratic function1.1.5 Zeros of a Quadratic Function1.1.6 Roots of a Quadratic Equation and its relation to

zeros of a function1.1.6.1 Solving Quadratic Equation

1.1.6.1.1 by Factoring1.1.6.1.2 by Completing the Square1.1.6.1.3 by Quadratic Formula

1.1.7 Nature of Roots1.1.8 Sum and Product of Roots1.1.9 Applications of Quadratic Equations

1.2. Rational Equations1.2.1. Rational Equations

Quarter 11. Algebra

1.1. Sequences and Series1.1.1. Review on Finding Patterns1.1.2. Arithmetic Sequence and Series1.1.3. Geometric Sequence and Series1.1.4. Other Sequences and Series

1.1.4.1 Harmonic Sequence1.1.4.2 Fibonacci Sequence

1.2 Polynomial Functions1.2.1 Polynomial Functions of Degree 1 and Degree 2

(Review)1.2.2 Polynomial Functions of Degree Greater than 2

Quarter 21.2.3 Synthetic Division1.2.4 Remainder Theorem1.2.5 Factor Theorem1.2.6 Zeros of a Polynomial Functions

1.2.7 Graphs of Polynomial Functions1.2.8 Applications of Polynomial Functions

2. Geometry2.1. Circles

2.1.1 Parts of a Circle




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1.2.2. Application of Rational Equations

Quarter 21.3. Variations

1.3.1. Direct1.3.2. Inverse1.3.3. Joint1.3.4. Combined

1.4. Radicals1.4.1. Rational Exponents1.4.2. Scientific Notations1.4.3. Transforming Expressions with Rational Exponent as

Radicals and vice versa1.4.4. Simplifying Radicals

1.4.5. Operations on Radicals1.4.6. Radical Equations1.4.7. Applications (include Surface Area and Volume)


2.1. Triangle Similarity2.1.1. SAS Similarity Theorem2.1.2. SSS Similarity Theorem2.1.3. AA Similarity Theorem

2.1.4. Right Triangle Similarity2.2. Enlargement and Reduction2.3. Scale Drawings2.4. Areas of Similar Plane Figure and Volumes of Similar Solid

Figures

2.1.2 Arcs and Angles2.1.3 Tangent Lines and Tangent Circles2.1.4 Power Theorems

2.2 Quadrilaterals

2.2.1 Conditions which guarantee that a quadrilateral is aparallelogram2.2.2 Cyclic quadrilaterals

Quarter 32.3 Coordinate Geometry

2.3.1 Distance Formula2.3.2 Equation of a Line2.3.3 Equation of a Circle

3. Probability and Statistics3.1. Measures of Position (Quantiles)

3.1.1. Quartiles3.1.2. Deciles3.1.3. Percentiles

Quarter 43.2. Fundamental Principle of Counting3.3. Combination3.4. Permutation3.5. Probability




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2.5. Transformations and Symmetry2.5.1 Tessellations2.5.2 Symmetry

2.5.2.1 with respect to a line

2.5.2.2 with respect to a point2.5.3 Translations (slides/glides)2.5.4 Reflections (flips)2.5.5 Rotations

Quarter 43. Trigonometry

3.1. Trigonometric Ratios3.2. Sine Law and Cosine Law3.3. Area of Triangles

3.4. Bearing

Proposed Tracking for Grades 11 and 12 (University-bound students)

Track Courses Grade 11 Grade 12


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Track 1 Science and engineering(1) General Math(2) Pre-Calculus

(1) Calculus for Sciences and Engineering(2) Probability and Statistics

Track 2 Economics, business and life sciences General Math(1) Calculus for Economics, Business and LifeSciences

(2) Probability and Statistics

Track 3 Humanities General Math Probability and Statistics


Domain/

Strand


Suggested Content: Domain/Strand Suggested Content: Domain/Strand General Math

1. Functions1.1. Exponential (graphs, equations)1.2. Inverse1.3. Logarithmic (graphs, equations)1.4. Applications

2. Personal Financial Management 2.1. Compound interest

2.2. Future value2.3. Instalment buying2.4. Truth in lending

3. Linear Programming 3.1. Review of System of Linear Inequalities in Grade 8

Probability and Statistics

1. Random Variables 1.1. Definition1.2. Expected value1.3. Variance and standard deviation1.4. Binomial random variable

2. Probability Distributions2.1. Binomial distribution

2.2. Poisson distribution2.2.1. As an approximation to the Binomial

2.3. Normal distribution2.3.1. Table of normal curve areas2.3.2. As an approximation to the Binomial


Domain/ Content Standard Performance Standards Content Standards Performance Standards


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Domain/Strand

Co te t Sta da d e o a ce Sta da ds Co te t Sta da ds e o a ce Sta da ds

3.2. Introduction to Linear Programming3.3. Solving Linear Programming Problems with and without

Mathematical Software

4. Logic 4.1. Propositional logic4.2. Propositional equivalences4.3. Predicates and quantifiers4.4. Rules of inference

3. Estimation3.1. Estimating population proportion3.2. Estimating population mean3.3. Estimating population variance3.4. Choosing a sample size

4. Testing 4.1. Basics of hypothesis testing4.2. Testing a claim about a proportion4.3. Testing a claim about a mean4.4. Testing a claim about variance or standard deviation

Pre-Calculus

1. Analytic Geometry 1.1. Review on Rectangular Coordinate System, Lines, and

Circles

1.2. Translation of Axes1.3. The Parabola1.4. The Ellipse1.5. The Hyperbola

2. Functions and Their Graphs2.1. Review on Functions2.2. Operations on Functions2.3. Functions as Mathematical Models2.4. Polynomial Functions and Their Graphs2.5. Rational Functions and Their Graphs

3. Sequences and Mathematical Induction3.1. Review of Sequences and Series in Grade 103.2. Sigma Notation3.3. Mathematical Induction3.4. The Binomial Theorem

Calculus for Economics, Business, and Life Sciences

1. The Derivative I 1.1. Introduction to Limits1.2. Infinite Limits and Limits at Infinity

1.3. Continuity1.4. The Derivative1.5. Basic Differentiation Rules1.6. Product and Quotient Rules1.7. The Chain Rule1.8. Applications of Derivative

2. The Derivative II 2.1. Continuous Compound Interest2.2. Derivatives of Logarithmic and Exponential Functions2.3. Implicit Differentiation2.4. Related Rates

3. The Derivative III 3.1. First Derivative and Graphs3.2. Second Derivative and Graphs3.3. Curve Sketching Techniques




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Domain/Strand

4. Trigonometry I 4.1. Review of Trigonometry in Grade 94.2. Circular Functions and Their Graphs4.3. Identities4.4. Sum and Difference Identities4.5. Double and Half-Angle Identities

5. Trigonometry II 5.1. Inverse Trigonometric Functions5.2. Trigonometric Equations5.3. Polar Coordinate System5.4. Graphs of Polar Equations5.5. Intersection of Polar Graphs

3.4. Optimization

4. Integration4.1. Antiderivatives and Indefinite Integrals4.2. Integration by Substitution4.3. Differential Equations Growth and Decay4.4. The Definite Integral4.5. Fundamental Theorem of Calculus4.6. Area between Curves4.7. Applications

Calculus for Sciences and Engineering

1. Limits1.1. Introduction to Limits1.2. Evaluating Limits1.3. One-Sided Limits1.4. Continuity1.5. Limits at Infinity and Horizontal Asymptotes1.6. Infinite Limits and Vertical Asymptotes1.7. Special Limits Involving Trigonometric Functions

2. Differentiation I 2.1. Derivatives and Tangents2.2. Rules of Differentiation (Product, Quotient, Chain Rules)2.3. Derivatives of Polynomial and Trigonometric Functions2.4. Implicit Differentiation and Higher Derivatives2.5. Derivatives of Exponential and Logarithmic Functions2.6. Applications: Rates of Change and Related Rates




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Domain/Strand

3. Differentiation II 3.1. First Derivative and Graphs3.2. Second Derivative and Graphs3.3. Graph Sketching3.4. Optimization Problems

4. Integration4.1. Antiderivatives4.2. Substitution Rule4.3. Area and The Definite Integral4.4. The Fundamental Theorem of Calculus4.5. Area between Curves

k to 12 mathematics curriculum guide

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