2010 sec yeariiicurriculumguidemathematics

2010 Secondary Education Curriculum
Mathematics

DEPARTMENT OF EDUCATION
Bureau of Secondary Education
Curriculum Development Division

2010 SECONDARY EDUCATION CURRICULUM

MATHEMATICS III

CURRICULUM GUIDE

1

Mathematics

General Standards in Mathematics

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

General Standard General Standard General Standard General Standard
First Year Level Second Year Level Third Year Level Fourth Year Level

The learner demonstrates understanding of The learner demonstrates understanding of The learner demonstrates understanding of The learner demonstrates understanding of
key concepts and principles of number and key concepts and principles of number key concepts and principles of number key concepts and principles of number
number sense as applied to measuring, sense and patterns in solving equations, sense, shapes and sizes and their sense, patterns and functions, data analysis
estimating, graphing, solving equations and generalizing relationships and solving applications to solving real-life problems and uses them in solving problems in real
inequalities, communicating problems in real life. involving geometric relationships. life.
mathematically and solving problems in real
life.

2

Mathematics

Mathematics
Concept Matrix

First Year Second Year Third Year Fourth Year
Real Number System Expressions with Rational Exponents Geometry of Shapes and Sizes Relations and Functions

Measurements Radical Expressions Geometric Relations Linear Functions

Writing Proofs Quadratic Functions

Algebraic Expressions Quadratic Equations Perpendicular Lines and Parallel Lines Polynomial Functions
• Laws of Exponents
• Special Products and Factors Radical Equations Triangle Congruence Exponential and Logarithmic
• Scientific Notation Functions
Inequalities in a Triangle

First-Degree Equations and Rational Algebraic Expressionsand Quadrilaterals Circular Functions
Inequalities in One Variable Equations
Similarity Trigonometric Identities and
Equations
Linear Equations and Inequalities in Variations
Two Variables

Systems of Linear Equations and Sequences and Series Circles Counting Techniques and Probability
Inequalities in Two Variables
Plane Coordinate Geometry Measures of Central Tendency and
Variability

3

Mathematics

MATHEMATICS III

General Standard:The learner demonstrates understanding of key concepts and principles of number sense, shapes and sizes and their applications to solving real life problems involving
geometric relationships.

QUARTER I (Geometry of Shapes and Sizes)

Stage 1: Results/Outcomes Stage 2: Assessment
STANDARDS ESSENTIAL Product/ At the Level of
Content Performance Understanding Question Performance Understanding Performance
The learner demonstrates The learner Many real-life objects How are geometric Models created Explanation Assessment of models
understanding of the key describes/illustrates in the environment can models reflected in • are drawn from real- Discuss the different created based on the
concepts of Geometry of plane figures, using be modeled many real-life objects? life objects. properties of a given following suggested criteria:
Shapes& Sizes. models satisfactorily geometrically. • illustrate different geometric figure and how it • drawn from real-life
and formulates plane figures and is seen and applied in real objects
intellectually solid figures. life. • models involve geometry
challenging situations Criteria: of shapes and sizes
involving geometric Clear
shapes and sizes then Situations formulated Coherent Tools: Rubrics for
finds solutions using a Systematic assessment of geometric
variety of strategies • are intellectually Thorough models created
with utmost accuracy. challenging.
• Involve geometry of Interpretation Assessment of situations
shapes and sizes. Describe how the different formulated based on the
• are worked out using geometric shapes are seen following suggested criteria:
a variety of strategies and used in the
with utmost accuracy. environment. • intellectually challenging
Criteria: • situations involve
Creative geometry of shapes and
Illustrative sizes
Insightful • situations are worked out
Significant using a variety of
strategies with utmost
Application accuracy
Pose intellectually
challenging situations
involving geometry of
shapes and sizes and solve

4

Mathematics

them. Tools: Rubrics for
Criteria: assessment of intellectually
Adaptive challenging situations
Appropriate formulated and worked out
Authentic
Efficient
Assessment using GRASPS:
Perspective
Develop insights from the Identify models of different
different properties geometric shapes as seen in
observed from a given many real-life objects (e.g.
geometric shape including roller skates, kitchen
its value in real life. utensils, product packaging,
etc.).
Criteria:
Credible
Create designs using
Perceptive
different geometric shapes.
Revealing

Empathy
Describe the difficulties one
can experience when
appropriate geometric
shapes are not in the
environment.
Criteria:
Receptive
Responsive
Sensitive

Self- Knowledge
Manifest understanding by
assessing how one can give
his/her best solution to a
problem/situation involving
geometric shapes and sizes.
Criteria:
Reflective
Relevant
Flexible

5

Mathematics

QUARTER I (Geometric Relations)

STANDARDS ESSENTIAL At the
Product/ Level of

The learner demonstrates The learner formulates Geometric relations How are the different Situations formulated Explanation Assessment of situations
understanding of the key intellectually that can be drawn geometric relations Discuss the relationships formulated based on the
concepts of Geometric challenging situations from different plane used to find solutions • are intellectually between and among angles following suggested criteria:
Relations. involving geometric figures facilitate the to intellectually challenging. and sides of a given
relations and finds solution of challenging situations • Involve geometric geometric figure and how • intellectually challenging
solutions using a intellectually involving plane relations. they are applied in real life. • situations involve
variety of strategies challenging situations. figures? • are worked out using Criteria: geometric relations
with utmost accuracy. a variety of strategies Clear • situations are worked out
with utmost accuracy. Coherent using a variety of
Systematic strategies with utmost
Thorough accuracy

Interpretation Tools: Rubrics for
Describe the relationships assessment of intellectually
between and among angles challenging situations
and sides of a given formulated and worked out
geometric figure and their
importance in real life
situations.
Criteria: Create designs, sketches or
Creative models of real-life objects
Illustrative applying the different
Insightful geometric relations.
Significant

Application
Use the different
relationships between and
among angles and sides of
a given geometric figure
and other concepts in
formulating and finding

6

Mathematics

solutions to intellectually
challenging situations.
Criteria:
Adaptive
Efficient
Practical
Relevant

Perspective
Develop insights from the
different relationships
related to angles and sides
of a given geometric figure.
Criteria:
Credible
Insightful
Perceptive
Revealing

Empathy
Describe how a person
feels for not knowing the
relationships that exist
between and among angles
and sides of a given
geometric figure.
Criteria:
Receptive
Responsive
Sensitive

Self-Knowledge
assessing how one can
give his/her best solution to
a problem/situation
involving geometric
relations.
Criteria:
Reflective

7

Mathematics

Relevant
Flexible

Mathematics III

General Standard: The learner demonstrates understanding of key concepts and principles of number sense, shapes and sizes and their applications to solving real life problems involving

QUARTER I (Writing Proofs)

STANDARDS ESSENTIAL At the
Product/ Level of

The learner demonstrates The learner Deductive and How can reasoning be Situations formulated Explanation Assessment of situations
understanding of the key communicates inductive reasoning used to understand Discuss one’s formulated based on the
concepts of Writing Proofs. mathematical can be used to and find solutions to • are intellectually thinking/ideas, reasoning, following suggested criteria:
thinking/ideas with understand and to find intellectually challenging. and points of view on a
coherence and clarity in solutions to challenging situations? • Involve writing given situation. • intellectually challenging
formulating and finding intellectually proofs. Criteria: • situations involve writing
solutions to challenging situations. • are worked out using Clear proofs
intellectually deductive and Coherent • situations are worked out
challenging situations. inductive reasoning. Systematic using deductive and
Thorough inductive reasoning

Compare and contrast assessment of intellectually
one’s thinking, reasoning, challenging situations
and points of view on a formulated and worked out
given situation.
Criteria:
Illustrative
Insightful
Significant
Application

8

Mathematics

Determine mathematical Assessment using GRASPS:
relationships in real life and
justify them. Create a situation involving
Criteria: group of people with
Adaptive different interests. Pose an
Efficient issue related to the given
Relevant situation for discussion and
exchange of views.
Perspective
Share one’s reasoning and
points of view about a given
situation.
Criteria:
Credible
Insightful
Perceptive
Revealing

Empathy
Show empathy when
someone shares his/her
thinking, reasoning, and
points of view about a given
situation.
Criteria:
Receptive
Responsive
Sensitive

Self- Knowledge
Assess one’s reasoning
and points of view about a
given situation.
Criteria:
Reflective
Relevant
Flexible

9

Mathematics

Mathematics III

General Standard: The learner demonstrates understanding of key concepts and principles of number sense, shapes and sizes and their applications to solving real life problems involving
QUARTERII (Perpendicular and Parallel Lines)

STANDARDS ESSENTIAL Product/ At the level of
The learner demonstrates The learner formulates Geometric How are perpendicular Situations formulated Explanation Assessment of situations
understanding of the key intellectually relationships between and parallel lines used Discuss the relationships formulated based on the
concepts of Perpendicular challenging situations and among in many intellectually • are intellectually that exist between and following suggested criteria:
and Parallel Lines. involving perpendicular perpendicular and challenging situations? challenging. among perpendicular and • intellectually challenging
and parallel lines and parallel lines can be • involve parallel lines as they are • situations involve
finds solutions using a applied in finding perpendicular and seen in some real-life perpendicular and parallel
variety of strategies solutions to many parallel lines. objects/situations. lines
with utmost accuracy. intellectually Criteria: • situations are worked out
• are worked out using
challenging situations. Clear using a variety of
a variety of
strategies with Coherent strategies with utmost
utmost accuracy. Systematic accuracy
Thorough
Tools: Rubrics for
assessment of intellectually
Interpretation challenging situations
Describe the relationships formulated and worked out
between and among
perpendicular and parallel Assessment using GRASPS:
lines and their importance
in real-life situations. Make a school development
Criteria: plan that focuses on
Illustrative improvement of facilities like
Insightful buildings or classrooms,
Significant roads, and other services.
Discuss the importance of
using perpendicular and
Application parallel lines in the plan.
Use the different properties
and theorems on

10

Mathematics

perpendicular and parallel
lines and other concepts in
formulating and finding
solutions to intellectually
Criteria:
Adaptive
Efficient
Relevant

Perspective
Develop insights from the
different properties and
theorems related to
perpendicular and parallel
lines.
Criteria:
Credible
Insightful
Perceptive
Revealing

Empathy
Show empathy on what a
person feels whenever
he/she is caught in a traffic
jam or in some other
unusual instances related
to perpendicular and/or
parallel lines.
Criteria:
Receptive
Responsive
Sensitive

Self-Knowledge
a problem/situation

11

Mathematics

involving parallel and
perpendicular lines.
Criteria:
Reflective
Relevant
Flexible

12

Mathematics

Mathematics III


QUARTER II (Triangle Congruence)

STANDARDS ESSENTIAL At the Level of
Product/
Content Performance Understanding Question Understanding Performance
Performance
The learner demonstrates The learner formulates Many real-life objects How are the different Situations formulated Explanation Assessment of situations
understanding of the key intellectually can be made by conditions for triangle Discuss the conditions that formulated based on the
concepts of Triangle challenging situations adopting different congruence applied in • are intellectually make triangles congruent. following suggested criteria:
Congruence. involving congruent designs that are finding solutions to challenging. Criteria: • intellectually challenging
triangles and finds generated using intellectually • involve triangle Clear • situations involve triangle
solutions using the congruent triangles. challenging situations? congruence Coherent congruence
different conditions for • are worked out using Justified • situations are worked out
triangle congruence a variety of Systematic using a variety of
with utmost accuracy. strategies with strategies with utmost
utmost accuracy Interpretation accuracy
Describe and illustrate the
different congruence Tools: Rubrics for
postulates for triangles. assessment of intellectually
Criteria: challenging situations
Illustrative formulated and worked out
Insightful
Significant
Application
Use the different triangle Create designs, sketches or
congruence postulates and models of real-life objects
other concepts in applying the different
formulating and finding conditions for triangle
solutions to intellectually congruence.

13

Mathematics

Criteria:
Adaptive
Efficient
Relevant

Perspective
Develop insights on what
makes two or more
triangles congruent.
Criteria:
Credible
Insightful
Perceptive
Revealing

Empathy
person feels whenever
he/she sees two or more
identical objects
.Criteria:
Receptive
Responsive
Sensitive

Self-Knowledge
a problem/situation
involving congruence of
triangles.
Criteria:
Reflective
Relevant
Flexible

14

Mathematics

Mathematics III


QUARTER II (Inequalities in a Triangle)

STANDARDS ESSENTIAL At the Level of
Product/
Content Performance Understanding Question Understanding Performance
Performance
The learner demonstrates The learner formulates The conditions for In what real-life Situations formulated Explanation Assessment of situations
understanding of the key intellectually triangle inequality can situations would you Discuss the relationships formulated based on the
concepts of Inequalities in challenging situations be applied in finding find the triangle • are intellectually between the sides of a following suggested criteria:
a Triangle. involving inequalities in solutions to inequality theorem challenging. triangle and how they are • intellectually challenging
a triangle and finds intellectually significant? • involve inequalities applied in real life. • situations involve
solutions using a challenging situations. in a triangle Criteria: inequalities in a triangle
variety of strategies • are worked out using Clear • situations are worked out
with utmost accuracy. a variety of Coherent using a variety of
strategies with Justified strategies with utmost
utmost accuracy Systematic accuracy

Describe the relationships assessment of intellectually
among the sides of a challenging situations
triangle and their formulated and worked out
importance in real-life
situations. Assessment using GRASPS:
Criteria:
Illustrative Make a proposal for the
Insightful construction of new roads in
Significant your locality and a

15

Mathematics

Application development plan for
Formulate and find rerouting scheme that would
solutions to intellectually minimize transportation
challenging situations using costs among residents.
the triangle inequality
theorem and other
concepts.
Criteria:
Adaptive
Efficient
Relevant

Perspective
Develop insights on how
triangles are formed.
Criteria:
Credible
Insightful
Perceptive
Revealing

Empathy
person feels whenever the
information or data,
materials that he needs, or
amount that he has are not
enough to perform or
complete a certain task.
Criteria:
Receptive
Responsive
Sensitive

Self-Knowledge
sharing knowledge on
triangle inequality and its
real-life applications.

16

Mathematics

Criteria:
Reflective
Relevant
Flexible

17

Mathematics

MATHEMATICS III

General Standard: The learner demonstrates understanding of key concepts and principles of number sense, shapes and sizes and their applications to solving real-life
problems involving geometric relationships.

QUARTER III(Quadrilaterals)
The learner The learner: Quadrilaterals have Where are Situations formulated: Explanation Assessment of situations
demonstrates • creates designs/ applications in real life quadrilaterals Discuss how the properties formulated based on the
understanding of the key models of that utilize such structural commonly found? • are intellectually of quadrilaterals are used in following suggested criteria:
concepts and properties the properties of designs, arts, etc. challenging designing certain objects
of Quadrilaterals. quadrilaterals. In what other • involve quadrilaterals and structures. • intellectually challenging
disciplines are they • are worked out using Criteria: • situations involve
• finds solutions to used? a variety of strategies Thorough quadrilaterals
intellectually with utmost accuracy. Coherent • situations are worked out
challenging Clear using a variety of
situations involving strategies with utmost
quadrilaterals by Interpretation accuracy.
applying a variety of Describe the differences
strategies with between/among special Tools: Rubrics for
utmost accuracy. parallelograms in terms of assessment of intellectually
the properties of their challenging situations
diagonals. formulated and worked out
Criteria:
Thorough Authentic Performance
Illustrative Task/s using G.R.A.S.P.S
Creative
Create three-dimensional
Application artworks using
Create models using the quadrilaterals.
properties of quadrilaterals.
Criteria:
Appropriate
Practical
Accurate
Relevant

18

Mathematics

Perspective
Develop insights on the
properties of quadrilaterals.
Criteria:
Perceptive
Open-minded
Sensitive
Responsive

Empathy
Show empathy by citing the
importance of quadrilaterals
in our daily lives.
Criteria:
Open
Sensitive
Responsive

Self-Knowledge
Manifest understanding of
quadrilaterals by citing its
importance in real-life.
Criteria:
Reflective
Responsive
Relevant

19

Mathematics

MATHEMATICS III
General Standard: The learner demonstrates understanding of key concepts and principles of number sense, shapes and sizes and their applications to solving real life

QUARTER III (Similarity)

The learner demonstrates The learner Knowledge of How is the Solutions to Explanation Assessment of situations formulated
understanding of the key creates, similarity is concept of situations involving Discuss similarities of figures such as based on the following suggested
concepts of Similarity. investigates, applied in finding similarity similarity of triangles and other polygons. criteria:
analyzes and dimensions of applied in real triangles are Criteria:
solves structures with the life? presented using Thorough • intellectually challenging
mathematical use of a scale mathematical Accurate • situations involve quadrilaterals
situations model. models. Justified • situations are worked out using a
involving similarity variety of strategies with utmost
through Interpretation accuracy.
appropriate and Describe how similar figures are seen and
accurate used in real life. Tools: Rubrics for assessment of
representations. Criteria: solutions to intellectually challenging
Illustrative situations
Meaningful
Justified Authentic Performance Task/s using
G.R.A.S.P.S
Application
Find solutions to intellectually challenging
. situations using the concept of similarity.
Criteria:
Appropriate
Practical
Accurate

Perspective
Develop appreciationof the applications of
similarity in the environment.
Criteria:

20

Mathematics

Appropriate
Practical

Empathy
Describe one’s feelings whenever he/she
sees identical objects.
Criteria:
Sensitive
Perceptive
Openness

Self-Knowledge
Manifest understanding by stating the
usefulness of similarity in solving
problems and in creating scale models of
objects.
Criteria:
Reflective
Responsive
Relevant

21

Mathematics

MATHEMATICS III

QUARTER IV (Circles)
The learner The learner Many engineering How is knowledge Situations Explanation Assessment of situations formulated
demonstrates creates, analyzes and architectural about circles and formulated: Discuss how arcs of a circle and central based on the following suggested criteria:
understanding and finds solutions designs involve other related terms and inscribed angles are measured
of key to intellectually arcs of a circle and applied in real-life? • are using models. • intellectually challenging
concepts of challenging central and intellectually Criteria: • situations involve circles
circles. situations involving inscribed angles. challenging. Thorough • situations are worked out through
circles and other • involve circles Coherent appropriate and accurate
related terms in • are worked out Clear representations
disciplines such as through
art, engineering, appropriate and Interpretation Tools: Rubrics for assessment of
architecture, accurate Describe the measures of arcs of a intellectually challenging situations
business, etc representations circle and inscribed and central angles formulated and worked out
through appropriate and explain the properties of chords,
and accurate secants, tangents, etc. Authentic Performance Task/s using
representations. Criteria: G.R.A.S.P.S
Thorough
Illustrative
Creative

Application
Find solutions to intellectually
challenging situations involving arcs of
a circle, central and inscribed angles,
chords, secants, tangents, etc.
Criteria:
Appropriate
Practical
Accurate
Relevant

22

Mathematics

Perspective
Develop insights on arcs of a circle,
central and inscribed angles, chords,
secants, tangents, etc.
Criteria:
Perceptive
Open-minded
Sensitive
Responsive

Empathy
Describe the difficulties one can
experience in an environment without
circles.
Criteria:
Open
Sensitive
Responsive

Self-knowledge
Manifest understanding by giving the
best solution to a real-life
problem/situation.
Criteria:
Reflective
Responsive
Relevant

23

Mathematics

MATHEMATICS III

QUARTER IV (Plane Coordinate Geometry)
The learner The learner Coordinate How are the Situations Explanation Assessment of situations formulated
demonstrates geometry has wide concepts of plane formulated: Discuss how the coordinate system is based on the following suggested criteria:
understanding • creates, practical coordinate used in real life.
of the key analyzes and applications. geometry applied • are Criteria: • intellectually challenging
concepts of finds solutions to in the real world? intellectually Thorough • situations involve plane coordinate
plane intellectually challenging. Coherent geometry
coordinate challenging • involve plane Clear • situations are worked out through
geometry situations coordinate appropriate and accurate
involving plane geometry Interpretation representations
coordinate • are worked out Describe how the concepts of plane
geometry. through coordinate geometry help in giving Tools: Rubrics for assessment of
appropriate and directions. intellectually challenging situations
• uses the accurate Criteria: formulated and worked out
concepts of representations Thorough
plane coordinate . Illustrative Authentic Performance Task/s using
geometry in Creative G.R.A.S.P.S
disciplines such
as navigation, Application
architecture, Find solutions to intellectually
business, etc challenging situations involving plane
through coordinate geometry.
appropriate and
accurate Criteria:
representations. Appropriate
Practical
Accurate
Relevant

24

Mathematics

Perspective
Develop insights from the different
properties and theorems related to
plane coordinate geometry.
Criteria:
Perceptive
Open-minded
Sensitive
Responsive

Empathy
Describe the difficulties one can
experience in real life if he/she lost in an
unfamiliar place and could not follow
directions in the map.
Criteria:
Open
Sensitive
Responsive

Self-Knowledge
Manifest understanding by giving
his/her best solution to a
problem/situation involving plane
coordinate geometry.
Criteria:
Reflective
Responsive
Relevant

25

Mathematics

Appendix

Resources:
ICT Tools
• http://www.deped.gov.ph/iSchool Web Board/Math Web Board
• http://www.deped.gov.ph/iSchool Web Board/skoool.ph
• http://www.deped.gov.ph/e-turo
• http://www.deped.gov.ph/BSE/iDEP
• http://www.pjoedu.wordpress/Philippine Studies/FREE TEXTBOOKS
• http://www.teacherplanet.com
• http://www.pil.ph/innovative teachers leadership award
• http://www.alcob.com/ICT Model School Network
• http://www.APEC Cyber Academy.com
• http://www.globalclassroom.net
• http://www.think.com
• http://www.rubistar.com
• Overhead projector/transparencies
• Computer/PC tablet/Interactive Whiteboard
• Graphing calculator
• CONSTEL CD/DVD materials
• CAI materials in CD/DVD format
• Intel Teach to the Future/ASEAN SchoolNet/FIT-ED/SMART School/Innovative Teachers Leadership
Award/sKwela/iSchool/Learn.ph/eskwelangbayan modules in PowerPoint format
• Authoring-enabled math storytelling enrichment modules ( e.g. Fibo the Frog Mathemajess’yan, etc.)
• Video clips/tapes
• Interactive digital games/puzzles (e.g. eDamath, 3D damath gaming, Cartesian coordinate system, etc.)
• E-TV episodes (Knowledge Channel, National Geographic Channel, Discovery Channel, BBC, etc.)
• Online/offline open-source teaching/learning materials
• Student/teacher-made PowerPoint/spreadsheet/word instructional materials with Hyperlinks
• Student/teacher-made webcam/digicam math storytelling materials
• Mathematical simulations

26

Mathematics

• Interactive flowchart/concept map/tree diagram/picture problem situation/secret message decoder
• Digital mathematical cartoon strips/humor/jokes/poster with hyperlinks
• eBooks/eTeachers manual with no hyperlinks
• Digital books/teaching guides with hyperlinks

Manipulative
• Games and puzzles (e.g. damath, chess-math, sungkamath, Sudoku, cross-number puzzle, etc.)
• Geoboard/rubber bands/strings
• Algebra tiles
• Cuisenaire rod
• Dice
• Domino/triangular domino
• Playing cards
• Mathemagic biscuit crackers (e.g. opposite sense in integers, etc.)

Print Materials
• Worksheets
• Workbooks
• Textbooks/supplementary reference materials/teachers manual
• Consumer education/global warming and climate change integration lesson exemplars
• Remedial/enrichment modules (e.g. EASE modules, distance learning/self-learning package, etc.)
• Enrichment math storytelling modules with indigenous cartoon characters (e.g. Max the Matrix & Co., etc.)
• Handouts/Activity Sheets/Cards
• Mathematical post card / mathematical cartoon strips/humors/quotes/jokes/jingle/slogan/themes/tarpaulin

Supplies and Materials
• Papers (graphing, bond, pad, manila, colored)
• School Supplies (Ruler/straightedge, Colored cartolina , Illustration board , Pairs of scissors, Masking tapes,Pentel pen)

27

2010 sec yeariiicurriculumguidemathematics

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