LEARNING COMPETENCIES GRADE 2 2010 mathematics

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(Philippine Elementary Learning Competencies)
BASIC EDUCATION CURRICULUM
MATHEMATICS
JUNE 2010
MATHEMATICS
BUREAU OF ELEMENTARY EDUCATION
Department of Education
Republic of the Philippines

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PHILIPPINE ELEMENTARY LEARNING COMPETENCIES - MATHEMATICS
Goal: Demonstrate understanding and skills in computing with considerable speed and accuracy, estimating, communicating, thinking analytically
and critically, and in solving problems in daily life using appropriate technology
GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI
STANDARDS STANDARDS STANDARDS STANDARDS STANDARDS STANDARDS
The Learner
 shows a clear
understanding of
the concept of
whole number up
to one hundred
including money
and enjoys using
the concept to
interpret and give
meaning to objects
and things that
he/she sees in
his/her
environment.
 understands the
concept of
addition and
subtraction of
whole numbers of
1- to 3- digit
numbers including
money and
appreciates using
them to solve
everyday problems.
 understands the
concept of halves
and fourths and
derives satisfaction
in applying the
The Learner
 shows a clear
understanding of
the concept of
whole numbers up
to one thousand
including money by
displaying
proficiency in
associating whole
numbers with
objects around him
as well as reading
and writing these
numbers in symbols
and in words.
 understands the
concept of the four
operations of whole
numbers and
applies the
concept in a
variety of problem
situations.
 displays a clear
understanding of
unit fractions and
enjoys/appreciates
applying the
concept in
separating an
The Learner
 understands the
concept of whole
numbers up to one
hundred thousand,
place value and
derives satisfaction
in counting,
rounding,
comparing and
using them in real-
life situation.
 shows improvement
in performing the
basic operations of
whole numbers
through the correct
use of regrouping,
estimating, mental
operations and
apply them in a
variety of problems.
 begins to
understand the
basic kinds of
fractions and enjoys
simplifying, ordering
and relating them
in day to day
situation.
 shows
The Learner
 shows mastery of
the concept of
whole numbers up
to billions and
enjoys giving the
place value and
rounding numbers.
the four operations,
estimation and
involving mental
computations
involving whole
numbers and
exhibits confidence
in solving problems
 understands the
concept of
decimals and
money and enjoys
reading and
writing, rounding,
renaming and
giving the place
value of decimals.
 demonstrates
understanding of
addition and
subtraction of
decimals and
The Learner
the concept s and
operations/series of
operations (MDAS)
of whole numbers
and uses the
operations in
solving real-life
problems
 shows
understanding of
the concepts of
fractions and apply
them through
renaming, ordering
dissimilar fractions
as well as
estimating.
 performs addition,
subtraction and
multiplication of
fractions and
makes use of this
knowledge to solve
everyday problems.
 understands the
concept of
reducing/expressin
g ratio to
lower/higher terms
The Learner
 understands the
concept of the
order of operations
(PEMDAS) of whole
numbers and
enjoys relating it to
a variety of
problem situation.
 enriches his/her
understanding of
decimals by
translating them in
expanded and
scientific notation.
 shows mastery in
performing the
operations involving
decimals and
enjoys using various
strategies in solving
problems.
 shows clear
understanding of
equivalent
fractions, finding
the LCD and
comparing and
ordering fractions.
performing the

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concept in
separating an
object or a group
of objects.
 understands that
things around
him/her differ and
that the differences
can be compared
and measured in
different ways.
object or group of
objects and
comparing them.
 understands and
appreciates the
basic properties of
geometric shapes
and applies them in
simple tessellation
and symmetry.
 understands the
basic concept of
measurement and
enjoys measuring,
describing and
estimating by using
standard units.
understanding of
the concept of
lines, tessellation
and symmetry and
finds satisfaction in
constructing and
relating to things in
their environment.
 extends his/her
understanding on
the concept and
application of time,
area and capacity
measures and
appreciates using
them to solve daily
life problems.
 shows appreciation
of the pictograph
through reading,
interpreting and
organizing data.
 begins to recognize
the basic parts of
calculator and
appreciates its
functions.
applies them in
problem solving.
 understands
differentiating,
ordering and
renaming fractions
and enjoys using
the knowledge in
everyday life
situation.
 performs addition,
subtraction and
multiplication of
fractions and
applies them to
solve everyday life
problems.
 Understands the
concept of angles
and plane figures
like square,
rectangle and
triangles; enjoys
constructing and
exploring similar
objects around
him/her.
 understands the
attributes of
perimeter, area
and volume and
enjoys measuring,
comparing
approximating and
applying the
formulas in solving
variety of problems.
and appreciates in
applying them to
daily life.
 understands the
concept of
renaming, rounding
and giving the
place value of
decimals and apply
the knowledge in
everyday life
situation.
 understands and
appreciates the
basic operations on
decimals and its
application to real-
world and
mathematical
situations.
 extends his
understanding of
percent, fractions,
ratios and decimals
to show relationship
to one another.
 understands the
attributes of circle
and 5 or more
sided polygons and
recognizes and
appreciates similar
things around him.
 The learner extends
his/her
understanding on
concept of
circumference,
basic operations of
fractions and finds
satisfaction in
applying them in
everyday problems.
 shows
understanding of
the attributes of
spatial figures and
enjoys their
functional use in
their daily life.
 extends his
understanding of
area through
surface area,
volume and
electric and water
meter reading and
applies them in
real-life situations.
of circle graph
through reading,
interpreting,
constructing and
finding average of
data.
 understands the
basic concept of
probability and
enjoys making
simple predictions
and telling
favorable
outcomes as
applied to real life
situations.

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I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1. Recognize
cardinal numbers
from 0 to 100
1.1 Identify
common
objects
according to:
1.1.1 color
1.1.2 size
(length,
height,
thickness)
1.1.3 shape
1.1.4 position
1.2 Classify sets
using common
objects
according to:
1.2.1 color
1.2.2 size
(length,
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1. Identify numbers
from 101 through
1000
1.1 Associate
numbers with
sets having
101 up to 500
objects/ things
and tell the
number of
objects
1.2 Associate
numbers with
sets having
501 up to 1000
objects/ things
and tell the
number of
objects
2. Read and write
numbers from 101
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1. Read and write
the numbers
through 100 000 in
symbols and in
words
1.1 Identify
cardinal
numbers
1.1.1 1000
through 10
000
1.1.2 10 001
though 100
000
1.2 Give the place
value of each
digit in four to
five-digit
numbers
1.3 Read numbers
through 100 000
of the bar graph
through reading,
interpreting,
constructing and
finding average of
data.
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1.Read and write
numbers through
millions in symbols
and in words
1.1 Identify
numbers from
100 001 through
millions/ billions
1.2 Give the place
value of each
digit in a six or
more digit
numbers
1.3 Read and
write numbers
through
millions/billions
in symbols
1.4 Read and
write numbers
area, volume and
temperature
measure and
enjoys making and
using measurement
in everyday life.
of line graph
through reading,
interpreting,
constructing and
finding average of
data.
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
REVIEW
1. Properties of
Whole Numbers
 Addition
 Multiplication
2. Operations of
Whole Numbers
through Problem
Solving:
 Addition
 Subtraction
 Multiplication
 Division
3. Perform series of
operations on
whole numbers
3.1 Interpret MDAS
rule correctly
3.2 Perform two to
four operations
 begins to
understand the
concept of
expression,
equation and
integers.
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1. Perform
operations on whole
numbers following
the correct order
(PEMDAS)
1.1 Give the
meaning of
exponent and
base
1.2 Give the value
of numbers
involving
exponents
1.3 Interpret
PEMDAS rule
correctly
1.4 Perform two
different
operations on
whole numbers
a. with or

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height,
thickness)
1.2.3 shape
1.2.4 position
1.3 Construct sets
with objects 1
to 10 in
1.3.1 the one
more
order
1.3.2 the one
less order
1.4 Compare two
sets using the
expressions
“fewer than”,
“more than”,
and “as many
as”
1.5 Order sets with
1 to 10 objects
from least to
greatest and
vice-versa
1.6 Associate
numbers with
sets having
objects 0 to 10
and tell the
number of
objects in a
set
1.7 Order numbers
0 to 10 from
least to
greatest and
vice-versa
1.8 Read and
through 1000 in
symbols and in
words
2.1 Read numbers
through 1000 in
symbols and in
words
2.2 Write numbers
through 1000 in
symbols and in
words
2.3 Give the place
value of each
digit in a three-
digit number
2.4 Write three-
digit numbers in
expanded form
2.5 Compare
numbers using
>, < and =
2.6 Order numbers
from 101 to
1000 from least
to greatest and
vice versa
3. Skip count by 50s
up to 1000
4. Identify the 11th
through the 20th
objects of given
sets from a given
point of reference
5. Read and write
ordinal numbers
from 11th through
the 20th
6. Identify and use
in symbols and
in words
1.4 Write numbers
through 100 000
in symbols and
in words
1.5 Write four to
five-digit
numbers in
expanded form
1.6 Express the
relationship of
numbers using
expressions "less
than",
“greater than”
and “equal to”
(> < =)
2. Round off
numbers to the
2.1 nearest tens
and hundreds
2.2 nearest
thousands and
ten thousands
3. Tell when a
number is odd or
even
4. Read and write
money in symbols
through 1000
4.1 Read money
value in symbols
through 1000
4.2 Write money
value in symbols
through 1000
4.3 Compare
through
millions/billions
in words
2. Round off
numbers to the
nearest
2.1 tens, hundreds,
thousands
2.2 ten thousands,
hundred
thousands
2.3 millions, billions
B. Comprehension of
Addition
1. Add six or more
digit numbers with
four or more
addends with
sums through
billions
1.1 without
regrouping
1.2 with
regrouping in
any two or
more places
2. Estimate the sum
of six or more digit
addends
3. Add mentally
two to three-digit
numbers with sums
up to 300 without
regrouping
4. Application of
Addition
4.1 Solve word
on whole
numbers
4. Subset of Whole
Numbers
4.1 Differentiate
prime and
composite
numbers
4.2 Find prime
factors of a
number
4.3 Give the
common
factors and
greatest
common factor
of given
numbers
- listing method
- prime
factorization
method
4.4 Give the
common
multiples and
least common
multiple of
given numbers
- listing method
- prime
factorization
method
II. RATIONAL NUMBERS
A. Comprehension of
Fraction
1. Change dissimilar
without
exponents
b. with or
without
parenthesis
or other
grouping
symbols
1.5 Perform more
than two
operations on
whole numbers
a. with or
without
exponents
b. with or
without
parenthesis
or other
grouping
symbols
2 Apply the order of
operations in
solving two to
three-step word
problems
2.1 Solve two to
three-step word
problems
involving whole
numbers
following the
steps in solving
two-step
problems

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write numbers
from 0 to 10 in
symbols
1.9 Tell the
relationship of
numbers from
0 to 10 using
the
expressions
“less than”,
“greater
than”, “equal”
1.10 Associate
numbers with
sets 11-50 and
identify the
number of
objects
1.11 Count by 1’s
through 50
1.12 Skip count by
2’s, 5’s and
10’s through
50
1.13 Associate
numbers with
sets having 51
up to 100
objects and
identify the
number of
objects in a
set
2. Read and write
numbers through
100 in symbols and
in words
2.1 Read numbers
the pattern of
naming ordinal
numbers e.g. 21st,
22nd, 23rd, 24th,
etc.
7. Read and write
money value
through 100
7.1 Read money in
symbols through
100
7.2 Express money
as pesos and
centavos
through 100
7.3 Compare
values of the
different
denominations of
coins and paper
bills through 100
using the relation
symbol
B. Comprehension of
Addition
1. Add two to three-
digit numbers with
sums up to 999
1.1 without
regrouping
1.2 with
regrouping
2. Add two to
three-digit
numbers with
zero in any of the
addends without
value of the
different
denominations
of coins and
bills through
1000
5. Express Roman
numbers through
M in Hindu-Arabic
symbols and vice
versa
5.1 Read and
write the value
of Roman
numbers in
Hindu-Arabic
and vice versa
5.1.1 I to L
5.1.2 L to C
5.1.2 C to D
5.1.3 D to M
B. Comprehension of
Addition
1. Add four to five-
digit numbers up
to four addends
with sums up to 99
999
1.1 without
regrouping
1.2 with
regrouping in
1.2.1 tens and
hundreds
places
1.2.2 thousands
and ten
problems
involving
addition of
whole numbers
including
money with
sums through
millions and
billions without
and with
regrouping
following the
steps in
problem solving
4.2 Solve mentally
one-step word
problems
involving
addition with
sums up to 300
without
regrouping
C. Comprehension of
Subtraction
1. Subtract five or
more digit
numbers from six
or more digit
numbers without
and with
regrouping in any
or all places and
involving three or
more zeros both in
the minuend and
subtrahend
1.1 Subtract five or
fractions to similar
fractions
1.1 Visualize
changing
dissimilar
fractions to
similar fractions
2. Identify equal
fractions using
regions and cross
product method
3. Change fractions
to lowest/higher
term (LCM/GCF)
4. Order dissimilar
fractions written in
different forms
from least to
greatest and vice
versa
5. Estimate fractions
close to 0, 2
1
, or 1
B. Comprehension of
Addition of
Fractions
1.Add similar and
in mixed forms
without and with
regrouping
1.1 Add two to
four similar
fractions
1.2 Visualize
addition of
dissimilar
fractions (using
A. Comprehension of
Decimals
1. Visualize
thousandths and
ten thousandths
1.1 Name a
decimal for a
given model
(region/blocks,
money, number
line, grid)
1.2 Use different
models to show
a given
decimal
(region/block,
money, number
line, grid)
2. Rename fractions
whose
denominators are
powers of 10 in
decimal form
3. Read and write
decimals through
ten thousandths
3.1 Identify the
value/place
value of each
digit in a given
decimal
3.2 Read decimals
through ten
thousandths
3.3 Write decimals
through ten
thousandths in
different

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from 11 through
100 in symbols
and in words
2.2 Write numbers
from 11 through
100 in symbols
and in words
2.3 Give the place
value of each
digit in a one to
two-digit
numbers
2.4 Regroup sets of
ones into sets of
tens and sets of
tens into
hundred using
objects
2.5 Write numbers
from 11 through
100 in
expanded form
3. Read and write
ordinal numbers 1st,
2nd, 3rd up to 10th
3.1 Identify the 1st,
2nd, 3rd up to
the 10th object
in a given set
from a given
set of reference
4. Read and write
money up to 50
4.1 Read and write
the symbol of 
for centavo and
for pesos
4.2 Tell the value of
regrouping with
sums up to 999
2.1 without
regrouping
2.2 with
regrouping
3. Show the
properties of
addition
3.1 Show the
zero/identity
property of
addition
3.2 Show the
commutative
property of
addition
3.3 Show the
associative
property of
addition
4. Add mentally
one to two-digit
numbers with
sums up to 50
5. Application of
Addition
5.1 Solve word
problems
involving
addition of
whole
numbers
including
money with
sums up to 999
without and
with
thousands
places
2.Estimate the sums
of three to five-
digit addends
3.Add mentally one
to two-digit
numbers with sums
up to 100 without
regrouping
4.Application of
Addition
4.1 Solve word
problems
involving
addition of
whole numbers
with sums up to
99 999 including
money
following the
steps in
problem solving
4.2 Solve mentally
one-step word
problems
involving
addition with
sums up to 100
without
regrouping
C. Comprehension of
Subtraction
1. Subtract three to
four-digit numbers
from four to five-
digit numbers with
more digit
numbers from
six or more digit
numbers
without
regrouping
1.2 Subtract five or
more digit
numbers from
six or more digit
numbers with
three
continuous or
non-continuous
zeros in both
minuends and
subtrahend and
with regrouping
in any or all
places
1.3 Estimate the
difference of
numbers with
four to six digits
2. Subtract mentally
numbers with
minuends up to
300 without
regrouping
3. Application of
Subtraction
3.1 Solve one-step
word problems
involving
subtraction of
whole numbers
including
money without
concrete and
visual/pictorial
models)
1.3 Add dissimilar
fractions
1.4 Add dissimilar
fractions and
whole numbers
1.5 Add whole
numbers and
mixed forms
1.6 Add mixed
forms and
dissimilar
fraction
1.7 Add mixed
forms
1.8 Estimate sum
2. Application of
Addition of
Fractions
2.1 Solve word
problems
involving
addition of
similar and
dissimilar
fractions without
or with
regrouping
following the
steps in problem
solving
C. Comprehension of
Subtraction of
Fractions
notations
 Standard
Notation
 Expanded
Notation
 Scientific
Notation
4. Compare and
order decimals
through ten
thousandths
5. Round decimals
through
thousandths
B. Comprehension of
Addition and
Subtraction of
Decimals
1. Add and subtract
decimals and
mixed decimals
through ten
thousandths
without or with
regrouping
1.1Estimate sums
and differences
of decimals
and mixed
decimals
1.2 Add and
subtract whole
numbers and
decimals
1.3 Add and
subtract
decimals

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a given set of
coins and paper
bills up to 50
4.3 Compare
values of the
different
denominations of
coins and paper
bills
4.4 through 50
using the relation
symbols
4.5 Skip count by
5s, 10s up to
50
B. Addition and
Subtraction of Whole
Numbers
Addition of Whole
Numbers
1. Add one to two-
digit numbers with
sum through 99
without and with
regrouping
1.1 Add two to
three one-
digit numbers
horizontally
and vertically
with sums up
to 18
1.1.1 Join two
sets with one
to nine
objects
regrouping
5.1.1 Analyze
the word
problem
5.1.1.1 Tell:
 what is
asked
 what is/
are given
 the word
clues
 the
operation
to be use
5.1.2 Transform
the word
problem into
a number
sentence
5.1.3 Use the
correct
operation
5.1.4 State
the complete
answer
C. Comprehension of
Subtraction
1. Subtract two to
three-digit
numbers with
minuends up to
999 without and
with regrouping
1.1 Illustrate how
subtraction is
used when:
1.1.1taking
minuends up to
99,999 without
and with
regrouping and
with zero difficulty
1.1 Subtract three-
digit number
from four to
five-digit
numbers with
minuends up to
99,999 without
regrouping
1.2 Subtract three
to four-digit
numbers from
four to five-digit
numbers with
regrouping
1.2.1 in the
thousands
place
1.2.2 in the ten
thousands
place
1.2.3 with zero
difficulty
2. Estimate the
difference of two
numbers with
three to four digits
3. Subtract mentally
two-digit numbers
with minuends up
to 99 without
regrouping
4. Application of
Subtraction
and with
regrouping
following the
steps in
problem-solving
3.2 Solve mentally
one-step word
problems
involving
subtraction
without
regrouping
following the
steps in
problem solving
4. Application of
Addition and
Subtraction
4.1 Solve two-step
word problems
involving
addition and
subtraction
including
money
following the
steps in solving
2-step problems
D. Comprehension of
Multiplication
1. Show the
properties of
multiplication
 Zero Property
 Identity
Property
 Distributive
1. Subtract fractions
and mixed forms
with common
denominators
without and with
regrouping
1.1 Visualize
subtraction of
fraction and
mixed form
(using concrete
and
visual/pictorial
models)
1.2 Subtract
whole numbers
from mixed
forms without
and with
regrouping
1.3 Subtract
fractions from
whole numbers
1.4 Subtract
fractions from
mixed numbers
without and
with regrouping
1.5 Subtract mixed
numbers from
whole numbers
1.6 Subtract mixed
numbers from
mixed numbers
(with similar
fractions)withou
t and with
regrouping
through ten
thousandths
without and
with regrouping
1.4 Add and
subtract mixed
decimals with
regrouping
1.5 Apply the
different
properties of
addition to
compute sums
mentally
1.6 Application of
addition and
subtraction of
decimals
1.6.1 Solve one
to three-step
word
problems
involving
addition and
subtraction of
decimals
including
money
following the
steps in
solving
problems
C. Comprehension of
Multiplication of
Decimals
1. Multiply decimals
and mixed

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1.1.2 Show the
relationship
of joining sets
to addition of
whole
numbers
1.1.3 Add two
one-digit
numbers
having sums
of :
- 6 and
less
- 7
through
10 (after
concept
of 1-10)
1.1.4 Illustrate
that any
given
number plus
zero is the
same
number
1.1.5 Show
that
changing the
order of two
addends
does not
affect the
sum
1.1.6 Add
three one-
digit numbers
having sums
up to 18
away from a
given set
1.1.2 finding a
missing
addend
1.2 Subtract two
to three-digit
numbers
without
regrouping
1.3 Subtract two
to three-digit
numbers with
regrouping
1.3.1 in the tens
place
without or
with zero
difficulty
1.3.2 in the
hundreds
place without
or with zero
difficulty
2. Use addition to
check
subtraction
3. Subtract
mentally one-
digit number
from one to two-
digit numbers
with minuends
up to 50 without
regrouping
4. Application of
Subtraction
4.1 Solve one-step
4.1 Solve one-step
word problems
involving
subtraction of
whole numbers
including
money with
minuends up to
99,999 without
and with
regrouping
following the
steps in
problem solving
4.2 Solve mentally
one-step word
problems
involving
subtraction
without
regrouping
4.3 Solve two-step
word problems
involving
addition and
subtraction of
whole numbers
including money
following the
steps in solving 2-
step problems
D. Comprehension of
Multiplication
1. Differentiate prime
and composite
numbers
1.1 Identify prime
Property of
Multiplication
over Addition
2. Multiply five or
more digit factors
by three to five-
digit factors
without and with
regrouping and
with zero in any of
the factors
2.1 Multiply five or
more digit
factors by
three- to five-
digit factors
without
regrouping
more digit
factors by
three- to five-
digit factors
with regrouping
more digit
factors having
one to three
zeros in both
factors without
and with
regrouping
more digit
factors by
multiples of 10,
100 and 1,000
3. Estimate the
2. Subtract dissimilar
fractions without
and with
regrouping
2.1 Visualize
subtraction of
dissimilar
fractions
2.2 Subtract
fractions from
mixed numbers
without and
with regrouping
2.3 Subtract mixed
numbers from
mixed numbers
without and
with regrouping
3. Application of
Subtraction of
Fractions
3.1 Solve word
problems
involving
subtraction of
fractions
following the
steps in
problem solving
3.2 Solve two-step
word problems
involving
addition and
subtraction of
fraction
following the
steps in solving
2-step problems
decimals through
thousandths
without and with
regrouping and
1.1 Estimate
products of
whole numbers
and decimals
1.2 Multiply one to
three-digit
factors by one
to two-digit
factors of whole
numbers and
decimals
without and
with regrouping
and with zero
difficulty
1.3 Multiply
hundredths by
hundredths
1.4 Multiply mixed
decimals by
mixed decimals
with
hundredths
1.5 Multiply
mentally
decimals by 10,
100 and 1,000
1.6 Multiply
mentally
decimals by 0.1,
0.01 and 0.001
2. Apply the
properties of

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1.1.7 Show
that
changing the
grouping of
three or more
addends
helps make
computation
easy and
does not
change the
sum
2. Add one to two-
digit numbers with
sums through 99
- without
regrouping
- with regrouping
3. Add mentally two
to three one-digit
numbers with sums
up to 18
4. Application of
Addition
4.1 Solve one-step
word problems
involving
addition of
whole
numbers
including
money with
sums up to 99
without and
with
regrouping
4.1.1 Analyze
the word
word problems
involving
subtraction of
whole
numbers
including
money with
minuends up
to 999 without
and with
regrouping
4.1.1 Analyze
the word
problem
4.1.1.1 Tell:
 what is
asked
 what
is/are
given
 the
word
clue/s
 the
operatio
n to be
used
4.1.2 Transform
the word
problem into
a number
sentence
4.1.3 Use the
correct
operation
4.1.4 State the
complete
answer
and
composite
numbers
2. Multiply two to
four-digit numbers
by one to two-
digit numbers
without and with
regrouping in any
or all places
2.1 Multiply two to
four-digit
numbers
without and
with regrouping
2.1.1 Show that
changing the
order and/or
regrouping in
multiplication
makes
computation
easy
(commutativ
e/
associative)
2.1.2 Multiply
two to four-
digit numbers
by one to
two-digit
numbers
without
regrouping
2.1.3 Multiply
two to four-
digit numbers
by one to
products of five or
more digits by two
to three-digit
numbers
4. Multiply mentally
two-digit numbers
with products up
to 200 without
regrouping
5. Application of
Multiplication
5.1 Solve word
problems
involving
multiplication of
whole numbers
including
money
following the
steps in
problem solving
5.2 Solve two-step
word problems
involving
multiplication and
any of addition/
subtraction
following the steps
in solving two-step
problems
E. Comprehension of
Division
1. Divide five or more
digit numbers by
three or more digit
numbers without
or with remainder
D. Comprehension of
Multiplication of
Fractions
1. Multiply fractions
1.1 fraction by a
whole number
1.2 mixed form by
a fraction
1.3 mixed form by
a mixed form
fractional units
3. Application of
multiplication of
fractions
3.1 Solve word
problems
involving
multiplication of
fractions
following the
steps in
problem solving
3.2 Solve two-step
word problems
involving
multiplication
and any of
addition and
subtraction
following the
steps in solving
two-step
problems
E. Comprehension of
Ratio
multiplication to
compute
products
2.1 Commutative
property of
multiplication
2.2 Associative
property of
multiplication
2.3 Distributive
property of
multiplication
over addition
3. Application of
multiplication of
decimals
3.1 Solve word
problems
involving
multiplication of
decimals
including
money followin
g the steps in
solving
problems
3.2 Solve two to
three-step word
problems
involving
addition,
subtraction and
multiplication of
decimals
including
money followin
g the steps in
solving two-step

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problem
4.1.1.1 Tell:
 what is
asked
 what
is/are
given
 the
word
clues
 the
operatio
n to be
used
4.2 Transform the
word problem
into a
number
sentence
4.3 Use the
correct
operation
4.4 State the
complete answer
Comprehension of
Subtraction
1. Subtract one to
two-digit
numbers from
one to two-digit
numbers with
minuends up to
99 without and
with regrouping
1.1 Visualize
situations
when
5. Application of
Addition and
Subtraction
5.1 Solve two-step
word problems
involving
addition and
subtraction of
two to three-
digit numbers
including
money
5.1.1 Analyze
the word
problems
5.1.1.1 Tell:
 what is
asked
 what
is/are
given
 the
word
clue/s
 the
hidden
question
 the
operatio
n to be
used
5.1.2 Transform
the word
problem into
a number
sentence
5.1.3 Use the
correct
two-digit
numbers with
regrouping
2.1.4 Multiply
two to four-
digit numbers
by one-digit
numbers with
zero in any of
the factors
2.1.5 Multiply
two to four-
digit numbers
by multiples
of 10 and 100
3. Estimate the
product of two to
four-digit numbers
by one to four-
digit numbers
two-digit numbers
by one-digit
numbers without
regrouping with
products up to
100
5. Application of
Multiplication
5.1 Solve one-step
word problems
involving
multiplication of
whole numbers
including
money
following the
steps in
and with zero
difficulty.
1.1 Divide five or
more digit
number by
three or more
digit numbers
without
remainder
1.2 Divide five or
more digit
numbers by
three or more
digit numbers
with remainder
1.3 Divide five or
more digit
numbers by three
or more digit
numbers with
zeros in the middle
or continuous
zeros in the
dividend
2. Divide multiples of
10 by 10 or 100 or
1000
3. Estimate the
quotient of five or
more digit
dividends by three
or more digit
divisors
4. Divide mentally
two to three-digit
numbers by one-
digit numbers
without remainder
1. Express the ratio of
two quantities
1.1 Visualize the
ratio of two
given sets of
objects
1.2 Express the
ratio of two
numbers by
using either
colon (:) or a
fraction
2. Reduce ratios to
lowest terms.
3. Identify equivalent
ratios
4. Application of
Ratios
4.1 Solve word
problems
involving ratio
following the
steps in solving
problems
F. Comprehension of
Decimals
1. Read and write
decimals through
thousandths
1.1 Rename
fractions whose
denominators
are powers of
10 in decimal
form and vice
versa
1.2 Give the
problems
D. Comprehension of
Division of Decimals
1. Estimate quotients
of whole numbers
and decimals
2. Divide
2.1 whole
numbers (two
to five-digit
dividends) by
decimals (one
to two- digit
divisors)
2.2 Differentiate
between
terminating and
repeating from
non-terminating
decimal
quotients
2.3 mixed
decimals by
whole numbers
2.3.1 Visualize
division using
money as
model
2.4 whole
numbers by
decimals and
mixed decimals
2.5 mixed
decimals by
mixed decimals
3. Divide decimals
by 10, 100, 1,000

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12
subtraction is
used
1.1.1 Remove a
subset from a
given set of
objects (taking
away)
1.1.1.1 Show
the
relationshi
p of the
removal
of a
group of
objects
from a
given set
to
subtractin
g of
whole
numbers
1.1.1.2 Show
that
subtractio
n is the
inverse of
addition
1.2 Subtract one-
digit numbers
with
minuends
through 18
(basic facts)
1.3 Subtract one
to two-digit
numbers with
minuends up
operation
5.1.4 State the
complete
answer
D. Comprehension of
Multiplication
1. Multiply one to
two-digit
numbers by one-
digit numbers
with products up
to 81
1.1 Multiply one-
digit by one-
digit number
with or without
regrouping
with products
up to 45
1.1.1 Show the
relationship
of putting
together two
or more sets
having the
same
number of
elements to
repeated
addition
1.1.2 Show
multiplication
of whole
numbers as
repeated
addition
using the
problem solving
5.2 Solve two-step
word problems
involving
multiplication as
well as
addition/
subtraction
including
money
following the
steps in solving
2-step problems
E. Comprehension of
Division
1. Divide two to
four-digit numbers
by one to two-
digit numbers
without or with
remainder and
1.1 Show that
renaming two
to three- digit
dividend helps
make
computation
easy
1.2 Divide two to
three-digit
numbers by
one-digit
numbers
without
remainder
1.3 Divide two to
5. Application of
Division
5.1 Solve one-step
word problems
involving
division of five
or more digit
numbers by
three or more
digit numbers
including
money
following the
steps in
problem solving
5.2 Solve two to
three-step word
problems
involving
division and any
one or two of
the other
fundamental
operations
learned
including
money
following the
steps in solving
two-step
problems
A. Comprehension of
Decimals and
Money
1. Read and write
place value of
each digit of a
given decimal
2. Round decimals
to the nearest
tenths and
hundredths
G. Comprehension of
Addition and
Subtraction of
Decimals
1. Add and subtract
decimals through
thousandths
without and with
regrouping
2. Add and subtract
mixed decimals
without and with
regrouping
3. Add and subtract
mixed decimals
from whole
numbers without
and with
regrouping
4. Application of
addition and
subtraction of
decimals
4.1 Solve word
problems
involving either
addition or
subtraction of
decimals
including
mentally
4. Divide decimals
by 0.1, 0.01, 0.001
mentally
5. Application of
division of
decimals
5.1 Solve word
problems
involving
division of
decimals
including
money followin
g the steps in
solving
problems
5.2 Solve two to
three-step word
problems
involving
decimals
including money
following the
steps in solving
two-step
problems
D. Comprehension of
Fractions
1. Write the fraction
described by a
region, set and
number line
2. Rename
fractions as
decimals and vice
versa

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13
to 99
1.3.1 without
regrouping
1.3.2 with
regrouping
2. Subtract
mentally one-
digit numbers
from minuends
up to 18 without
regrouping
3. Application of
Subtraction
3.1 Solve word
problems
involving
subtraction
of whole
numbers
including
money with
minuends up
to 99 without
and with
regrouping
3.1.1Analyze the
word
problems
3.1.1.1 Tell:
 what is
asked
 what
is/are
given
 the
word
clues
 the
number line
or array, etc.
1.1.3 Transform
an addition
sentence into
a
multiplication
sentence
1.1.4 Identify
the parts of a
multiplication
sentence
1.1.5 Show that
any number
multiplied by
one (1) is the
same
number
1.1.6 Show that
zero
multiplied by
any number
is zero and
vice versa
1.2 Give the
factors of a
given
number
1.3 Multiply one
to two-digit
numbers by
one-digit
number with
products up
to 81
1.4 Multiply
mentally
one-digit
three-digit
numbers by
one-digit
number with
remainder
1.4 Divide two to
three-digit
numbers by
multiples of 10
up to 90
1.5 Divide two to
three-digit
numbers by
one to two-digit
numbers with
zero difficulty
1.6 Divide three to
four-digit
numbers by
one to two-digit
numbers
without or with
remainder and
with zero
difficulty
1.6.1 Divide three
to four-digit
numbers by
one-digit
number without
remainder
1.6.2 Divide three
to four-digit
numbers by
one to two-digit
numbers with
remainder
1.6.3 Divide three
common fractions
in decimal form
through
hundredths
1.1 Visualize
common
fractions as
decimals using
models like
blocks, grid and
money
1.2 Write common
fractions in
decimal form
1.3 Read and
write decimal
numbers
through
hundredths
1.4 Rename
fractions whose
denominators
are 10 and 100
in decimal form
and vice versa
1.5 Give the place
value of each
digit of a given
decimal
through
hundredths
2. Express money as
pesos/centavos
3. Round decimal to
the nearest tenths
B. Comprehension of
Addition and
money
following the
steps in
problem solving
4.2 Solve two-step
word problems
involving
addition and
subtraction of
decimals money
following the
steps in solving
two-step
problems
H. Comprehension of
Multiplication of
Decimals
1.1 Visualize
multiplication of
decimals using
models
1.2 Multiply tenths
by another
tenths
1.3 Multiply
hundredths by
tenths and vice
versa
2. Multiply mixed
decimals with
tenths and
hundredths by
whole numbers
3. Multiply mixed
decimals by
mixed decimals
3. Form equivalent
fractions
4. Solve for the
missing terms in a
pair of equivalent
fractions
5. Reduce
fractions to lowest
terms
6. Change mixed
numbers to
improper fractions
and vice versa
7. Estimate fractions
close to 0, 2
1
or 1
8. Find the least
common
denominator
(LCD) of a set of
fraction
9. Compare
fractions and
mixed forms using
9.1 fraction sense,
visual
reasoning,
renaming to like
forms
9.2 cross products
method
9.3 LCD method
10. Order fractions
in simple and
mixed forms in
ascending or
descending order
F. Comprehension of

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14
operatio
n to be
used
3.1.2 Transform
the word
problem
into a
number
sentence
3.1.3 Use the
correct
operation
3.1.4 State the
complete
answers
A. Comprehension of
Fractions
1. Recognize
2
1
and
4
1
of a
whole
2. Separate a
whole object
into
halves/fourths
3. Separate group
of objects into
halves/fourths
III. MEASUREMENT
A. Comprehension of
Time Measure
1. Tell the number
numbers with
products up
to 81 without
regrouping
2. Application of
Multiplication
2.1 Solve one-step
word problems
involving
multiplication
of whole
numbers
including
money
2.1.1 Analyze
the word
problem
2.1.1.1 Tell:
 what is
asked
 what
is/are
given
 the
word
clue/s
 the
operatio
n to be
used
2.1.2 Transform the
word problem
into a number
sentence
2.1.3 Use the
correct
operation
2.1.4 State the
to four-digit
numbers by
one to two-digit
numbers with
zero difficulty
5 by 5
10 by 10 and 100
4. Estimate the
quotient of two to
four-digit numbers
by one to two-
digit numbers
5. Divide mentally
two-digit numbers
through 99 by
one-digit numbers
without remainder
6. Application of
Division
6.1 Solve one-
step word
problem
involving
division of two
to four-digit
numbers by
one to two-digit
numbers
including
money
following the
steps in solving
problems
6.2 Solve two-step
word problems
involving
Subtraction of
Decimals
1. Add and
subtract decimals
through
hundredths
without and with
regrouping
1.1 Add decimals
through
hundredths
without and
with regrouping
1.2 Subtract
decimals
through
hundredths
without or with
regrouping
2. Add and subtract
mixed decimals
with regrouping
2.1 Add mixed
decimals with
regrouping
2.2 Subtract mixed
decimals with
regrouping
3. Application of
addition and
subtraction of
decimals
3.1 Solve word
problems
involving either
addition or
subtraction of
decimals
with tenths and
hundredths
by 10 and 100
mentally by 0.1,
and 0.01
6. Application of
Multiplication of
Decimals
6.1 Solve word
problems
involving
multiplication of
decimals
including money
following the
steps in solving
problems
I. Comprehension of
Division of Decimals
1. Divide decimals
through
hundredths
1.1Visualize
division of
decimals using
models
1.2 Divide
decimals by
decimals
through
hundredths
1.3 Divide
decimals by
whole numbers
2. Application of
Addition and
Subtraction of
Fractions
1. Visualize addition
and subtraction of
fractions (using
concrete and
visual/ pictorial
models)
2. Estimate sums and
differences of
fractions in simple
and mixed forms
3. Add and subtract
similar fractions in
simple or mixed
forms without
regrouping
4. Add and subtract
similar fractions in
simple or mixed
forms with
regrouping
5. Add and subtract
in simple or mixed
forms without
regrouping
6. Add and subtract
in simple or mixed
forms with
regrouping
7. Add mentally
similar fractions
using the
properties of
addition

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15
of days in a
week; months
in a year using
the calendar
2. Indicate time to
the hour/half
hour
2.1 Show that 60
minutes
make an
hour
2.2 Express the
relationship
between
the “hour
hand” and
the “minute
hand” of
the clock
3. Indicate time to
the nearest 15
minutes of an
hour like 1:15,
1:30, 1:45
4. Read and write
time as shown on
the clock
B. Comprehension of
Linear Measure
1. Make
measurement
using non-
standard units of
linear measures
2. Compare
among the non-
standard units of
complete
answer
2.2 Solve two-step
word problems
involving
multiplication of
whole numbers
as well as
addition and
subtraction
including money
following the
steps in solving 2-
step problem
E. Comprehension of
Division
1. Divide whole
numbers with
dividends
through 81 by
one-digit divisors
1.1 Show division
 by partition
(including the
equal parts of
a number)
 by distribution
(finding how
many times a
number is
contained in a
given number)
 as repeated
subtraction
 as inverse of
multiplication
1.2 Identify the
division and any
one of the
fundamental
operations
including
money
following the
steps in solving
2-step problems
6.3 Solve three-
step word
problems
involving
division and any
two of the other
fundamental
operations
including
money
following the
steps in solving
2-step problems
II. Rational Numbers
A. Comprehension of
Fractions
1. Order fractions
less than
one/equal to
one/more than
one
1.1 Identify
fractions less
than one
1.2 Identify
fractions equal
to one
including
money
following the
steps in
problem solving
3.2 Solve one to
two-step word
problems
involving
addition and
subtraction of
decimals
including money
following the
steps in solving
two-step
problems
C. Comprehension of
Fractions
1. Differentiate
fractions including
those with
denominators of
10 and 100
1.1 Identify proper
fraction/
improper
fraction/mixed
forms from a
given set of
fractions
including those
with
denominators
of 10 and 100
1.1.1 Identify
fractions
Division of
Decimals
2.1 Solve word
problems
involving
division of
decimals
following the
steps in
problem solving
J. Comprehension of
Percent
1. Relate fractions,
ratios, decimals
and percent
1.1 Visualize the
meaning of
percent (%)
1.2 Give the
relationship
 among
fractions, ratios
and percents
(with visual
models)
 between
percent and
decimal (with
visual models)
 among
fractions, ratios,
decimals and
percents
2. Give the meaning
of the elements
used in solving
percentage
8. Application of
addition and
subtraction of
fractions
8.1 Solve word
problems
involving
addition or
subtraction of
fractions in
simple or mixed
forms with or
without
regrouping follo
wing the steps
in solving
problems
8.2 Solve two-step
word problems
involving
addition and
subtraction of
fractions in
simple and
mixed forms
without and
with
regrouping follo
wing the steps
in solving two-
step problems
G. Comprehension of
Multiplication of
Fractions
1. Simplify factors by
cancellation
method before

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16
linear measure in
terms of
consistency and
accuracy
C. Comprehension of
Mass Measure
1. Measure mass
using non-
standard units of
mass measures
2. Compare
among the non-
standard units of
mass measure in
terms of
consistency and
accuracy
D. Comprehension of
Area
1. Measure area
using non-
standard units
2. Compare
among the non-
standard units of
measuring area
in terms of
consistency and
accuracy
E. Comprehension of
Capacity
1. Measure
capacity using
non-standard
units
parts of a
division
sentence
1.3 Transform a
division
sentence into
multiplication
sentence
and vice
versa
1.4 Divide one to
two-digit
numbers by
one-digit
numbers
1.5 Divide two-
digit numbers
with
dividends
through 81
2. Application of
Division
2.1Solve one-step
word problems
involving
division of
whole
numbers with
dividends up
to 81
2.1.1 Analyze
the word
problem
2.1.1.1 Tell:
 what is
asked
 what is/are
given
1.3 Comprehend
fractions more
than one
1.3.1 Recognize
fractions
more than
one
1.3.2 Separate
group of
objects to
show
fractions
more than
one
1.3.3 Read and
write
fractions
more than
one in
symbols and
words
1.4 Compare
fractions less
than one/
equal to one/
more than one
with the same
denominator
1.5 Order fractions
less than
one/equal to
one/more than
one with the
same
denominator in
increasing or
decreasing
order
using regions,
sets and
number line
1.1.2 Use
fraction to
represent
division
1.2 Identify similar
and dissimilar
fractions from a
given set of
fractions
2. Order similar
fractions written in
different forms
from least to
greatest and vice
versa
3. Change improper
fraction to mixed
forms and vice
versa
4. Change one (1) to
fraction form and
vice versa
5. Rename decimals
to fractions
D. Comprehension of
Addition and
Subtraction of
Fraction
1. Add similar
fractions and
whole numbers
without
regrouping
1.1 Visualize
problems
2.1 Percentage
2.2 Rate or
Percent
2.3 Base
3. Determine the
percentage of a
number
3.1 Identify the
base percentage
and rate in a
problem
3.2 Find the
percentage in a
given problem
3.3 Solve word
problems involving
finding the
percentage
III. Geometry
A. Comprehension of
Polygons
1. Describe five or
more sided
polygons
1.1 Identify five or
more sided
polygons
1.2 Illustrate five or
more sided
polygons
2. Describe similar
and congruent
polygons
2.1 Visualize
congruent
multiplying
in simple and
mixed forms
3. Show that
multiplying a
fraction by its
reciprocal is equal
to 1
4. Application of
Multiplication of
Fractions
4.1 Solve word
problems
involving
multiplication of
numbers in
mixed
forms following
the steps in
solving
problems
4.2 Solve two to
three-step word
problems
involving
addition,
subtraction,
and
multiplication of
numbers in
mixed forms
following the
steps in solving
two-step
problems
H. Comprehension of

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2. Compare
among the non-
standard units of
capacity
measure in terms
of accuracy of
measurement
 the word
clue/s
 the
operation
to be used
2.1.2 Transform
the word
problem into
a number
sentence
2.1.3 Use the
correct
operation
2.1.4 State the
complete
answer
2.2 Solve two-step
word problem
involving
division of
whole
numbers as
well as
addition/
subtraction/
multiplication
including
money
following the
steps in solving
2-step
problem
2.2.1 Analyze
the word
problem
2.2.1.1 Tell:
 what is
asked
2. Change fractions
to lowest forms
2.1 Find the
greatest
common factor
(GCF) of two
given number
2.2 Reduce
fractions to
lowest terms
III. Geometry
A. Comprehension of
Line and Line
Segment
1. Distinguish
perpendicular,
parallel and
intersecting lines
1.1 Visualize
perpendicular,
parallel and
intersecting
lines
1.2 Identify
perpendicular,
parallel and
intersecting
lines
2. Draw congruent
line segments
2.1 Visualize
congruent line
segments
2.2 Identify
congruent line
segments
addition of
similar fractions
1.2 Add similar
fractions
1.3 Add a fraction
and a whole
number
1.4 Add mentally
similar fractions
2. Subtract similar
fractions without
regrouping
2.1 Visualize
subtraction of
similar fractions
2.2 Subtract similar
fractions
2.3 Subtract a
fraction from a
whole number
2.4 Subtract
mentally similar
fractions
3. Application of
Addition and
Subtraction of
Fractions
3.1 Solve word
problems
involving
addition of
similar fractions
without
regrouping
following the
steps in
problem solving
3.2 Solve word
polygons
2.2 Identify
congruent
polygons
2.3 Illustrate
congruent
polygons
2.4 Visualize similar
polygons
2.5 Identify similar
polygons
2.6 Illustrate similar
polygons
3. Describe a circle
3.1 Visualize circle
3.2 Identify the
parts of a circle
(radius and
diameter)
3.3 Illustrate circles
with different
radii
IV. Measurement
A. Comprehension of
Circumference of a
Circle
1. Find the
circumference of
a circle in
centimetre/ metre
1.1 Visualize the
circumference
of a circle
1.2 Derive a
formula for
finding the
Division of
Fractions
1. Visualize division
of a whole
number by a
fraction; a fraction
by another
fraction
2. Divide a fraction
by a fraction
3. Divide a whole
number by a
fraction and vice
versa
4. Divide mixed
number by a
fraction and vice
versa
5. Divide mixed
number by a
whole number
and vice versa
6. Divide mixed
number by a
mixed number
7. Application of
Division of Fraction
7.1 Solve word
problems
involving
division of
fractions followi
ng the steps in
solving
problems
7.2 Solve two to
three-step word
problems

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18
 what
is/are
given
 the
word
clue/s
 the
hidden
question
 the
operatio
ns to be
used
2.2.1.2Transform
the word
problems into a
number
sentence
2.2.2 Use the
correct
operation
2.2.3 State
the complete
answer
A. Comprehension of
Unit Fractions
1. Identify 3
1
, 5
1
, 6
1
of a given
whole/group of
objects
2. Read and write 3
1
,
5
1
, 6
1
in symbols
and in words
3. Identify other unit
3. Determine which
motion turn, flip or
slide creates a
given tessellation
4. Form simple
symmetrical
designs out of
given shapes
IV. Measurement
A. Comprehension of
Time Measure
1. Convert time
measure from
smaller to larger
units and vice
versa
1.1 seconds to
minutes,
minutes to
hours, hours to
day
1.2 days to years,
years to days
2. Find the exact
time between
dates
3. Application of
time measure
3.1 Solve one-
step word
problems
involving time
measure
following the
steps in
problem solving
problems
involving
subtraction of
similar fractions
without
regrouping
following the
steps in
problem solving
E. Comprehension of
Multiplication of
Fractions
1.1 Visualize
multiplication of
fractions (visual
models)
1.2 Find a
fractional part
of a whole
number of a
fraction
1.2.1 Translate
expressions
such as:
2
1
of 6 ,
3
2
of 6
1
1.3 Multiply a
fraction by
another
fraction
2. Application of
Multiplication
2.1 Solve word
problems
involving
distance
around a circle
1.3 Find the
circumference
of the given
circle
2. Application of
Circumference
2.1 Solve word
problems
involving
circumference
measure
following the
steps in
problem solving
B. Comprehension of
Area
1. Convert one
square unit of
measure to a
larger or smaller
unit
2. Find the area of
trapezoid and
circle in square
metres/
centimetres
1.1 Visualize the
area of
trapezoid and
circle
2.2 Derive a
formula for
finding the area
of trapezoid
and circle
involving all
operations on
fractions followin
g the steps in
solving two-step
problems
I. Comprehension of
Ratio and
Proportion
1. Form ratio and
proportion for
groups of
objects/numbers
1.1 Visualize the
meaning of
proportion
1.2 Tell whether
two ratios make
a proportion
1.3 Find a missing
term in a
proportion
2. Application of
Ratio and
proportion
2.1 Set up a
proportion for a
given situation
2.2 Solve word
problems with:
 Direct
proportion
 Partitive
proportion
 Inverse
proportion

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19
fractions
4. Read and write
other unit fractions
in symbols and in
words
5. Compare other
unit fractions using
relation symbols
B. Comprehension of
Other Fractions
Less Than One
2. Identify other
fractions less
than one
2.1 Recognize
fractional
parts of a
whole
2.2 Separate a
whole or
group of
objects into
fractional
parts
2.3 Read and
write other
fractions less
than one in
symbols and
in words
III. Geometry
A. Comprehension of
Shapes
1. Identify different
shapes common
B. Comprehension of
Area
1. Find the area of a
figure in square
centimetres/
metres
1.1 Visualize the
area of a
rectangle
1.2 Visualize the
area of a
square
1.3 Derive a
formula for
finding the area
of a rectangle/
square
2. Application of
concept of area
2.1 Solve word
problems involving
area of
rectangle/square
following the steps
in problem solving
C. Comprehension of
Capacity
1. Find capacity
using standard
units of measure
(base unit: litre)
2. Convert capacity
measure from
smaller to larger
units and vice
versa (ml to L; L to
ml)
multiplication of
fractions
following the
steps in
problem solving
III. GEOMETRY
A. Comprehension of
Angles and Plane
Figures
1. Describe different
kinds of angles
1.1 Visualize
different kinds
of angles
1.2 Identify parts
of an angle
1.3 Name
different kinds
of angles such
as right, acute
and obtuse
1.4 Classify angles
as right, acute
or obtuse
1.5 Identify
congruent
angles
1.6 Draw
congruent
angles
2. Describe plane
figures according
to their sides,
corners and their
functional use
2.1 square
2.3 Find the area
of trapezoid
and circle
3. Application of
Measurement of
Area
32.1 Solve word
problems
involving area
of trapezoid
and circle
following the
steps in
problem solving
C. Comprehension of
Volume
1. Find the volume of
cube/ rectangular
prism
1.1 Name the unit
of measure
used for
measuring the
volume of
cube/
rectangular
prism
1.2 Convert one
cubic unit of
measure to a
larger or smaller
unit
1.3 Derive a
formula for
finding the
volume of
cube/
J. Comprehension of
Percent
1.Review the
meaning of the
elements used in
solving
percentage
problems
1.1 Percentage
1.2 Rate or
Percent
1.3 Base
2. Determine the
percentage, rate
and base in a
given problem
2.1 Set up a
proportion to
solve problems
2.2 Solve the three
types of
percentage
problems
2.2.1 Find the
percentage
when the
rate and
base are
given
2.2.2 Find the
rate or
percent
when the
percentage
and base are
given
2.2.3 Find the
base when

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20
at home and in
the school
2. Classify shapes
according to
numbers of sides
and corners
2.1 Describe
shapes
according to
number of
sides
2.2 Describe
shapes
according to
number of
corners
2.3 Compare
shapes
according to
number of
sides and
corners
3. Tessellate a
surface using
triangles and
squares
4. Identify
shapes/figures
that show
symmetry
IV. Measurement
A. Comprehension of
Time Measure
1. Use the calendar
to tell the
number of:
3. Application of
measurement of
capacity
3.1 Solve word
problems
involving
capacity
measure
following the
steps in
problem solving
V. Graphs
A. Comprehension of
Pictograph
1. Interpret data
presented in a
pictograph
1.1 Name the
following parts
of a pictograph
a. title
b. legend
c. labels
1.2 Interpret the
graph
2. Construct
pictograph
2.1 Organize data
in a pictograph
VI. Calculator
1. Identify the parts
of a calculator
2. Tell the function of
2.2 rectangle
2.3 triangle
2.3.1 parts
2.3.2 types
according to
sides
2.3.3 types
according to
angles
3. Illustrate three or
four-sided plane
figures using ruler
and protractor
IV. MEASUREMENT
A. Comprehension of
Perimeter
1. Find the perimeter
of regular
polygons
1.1 triangle
1.2 quadrilateral
1.3 pentagon, etc.
2. Derive a formula
for finding the
perimeter of
regular polygons
3. Find the
perimeter of
irregular polygons
4. Application of
Perimeter
4.1 Solve word
problems
involving
perimeter
measures
rectangular
prism
2. Application of
Measurement of
Volume
2.1 Solve word
problem
involving
measurement
of volume
following the
steps in
problem solving
D. Comprehension of
Temperature
Measure
1. Give body/
weather
temperature using
degree Celsius
1.1 Identify the
parts of a
thermometer
1.2 Read a
thermometer
2. Application of
Temperature
Measure
2.1 Solve word
problem
involving
body/weather
temperature
following the
steps in
problem solving
the
percentage
or rate are
given
3. Compute
common
percentage
problems mentally
4. Solve word
problems involving
finding the
percentage/rate/
base
4.1 Percent of
increase/
decrease
 Discounts
 Original Price
 Rate of
Discount
 Sale Price
 Marked-up
Price
4.2 Commission
 Rate of
Commission
 Amount of
commission
 Total Sales
 Net Sales/
Income
4.3 Sales Tax
 Rate of Sales
Tax
 Selling Price
4.4 Simple Interest
 Principal
Rate

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21
1.1 weeks in a
month
1.2 days in a
month
1.3 months in a
year
1.4 weeks in a
year
1.5 days in a
year
2. Determine the
number of days
in a given
number of
 weeks
 months
3. Tell the time
using the digital
clock
4. Compare the
digital clock and
analog clock (a
clock with
minute and hour
hands)
5. Application of
time measure
5.1 Solve simple
word problems
involving time
without
conversion of
standard units
B. Comprehension of
Linear Measure
1. Make
measurement
each part of a
calculator
following the
steps in
problem solving
B. Comprehension of
Area
1. Find the area of
parallelogram
and triangle in
square metre/
centimetre
1.1 Derive a
formula for
finding the area
of a:
1.1.1parallelogr
am
1.1.2 triangle
1.2 Find the area
of
parallelogram
and triangle
2. Solve word
problems involving
the area of
parallelogram
and triangle
following the steps
in problem solving
C. Comprehension of
Volume
1. Make
measurement
using non-
standard units:
 cubes
 marbles
V. Graphs
A. Comprehension of
Line Graph
1. Read/Interpret
data presented in
a line graph
2. Construct a line
graph
2.1 Organize data
in a line graph
3. Find the average
of data presented
in a line graph
 Time
 Total Amount
Due
III. GEOMETRY
A. Comprehension of
Spatial Figures
1. Describe different
spatial figures
1.1 Visualize the
different spatial
figures, cube,
prism, cylinder,
sphere,
pyramid, cone,
etc.
1.2 Identify the
nets of the
following spatial
figures:
cube, prism,
cylinder,
sphere,
pyramid, and
cone
1.3 Identify the
different spatial
figures and their
functional use
1.4 Illustrate the
different spatial
figures
IV. Measurement
A. Comprehension of
Surface Area

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22
using standard
units of linear
measure (metre:
base unit)
2. Approximate
measurement of
length, width,
height and
distance
C. Comprehension of
Mass Measure
1. Make
measurement
using standard
units of mass
measure (gram:
base unit)
2. Approximate
measurement of
mass
3. Investigate
accuracy in
measuring mass
and quantity of
things bought
e.g. knowledge
in using the
weighing scale
D. Comprehension of
Capacity
1. Make
measurement
using standard
units of capacity
measure (litre:
base unit)
2. Compare among
the non-standard
units of measuring
volume in terms of
consistency and
accuracy
3. Approximate
measurement of
volume
IV. Graphs
A. Comprehension of
Bar Graph
1. Read and
interpret data
presented in a bar
graph
1.1 Read the
following parts
of a bar graph
a. title
b. legend
c. labels
1.2 Interpret bar
graphs
2. Construct bar
graphs
2.1 Organize data
in a bar graph
3. Find the average
of data presented
in a bar graph
1. Find the surface
area of cubes,
prisms, and
cylinders
1.1 Identify the
faces of solid
1.2 Name the unit
of measure
used for
measuring the
surface area of
solids
1.3 Derive a
formula for
finding the
surface area of:
 cubes
 prisms
 cylinders
2. Application of
Measurement of
Surface Area
2.1 Solve word
problems
involving
measurement
of surface
area following
the steps in
solving
problems
B. Comprehension of
Volume
1.Find the volume of
a solid
1.1 Name the unit
of measure

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23
2. Approximate
measurement of
capacity
E. Comprehension of
Area
1. Find the area of
a given figure
using the square
units
1.1 Visualize plane
figures in square
units
1.2 Tell the number
of square units
covering a given
plane figure
used for
measuring the
volume of solids
1.2 Convert one
cubic unit of
measure to a
larger or smaller
unit
1.3 Derive a
formula for
finding the
volume of solids
like:
 cylinders
 pyramids
 cones
2. Application of
Measurement of
Volume
2.1 Solve word
problems
involving
measurement
of volume
following the
steps in solving
problems
C.Comprehension of
Meter Reading
1.Read and
interpret readings
from:
1.1 electric meter
1.2 water meter
2. Solve word
problems involving
electric and water

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consumptions
V. Graphs
A. Comprehension of
Circle Graph
1. Read and
interpret data
presented in a
circle graph
2. Construct a circle
graph
2.1 Organize data
in a circle
graph
VI. Simple Probability
1. Make simple
predictions
2. Tell the number of
favorable
outcomes/
chances
VII. Introduction to
Algebra
A. Comprehension of
Integers
1. Visualize integers
in their order on a
number line
2. Compares
integers
3. Order integers in
increasing/
decreasing order

12/3/2010
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B. Expressions and
Equations
1. Give the meaning
of expression and
equation
2. Differentiate
expression from
equation

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