Download Math 5 - SYLLABUS

SYLLABUS IN MATHEMATICS 5
FIRST QUARTER
PROGRAM
STANDARD
GRADE LEVEL
STANDARD
CONTENT
STANDARD
The learner demonstrates understanding and appreciation of key concepts and principles
of mathematics as applied - using appropriate technology - in problem solving, critical
thinking, communicating, reasoning, making connections, representations, and decisions in
real life.
The learner demonstrates understanding and appreciation of key concepts and skills
involving numbers and number sense (divisibility, order of operations, fractions and decimals
including money, ratio and proportion, percent, integers); geometry (plane and solid figures);
patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area,
surface area, volume, and meter reading); and statistics and probability (tables, pie graphs,
and experimental and theoretical probability) as applied - using appropriate technology - in
critical thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner…
1. demonstrates understanding of whole numbers up to 10, 000,000.
2. demonstrates understanding of order of operations and the four fundamental
operations involving whole numbers.
PERFORMANCE
STANDARD
The learner…
1. is able to recognize and represent whole numbers up to 10 000 000 in various forms
and contexts.
2. is able to apply order of operations and the four fundamental operations involving
whole numbers in mathematical problems and real-life situations.
TIME FRAME
TOPICS

Orientation

Numbers Beyond 100 000
Week 1
Value: Responsibility
LEARNING COMPETENCIES
The learner…
 reviews school rules and regulations
 gets to know his/her classmates and
teachers
ASSESSMENT
 Recitations
 Group sharing
 Presentations
 Journal
The learner…
 M5NS-Ia-1.5: visualizes with
emphasis on numbers 100 001 – 10
000 000
Formative:
 Drills and
practices
 Recitation
 Journal writing

Week 2

Comparing Numbers

Approximation
Value: Social awareness;
Accuracy
Week 3
M5NS-Ia-9.5: reads and writes
numbers up to 10 000 000 in
symbols and in words
The learner…
 M5NS-HAU-Ic-1.1: compares and
orders numbers up to ten millions

M5NS-Ia-15.3: rounds numbers to
the nearest hundred thousand and
million.
Summative:
 Reading and
Writing Numbers
 Quiz
 Group Activity –
Forming
Numbers
Formative:
 Drills
 Group activity
Summative:
 Comparing and
Ordering
Numbers up to
Ten Millions
 Rounding Off
Numbers
 Quiz

Multiplication
Values: Speed and accuracy
Week 4
The learner…
Formative:
 M5NS-HAU-Id-1.1: multiplies
 Drills and
numbers up to 3-digit numbers by up
Exercises
to 2-digit numbers without or with
regrouping.
Summative:
 Multiplying
Whole Numbers
 M5NS-HAU-Id-1.2: multiplies a
whole number by tens, hundreds
 Speed Test
and thousands.
 Quiz
Week 5
First Mid-Quarter Exam

Division
Values: Speed and accuracy
Week 6
The learner…
 M5NS-HAU-If-1.1: divides 3- to 4digit numbers by 1- to 2-digit
numbers without and with
remainder.


Word Problems
Values: Analysis and critical
thinking
Week 7
M5NS-HAU-If-1.2: divides a whole
number by tens, hundreds and
thousands.
Formative:
 Drills
Summative:
 Dividing Whole
Numbers
 Speed Test
 Quiz
The learner…
 M5NS-HAU-Ig-1.1: solves multi-step Formative:
 Drills
routine and non-routine word
 Think-Pair-Share
problems involving the 4 operations.

M5NS-HAU-Ig-1.2: creates
problems involving the four
operations of whole numbers
including money, with reasonable
answers.
Summative:
 Problem Solving
 Group Activity
 Quiz

Order of Operations
Values: Respect for laws;
obedience
The learner…
 M5NS-Ic-61.2: states, explains and
interprets the MDAS, PMDAS or
GMDAS rule

M5NS-Id-62.2: performs a series of
two or more operations
Week 8
Prime and Composite Numbers
Prime Factorization
Values: Value one’s worth as a
person
Week 9
Week 10
Formative:
 Drills and
Practices
 Group Activity
Summative:
 Simplifying a
Series of
Operations on
Whole Numbers
Using MDAS,
PMDAS or
GMDAS Rule
 Quiz
The learner…
Formative:
 M5NS-HAU-Ii-1.1: identifies and
 Drills and
differentiate prime and composite
Exercises
numbers.
 Recitation
 M5NS-HAU-Ii-1.2: state the
Summative:
prime factors of numbers.
 Quiz
 First
Computation Skill
Test
 Performance
Task
First Quarter Exam
SYLLABUS IN MATHEMATICS 5
SECOND QUARTER
PROGRAM
STANDARD
The learner demonstrates understanding and appreciation of key concepts and principles
of mathematics as applied - using appropriate technology - in problem solving, critical
thinking, communicating, reasoning, making connections, representations, and decisions in
real life.
The learner demonstrates understanding and appreciation of key concepts and skills
involving numbers and number sense (divisibility, order of operations, fractions and decimals
including money, ratio and proportion, percent, integers); geometry (plane and solid figures);
patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area,
surface area, volume, and meter reading); and statistics and probability (tables, pie graphs,
and experimental and theoretical probability) as applied - using appropriate technology - in
critical thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner demonstrates understanding of divisibility, factors and multiples, and the four
fundamental operations involving fractions.
The learner is able to apply divisibility, factors and multiples, and the four fundamental
operations involving fractions in mathematical problems and real-life situations.
GRADE LEVEL
STANDARD
CONTENT
STANDARD
PERFORMANCE
STANDARD
TIME
FRAME
TOPICS
LEARNING COMPETENCIES
The learner…

Divisibility Rules

M5NS-Ib-58.1: uses divisibility
rules for 2, 5, and 10 to find the
common factors of numbers.

M5NS-Ib-58.2: uses divisibility
rules for 3, 6, and 9 to find the
common factors.

M5NS-Ib-58.3: uses divisibility
rules for 4, 8, 11 and 12 to find the
Value: Wise decision making
Week 1
ASSESSMENT
Formative:
 Recitation
 Written exercises
 Game (Sa Pula,
Sa Puti)
 Journal Writing
(Uses of
divisibility rules)
Summative:
 Test
common factors.


Factors and Multiples
Values: Diligence and
enthusiasm in doing one’s work



Fractions
Values: Being focused on one’s
tasks; equality

Week 4
Fractions in Lowest Term
Values: Speed and accuracy
M5NS-Ic-59: solves problems
involving divisibility rules
M5NS-Id-68.2: finds the common
factors and the GCF of 2–4
numbers using continuous division.
M5NS-Id-69.2: finds the common
multiples and LCM of 2–4 numbers
using continuous division.
M5NS-Ie-70.2: solves real-life
problems involving GCF and LCM
of 2-3 given numbers.
Formative:
 Oral and Written
Drills
Summative:
 Test
The learner…


Performance
Task
The learner…

Week 2-3

M5NS-HAU-IId-1.1: identifies
proper fractions, improper
fractions, and mixed numbers.
M5NS-HAU-IId-1.2: changes
improper fraction to mixed number
and vice versa.
The learner…

M5NS-HAU-IId-1.3: changes
fractions to lowest term
Formative:
 Recitation
 Oral and Written
Drills
Summative:
 Test
Formative:
 Oral and Written
Drills
 Recitation
Summative:
 Test
Week 5
Second Mid-Quarter Exam

Addition and Subtraction
of Proper Fractions
The learner…

Values: Accuracy, patience,
cooperation
Week 6



Addition and Subtraction
Involving Mixed Numbers
M5NS-HAU-IIf-1.1: represents
addition and subtraction of proper
fractions using concrete and
pictorial models.
M5NS-HAU-IIf-1.2: estimates
sums and differences of proper
fractions.
Formative:
 Oral and Written
Drills
 Group Activity
Summative:
 Test
M5NS-HAU-IIf-1.3: adds and
subtracts proper fractions.
The learner…

Values: Orderliness in doing
one’s work; cooperation
M5NS-HAU-IIg-1.1: represents
addition and subtraction of mixed
numbers using concrete and
pictorial models.

M5NS-HAU-IIg-1.2: estimates
sums and differences of mixed
numbers.

M5NS-HAU-IIg-1.3: adds and
subtracts mixed numbers.

M5NS-If-87.2 :solves routine and
non-routine problems involving
addition and/or subtraction of
fractions using appropriate
Week 7
Formative:
 Oral and Written
Drills
 Group Activity
Summative:
 Test
problem solving strategies and
tools.

Multiplication of Fractions
Values: Accuracy; generosity
Week 8
The learner…

M5NS-Ig-89: visualizes
multiplication of fractions using
models.

M5NS-Ig-90.1: multiplies fractions
and mixed numbers.


Division of Fractions
Value: Sharing
M5NS-HAU-IIh-1.1:finds a
fractional part of a whole number
or of a fraction.
The learner…


Week 9

Problem Solving
Values: Critical and analytical
thinking
M5NS-Ii-95: visualizes division of
fractions.
M5NS-Ii-96.1: divides
- simple fractions
- whole numbers by a fraction
and vice versa
The learner…

M5NS-Ij-97.1: solves problems
involving addition, subtraction,
multiplication and division of
fractions and mixed numbers
using the appropriate strategies.
Formative:
 Seatwork and
Board work
 Group Work
Summative:
 Test
Formative:
 Seatwork
 Board work
 Recitation
Summative:
 Test
Formative:
 Drills
 Pair-Share
Summative:
 Test
 Performance
Task
 Second
Computation
Skill Test
Week 10
Second Quarter Exam
SYLLABUS IN MATHEMATICS 5
THIRD QUARTER
PROGRAM
STANDARD
The learner demonstrates understanding and appreciation of key concepts and principles
of mathematics as applied - using appropriate technology - in problem solving, critical
thinking, communicating, reasoning, making connections, representations, and decisions in
real life.
The learner demonstrates understanding and appreciation of key concepts and skills
involving numbers and number sense (divisibility, order of operations, fractions and decimals
including money, ratio and proportion, percent, integers); geometry (plane and solid figures);
patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area,
surface area, volume, and meter reading); and statistics and probability (tables, pie graphs,
and experimental and theoretical probability) as applied - using appropriate technology - in
critical thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner…
1. demonstrates understanding of decimals.
2. demonstrates understanding of the four fundamental operations involving decimals
and ratio and proportion.
3. demonstrates understanding of percent.
GRADE LEVEL
STANDARD
CONTENT
STANDARD
The learner…
1. 1.is able to recognize and represent decimals in various forms and contexts.
2. is able to apply the four fundamental operations involving decimals and ratio and
proportion in mathematical problems and real-life situations.
3. is able to apply percent in mathematical problems and real-life situations
PERFORMANCE
STANDARD
TIME
FRAME
TOPICS

Week 1-2
Decimals
Values: Appreciation
for parents, gratitude;
Sportsmanship
LEARNING COMPETENCIES
The learner…

M5NS-IIa-101.2: gives the place value
and the value of a digit of a given
decimal number through ten
ASSESSMENT
Formative:
 Oral and Written Drills
 Recitation
 Seatwork
thousandths.

Multiplication of
Decimals

M5NS-IIa-102.2: reads and writes
decimal numbers through ten
thousandths.

M5NS-IIa-103.2: rounds decimal
numbers to the nearest hundredth and
thousandth

M5NS-IIb-104.2: compares and
arranges decimal numbers.

M5NS-HAU-IIIb-1.1:expresses decimals
as fractions and vice versa
The learner…

M5NS-IId-110: visualizes multiplication
of decimal numbers using pictorial
models.

M5NS-IId-111.1: multiplies decimals up
to 2 decimal places by 1- to 2-digit
whole numbers.
Formative:
 Oral and Written Drills
 Recitation

M5NS-IId-111.2: multiplies decimals
with factors up to 2 decimal places.
Summative:
 Test

M5NS-HAU-IIIc-1.1: multiplies decimal
numbers by multiples of 10, 100 and 1
000.

M5NS-HAU-IIIc-1.2:multiplies decimals
mentally by 0.1, 0.01, 10 and 100.
Values: Speed and
accuracy
Week 3
Summative:
 Test

Division of
Decimals
The learner…

M5NS-IIf-115: visualizes division of
decimal numbers using pictorial models.

M5NS-IIf-116.1: divides decimals with
up to 2 decimal places.

M5NS-IIf-116.2: divides whole numbers
with quotients in decimal form.

M5NS-HAU-IIId-1.1:divides decimals by
multiples of 10, 100 and 1 000.

M5NS-HAU-IIId-1.2:analyzes and
solves word problems involving
multiplication and division of decimals
including money.
Values: Speed and
accuracy
Week 4
Week 5
Formative:
 Oral and Written Drills
 Recitation
 Seatwork and Board
work
Summative:
 Test
Third Mid-Quarter Exam

Ratio
Value: Equality
The learner…

M5NS-IIh-122: visualizes the ratio of
two given sets of objects.

M5NS-IIh-123: expresses the ratio of
two numbers using either the colon(:) or
a fraction.
Formative:
 Oral and Written Drills
 Group Activity: Finding
the Ratio in a Set of
Coins
 Recitation

M5NS-IIi-124: identifies and writes
equivalent ratios.
Summative:
 Test

M5NS-IIi-125: expresses ratios in their
Week 6
simplest forms.


Proportion
Values: Equality and
respect
The learner…

M5NS-IIj-127: defines and describes a
proportion.

M5NS-HAU-IIIg-1.1:tells whether two
ratios make a proportion
M5NS-IIi-126: finds a missing term in a
proportion

M5NS-HAU-IIIg-1.2:sets up a proportion
for a given situation.
Summative:
 Test
M5NS-IIj-128: recognizes when two
quantities are in direct proportion.


Percent
Value: Thriftiness;
Speed and accuracy
Formative:
 Oral and Written Drills
 Recitation
 Seatwork
 Board work

Week 7

M5NS-IIi-126: finds the missing term in
a pair of equivalent ratios.
M5NS-HAU-IIIg-1.3:solves problems
involving ratio and direct proportion.
The learner…

M5NS-IIIa-136: visualizes percent and
its relationship to fractions, ratios, and
decimal numbers using models.

M5NS-IIIa-137: defines percentage, rate
or percent, and base.

M5NS-IIIa-138: identifies the base,
Week 8-9
Formative:
 Oral and Written Drills
 Seatwork
 Recitation
Summative:
 Test
 Performance Task
 Third Computation Skill
Test
percentage, and rate in a problem.
Week 10

M5NS-IIIb-139: finds the percentage in
a given problem.

M5NS-IIIb-140: analyzes and solves
problems involving percentage using
appropriate strategies and tools.
Third Quarter Exam
SYLLABUS IN MATHEMATICS 5
FOURTH QUARTER
PROGRAM
STANDARD
The learner demonstrates understanding and appreciation of key concepts and principles
of mathematics as applied - using appropriate technology - in problem solving, critical
thinking, communicating, reasoning, making connections, representations, and decisions in
real life.
The learner demonstrates understanding and appreciation of key concepts and skills
involving numbers and number sense (divisibility, order of operations, fractions and decimals
including money, ratio and proportion, percent, integers); geometry (plane and solid figures);
patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area,
surface area, volume, and meter reading); and statistics and probability (tables, pie graphs,
and experimental and theoretical probability) as applied - using appropriate technology - in
critical thinking, problem solving, reasoning, communicating, making connections,
representations, and decisions in real life.
The learner…
1. demonstrates understanding of polygons, circles, and solid figures.
2. demonstrates understanding of circumference.
3. demonstrates understanding of area, volume and temperature.
GRADE LEVEL
STANDARD
CONTENT
STANDARD
PERFORMANCE
STANDARD
TIME
FRAME
The learner…
1. is able to construct and describe polygons, circles, and solid figures.
2. is able to apply knowledge of circumference in mathematical problems and real-life
situations.
3. is able to apply knowledge of area, volume and temperature in mathematical problems
and real-life situations.
TOPICS
LEARNING COMPETENCIES
The learner…

Week 1
Angles
Value: Appreciation of
the uses of angles

M5NS-HAU-IVa-1.1: identifies that
angles on a straight line add up to
1800.
ASSESSMENT
Formative:
 Recitation
 Seatwork
 Board Work
Summative:

Triangles

M5GE-HAU-IVa-1.2:identifies that
angles at a point add up to 3600.

M5GE-HAU-IVa-1.3:identifies that
vertically opposite angles are equal.
The learner…


M5GE-HAU-IVa-1.4:identifies and
describes the different kinds of
triangles: acute, right, obtuse, scalene,
isosceles, equilateral, equiangular.
M5GE-HAU-IVa-1.5:determines the
sum of the angles in a triangle.

Test
Formative:
 Recitation
 Seatwork
 Board Work
Summative:
 Test

4-sided Figures

Polygons
Value: Appreciation of
beauty of shapes
around us
Week 2
The learner…

M5GE-HAU-IVb-1.1:identifies and
describes the different kinds of
quadrilaterals: parallelograms,
trapezoid, rhombus

M5GE-HAU-IVb-1.2:finds the unknown
angles using angle properties in
geometrical figures such as a
parallelogram, rhombus and trapezoid.

M5GE-IIIc-19: visualizes, names, and
describes polygons with 5 or more
sides.

M5GE-IIIc-20: describes and
compares properties of polygons
(regular and irregular polygons).

M5GE-IIIc-21: draws polygons with 5
or more sides.
Formative:
 Oral and Written Drills
 Recitation
 Seatwork
 Board Work
Summative:
 Group Activity: Using
Triangles and 4-sided
Figures to Form Shapes
 Test

M5GE-HAU-IVb-1.3:represents
congruent polygons using models.
The learner…

Week 3
Circles
Value: Appreciation of
beauty of shapes
around us

M5GE-IIId-23.1: visualizes and
describes a circle.

M5GE-IIId-23.2: identifies the terms
related to a circle.

M5GE-IIIe-24: draws circles with
different radii using a compass.
Formative:
 Recitation
 Seatwork
 Board Work
Summative:
 Test
 Performance Task
(Tessellation)

Solid Figures
Values: Patience and
accuracy

Circumference
Values: Accuracy;
Respect for others’
property
The learner…

M5GE-HAU-IVc-1.1:visualizes and
describes solid figures.

M5GE-HAU-IVc-1.2:makes models of
different solid figures: cube, prism,
pyramid, cylinder, cone, and sphere
using plane figures.
The learner…

M5ME-IIIh-67: visualizes
circumference of a circle.

M5ME-IIIh-68: measures
circumference of a circle using
appropriate tools.

M5ME-IIIi-69: derives a formula in
finding the circumference of a circle.

M5ME-IIIi-70: finds the circumference
of a circle.
M5ME-IIIj-71: solves problems
involving circumference of a circle.
Week 4

Week 5
Fourth Mid-Quarter Exam
Formative:
 Seatwork
 Board Work
Summative:
 Test

Area of a Circle
Value: Speed and
accuracy
The learner…

M5ME-IVa-72: visualizes area of a
circle.
Formative:
 Oral and Written Drills
 Board Work
 Group Work

M5ME-IVa-73: derives a formula in
finding the area of a circle.
Summative:
 Test

M5ME-IVa-74: finds the area of a
circle.
Week 6


Volume
Value: Accuracy
M5ME-IVb-75: solves problems
involving area of a circle.
The learner…


Week 7-8

M5ME-HAU-IVg-1.3: converts one
cubic unit of measure to a larger or
smaller unit.
M5ME-HAU-IVg-1.4: describes the
volume of a cube and a rectangular
prism.
Formative:
 Seatwork
 Board Work
 Group Work
Summative:
 Test
M5ME-IVd-81: derives a formula for
finding the volume of a cube and a
rectangular prism.


Week 9
Temperature
Value: Environmental
awareness and
concern
M5ME-IVe-83: solves problems
involving volume of a cube and a
rectangular prism using appropriate
formulas and procedures.
The learner…

M5ME-IVf-1: describes and estimates
the temperature inside and outside the
classroom.
Formative:
 Exploration: Describe
and measure the
temperature inside and
outside the classroom,

Week 10
M5ME-IVf-2: identifies the parts of a
thermometer.

M5ME-IVf-3: reads a thermometer.

M5ME-IVf-4: converts degree
Fahrenheit to degree Celsius and vice
versa.

M5ME-IVf-87: solves problems
involving temperature.
Fourth Quarter Exam


body temperature and
temperature at melting
point.
Seatwork
Board Work
Summative:
 Test
 Fourth Computation
Skill Test