2010 sec yeariiicurriculumguidemathematics

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2010 Secondary Education Curriculum Mathematics

DEPARTMENT OF EDUCATION Bureau of Secondary Education

Curriculum Development Division

2010 SECONDARY EDUCATION CURRICULUM

MATHEMATICS III

CURRICULUM GUIDE

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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 First Year Level

General Standard Second Year Level

General Standard Third Year Level

General Standard Fourth Year Level

The learner demonstrates understanding of key concepts and principles of number and number sense as applied to measuring, estimating, graphing, solving equations and inequalities, communicating mathematically and solving problems in real life.

The learner demonstrates understanding of key concepts and principles of number sense and patterns in solving equations, generalizing relationships and solving problems in real life.

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.

The learner demonstrates understanding of key concepts and principles of number sense, patterns and functions, data analysis and uses them in solving problems in real life.

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Mathematics Concept Matrix

First Year Second Year Third Year Fourth Year

Real Number System Measurements

Expressions with Rational Exponents Radical Expressions

Geometry of Shapes and Sizes Geometric Relations Writing Proofs

Relations and Functions Linear Functions Quadratic Functions

Algebraic Expressions

• Laws of Exponents

• Special Products and Factors

• Scientific Notation

Quadratic Equations Radical Equations

Perpendicular Lines and Parallel Lines Triangle Congruence Inequalities in a Triangle

Polynomial Functions Exponential and Logarithmic Functions

First-Degree Equations and Inequalities in One Variable Linear Equations and Inequalities in Two Variables

Rational Algebraic Expressionsand Equations Variations

Quadrilaterals Similarity

Circular Functions Trigonometric Identities and Equations

Systems of Linear Equations and Inequalities in Two Variables

Sequences and Series Circles Plane Coordinate Geometry

Counting Techniques and Probability Measures of Central Tendency and Variability

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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 At the Level of Content Performance Understanding Question

Product/ Performance Understanding Performance

The learner demonstrates understanding of the key concepts of Geometry of Shapes& Sizes.

The learner describes/illustrates plane figures, using models satisfactorily and formulates intellectually challenging situations involving geometric shapes and sizes then finds solutions using a variety of strategies with utmost accuracy.

Many real-life objects in the environment can be modeled geometrically.

How are geometric models reflected in many real-life objects?

Models created

• are drawn from real-life objects.

• illustrate different plane figures and solid figures.

Situations formulated

• are intellectually challenging.

• Involve geometry of shapes and sizes.

• are worked out using a variety of strategies with utmost accuracy.

Explanation Discuss the different properties of a given geometric figure and how it is seen and applied in real life.

Criteria: Clear Coherent Systematic Thorough

Interpretation Describe how the different geometric shapes are seen and used in the environment.

Criteria: Creative Illustrative Insightful Significant

Application Pose intellectually challenging situations involving geometry of shapes and sizes and solve

Assessment of models created based on the following suggested criteria:

• drawn from real-life objects

• models involve geometry of shapes and sizes

Tools: Rubrics for assessment of geometric models created Assessment of situations formulated based on the following suggested criteria:

• intellectually challenging

• situations involve geometry of shapes and sizes

• situations are worked out using a variety of strategies with utmost accuracy

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them.

Criteria: Adaptive Appropriate Authentic Efficient

Perspective Develop insights from the different properties observed from a given geometric shape including its value in real life.

Criteria: Credible Perceptive 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

Tools: Rubrics for assessment of intellectually challenging situations formulated and worked out

Assessment using GRASPS: Identify models of different geometric shapes as seen in many real-life objects (e.g. roller skates, kitchen utensils, product packaging, etc.). Create designs using different geometric shapes.

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QUARTER I (Geometric Relations)

Stage 1: Results/Outcomes Stage 2: Assessment STANDARDS ESSENTIAL At the

Level of Content

Performance Understanding Question


The learner demonstrates understanding of the key concepts of Geometric Relations.

The learner formulates intellectually challenging situations involving geometric relations and finds solutions using a variety of strategies with utmost accuracy.

Geometric relations that can be drawn from different plane figures facilitate the solution of intellectually challenging situations.

How are the different geometric relations used to find solutions to intellectually challenging situations involving plane figures?



• Involve geometric relations.


Explanation Discuss the relationships between and among angles and sides of a given geometric figure and how they are applied in real life.


Interpretation Describe the relationships between and among angles and sides of a given geometric figure and their importance in real life situations.

Criteria: Creative Illustrative Insightful Significant

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

Assessment of situations formulated based on the following suggested criteria:


• situations involve geometric relations



Assessment using GRASPS: Create designs, sketches or models of real-life objects applying the different geometric relations.

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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 Manifest understanding by assessing how one can give his/her best solution to a problem/situation involving geometric relations.

Criteria: Reflective

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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 geometric relationships.

QUARTER I (Writing Proofs)


STANDARDS ESSENTIAL At the Level of

Content

Performance Understanding Question Product/

Performance Understanding Performance

The learner demonstrates understanding of the key concepts of Writing Proofs.

The learner communicates mathematical thinking/ideas with coherence and clarity in formulating and finding solutions to intellectually challenging situations.

Deductive and inductive reasoning can be used to understand and to find solutions to intellectually challenging situations.

How can reasoning be used to understand and find solutions to intellectually challenging situations?



• Involve writing proofs.

• are worked out using deductive and inductive reasoning.

Explanation Discuss one’s thinking/ideas, reasoning, and points of view on a given situation. Criteria:

Clear Coherent Systematic Thorough

Interpretation Compare and contrast one’s thinking, reasoning, and points of view on a given situation.

Criteria: Illustrative Insightful Significant

Application



• situations involve writing proofs

• situations are worked out using deductive and inductive reasoning


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Determine mathematical relationships in real life and justify them.

Criteria: Adaptive Efficient Relevant

Perspective Share one’s reasoning and points of view about a given situation.


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.


Assessment using GRASPS: Create a situation involving group of people with different interests. Pose an issue related to the given situation for discussion and exchange of views.

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Mathematics III


QUARTERII (Perpendicular and Parallel Lines)

Stage 1: Results/Outcomes Stage 2: Assessment STANDARDS ESSENTIAL At the level of

Content Performance Understanding Question Product/

Performance Understanding Performance The learner demonstrates understanding of the key concepts of Perpendicular and Parallel Lines.

The learner formulates intellectually challenging situations involving perpendicular and parallel lines and finds solutions using a variety of strategies with utmost accuracy.

Geometric relationships between and among perpendicular and parallel lines can be applied in finding solutions to many intellectually challenging situations.

How are perpendicular and parallel lines used in many intellectually challenging situations?



• involve perpendicular and parallel lines.


Explanation Discuss the relationships that exist between and among perpendicular and parallel lines as they are seen in some real-life objects/situations.


Interpretation Describe the relationships between and among perpendicular and parallel lines and their importance in real-life situations.


Application Use the different properties and theorems on



• situations involve perpendicular and parallel lines


Tools: Rubrics for assessment of intellectually challenging situations formulated and worked out Assessment using GRASPS: Make a school development plan that focuses on improvement of facilities like buildings or classrooms, roads, and other services. Discuss the importance of using perpendicular and parallel lines in the plan.

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perpendicular and parallel lines and other concepts in formulating and finding solutions to intellectually challenging situations.


Perspective Develop insights from the different properties and theorems related to perpendicular and parallel lines.


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 Manifest understanding by assessing how one can give his/her best solution to a problem/situation

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involving parallel and perpendicular lines.


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Mathematics III


QUARTER II (Triangle Congruence)


STANDARDS ESSENTIAL At the Level of Content


Product/ Performance

Understanding Performance

The learner demonstrates understanding of the key concepts of Triangle Congruence.

The learner formulates intellectually challenging situations involving congruent triangles and finds solutions using the different conditions for triangle congruence with utmost accuracy.

Many real-life objects can be made by adopting different designs that are generated using congruent triangles.

How are the different conditions for triangle congruence applied in finding solutions to intellectually challenging situations?



• involve triangle congruence

• are worked out using a variety of strategies with utmost accuracy

Explanation Discuss the conditions that make triangles congruent. Criteria:

Clear Coherent Justified Systematic

Interpretation Describe and illustrate the different congruence postulates for triangles. Criteria:

Illustrative Insightful Significant

Application Use the different triangle congruence postulates and other concepts in formulating and finding solutions to intellectually challenging situations.



• situations involve triangle congruence



Assessment using GRASPS: Create designs, sketches or models of real-life objects applying the different conditions for triangle congruence.

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Perspective Develop insights on what makes two or more triangles congruent. Criteria:

Credible Insightful Perceptive

Revealing

Empathy Show empathy on what a person feels whenever he/she sees two or more identical objects .Criteria:

Receptive Responsive Sensitive

Self-Knowledge Manifest understanding by assessing how one can give his/her best solution to a problem/situation involving congruence of triangles. Criteria:

Reflective Relevant Flexible

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Mathematics III


QUARTER II (Inequalities in a Triangle)


STANDARDS ESSENTIAL At the Level of Content


Product/ Performance

Understanding Performance

The learner demonstrates understanding of the key concepts of Inequalities in a Triangle.

The learner formulates intellectually challenging situations involving inequalities in a triangle and finds solutions using a variety of strategies with utmost accuracy.

The conditions for triangle inequality can be applied in finding solutions to intellectually challenging situations.

In what real-life situations would you find the triangle inequality theorem significant?



• involve inequalities in a triangle

• are worked out using a variety of strategies with utmost accuracy

Explanation Discuss the relationships between the sides of a triangle and how they are applied in real life.

Criteria: Clear Coherent Justified Systematic

Interpretation Describe the relationships among the sides of a triangle and their importance in real-life situations.




• situations involve inequalities in a triangle



Assessment using GRASPS: Make a proposal for the construction of new roads in your locality and a

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Application Formulate and find solutions to intellectually challenging situations using the triangle inequality theorem and other concepts.


Perspective Develop insights on how triangles are formed.

Criteria: Credible Insightful Perceptive

Revealing

Empathy Show empathy on what a 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 Manifest understanding by sharing knowledge on triangle inequality and its real-life applications.

development plan for rerouting scheme that would minimize transportation costs among residents.

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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)



Performance Understanding Performance The learner demonstrates understanding of the key concepts and properties of Quadrilaterals.

The learner:

• creates designs/ models of that utilize the properties of quadrilaterals.

• finds solutions to intellectually challenging situations involving quadrilaterals by applying a variety of strategies with utmost accuracy.

Quadrilaterals have applications in real life such structural designs, arts, etc.

Where are quadrilaterals commonly found? In what other disciplines are they used?

Situations formulated:

• are intellectually challenging

• involve quadrilaterals


Explanation Discuss how the properties of quadrilaterals are used in designing certain objects and structures. Criteria: Thorough Coherent Clear

Interpretation Describe the differences between/among special parallelograms in terms of the properties of their diagonals. Criteria: Thorough Illustrative Creative

Application Create models using the properties of quadrilaterals. Criteria: Appropriate Practical Accurate Relevant



• situations involve quadrilaterals

• situations are worked out using a variety of strategies with utmost accuracy.

Tools: Rubrics for assessment of intellectually challenging situations formulated and worked out Authentic Performance Task/s using G.R.A.S.P.S Create three-dimensional artworks using quadrilaterals.

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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

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MATHEMATICS III


QUARTER III (Similarity)


STANDARDS ESSENTIAL At the level of Content Performance Understanding Question


The learner demonstrates understanding of the key concepts of Similarity.

The learner creates, investigates, analyzes and solves mathematical situations involving similarity through appropriate and accurate representations.

Knowledge of similarity is applied in finding dimensions of structures with the use of a scale model.

How is the concept of similarity applied in real life?

Solutions to situations involving similarity of triangles are presented using mathematical models.

.

Explanation Discuss similarities of figures such as triangles and other polygons. Criteria: Thorough Accurate Justified

Interpretation Describe how similar figures are seen and used in real life. Criteria: Illustrative Meaningful Justified

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:



• situations involve quadrilaterals

• situations are worked out using a variety of strategies with utmost accuracy.

Tools: Rubrics for assessment of solutions to intellectually challenging situations Authentic Performance Task/s using G.R.A.S.P.S

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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

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MATHEMATICS III


QUARTER IV (Circles)



Performance Understanding Performance The learner demonstrates understanding of key concepts of circles.

The learner creates, analyzes and finds solutions to intellectually challenging situations involving circles and other related terms in disciplines such as art, engineering, architecture, business, etc through appropriate and accurate representations.

Many engineering and architectural designs involve arcs of a circle and central and inscribed angles.

How is knowledge about circles and other related terms applied in real-life?



• involve circles

• are worked out through appropriate and accurate representations

Explanation Discuss how arcs of a circle and central and inscribed angles are measured using models. Criteria: Thorough Coherent Clear

Interpretation Describe the measures of arcs of a circle and inscribed and central angles and explain the properties of chords, secants, tangents, etc. Criteria: 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


• intellectually challenging • situations involve circles

• situations are worked out through appropriate and accurate representations


Authentic Performance Task/s using G.R.A.S.P.S

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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

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MATHEMATICS III


QUARTER IV (Plane Coordinate Geometry)



Performance Understanding Performance The learner demonstrates understanding of the key concepts of plane coordinate geometry

The learner

• creates, analyzes and finds solutions to intellectually challenging situations involving plane coordinate geometry.

• uses the concepts of plane coordinate geometry in disciplines such as navigation, architecture, business, etc through appropriate and accurate representations.

Coordinate geometry has wide practical applications.

How are the concepts of plane coordinate geometry applied in the real world?



• involve plane coordinate geometry

• are worked out through appropriate and accurate representations.

Explanation Discuss how the coordinate system is used in real life. Criteria: Thorough Coherent Clear

Interpretation Describe how the concepts of plane coordinate geometry help in giving directions. Criteria: Thorough Illustrative Creative

Application Find solutions to intellectually challenging situations involving plane coordinate geometry. Criteria: Appropriate Practical Accurate Relevant


• intellectually challenging • situations involve plane coordinate

geometry

• situations are worked out through appropriate and accurate representations


Authentic Performance Task/s using G.R.A.S.P.S

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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

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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

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• 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)

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