Math Curriculum Guide Grades 1-10 December 2013 PDF
Math Curriculum Guide Grades 1-10 December 2013 PDF
Math Curriculum Guide Grades 1-10 December 2013 PDF
Department of Education
DepEd Complex, Meralco Avenue
Pasig City
K to 12 Curriculum Guide
MATHEMATICS
(Grade 1 to Grade 10)
December 2013
K to 12 BASIC EDUCATION CURRICULUM
CONCEPTUAL FRAMEWORK
Mathematics is one subject that pervades life at any age and in any circumstance. Thus, its value goes beyond the classroom and the school. Mathematics
as a school subject, therefore, must be learned comprehensively and with much depth.
The twin goals of mathematics in the basic education levels, K-10, are Critical Thinking and Problem Solving.
Critical thinking, according to Scriven and Paul (1987) is the intellectually disciplined process of actively and skilfully conceptualizing, applying, analyzing,
synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.
On the other hand, according to Polya (1945 & 1962), mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to a
problem that is unknown.
These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills and processes, desirable values and
attitudes, and appropriate tools, taking into account the different contexts of Filipino learners.
There are five content areas in the curriculum, as adopted from the framework prepared by MATHTED & SEI (2010): Numbers and Number Sense, Measurement,
Geometry, Patterns and Algebra, and Probability and Statistics.
The specific skills and processes to be developed are: knowing and understanding; estimating, computing and solving; visualizing and modelling; representing and
communicating; conjecturing, reasoning, proving and decision-making; and applying and connecting.
The following values and attitudes are to be honed as well: accuracy, creativity, objectivity, perseverance, and productivity.
We recognize that the use of appropriate tools is necessary in teaching mathematics. These include: manipulative objects, measuring devices, calculators and
computers, smart phones and tablet PCs, and the Internet.
We define context as a locale, situation, or set of conditions of Filipino learners that may influence their study and use of mathematics to develop critical thinking and
problem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, as well as the learners prior knowledge and
experiences.
The framework is supported by the following underlying learning principles and theories: Experie ntial and Situated Learning, Reflective Learning, Constructivism,
Cooperative Learning and Discovery and Inquiry-based Learning. The mathematics curriculum is grounded in these theories.
Experiential Learning as advocated by David Kolb is learning that occurs by making sense of direct everyday experiences. Experiential Learning theory defines learning
as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience"
(Kolb, 1984, p. 41). Situated Learning, theorized by Lave and Wenger, is learning in the same context in which concepts and theories are applied.
Reflective Learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations. Deeper learning occurs when
learners are able to think about their experiences and process these, allowing them the opportunity to make sense of and derive meaning from their experiences.
Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connect them to new
ideas.
Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task.
The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery Learning and Inquiry-based Learning
(Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships, and concepts.
Mathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic, and reasoning. Mathematics is also a tool of science
and a language complete with its own notations and symbols and grammar rules, with which concepts and ideas are effectively expressed.
The contents of mathematics include Numbers and Number Sense, Measurement, Geometry, Patterns & Algebra and Statistics and Probability.
Numbers and Number Sense as a strand include concepts of numbers, properties, operations, estimation, and their applications.
Measurement as a strand includes the use of numbers and measures to describe, understand, and compare mathematical and concrete objects. It focuses on
attributes such as length, mass and weight, capacity, time, money, and temperature, as well as applications involving perimeter, area, surface area, volume, and angle
measure.
Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoning, and geometric modelling and
proofs.
Patterns and Algebra as a strand studies patterns, relationships, and changes among shapes and quantities. It includes the use of algebraic notations and
symbols, equations, and most importantly, functions, to represent and analyze relationships.
Statistics and Probability as a strand is all about developing skills in collecting and organizing data using charts, tables, and graphs; understanding, analyzing and
interpreting data; dealing with uncertainty; and making predictions about outcomes.
The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it pro vides necessary concepts and life
skills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens of the Philippines.
K3 46 7 10
At the end of Grade 6, the learner demonstrates At the end of grade 10, the learner
At the end of Grade 3, the learner demonstrates understanding and appreciation of key concepts and skills demonstrates understanding and appreciation of key
understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers, concepts and skills involving numbers and number sense
involving numbers and number sense (whole numbers up number theory, fractions, decimals, ratio and proportion, (sets and real numbers); measurement (conversion of
to 10,000 and the four fundamental operations including percent, and integers);measurement (time, speed, units); patterns and algebra (linear equations and
money, ordinal numbers up to 100th, basic concepts of perimeter, circumference and area of plane figures, inequalities in one and two variables, linear functions,
fractions); measurement (time, length, mass, capacity, volume and surface area of solid/space figures, systems of linear equations, and inequalities in two
area of square and rectangle); geometry (2-dimensional temperature and meter reading); geometry (parallel and variables, exponents and radicals, quadratic equations,
and 3-dimensional objects, lines, symmetry, and perpendicular lines, angles, triangles, quadrilaterals, inequalities, functions, polynomials, and polynomial
tessellation); patterns and algebra (continuous and polygons, circles, and solid figures); patterns and algebra equations and functions); geometry (polygons, axiomatic
repeating patterns and number sentences); statistics and (continuous and repeating patterns, number sentences, structure of geometry, triangle congruence, inequality
probability (data collection and representation in tables, sequences, and simple equations); statistics and and similarity, and basic trigonometry);statistics and
pictographs and bar graphs and outcomes)as applied - probability (bar graphs, line graphs and pie graphs, probability (measures of central tendency, variability and
using appropriate technology - in critical thinking, simple experiment, and experimental probability) as position; combinatorics and probability) as applied - using
problem solving, reasoning, communicating, making applied -using appropriate technology - in critical thinking, appropriate technology - in critical thinking, problem
connections, representations, and decisions in real life. problem solving, reasoning, communicating, making solving, communicating, reasoning, making connections,
connections, representations, and decisions in real life. representations, and decisions in real life.
Time Allotment:
Grade 1 2 3 4 5 6 7 8 9 10
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
_
Lesson Guide in Elem.
50. constructs equivalent number
Math Grade 1 p. 184
expression using addition and
M1AL-IIIh-8
subtraction.
e.g. 6 + 5 = 12 - 1
Lesson Guide in Elem.
51. identifies and creates patterns to
Math Grade 1 pp. 39 41;
compose and decompose using
57 63
addition. M1AL-IIIi-9
e.g. 7 = 0 + 7, 1 + 6, 2 + 5, 3 + 4, 4 +
3, 5 + 2, 6 + 1, 7 + 0
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
Patterns and demonstrates is able to apply 67. determines the missing term/s in
Algebra understanding of knowledge of a given continuous pattern using
continuous patterns using continuous patterns two attributes (any two of the
two attributes and using two attributes following: figures, numbers,
mathematical sentences and number sentences colors, sizes, and orientations,
involving multiplication involving multiplication etc.)
M2AL-IIIj-3
and division of whole and division using 2, 3, e.g.
numbers using 2, 3, 4, 5 4, 5 and 10 only in
and 10 only. various situations. 1, A, 2,B,3,C,__,__
1 , 2 , 3 , 4 __
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
The learner... The learner... The learner...
Grade 3- FIRST QUARTER
Lesson Guide in Elem.
Numbers and 1. demonstrates 1. is able to recognize, Math 3 pp. 1 14
Number understanding of represent, compare, 1. visualizes numbers up to 10 000 with BEAM LG Gr. 3 Module 1.1
M3NS-Ia-1.3
Sense whole numbers up and order whole emphasis on numbers 1001 - 10000. Whole Numbers
to 10 000, ordinal numbers up to 10
numbers up to 000, and money up Lesson Guide in Elem.
100th, and money up to PhP1000 in Math 3 pp. 15 17
to PhP1000. various forms and 2. gives the place value and value of a BEAM LG Gr. 3 Module 1.1
contexts. M3NS-Ia-10.3
digit in 4- to 5-digit numbers. Whole Numbers
2. demonstrates MTB-MLE Group
understanding of 2. is able to recognize Teachers Guide
addition and and represent, Lesson Guide in Elem.
subtraction of whole ordinal numbers up Math 3 pp. 18 - 27
numbers including to 100th in various 3. reads and writes numbers up to 10 BEAM LG Gr. 3 Module 1.1
money forms and contexts. M3NS-Ia-9.3
000 in symbols and in words. Whole Numbers
MTB-MLE Group
3. is able to apply Teachers Guide
addition and
Lesson Guide in Elem.
subtraction of whole
Math 3 pp. 37 40
numbers including
BEAM LG Gr. 3 Module 1.2
money in 4. rounds numbers to the nearest ten,
M3NS-Ib-15.1 Whole Numbers
mathematical hundred and thousand..
DLP Gr. 4 Module 5
problems and real-
MTB-MLE Group
life situations.
Teachers Guide
BEAM LG Gr. 3 Module 1.1
5. compares numbers up to Whole Numbers
M3NS-Ib-12.3 MTB-MLE Group
10 000 using relation symbols.
Teachers Guide
MTB-MLE Group
6. orders 4- to 5-digit numbers in Teachers Guide
M3NS-Ib-13.3
increasing or decreasing order.
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
The learner The learner The learner
Grade 4- FIRST QUARTER
1. visualizes numbers up to 100 000 with BEAM LG Gr.3 Module 1.1
Numbers and 1. demonstrates 1. is able to recognize and emphasis on numbers 10 001 M4NS-Ia-1.4 Whole Numbers
Number understanding of represent whole 100 000.
Sense whole numbers up to numbers up to 100,000 2. gives the place value and value of a
100,000. in various forms and M4NS-Ia-10.4
digit in numbers up to 100 000.
contexts.
3. reads and writes numbers up to BEAM LG Gr.3 Module 1.1
2. demonstrates
hundred thousand in symbols and in M4NS-Ia-9.4 Whole Numbers
understanding of 2. is able to apply
words.
multiplication and multiplication and
BEAM LG Gr.3 Module 1.1
division of whole division of whole 4. rounds numbers to the nearest
M4NS-Ib-5.2 Whole Numbers
numbers including numbers including thousand and ten thousand.
DLP Gr. 4 Module 6
money. money in mathematical
problems and real-life 5. compares numbers up to 100 000
M4NS-Ib-12.4
situations. using relation symbols.
Numbers and 1. demonstrates 1. is able to apply 22. identifies factors of a given number up M4NS-IIa-64
Number understanding of knowledge of to 100.
Sense factors and factors and
multiples and multiples, and 23. identifies the multiples of a given M4NS-IIa-65
addition and addition and number up to 100.
subtraction of subtraction of BEAM LG Gr.5 Module 1
fractions. fractions in Subsets of Whole
mathematical Numbers, Gr. 6 Number
2. demonstrates problems and real- 24. differentiates prime from composite Theory
understanding of life situations. M4NS-IIb-66
numbers. Lesson Guide in Elem.
improper fractions Math Gr. 5 p. 30
and mixed numbers 2. is able to MISOSA Gr. 5 Module Prime
recognize and and Composite Numbers
represent improper BEAM LG Gr.5 Module 1
fractions and mixed Subsets of Whole Numbers
numbers in various 25. writes a given number as a product of M4NS-IIb-67
DLP Gr. 5 Module 10
forms and contexts. its prime factors.
MISOSA Gr. 5 Module
Prime Factors of a Number
26. finds the common factors and the BEAM LG Gr.5 Module 1
greatest common factor (GCF) of two Subsets of Whole Numbers
M4NS-IIc-68.1
numbers using the following methods: Lesson Guide in Elem.
listing, prime factorization, and Math Gr. 5 p.33
continuous division.
K to 12 Mathematics Curriculum Guide December 2013 Page 44 of 109
K to 12 BASIC EDUCATION CURRICULUM
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
The learner The learner The learner
27. finds the common multiples and least Lesson Guide in Elem.
common multiple (LCM) of two Math Gr. 5 p.44
M4NS-IIc-69.1
numbers using the following methods: MISOSA Gr. 5 Module
listing, prime factorization, and Least Common Multiple
continuous division.
28. solves real-life problems involving GCF
M4NS-IId-70.1
and LCM of 2 given numbers .
29. creates problems with reasonable
answers involving GCF and LCM of 2 M4NS-IId-71.1
given numbers.
BEAM LG Gr.4 Module 8
Fractions
30. identifies proper fractions, improper
M4NS-IIe-79.2 DLP Gr. 4 Module 57
fractions, and mixed numbers.
Lesson Guide in Elem.
Math Gr. 4 p.192
BEAM LG Gr.4 Module 8
Fractions
DLP Gr. 4 Module 61, Gr. 6
Module 26
31. changes improper fraction to mixed Lesson Guide in Elem.
M4NS-IIe-80
numbers and vice versa. Math Gr. 4 p.209, Gr. 6 p.
170
MISOSA Module Gr. 4
Improper to Mixed
Numbers
BEAM LG Gr.3 Module 2
Fractions; Gr. 6 Module 7
32. changes fractions to lowest forms. M4NS-IIe-81
Lesson Guide in Elem.
Math Gr. 6 p.166
BEAM LG Gr.4 Module 9
Addition and Subtraction of
Fractions
33. visualizes addition and subtraction of M4NS-IIf-82.1
Lesson Guide in Elem.
similar fractions.
Math Gr. 4 p. 209, Gr. 5
p.124
1 2 3 4 5 6 7 ____
54. finds the missing number in an
equation involving properties of
M4AL-IIIe-13
operations. (e.g. (4+__ ) + 8 = 4 +
( 5 + __)
55. finds the elapsed time in minutes and
Measurement demonstrates is able to apply the M4ME-IIIf-11
seconds.
understanding of the concepts of time,
56. estimates the duration of time in
concept of time, perimeter, area, and M4ME-IIIf-12
minutes.
perimeter, area, and volume to mathematical
volume. problems and real-life 57. solves problems involving elapsed time. M4ME-IIIg-13
situations.
58. visualizes the perimeter of any given
M4ME-IIIg-48
plane figure in different situations.
DLP Gr. 4 Module 84
59. measures the perimeter of any given
M4ME-IIIh-49
figure using appropriate tools.
60. derives the formula for perimeter of BEAM LG Gr.4 Module 18
M4ME-IIIh-50
any given figure. Perimeter
K to 12 Mathematics Curriculum Guide December 2013 Page 49 of 109
K to 12 BASIC EDUCATION CURRICULUM
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
The learner The learner The learner
BEAM LG Gr.4 Module 18
Perimeter
61. finds the perimeter of triangles,
DLP Gr. 4 Module 82, 83,
squares, rectangles, parallelograms, M4ME-IIIi-51
86
and trapezoids.
Lesson Guide in Elem.
Math Gr. 4 p.302, 305
62. solves routine and non-routine BEAM LG Gr.4 Module 18
problems in real-life situations Perimeter
involving perimeter of squares and M4ME-IIIi-52 Lesson Guide in Elem.
rectangles, triangles, parallelograms, Math Gr. 4 p.309
and trapezoids.
63. differentiates perimeter from area. M4ME-IIIj-53
64. converts sq. cm to sq. m and vice
M4ME-IIIj-54
versa.
Grade 4- FOURTH QUARTER
65. finds the area of irregular figures made
up of squares and rectangles using sq. M4ME-IVa-55
cm and sq. m.
66. estimates the area of irregular plane
figures made up of squares and M4ME-IVa-56
rectangles.
BEAM LG Gr.4 Module 13
Area
67. derives the formulas for the area of
DLP Gr. 4 Module 85
triangles, parallelograms, and M4ME-IVb-57
Lesson Guide in Elem.
trapezoids.
Math Gr. 4 p.315, 317,
321, 325
BEAM LG Gr.4 Module 13
Area, Gr. 5 Module 14
Area
68. finds the area of triangles, DLP Gr. 4 Module 48, Gr. 5
parallelograms and trapezoids using sq. M4ME-IVb-58 Module 47, 50
cm and sq. m. Lesson Guide in Elem.
Math Gr. 5 p.372, 377, Gr.
6 p. 373, 378
MISOSA Module Gr.5
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
The learner The learner The learner
Grade 5- FIRST QUARTER
DLP Gr. 3 Module 1, Gr. 4
Numbers and Module 1
Number 1. demonstrates 1. is able to recognize BEAM LG Gr. 4 Module 1-
1. visualizes numbers up to 10 000 000
Sense understanding of and represent whole Whole Numbers
with emphasis on numbers 100 001 M5NS-Ia-1.5
whole numbers up to numbers up to 10 000 Lesson Guide in Elem.
10 000 000.
10 000 000. 000 in various forms Math Gr. 4 p. 1
and contexts. MISOSA Gr. 4 Module
2. demonstrates Numbers through Billions
understanding of 2. is able to apply DLP Gr. 3 Module 3, Gr. 4
divisibility, order of divisibility, order of Module 3
operations, factors operations, factors and BEAM LG Gr. 4 Module 1-
2. reads and writes numbers up to
and multiples, and the multiples, and the four M5NS-Ia-9.5 Whole Numbers, Gr. 5
10 000 000 in symbols and in words.
four fundamental fundamental operations Module 1
operations involving involving fractions in Lesson Guide in Elem.
fractions mathematical problems Math Gr. 4 p. 7, Gr. 5 p. 1
and real-life situations. DLP Gr. 3 Module 6, Gr. 5
Module 4
BEAM LG Gr. 4 Module
3. rounds numbers to the nearest Rounding Off Numbers
M5NS-Ia-15.3
hundred thousand and million. Lesson Guide in Elem.
Math Gr. 4 p. 13
MISOSA Gr. 4 Module
Rounding Numbers
DLP Gr. 4 Module 4, Gr. 5
4. uses divisibility rules for 2, 5, and 10
Module 1, 12
to find the common factors of M5NS-Ib-58.1
Lesson Guide in Elem.
numbers.
Math Gr. 5 p.48
DLP Gr. 5 Module 1, 12
5. uses divisibility rules for 3, 6, and 9 to Lesson Guide in Elem.
M5NS-Ib-58.2
find common factors. Math Gr. 5 p.51, 57
Patterns and demonstrates 1. is able to apply the 71. formulates the rule in finding the next
Algebra understanding of the knowledge of sequence term in a sequence.
concept of sequence and in various situations. e.g.
solving simple equations. 1, 3, 7,15, (15 x 2+1) M5AL-IIIf-6
2. is able to use different Possible answers:
problem solving (x 2 + 1)
strategies. (+2, +4, +8, +16)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
The learner The learner The learner
Grade 6- FIRST QUARTER
Lesson Guide in Elem.
Numbers and demonstrates is able to apply the four Math Gr. 6 p. 203, 207,
Number understanding of the four fundamental operations 212, 216, 219, 223
Sense fundamental operations involving fractions and 1. adds and subtracts simple fractions and DLP Gr. 6 Module 31, 32
involving fractions and decimals in mathematical mixed numbers without or with M6NS-Ia-86 BEAM LG Gr. 6 Module 8A
decimals. problems and real-life regrouping. MISOSA Modules Gr.5 and
situations. 6 Subtraction of Mixed
Numbers
Measurement demonstrates is able to apply knowledge 70. determines the relationship of the
understanding of volume of volume of solid figures volume between
of solid figures and and meter reading in 70.1 a rectangular prism and a
M6ME-IVa-95
meter reading. mathematical problems and pyramid;
real-life situations. 70.2 a cylinder and a cone;
70.3 and a cylinder and sphere.
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
Measurement demonstrates is able to formulate real-life 1. illustrates what it means to measure. M7ME-IIa-1
understanding of the key problems involving 2. describes the development of
concepts of measurement. measurements and solve measurement from the primitive to
M7ME-IIa-2
these using a variety of the present international system of
strategies. units.
3. approximates the measures of
quantities particularly length ,
M7ME-IIa-3
weight/mass, volume, time, angle
and temperature and rate.
4. converts measurements from one
unit to another in both Metric and M7ME-IIb-1
English systems.***
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
*** Suggestion for ICT enhanced lesson when available and where appropriate
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
Patterns and demonstrates is able to formulate real-life 1. factors completely different types
Algebra understanding of key problems involving factors of of polynomials (polynomials with
concepts of factors of polynomials, rational common monomial factor,
polynomials, rational algebraic expressions, linear difference of two squares, sum and M8AL-Ia-b-1
algebraic expressions, equations and inequalities in difference of two cubes, perfect
linear equations and two variables, systems of square trinomials, and general
inequalities in two linear equations and trinomials).
variables, systems of linear inequalities in two variables 2. solves problems involving factors
M8AL-Ib-2
equations and inequalities and linear functions, and of polynomials.
in two variables and linear solve these problems
functions. accurately using a variety of 3. illustrates rational algebraic
M8AL-Ic-1
strategies. expressions.
4. simplifies rational algebraic
M8AL-Ic-2
expressions.
5. performs operations on rational
M8AL-Ic-d-1
algebraic expressions.
6. solves problems involving rational
M8AL-Id-2
algebraic expressions.
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
*** Suggestion for ICT enhanced lesson when available and where appropriate
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
Grade 9- FIRST QUARTER
BEAM Second Year
demonstrates is able to investigate Module 4 (TG)
Patterns and understanding of key thoroughly mathematical EASE Module Second Year
Algebra concepts of quadratic relationships in various Quadratic Equations
equations, inequalities and situations, formulate real- M9AL-Ia-1
1. illustrates quadratic equations. Module 3
functions, and rational life problems involving Chapter 2
algebraic equations. quadratic equations, Quadratic Equations pp.44-
inequalities and functions, 46 (LM)
and rational algebraic
equations and solve them BEAM Second Year
using a variety of Module 4 (TG)
2. solves quadratic equations by: (a)
strategies. EASE Module Second Year
extracting square roots; (b) factoring;
M9AL-Ia-b-1 Quadratic Equations,
(c) completing the square; and (d)
Module 3
using the quadratic formula.
Chapter 2Quadratic
Equations pp.47-53(LM)
BEAM Second Year,
Module 4 (TG)
EASE Module Second Year
3. characterizes the roots of a quadratic Quadratic Equations,
M9AL-Ic-1
equation using the discriminant. Module 3
Chapter 2
Quadratic Equations pp.53-
59 (LM)
BEAM Second Year
Module 4 (TG)
4. describes the relationship between the
EASE Module Second Year
coefficients and the roots of a
M9AL-Ic-2 Quadratic Equations,
quadratic equation.
Module 3 Chapter 2
Quadratic Equations pp.53-
59 (LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Second Year
Module 4 (TG)
LM
5. solves equations transformable to EASE Module Second Year
quadratic equations (including M9AL-Ic-d-1 Quadratic Equations,
rational algebraic equations). Module 3
Chapter 2
Quadratic Equations pp.53-
59 (LM)
BEAM Second Year
Module 4 (TG)
EASE Module Second Year
6. solves problems involving quadratic
Quadratic Equations,
equations and rational algebraic M9AL-Ie-1
Module 3
equations.
Chapter 2
Quadratic Equations pp.61-
64 (LM)
APEX Chapter 3
Quadratic Functions
8. solves quadratic inequalities. M9AL-If-2
Lessons 18-19 pp.203-217
(LM)
APEX Chapter 3
9. solves problems involving quadratic Quadratic Functions
M9AL-If-g-1
inequalities. Lessons 18-19 pp.203-217
(LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Fourth Year
Module 3
Math IV: Advanced
Algrebra, Trigonometry
and Statistics (Lesson
12. transforms the quadratic function Plans) 2002 BEC (Week 8)
defined byy = ax2 + bx + cinto the M9AL-Ih-1 pp.31-32 (TG)
formy = a(x h)2 + k. EASE Module Fourth Year
Quadratic Equations,
Module 1
APEX Chapter 3
Quadratic Functions
Lesson 2 pp.101-105 (LM)
13. graphs a quadratic function: (a) BEAM Fourth Year, Module
domain; (b) range; (c) intercepts; 3 (TG)
(d) axis of symmetry; (e) vertex; M9AL-Ig-h-i-1 EASE Module Fourth Year
(f) direction of the opening of the Quadratic Equations,
parabola. Module 1 (LM)
BEAM Fourth Year
Math IV: Advanced
Algebra, Trigonometry,
and Statistics (Lesson
14. analyzes the effects of changing
Plans) 2002 BEC (Week 8-
the values of a, h and k in the
M9AL-Ii-2 9) pp.37-41 (TG)
equation y = a(x h)2 + k of a
EASE Module Fourth Year,
quadratic function on its graph.***
Module 2
APEX Chapter 3
Quadratic Functions
Lesson 2 pp.120-125 (LM)
EASE Module Fourth Year
Quadratic Functions,
15. determines the equation of a
Modules 3 and 4
quadratic function given: (a) a
M9AL-Ij-1 APEX Chapter 3
table of values; (b) graph; (c)
Quadratic Functions
zeros.
Lesson 1 pp.92-100
Lesson 13 pp.165-171(LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
Math IV: Advanced
Algebra, Trigonometry,
and Statistics (Lesson
Plans) 2002 BEC (Week 8-
9) pp.37-41 (TG)
16. solves problems involving EASE Module Fourth Year
quadratic functions. M9AL-Ii-j-2
Quadratic Functions,
Modules 3 and 4
APEX Chapter 3
Quadratic Functions
Lesson 14 pp.172-183
(LM)
Grade 9- SECOND QUARTER
BEAM Second Year,
Patterns and demonstrates is able to formulate and Module 8 (TG)
Algebra understanding of key solve accurately problems EASE Module Second Year
concepts of variation and involving radicals. 17.illustrates situations that involve the Variations
M9AL-IIa-1
radicals. following variations: (a) direct; (b) Modules 1-3
inverse; (c) joint; (d) combined. Chapter 4 Variation
pp.102-121 (LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Second Year,
Module 9 (TG)
Ease Module Second Year
20.applies the laws involving positive Integral Exponents,
integral exponents to zero and M9AL-IId-1 Modules 2
negative integral exponents. Chapter 5 Integral
Exponents pp.122-135
(LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Second Year,
Module 10 (TG)
EASE Module Second Year
Radical Expressions,
25.simplifies radical expressions using the
M9AL-IIg-1 Module 3
laws of radicals.
Chapter 6 Radical
Expressions pp.152-156
(LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
Grade 9- THIRD QUARTER
BEAM Third Year
Geometry demonstrates is able to investigate, Module 12 (TG)
understanding of key analyze, and solve APEX Lesson 1-7
concepts of quadrilaterals problems involving
Quadrilaterals
(parallelograms, quadrilaterals
trapezoids, kites) and (parallelograms, trapezoids, Geometry Chapter 1
triangle similarity. kites) and triangle similarity 29. identifies quadrilaterals that are M9GE-IIIa-1 Geometry of Shape and
through appropriate and parallelograms. Size
accurate representation. Quadrilaterals p.17 Chapter
4 Quadrilaterals
4.1.3 The Parallelogram
and its properties p.124
(LM)
BEAM Third Year
Module 12 (TG)
30. determines the conditions that Geometry Chapter 4
guarantee a quadrilateral a Quadrilaterals
M9GE-IIIa-2 4.2. Conditions which
parallelogram.
guarantee that a
quadrilateral is a
parallelogram p.132 (LM)
EASE Module Third Year
31. uses properties to find measures of
angles, sides and other quantities M9GE-IIIb-1 Properties of Quadrilaterals
involving parallelograms. Module 1 (LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
34. proves theorems on trapezoids and
M9GE-IIId-2
kites.
EASE Module Third Year
35. solves problems involving
M9GE-IIIe-1 Properties of Quadrilaterals
parallelograms, trapezoids and kites.
Module 1 (LM)
BEAM Third Year
Module 15 (TG)
EASE Module Third Year
Similarity
Module 1
36. describes a proportion. M9GE-IIIf-1 APEX Math Triangles Unit 4
Lesson 1-10
Geometry Chapter 5
Similarity
5.1. Ratio and Proportion
p.145 (LM)
BEAM Third Year
Module 15
37. applies the fundamental theorems of APEX Math Triangles Unit 4
M9GE-IIIf-2 Lesson 1-10
proportionality to solve problems
involving proportions. Geometry Chapter 5
Similarity
5.1. Ratio and Proportion
p.145
BEAM Third Year, Module
16 (TG)
EASE Module Third Year
Similar Triangles, Module 2
APEX Math Triangles Unit 4
38. illustrates similarity of figures. M9GE-IIIg-1
Lesson 1-10
Geometry Chapter 5
5.2. Similarity between
triangles p.149 (LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Third Year, Module
16
(TG)
EASE Module Third Year
39. proves the conditions for similarity of
Similar Triangles, Module 2
triangles. ***
APEX Math Triangles Unit 4
39.1 SAS similarity theorem
39.2 SSS similarity theorem M9GE-IIIg-h-1 Lesson 1-10
39.3 AA similarity theorem Geometry Chapter 5
39.4 right triangle similarity theorem Similarity
39.5 special right triangle theorems 5.2.4. Basic Similarity
Theorems p.157
5.4. Similarities in Right
Triangles p.166 (LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Third Year, Module
16 (TG)
EASE Module Third Year
Similarity, Module 3
APEX Math Similarity of
Triangles Unit 4
42. solves problems that involve triangle
M9GE-IIIj-1 Lesson 11-16
similarity and right triangles.***
Geometry Chapter 5
Similarity
5.5. Problems Involving
Similar Triangles and Other
Special Right Triangles
p.175 (LM)
Grade 9- FOURTH QUARTER
BEAM Fourth Year, Module
demonstrates is able to apply the
Geometry understanding of the basic concepts of trigonometric 43. illustrates the six trigonometric ratios: 13 (TG)
concepts of trigonometry. ratios to formulate and sine, cosine, tangent, secant, M9GE-IVa-1 EASE Module Fourth Year
solve real-life problems with cosecant, and cotangent. Triangle Trigonometry,
precision and accuracy Module 1 (LM)
44. finds the trigonometric ratios of
M9GE -IVb-c-1
special angles.
BEAM Fourth Year, Module
13 (TG)
45. illustrates angles of elevation and EASE Module Fourth Year
M9GE-IVd-1
angles of depression. Triangle Trigonometry,
Module 2 (LM)
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY LEARNING
CONTENT STANDARDS CODE
MATERIALS
The learner... The learner... The learner...
BEAM Fourth Year, Module
13 (TG)
EASE Module Fourth Year
Triangle Trigonometry,
47. illustrates laws of sines and cosines. M9GE-IVf-g-1 Module 2 Math IV:
Advanced Algebra.
Trigonometry, and
Statistics (Lesson Plans)
2002 EBEC (Week 6-7)
pp.50-56 (LM)
BEAM Fourth Year, Module
48. solves problems involving oblique 13 (TG)
triangles. M9GE-IVh-j-1 EASE Module Fourth Year
Triangle Trigonometry,
Module 2 (LM)
*** Suggestion for ICT enhanced lesson when available and where appropriate
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
Statistics demonstrates is able to use precise 33. illustrates the permutation of objects. M10SP-IIIa-1
and Probability understanding of key counting technique and
concepts of combinatorics probability in formulating 34. derives the formula for finding the
and probability. conclusions and making number of permutations of n objects M10SP-IIIa-2
decisions. taken r at a time.
35. solves problems involving M10SP-IIIb-1
permutations.
36. illustrates the combination of objects. M10SP-IIIc-1
37. differentiates permutation from
combination of n objects taken r at M10SP-IIIc-2
a time.
38. derives the formula for finding the
number of combinations of n objects M10SP-IIId-1
taken r at a time
39. solves problems involving
M10SP-IIId-e-1
permutations and combinations.
40. illustrates events, and union and
M10SP-IIIf-1
intersection of events.
41. illustrates the probability of a union of
M10SP-IIIg-1
two events.
42. finds the probability of A B . M10SP-IIIg-h-1
PERFORMANCE
CONTENT STANDARDS LEARNING COMPETENCY
CONTENT STANDARDS CODE LEARNING MATERIALS
Statistics and demonstrates is able to conduct 45. illustrates the following measures of
M10SP-IVa-1
Probability understanding of key systematically a mini- position: quartiles, deciles and
concepts of measures of research applying the percentiles.***
position. different statistical 46. calculates a specified measure of
methods. M10SP-IVb-1
position (e.g. 90th percentile) of a set
of data.
47. interprets measures of position. M10SP-IVc-1
48. solves problems involving measures of
M10SP-IVd-e-1
position.
*** Suggestion for ICT enhanced lesson when available and where appropriate
Communicating the use of notations, symbols, figures, equations and functions to convey mathematical ideas.
Computing the skill of calculating using correct algorithms, procedures and tools to arrive at a final exact result.
Conjecturing the skill of formulating mathematical theories that still need to be proven.
Connecting the skill of integrating mathematics to other school subjects and other areas in life.
the theory that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connects them to new ideas
Constructivism
that are encountered.
a locale, situation, or set of conditions of students that may influence their study and use of mathematics to develop critical thinking and
Context
problem solving skills.
Cooperative Learning learning that is achieved by working with fellow learners as they all engage in a shared task.
Creativity the skill of using available procedures in Mathematics and non-conventional methods to solve a problem and produce answers.
the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information
Critical Thinking gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action (Scriven&
Paul, 1987).
Decision-making the skill of arriving at a choice or decision based on sound, logical procedures and mathematical analyses.
Discovery Learning learning that is achieved by allowing students to discover new ideas using their experiences (Bruner, 1961).
Estimating the skill of roughly calculating or judging a numerical value or quantity.
Experiential Learning learning that occurs by making sense of direct everyday experiences (Kolb, 1984)
Inquiry-based Learning learning that focuses on students asking questions and finding answers to their questions using their personal experiences.
Knowing and
meaningful acquisition of concepts that include memorizing and recalling of facts and procedures
Understanding
Mathematical Problem
finding a solution to a problem that is unknown (Polya, 1945 & 1962).
Solving
Modeling the use of functions and graphs to represent relationships between and among quantities in a phenomenon.
the quality of judging, evaluating and making decisions based on mathematical facts and results without being influenced by subjective
Objectivity
conditions.
Perseverance firmness in finishing a task despite difficulties and obstacles.
Productivity the quality of pursuing an activity to arrive at a meaningful and useful result or product.
K to 12 Mathematics Curriculum Guide December 2013 Page 107 of 109
K to 12 BASIC EDUCATION CURRICULUM
GLOSSARY
Proving the skill of demonstrating the truth or falsity of a theory using reasoning and arguments.
Reasoning the process of explaining using sound analyses, following the rules of logic.
Solving to find the answer to an algebraic or mathematical problem using any procedures and tools available.
using ones creativity and imagination to produce images, pictures and other means to represent and understand mathematical concepts
Visualizing
(MATHTED & SEI, 2010).
Sample: M7AL-IIg-2
-
Patterns and Algebra AL
Roman Numeral
*Zero if no specific quarter
Quarter Second Quarter II
Lowercase Letter/s
*Put a hyphen (-) in between Measurement ME
letters to indicate more than a
Week Week seven g
specific week
-
Solves problems involving Statistics and Probability SP
Arabic Number Competency
algebraic expressions
2