Math 8 Syllabus

La Consolacion University Philippines

I. SUBJECT SYLLABUS: Mathematics 8

II. CURRICULUM:

K to 12III. SUBJECT DESCRIPTION:

Mathematics 8 deals with key concepts and skills under the K-12 curriculum namely number sense, measurement, algebra, geometry, probability and statistics. Specifically, Grade 8 students are expected to manifest mastery on special products and factors, rational algebraic expressions, relations and functions, system of linear equations and inequalities in two variables, axiomatic development of geometry, triangle congruence and inequalities in a triangle, measures of variability and basic concepts of probability. These concepts are being applied in solving problems for the students to develop analytical and critical thinking. Values are also integrated in order for the students to be developed not only intellectually but also morally and spiritually.

Pre requisite:

Mathematics 7Number of Units:1.0

IV. GRADE LEVEL STANDARD:The learner demonstrates understanding of key concepts and principles of algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. V. GENERAL OBJECTIVES:At the end of Grade 8, the students are expected to demonstrate understanding of concepts and skills related to quadratic equations, quadratic functions, inequalities, rational algebraic equation, variation, radical exponents, similarity, quadrilaterals and triangle trigonometry and others and apply them in solving problems. VI. DAILY ROUTINE: Opening and Closing Prayer

Checking of Uniform and ID

Checking of Attendance

Checking of the Cleanliness of the room

Presentation of Specific Learning Objectives

Motivation/Recall/ReviewFIRST QUARTER Quarter Objectives: At the end of the First Quarter, the students are expected to:1. recognize special products and factor polynomials. 2. perform operations on rational expressions.3. manifest patience an critical thinking ind solving special products and multiplication of polynomials. Content Standards:

The learner demonstrates understanding of key concepts of special products and factors of polynomials and operations rational expressions.

Performance Standards:

The learner is able to recognize special products and factor polynomials, perform operations on rational expressions, manipulate algebraic expressions with integral exponents.

LEARNING OBJECTIVESCONTENTSAPPROXIMATE WEEK ALLOTMENTSUGGESTED LEARNING ACTIVITIESSUGGESTED INSTRUCTIONAL MATERIALSPOSSIBLE VALUES TO BE INTEGRATEDSUGGESTED PERFORMANCE TASKREMARKS

At the end of the First Quarter, the students are expected to:1. identify polynomials which are special products: polynomials with common monomial factors, trinomials that are squares of binomials, trinomials that are products of the sum and difference of two terms, and trinomials that are products of two binomials1.Special Products and Factors1.1. Identifying Special Products

Week 1-2 Discussion Guided Discovery

Think pair

Drill

Comparing and Contrasting

Consolidation and Pratice LCD

Laptop OHP

Manila Paper

Cartolina

Analytical and

Critical Thinking

Patience

Cooperation Oral Recitation

Quiz

Work Sheets

2. find special products of: square of a binomial, square of a multinomial, sum and difference of two terms, cube of a binomial, and product of the special case of multiplying a binomial and a trinomial. 3. Solve problems that involve polynomials and their products

1.2. Square of a Binomial

1.3. Square of a Multinomial

1.4. Product of the Sum and Difference of two terms

1.5. Cube of a Binomial

1.6. Product of the special case of multiplying a binomial and a trinomial.

Week 3-4 Mental Calculation Individual Practice LCD Laptop Cartolina Manila Paper

OHP Fairness Teamwork

Respect Think Pair (Students will be paired and ask them to solve problems in pair)

Quiz

Book Activity

4.factors completely different types of polynomials (polynomials with common monomial factors, difference of two squares, perfect square trinomials, sum and difference of two cubes,and general trinomials) using special formulas, grouping and other techniques. 5. solve problems that involve polynomials and their products.

1.7. Common Monomial Factor1.8. Factors of Difference of Two Squares1.9. Factors of the Perfect Square Trinomial

1.10. Factors of Quadratic Trinomials1.11. Factors of Sum or Difference of Two Cubes

Week 5-6 Discussion

Comparing and Contrasting Mental Mathematics

Group work LCD

Laptop Cartolina Manila Paper

OHP Tolerance Focus

Positive

outlook

Creativity

Persistence Board

Work

Book

activity

Quiz

Integration Period and 1st Periodical TestWeek 7-8

SECOND QUARTER

Quarter Objectives:

At the end of the Second Quarter, the students are expected to:

1. demonstrate knowledge and skills in rectangular coordinate system, relations and functions;

2. solve problems involving rectangular coordinate system, relations and functions and

3. manifest the value of analytical and critical thinking, patience, perseverance, hard work and determination.

Content Standards:

The learner demonstrates understanding of key concepts of linear functions and their graphs, linear equations and inequalities.


The learner is able to explore the rectangular coordinate system, explore the concept of a relations and a function, explore the linear function, its equation and graph, graph linear inequalities in two variables, explore and solve systems of linear equations and inequalities in two variables.

LEARNING OBJECTIVESCONTENTSAPPROXIMATE WEEK ALLOTMENTSUGGESTED LEARNING ACTIVITIESSUGGESTED INSTRUCTIONAL MATERIALSPOSSIBLE VALUES TO BE INTEGRATEDSUGGESTED PERFORMANCE TASKREMARKS

At the end of the Second Quarter, the students are expected to:

1. Review basic concepts and skills of fraction

2. Define and illustrate rational expressions

3. Simplify rational expressions

4. Solve problems involving simplification of rational expressions

2. Rational Algebraic Expression2.1. Reviewing Fractions

2.2. Simplifying Rational Expressions

Week 1 Discussion

Guided Discovery

Following directions

LCD

Laptop Cartolina Manila Paper

OHP Respect for Others

Self- Confidence

Responsibility in Doing Ones Work

Sharing The students will be asked to look for a partner and solve the given activity by the teacher.

Book Activity

Quiz

4. Review concepts and skills related to positive exponents

5. Define and interpret zero and negative exponents

6. Evaluate algebraic expressions involving integral exponents

7. Simplify algebraic expressions involving integral exponents3. Algebraic Expressions with Integral Exponents

3.1. Reviewing the Concepts Related to Positive Integral Exponents

3.2. Zero and Negative ExponentsWeek 2-3 Drill and review

Discussion LCD

Laptop Cartolina OHP Law and Order

Paradigm Shift Recitation

Seatwork

Quizzes

Homework

8. Describe the rectangular coordinate system and its uses

9. Define and illustrate the coordinate axes, the origin and a point on the coordinate plane

10. Describe and plot positionsRelations and Functions4.1. The Rectangular Coordinate SystemWeek 4 Word Analysis

Discussion Trivia questions

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Love and Peace

Heroism

Respect Quiz

Worksheet

11. Define and illustrate relations

12. Define and illustrate a function

13. Determine if a given relation is a function using a table of ordered pairs, graphs and equations

14. Differentiate between dependent and independent variables

15. Define and describe the domain and range of a variable4.2. Relations

4.3. FunctionsWeek 5 Discussion

Real life situations demonstration

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Friendship Individuality and Society Seatwork, Quiz , Worksheet

16. Sketch the graph of the functions

17. Determine the domain and range of the functions

18. Determine whether the graph of a relation is a function or not

19. Determine the sum, difference product, and quotient of two functions and determine the domain of resulting relation

20. Find the composition of two functions and determine its domain

4.4. Graphs of Functions

4.5. Operations with FunctionsWeek 6 Exposition

Cooperative learning

Vocabulary building

Discovery learning Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Positive outlook

Reflection

Cooperation Quiz Group work Worksheet

Board Work

21. Define and describe a linear function using its points, equation, and graph

22. Find the domain and range of a linear function

23. Define and illustrate the meaning of a slope of a line

24. Find the slope of a line given two points, a table of values or list of ordered pairs, its equation and graph

25. Graph a linear function given (a) any two points; (b) the x- and y-intercepts; (c) the slope and a point on the line

26. Characterize the graph of a linear function in terms of its intercepts and slope Linear Functions

5.1. Definition of Linear Function5.2. Graph of Linear FunctionWeek 7 Practical Work

Guided learning discovery

Cooperative Learning Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Cooperation Aesthetic beauty

Perseverance Worksheet Seatwork Quizzes

Homework

Portfolio of Graphs

27. Write linear equation Ax+By=C in the form y=mx+b, and vice versa

28. Find the equation of a line given (a) two points; (b) the slope and a point; (c) the slope and its intercept5.3. Equations of Linear FunctionsWeek 8 Exposition

Mathematical Investigation

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP Orderliness

Perseverance Seatwork

Worksheet

Quiz

29. Solve problems involving linear functions and linear patterns 5.4. Problems Involving Linear Functions and Linear Patterns Discussion

Graphic Organizer Blackboard

Chalk

Eraser

Cartolina

OHP Promote recycling and saving

Integration Period & 2nd Periodical Test

Proposed Projects / Activities:

Puzzle and game boards integrating the concept learned in rational expression.

THIRD QUARTER

Quarter Objectives:

At the end of the Third Quarter, the students are expected to:

1. demonstrate knowledge and skills in axiomatic development of geometry, triangle congruence and inequalities in triangles ;

2. apply the concepts of triangle congruence and inequalities in triangles; and

3. manifest the value of analytical and critical thinking skills, patience, determination, honesty, hard work and love for knowledge.

Content Standards:

The learner demonstrates understanding of axiomatic development of geometry, triangle congruence, inequalities in triangles and parallel and perpendicular lines.


The learner is able to engage in formal arguments, reason and proof, prove triangle congruence, explore situations involving inequalities in triangles, prove results involving parallel and perpendicular lines.

LEARNING OBJECTIVESCONTENTSAPPROXIMATE TIME ALLOTMENTSUGGESTED LEARNING ACTIVITIESSUGGESTED LEARNING MATERIALSPOSSIBLE VALUES TO BE INTEGRATEDSUGGESTED EVALUATIVE ACTIVITIESREMARKS

At the end of the Third Quarter, the students are expected to:

1. Define and describe systems of linear equation using practical situations and mathematical expressions

2. Identify which given systems of linear equations have graphs that are parallel, that intersect, and that coincide

3. Graph systems of linear equations

4. Solve systems of linear equation by graphing

5. Solve systems of linear equation by substitution

6. Solve systems of linear equation by elimination

7. Solve systems of linear equations by using determinants

Systems of Linear Equations and Inequalities in Two Variables6.1. Systems of Linear Equations in Two Variables6.2. Solving Systems of Linear Equations by Graphing6.3. Solving Systems of Linear Equations by Substitution

6.4. Solving Systems of Linear Equations by Elimination

6.5. Solving Systems of Linear Equations by using determinants

Week1 & 2 Discussion

Association Real life translation

Practical Work

Exposition Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Patience Respect

Good Health

Morality Quiz

Seatwork Review/Drill

Homework

6.6. Solving Problems Involving Systems of Linear Equations6.7. Linear Inequalities in Two Variables

6.8. Systems of Linear InequalitiesWeek 3 Discussion

Board Work

Solving

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

9. write rules or formulas involving inverse variation;

10. identify the constant of variation;

11. evaluate formulas involving inverse variation;

12. express inverse property as a proportion;

13. solve verbal problemsAxiomatic Development of Geometry7.1. Conditional and Biconditional Statements7.2. Reasoning in Geometry

7.3. Undefined Terms, Postulates and Theorems

Week 4 Discussion

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Cooperation

Responsibility Quiz

Seatwork

14. determine the constant of variation;

15. solve problems involving joint variationTriangle Congruence8.1. Conditions for Triangle Congruence Week 5 & 6 Discussion

Guided Discovery Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Cooperation

Patience

Determination

Self-Confidence

Quiz

Seatwork

16. simplify and evaluate numerical expressions involving integral exponents (positive, negative, zero);

17. rewrite algebraic expressions with zero and negative exponents and be able to simplify them;8.2. Applying the Conditions for Triangle CongruenceWeek 7 & 8 Discussion

Problem Analysis

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Analytical and Critical thinking

Love for Knowledge

Responsibility in doing ones work

Cooperation Group Activity

Seatwork

Quiz

18. define radical expressions;

19. name and describe the parts of radical expression;

20. rewrite 8.3. Congruence in an Isosceles Triangle Discussion


Chalk

Eraser

Manila Paper

Cartolina Responsibility

Patience

Determination Group Activity

Worksheet

Seatwork

Integration Period and 3rd Periodical Test

Proposed Projects / Activities:

The Multinomial Theorem

Sing Me A Math Song

Quiz Bee

FOURTH QUARTER

Quarter Objectives:

At the end of the Fourth Quarter, the students are expected to: 1. demonstrate knowledge and skills in variability and probability;

2. solve problems involving variability and probability; and

3. manifest the value of analytical and critical thinking, patience, hard work, determination, honesty, cooperation and responsibility.

Content Standards:

The learner demonstrates understanding of key concepts of measures of variability of data and basic concepts of probability.


The learner is able to explore the concept of measure of variability, discuss the basic concepts of probability and solve simple problems involving probabilities of events.

LEARNING OBJECTIVESCONTENTSAPPROXIMATE TIME ALLOTMENTSUGGESTED LEARNING ACTIVITIESSUGGESTED LEARNING MATERIALSPOSSIBLE VALUES TO BE INTEGRATEDSUGGESTED EVALUATIVE ACTIVITIESREMARKS

At the end of the Fourth Quarter, the students are expected to:1. Apply the postulates and theorems on triangle congruence involving overlapping triangles

2. Apply the postulates and theorems to right triangle congruence to prove statements on congruence involving parts of right triangles

8.4. Overlapping Triangles

8.5. Right Triangle Congruence and Problems Involving Altitudes and MediansWeek 1-2 Discussion


Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP

Analytical and Critical Thinking

Cooperation


Simplicity Quiz

Seatwork

Book Activity

3. Apply theorems concerning bisectors and perpendicular lines to prove statements on congruence8.6. Theorems Concerning Bisectors and Perpendicular LinesWeek 3 Discussion

Drill

Derivation

Blackboard

Chalk

Eraser

Manila Paper

Cartolina

OHP


Self-Confidence

Sharing ones knowledge to others The students will be asked to solve by twos and discuss their answers to the whole class

4. State and illustrate the theorems on triangle inequalities5. Apply the theorems on triangle inequalities to:

a. determine possible measures for the angles and sides of triangles

b. justify claims about the unequal relationships between sides and angle measure

c. apply theorems on triangle inequalities to prove results involving triangle inequalities

6. Define parallel and perpendicular lines7. Illustrate and prove properties of parallel lines

8. Determine and prove the conditions under which lines and segments are parallel or perpendicular

9. Recall the different kinds of quadrilaterals and identify those that are parallelograms

10. Determine the conditions that makes quadrilateral a parallelogram

11. Use properties to find measures of angles, sides, and other quantities involving parallelogram

8.7. Inequalities in Triangle

8.8. Parallel and Perpendicular Lines

8.9. Quadrilaterals Week 4 Discussion



Chalk

Eraser

Manila Paper

Cartolina

OHP


Willingness to Learn

Cooperation


Self-Confidence Seatwork

Quiz

Work sheet

12. Recall the meaning and interpretation of the mean, median, and mode of ungrouped and extend them to group dataMeasures of Variability

9.1. Reviewing Measures of Central Tendency

Week 5 Discussion



Chalk

Eraser

Manila Paper

Cartolina

OHP



Cooperation



Quiz

Work sheet

13. Discuss the meaning of variability

14. Calculate the different measures of variability of a given set of data

a. Range

b. Average deviation

c. Standard deviation

15. Describe a set of data using measures of central tendency and measures of variability9.2. Measures of DispersionWeek 6 Discussion



Chalk

Eraser

Manila Paper

Cartolina

OHP



Cooperation



Quiz

Work sheet

16. Define an experiment, outcome, sample space and event

17. Count the number of occurrence of an outcome in an experiment and organize them using a diagram, systematic listing and the fundamental counting principle

18. Define and discuss the probability of an event

19. Interpret the meaning of experimental probability of an event

20. Differentiate between an experimental probability and theoretical probability

21. Solve simple problems involving probabilities of events 9.3. The Fundamental Principle of Counting

9.4. Probability of an EventWeek 7 Discussion



Chalk

Eraser

Manila Paper

Cartolina

OHP



Cooperation



Quiz

Work sheet

Integration Period and 4th Periodical Test

REFERENCES

A. Printed References

Diaz, Z. B. & Mojica, M. P., et. al (2013) Next century mathematics 8. Quezon City: Phoenix Publishing House, Inc.Glorial, J.C. & Guadayo, J. L., et. al (2013) 21st century mathematics: A vision for a better future. Quezon City: Phoenix Publishing House, Inc.Catan, Sr. C.M., OSA, De Jesus, M. B. B.,Gonzales, Rev. Fr. R. B.,MS and Dulay, Sr. L. M.,ICM.(2002) Transformative education: a source book for basic education Vol. 1. Quezon City: Phoenix Publishing House, Inc.

McConnel, J. W., et.al. (2002) Algebra - 2nd edition. Chicago, Illinois: Pearson Education Inc.

Orines, F. B. and Mendoza, M. O.(2003) Intermediate algebra. Quezon City: Phoenix Publishing House, Inc.

Orines, F. B., Diaz, Z. E. and Mojica, M. P. (2007) Next century mathematics: intermediate algebra.

Quezon City: Phoenix Publishing House, Inc.

Oronce, O. A. and Mendoza, M. O.(2003) Exploring mathematics II: intermediate algebra. Manila: Rex

Printing Company, Inc.

Oronce, O. A. and Mendoza, M. O.(2007) e-Math II: intermediate algebra worktext in mathematics for second year high school. Manila: Rex Bookstore Inc.B. Internet References

Special Products. Retrieved May 30, 2014 from http://www.mathsisfun.com/algebra/special-binomial-products.html

Math Functions, Relations, Domain, and Range. Retrieved May 30, 2014 from

http://www.mathwarehouse.com/algebra/relation/math-function.phpEquations. Retrieved May 31, 2010 from http://en.wikibooks.org/wiki/Algebra#Equations_and_functions_.28second_year_algebra29Systems of Linear Equation. Retrieved May 31, 2010 from http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/linear.html

Absolute Value. Retrieved May 31, 2007 from http://www.purplemath.com/modules/systlin1.htm

Factoring Numbers. Retrieved May 31, 2007 from http://www.purplemath.com/modules/syslneq.htm

Solving Absolute Value. Retrieved May 31, 2007 from http://www.purplemath.com/modules/quadform.htm

Solving Linear Equations. Retrieved May 31, 2007 from http://www.purplemath.com/modules/fcns2.htm

Simplifying with Exponents. Retrieved May 31, 2007 from http://www.purplemath.com/modules/solvquad.htm

Graphing Radical Equations. Retrieved May 31, 2007 from http://www.purplemath.com/modules/variatn.htm Revised by:

Checked by:

Approved by:

Mr. Jeffrey M. Tinagan

Mr. Rorimar L. Mallari

Prof. Enrico F. RosalesMathematics Teacher

SAC Mathematics

BED Principal

Date of Revision: May 2014621

Documents

Math 8 Syllabus