## Transcript

(Phi li ppi ne El e mentary Learni ng Compe te nci e s)
BASIC EDUCATION CURRICULUM
MATHEMATICS
1
MATHEMATICS
DESCRIPTION
Mathematics in Grades 1 and 2 includes the study of whole numbers, addition and subtraction, basic facts of multiplication and division,
basics of geometry, fractions, metric and local measurements, the use of money and their application to practical problems based on real
life activities.
Grades 3 and 4 deals with the study of whole numbers, the four fundamental operations, fractions and decimals including money, angles,
plane figures, measurement and graphs.
In Grades 5 and 6 the child is expected to have mastered the four fundamental operations of whole numbers, performs skills in decimals
and fractions, conceptualize the meaning of ratio and proportion, percent, integers, simple probability, polygons, spatial figures,
measurement and graphs. Simple concepts in Algebra is also introduced to be articulated in the high school.
Besides further development of the basic mathematical skills, the child is expected to solve problems related to business and industrial
activities in the community.
TIME ALLOTMENT
Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6
Daily 80 80 80 60 60 60
Weekly 400 400 400 300 300 300
The 20-minute increase in the daily time allotment is given to ensure that all lessons are finished and there will be more activities that
involve grouping practical investigations and problem solving. Pupils learn more if they have hands on or manipulative and interactive
activities, learn on their own, explore, discover, generalize and apply what they learned in their daily life.
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EXPECTATIONS
At the end of Grade VI, the child is expected to have mastered the concepts and operations of whole numbers; demonstrate
understanding of concepts and perform skills on decimals, fractions, ratio and proportion, percent, integers, simple probability, geometry,
measurement, and graphs; integers; exact and estimated computation of the four fundamental operations involving decimals, money,
fractions and measurement; and apply the concepts learned in solving problems.
At the end of Grade V, the child is expected to have mastered the concepts and operations of whole numbers; demonstrate
understanding of concepts and perform skills on fractions, decimals including money, ratio, percent, geometry, measurement and graphs;
exact and estimated computation of the four fundamental operations on rational numbers including money and measurement and apply
the concepts learned in solving problems.
At the end of Grade IV, the child is expected to demonstrate understanding of concepts and perform skills of whole numbers up to
millions and billions including money, decimals, fractions, geometry, graphs and scales; exact and estimated computation on the four
fundamental operations; and apply the concepts learned to solve problems.
At the end of Grade III, the child is expected to demonstrate understanding of concepts and skills on whole numbers up to one hundred
thousand, fractions, measurement and graphs; perform the four fundamental operations of whole numbers and measurement; and apply
the concepts learned in solving problems.
At the end of Grade II, the child is expected to demonstrate understanding of concepts and skills on whole numbers up to one thousand
including basics of geometry; perform addition and subtraction of 3 to 4-digit numbers, understand basic facts of multiplication and
division; and apply the concepts learned to solve problems.
At the end of Grade I, the child is expected to demonstrate understanding of basic concepts and skills on whole numbers up to one
hundred including money and measurement; perform addition and subtraction of 1 to 3-digit numbers; and apply the concepts learned to
solve problems.
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
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ELEMENTARY MATHEMATICS
I II III IV V VI
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1. Recognize cardinal
numbers from 0 to 100
1.1 Identify common
objects
according to
color
- size
- shape
1.2 Classify sets
using common
objects
according to
color,
- size
- shape
1.3 Order sets with 1
to 10 objects
from least to
greatest and
vice-versa
1.4 Construct sets
with objects 1 to
10 in
1.4.1 – the one more order
1.4.2 – the one less order
1.5 Compare 2 sets
using the
expressions
“fewer than”,
“more than”, and
“as many as”
1.6 Associate
numbers with
sets having
objects 0 to 10
1.7 Tell the number
of objects in a
given set of 10 or
less
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
1.2 Associate numbers with
sets having 501 up to
1000 objects/ sets
2. Read and write numbers
from 101 through 1000
in symbols and in words
2.1 Give the place value of
each digit in a 3-digit
number
2.2 Read numbers through
1000 in symbols and in
words
2.3 Write numbers through
1000 in symbols and in
words
2.4 Write 3-digit numbers in
expanded form
2.5 Compare numbers using
>, < and =
3. Skip count numbers by
50s up to 1000
4. Read and write ordinal
numbers from 11
th
through the 20
th
objects
of given sets from a
given point of reference
4.1 Identify the 11
th
through
the 20
th
objects of given
sets from a given point
of reference
4.2 Identify ordinal numbers
up to the 20
th
5. Identify the pattern of
naming ordinal numbers
e.g. 21
st
, 22
nd
, 23
rd
, 24
th
,
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 4 to
5 digit numbers
1.3 Read numbers
through 100 000 in
symbols and in
words
1.4 Write numbers
through 100 000 in
symbols and in
words
1.5 Express the
relationship of
numbers using
expressions "less
than" greater than
and equal to (> < =)
1.6 Write 4 to 5 digit
numbers in
expanded form
2. Round number 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
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 6 or
more digit
numbers
1.3 Read and write
numbers through
millions/billions in
symbols
1.4 Read and write
numbers through
millions/billions in
words
2. Round off numbers to
the nearest
2.1 tens
2.2 hundreds
2.3 thousands
2.4 ten thousands
2.5 hundred
thousand
2.6 millions
2.7 billions
B. Comprehension of
Addition
1. Add 6 or more digit
numbers with 4 or more
addends with sums through
billions
1.1 without regrouping
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
REVIEW
1. Place Value
2. Properties of Whole
Numbers
• •• • Addition
• •• • Multiplication
3. Rounding numbers
4. Operations of Whole
Numbers:
• •• • Adding and Subtracting
• •• • Multiplying Whole
Numbers
• •• • Dividing Whole
Numbers
5. Problem Solving Involving
Large Numbers: 1-step
and 2- to 3-step
1. Subset of Whole Numbers
1.1 Differentiate odd from
even numbers
1.2 Give the common factors
of given numbers
1.3 Identify prime and
composite numbers
1.4 Find prime factors of a
number
1.5 Show multiples of a
given number by 10,
100
1.6 Find the least common
multiple of a set of
numbers
1.7 Tell when a number is
divisible by another
number (Divisibility
Rules)
I. WHOLE NUMBERS
A. Comprehension of
Whole Numbers
1. Comprehend the order of
operations on whole
numbers
1.1 Follow the correct order
of operations (PEMDAS
Rule) when solving
expressions/equations
having more than one
operations
1.1.1 Give the
meaning of
- Expression
- Equation
- Exponent
- Base
1.1.2 Evaluate an
expression involving
exponents
1.1.3 Evaluate an
expression with two different
operations with or without
exponents and
parenthesis/grouping
symbols
1.1.4 Evaluate an
expression with more than 2
operations with or without
exponents and
parenthesis/grouping
symbols
1.2 Apply the order of
operations in solving 2-3
step word problems
4
I II III IV V VI
1.8 Order numbers 1
to 10 including
zero from least to
greatest and
vice-versa
1.9 Read and write
numbers from 0
to 10 in symbols
1.10 Tell the relationship
of numbers using
the expressions
“less than”, “greater
than”, “equal”
1.11 Count by 1’s through 50
1.12 Identify numbers in sets
having 11 to 50 objects
1.13 Skip count by 2’s, 5’s
and 10 through 50
1.14 Associate numbers
with sets having 51 up
to 100 objects/things
2. Read and write numbers
through 100 in symbols
and in words
2.1 Give the place value
of each digit in a 1-
to 2-digit numbers
2.2 Read numbers from
11 through 100 in
symbols and in words
2.3 Write numbers from
11 through 100 in
symbols and in words
2.4 Write numbers from
11 through 100 in
expanded form
2.5 Regroup sets of
ones into sets of
tens and sets of
tens into hundreds
using objects
etc.
6. Use the pattern of naming
ordinal numbers beyond
20
7. Read and write money
value through P100
7.1 Read money in symbols
through P100
7.2 Express money as pesos
and centavos through
P100
7.3 Compare values of the
different denominations
of coins and paper bills
through P100 using the
relation symbol
8. Express Roman numbers
in equivalent Hindu-
Arabic through L (50)
8.1 Read and write Roman
numbers through L
8.2 Change Roman numbers
in equivalent Hindu-
Arabic through L and
vice-versa
B. Comprehension of
Addition
1. Add 2- to 3-digit numbers
with sums up to 999
1.1 without regrouping in
short form
1.2 with regrouping
2. Add 2- to 3-digit numbers
with zero in any of the
addends without
regrouping with sums up
to 999
3. Add 2- to 3-digit numbers
with zero in any of the
addends with regrouping
with sums up to 999
4. Show properties of
addition in adding
numbers
4.1 Read money value
in symbols through
1000
4.2 Write money value in
symbols through
1000
4.3 Compare 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 L to C
5.1.2 C to D
5.1.3 D to M
B.
1. Comprehension of
Addition
1.1 Add 4 to 5 digit
numbers up to four
addends with sums up
to 100 000
1.1.1 Without
regrouping in short
forms
1.1.2 With regrouping in
1.1.2.1 Tens and
hundreds places
1.1.2.2 Thousands
and ten thousands
places
1.2 Estimate the sums of
3 to 5 digit addends
1.3 Add mentally 1 to 2
digit numbers with
sums up to 100 without
regrouping
1.2 with regrouping in:
- any two or
more places
- all places
2. Show the properties of
addition
2.1 Commutative
Property
2.2 Associative
Property
2.3 Identity Property
3. Estimate the sum of 6 or
more digit addends
4. Add mentally 2 to 3 digit
numbers with sums up
to 300 without regrouping
5. Application of Addition
5.1 Solve word problems
involving addition of
whole numbers
including money
with sums through
millions and billions
without and with
regrouping
5.1.1 Analyze the
word problem
5.1.1.1 Tell:
- what is
asked
- what is/are
given
- the word
clue/s
- the
operation
to be used
5.1.2 Transform the
word
problem into
a number
sentence
5.1.3 Use the
correct
operation
A. Comprehension of
Fraction
1. Change dissimilar
fractions to similar
fractions
1.1 Visualize changing
dissimilar fractions to
similar fractions
1.2 Identify equal fractions
1.2.1 Use cross product to
determine whether 2
fractions are equal
1.3 Change fractions to
lower/higher term
(LCM/GCF)
2. Estimate fractions close to
0,
2
1
, or 1
B. Comprehension of
Addition Fraction
1. Add numbers in mixed
forms with similar and
dissimilar fractions
without and with
regrouping
1.1 Add two to four similar
fractions
1.2 Visualize addition of
dissimilar fractions
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 form and a
dissimilar fraction
1.7 Add mixed forms
1.8 Estimate sum
1.9 Add mentally two
fractional units with
similar denominators
2. Application of Addition of
Fractions
1.2.1 Write an equation
to solve multi-step word
problems
1.2.2 Solve 2-3 step
word problems involving
whole numbers
1.3 Describe answer in a
complete sentence with
proper units/labels
II. RATIONAL NUMBERS
A. Comprehension of
Decimals
1. Visualize ones, tenths,
hundredths and thousandths
1.1 Name a decimal for
a given model
(region/blocks, money,
number line)
1.2 Use different models
to show a given decimal
(region/block, money,
number line)
2. Rename fractions whose
denominators are power of
10 in decimal form
3. Read and write decimals
through ten thousandths
3.1 Identify the
value/place value of a digit in
a given decimal
3.2 Read decimals
through ten thousandths
3.3 Write decimals
through ten thousandths in
different notations
5
I II III IV V VI
3, Read and write ordinal
numbers 1
st
, 2
nd
, 3
rd
up to
10
th
in a given set
3.1 Identify the 1
st
, 2
nd
,
3
rd
up to the 10
th
object
in a given set
4. Read and write money
up to P 50.00
4.1 Read and write the
symbol of c for
centavo and P for
pesos
4.2 Tell the value of a
given set of coins and
paper bills up to P50
4.3 Compare values of
the different
denominations of
coins and paper bills
through P50 using
the relation symbols.
4.4 Skip count by P5s,
P10s up to P50s
B. Comprehension of
Addition
1. Add two to three 1-
digit numbers with
sums up to 18
horizontally and
vertically
1.1 Join two sets
with 1 to 9
objects
1.2 Show the
relationship of
joining sets to
addition of whole
numbers
1.3 Add two 1-digit
numbers having
sums of :
- 6 and less
- 7 through 10
(after concept
of 1-10)
4.1 Show the commutative
property of addition in
adding numbers
4.2 Show the associative
property of addition in
adding numbers
5. Add mentally 1- to 2-digit
numbers with sum up to
50
6. Application of Addition
6.1 Solve word problems
involving addition of
whole numbers
including money with
sums up to 999 without
and with regrouping
6.1.1 Analyzes word problem
6.1.1.1 Tell:
• •• • what is asked
• •• • what is/are given
• •• • the word clues
• •• • the operation to
be used
6.1.2 Transform the word
problem into a number
sentence
6.1.3 Use the correct
operation
6.1.4 State the complete
answer
C. Comprehension of
Subtraction
1. Subtract 2- to 3-digit
numbers with minuends
up to 999 without and
with regrouping
1.1 Illustrate how subtraction
is used when:
1.1.1 Taking away from the
given set
1.1.2 Comparing two sets
1.1.3 Finding a missing
addend
2. Application of Addition
2.1 Solve word problems
involving addition of
whole numbers with
sums up to 100 000
including money
following the steps
in problem solving
2.2 Solve mentally 1 step
word problems
involving addition
with sums up to
100 without
regrouping
C.
1. Comprehension of
Subtraction
1.1 Subtract 3 to 4 digit
numbers from 4
to 5 digit numbers
with minuends up to
100 000 without and
with regrouping
and with zero difficulty
1.1.1 Subtract 3 digit
number from 4 to 5
digit numbers with
minuends up to
100 000 without
regrouping
1.1.2 Subtract 4 digit
number from 4 to 5
digit numbers with
minuends up to
100 000 without
regrouping
1.1.3 Subtract 3 to 4
digit numbers from
4 to 5 digit numbers
with regrouping
1.1.3.1 in the tens
place
1.1.3.2 in the
hundreds place
1.1.3.3 in the
thousands place
5.1.4 State the
complete
answer
5.2 Solve mentally 1 step
word problems involving
addition with sums up to 300
without regrouping
C. Comprehension of
Subtraction
1. Subtract 5 or more
digit numbers from 6
or more digit numbers
without and with
regrouping in any or
all places and
involving three or
more zeros in the
minuend.
1.1 Subtract 5 or more
digit numbers from
6 or more digit
numbers without
regrouping
1.2 Subtract 5 or more
digit numbers from
6 or more digit
numbers with
regrouping
1.2.1 having zeros
in the
minuends
and/or
subtrahend
1.2.2 with three
continuous
or non-
continuous
zeros in both
minuends
and
subtrahend
and with
regrouping in
any or all
places
2.1 Solve word problems
involving addition of
similar and dissimilar
fractions without or with
regrouping
2.1.1 Analyze the word
problem
2.1.1.1 Tell:
- what is asked
- what is/are given
- the word clue
- the operation to be
used
2.1.2 Transform word
problem into a number
sentence
2.1.3 Use the correct
operation
2.1.4 State the complete
answer
C. Comprehension of
Subtraction of Fractions
1. Subtract fractions and
mixed forms with common
denominators without and
with regrouping
1.1 Visualize subtraction of
fractions
1.2 Subtract whole numbers
from mixed forms
1.3 Subtract mixed numbers
from mixed numbers
(with similar fractions)
1.4 Subtract fractions from
whole numbers
1.5 Subtract fractions from
mixed numbers
1.6 Subtract mixed numbers
from whole numbers
2. Subtract Dissimilar
Fractions
2.1 Visualize subtraction of
dissimilar fractions
2.2 Subtract fractions from
mixed numbers
- Standard Notation
- Expanded Notation
4. Compare and order
decimals through ten
thousandths
5. Round decimals through
ten thousandths
B. Comprehension of
Addition and Subtraction
of Decimals
1. Estimate sums and
differences of whole
numbers and decimals
2. Add and subtract whole
numbers and decimals
3. Add and subtract
decimals through ten
thousandths without and with
regrouping (with
concrete/visual models)
4. Add and subtract mixed
decimals with regrouping
5. Apply the different
properties of addition to
compute sums mentally
5.1 Commutative property of
addition
6. Application of addition and
subtraction of decimals
6.1 Write an equation to
solve word problems
6.2 Solve 1 to 3-step
word problems involving
addition and subtraction of
decimals including money
6
I II III IV V VI
1.4 Illustrate that any
given number
plus zero is the
same number
1.5 Show that
changing the
order of two
addends does
not affect the
sum
1.6 Add three 1-digit
numbers having
sums up to 18
1.7 Show that
changing the
grouping of three
or more addends
helps make
computation
easy
2. Add mentally two to
three 1-digit numbers
with sums up to 18
3. Add 1-to 2-digit
numbers with sum
through 99
- without regrouping
- with regrouping
4. Application of Addition
4.1 Solve 1-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 problem
4.1.1.1 Tell
- what is asked
- what is/are given
- the word clues
- the operation to
be used
1.2 Subtract 2- to 3-digit
numbers with
regrouping
1.2.1 in the tens place
without or with zero
1.2.2 in the hundreds place
value without or with
zero difficulty
1.2.3 in the tens and
hundreds place without
or with zero difficulty
2. Use addition to check
subtraction
3. Subtract mentally 1-digit
number from 1 and 2
digit numbers with
minuends up to 50
without regrouping
4. Application of Subtraction
4.1 Solve 1-step 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 operation 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
5. Application of Addition and
Subtraction
5.1 Solve 2-step word
problems involving
addition and subtraction
of 2- to 4-digit numbers
1.1.3.4 in the ten
thousand place
1.1.3.5 with zero
difficulty in either
tens or hundreds
place
1.1.4 Estimate the
difference of two
numbers with 3 to 4
digits
1.2 Subtracts mentally 2
digit numbers with
minuends up to 99
without regrouping
2. Application of
Subtraction
2.1 Solve 1 step word
problems involving
subtraction of whole
numbers including
money with
minuends up to
100 000 without
and with regrouping
following the steps
in problem solving
2.2 Solve mentally 1 step
word problems
involving
subtraction without
regrouping
3. Application of Addition
and Subtraction
3.1 Solve 2 step word
problems involving
addition and
subtraction of whole
numbers including
money following
the steps in problem
solving
D.
1. Comprehension of
Multiplication
1.1 Multiply 2 to 4 digit
numbers by 1 to 2
digit numbers
1.3 Estimate the
difference of two
numbers with four
to six digits
2. Subtract mentally
numbers with minuends up
to 300 without regrouping
3. Application of Subtraction
3.1 Solve 1-step word
problems involving
subtraction of whole
numbers including
money without and
with regrouping
3.1.1 Analyze the
word problem
3.1.1.1 Tell:
- what is
asked
- what is/are
given
- the word
clue/the
operation
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
answer
3.2 Solve mentally 1- step
word problems
involving subtraction
without regrouping
4. Application of Addition
and Subtraction
4.1 Solve 2-step word
problems involving
addition and
subtraction
including money
2.3 Subtract mixed numbers
from mixed numbers
3. Subtract mentally similar
fractions
4. Application of Subtraction
of Fractions
4.1 Solve word problems
involving subtraction
of fractions
4.1.1 Analyze word problems
4.1.1.1 Tell:
- what is asked
- what is/are given
- the word clue
- the operation 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
5. Application of Addition and
Subtraction of
Fractions
5.1 Solve 2-step word
problems involving
addition and
subtraction of fraction
D. Comprehension of
Multiplication of Fractions
1. Multiply fractions by whole
number, mixed form by a
fraction
1.1 Visualize multiplication of
fractions
1.2 Find a fractional part of a
number
1.2.1 Translate expressions
such as “
2
1
of
3
2
1.3 Multiply
1.3.1 fraction by another
fraction
6.3 Describe answer in a
complete sentence with
proper labels/units
C. Comprehension of
Multiplication of Decimals
1. Estimate products of
whole numbers and decimals
2. Multiply up to 3 digit
factors by 1 to 2 digit factors
without and with regrouping
and with zero difficulty
3. Multiply hundredths by
hundredths
4. Multiply mixed
decimals by mixed decimals
with hundredths
5. Multiply mentally
decimals by 10, 100 and
1,000
6. Multiply mentally
decimals by .01, 0.01 and
0.001
7. Apply the properties
of multiplication to compute
products
7.1 Commutative
property of multiplication
7.2 Associative
property of multiplication
7.3 Distributive
property of multiplication
over addition
8. Application of
multiplication of decimals
7
I II III IV V VI
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
C. Comprehension of
Subtraction
1. Subtract 1-to 2-digit
numbers from 1-to2
digit numbers with
minuends up to 99
without and with
regrouping
1.1 Visualize
situations when
subtraction is
used
1.1.1 Remove a
subset from
a given set
of objects
(taking
away
1.1.1.1 Show the
relationship
of the
removal of a
group of
objects
from a given
set to
subtracting of
whole
numbers
1.1.1.2 Compare two
given sets
(more or less
in number)
including money
5.1.1 Analyze the word
problems
5.1.1.1 Tell:
- what is asked
- the word clue/s
- the hidden question
- the operation to be
used
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
D. Comprehension of
Multiplication
1. Multiply 1- to 2-digit
numbers by a 1-digit
number with products up
to 81
1.1 Multiply 1-digit by 1-digit
number with or without
regrouping with products
up to 45
1.1.1 Show the relationship
of putting together 2
or more number of
elements to repeated
addition
1.1.2 Show multiplication of
whole numbers as
repeated addition on 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 Give the factors of a
given number
1.1.6 Show that a number
multiplied by 1 is the
without and with
regrouping in all
places
1.1.1 Multiply 2 to 4
digit numbers
without and with
regrouping
1.1.1.1 Show that
changing the order
and/or regrouping
in multiplication
makes computation
easy
1.1.1.2 Multiply 2 to 4
digit numbers by
1 to 2 digit numbers
without regrouping
1.1.1.3 Multiply 2 to 4
digit numbers by 1
to 2 digit numbers
with regrouping
1.1.1.4 Multiply 2 digit
numbers by 1 digit
number with zero
in the multiplicand
1.1.1.5 Multiply 3 to 4
digit numbers by
1 digit numbers with
zero in the
multiplicand
1.1.1.6 Multiply 2 to 4
digit numbers
by multiples of 10
1.1.1.7 Multiply 2 to 4
digit numbers by
multiples of 100
1.1.2 Estimate the
product of 2 to 3
digit factors by 1 to
2 digit factors
1.1.3 Estimate the
product of 4 digit
factors by 1 to 2
digit factors
1.1.4 Multiply mentally 2
digit numbers by
1 digit numbers
4.1.1 Tell:
- what is
asked
- what is/are
given
- the word
clue/s
- the hidden
question
- the
operation 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
D. Comprehension of
Multiplication
1. Multiply 5 or more
factors by 3 to 5 digit
factors without and
with regrouping and
with zero difficulty
1.1 Multiply 5 or more
digit factors by 3
digit factors
without and with
regrouping
1.2 Multiply 5 or more
digit factors by 4
to 5 digit factors
without and with
regrouping
1.3 Multiply 5 or more
digit factors
having one to
three zeros in both
factors without
regrouping
1.3.2 fraction by a whole
number
1.3.3 mixed form by a
fraction
1.3.4 mixed form by a mixed
form
2. Multiply mentally fraction
units
3. Application of
multiplication of fractions
3.1 Solve word problems
involving multiplication of
fractions
3.1.1 Analyze the word
problem
3.1.1.1 Tell:
- what is asked
- what is/are given
- the word clue
- the operation to be
used
3.1.2 Transform the word
problem into number
sentence
3.1.3 Use the determined
operations
3.1.4 State the complete
answer
4. Application of
Multiplication
E. Comprehension of Ratio
and Proportion
Reducing ratios to lowest
terms
1. Express the ratio of two
numbers
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. Forms Proportion for
Numbers
8.1 Write an equation to
solve word problems
8.2 Solve word problems
involving multiplication of
decimals including money
8.3 Solve 2 to 3 step word
problems involving addition,
subtraction and multiplication
of decimals including money
8.4 Describe the answer in
a complete sentence with
proper labels/units
D. Comprehension of
Division of Decimals
1. Estimate problems of
whole numbers and decimals
2. Divide
2.1 Whole numbers (2-5
digit dividends by decimals
(1-2 digit divisions)
2.2 Recognize and
differentiate between
terminating and repeating
from non-terminating decimal
quotients
2.2.1 Recognize and
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
8
I II III IV V VI
1.1.1.3 Find a
missing
addend
1.1.1.3.1 Show that
subtraction is the
inverse of
addition
1.2 Subtract 1-digit nos.
with minuends
through 18 (basic
facts)
1.3 Subtract 1-to 2-digit
numbers with
minuends
up to 99
1.3.1 without
regrouping
1.3.2 with regrouping
1.3.3 Subtract 2-digit
without regrouping
1.3.4 Subtract 2-
digit with
regrouping
2. Subtract mentally 1-
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
3.1.1 Analyze
the word
problems
3.1.1.1 Tell:
- what is
asked
- what is/are
given
same number
1.1.7 Show that zero
multiplied by a
number is zero
1.2 Multiply 1- to 2-digit
numbers by 1-digit
number with products
up to 81
1.3 Multiply mentally 1-digit
numbers with
products up to 81
without regrouping
2. Application of
Multiplication
2.1 Solve 1-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 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
3. Application of
Multiplication and Any
of Addition/
Subtraction
3.1 Solve 2- to 3-step word
problems involving
multiplication of whole
numbers including
money
without regrouping
with products up to
100
2. Application of
Multiplication
2.1 Solve word problems
involving
multiplication of
whole numbers
including money
following the steps
in problem solving
3. Application of
Multiplication and any
one of Addition/
Subtraction
3.1 Solve 2-3 step word
problems involving
multiplication and
any one of addition/
subtraction
following the steps
in problem solving
E.
1. Comprehension of
Division
1.1 Divide 2 to 4 digit
numbers by 1 to
2 digit numbers
without or with
remainder and with
zero difficulty
1.1.1 Divide 2 to 3 digit
numbers by
1 digit number
without/with
remainder
1.1.1.1 Show that
renaming 2 to 3
digit numbers help
make
computation easy
1.1.1.2 Divide 2 to 3
digit numbers by
1 digit number
without remainder
1.4 Multiply 5 or more
digit factors
having one to
three zeros in both
factors with
regrouping in all
places.
1.5 Multiply 5 digit or
more factors by
multiples of 10,
100 and 1,000
2. Show the properties of
multiplication
- Commutative
- Associative
- Zero Property
- Identity Property
- Distributive Property of
Multiplication over
Addition
3. Estimate the products of
two factors with 5 or more
digits by 2 to 3-digit numbers
4. Multiply mentally 2-digit
numbers with products
up to 200 without
regrouping
5. Write numbers in
exponent form
6. Write numbers in
standard form to
scientific notation and
vice-versa
6.1 Write number in
standard form to
scientific notation
6.2 Write number in
scientific notation
to standard form
7. Application of
Multiplication
7.1 Solve word problems
involving multiplication of
whole number including
money
F. Comprehension of
Decimals
1. Read and write decimals
through thousandths
1.1 Rename in decimal form
fraction whose denominators
are powers of 10
1.2 Give the place value of
each digit of a given decimal
2. Round decimals to the
nearest tenths/hundredths/
thousandths
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 with regrouping
• •• • Subtract mixed
decimals with
regrouping
• •• • Subtract mixed
decimals from whole
numbers
3. Application of addition and
subtraction of decimals
3.1 Solve word problems
involving either addition or
subtraction of decimals
including money
3.2 Solve 2-step word
problems involving addition
and subtraction of decimals
including money
H. Comprehension of
Multiplication of Decimals
1. Multiply mixed decimals
and whole numbers
1.1 Visualize multiplication of
2.4 Whole numbers by
decimals and mixed
decimals
2.5 Mixed decimals by
mixed decimals
3. Divide decimals by 10,
100, 1,000 mentally
4. Divide decimals by 0.1,
0.01, 0.001 mentally
5. Application of division of
decimals
5.1 Write an equation to
solve problems
5.2 Solve word problems
involving division of decimals
including money
5.3 Solve 2 to 3 step word
problems involving decimals
including money
5.4 Describe the answer in
a complete sentence with
proper labels/units
E. Comprehension of
Number Theory and
Fractions
1. Comprehension of number
theory and concepts
1.1 Generalize when a
number is divisible by
another number divisibility
rules
1.2 Identify prime and
composite numbers
1.3 Enumerate factors and
multiples of given numbers
9
I II III IV V VI
- the word clues
- the operation
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
II. Rational Numbers
A. Comprehension of
Fractions
1. Recognize 1/ 2
and 1/ 4 of a
whole
2. Separate a whole
object into
halves/fourths
3. Separate group of
objects into
halves/fourths
IV. MEASUREMENT
A. Comprehension of
time measure
1. Tell the number 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 Tell time using
digital clock
3. Indicate time to the
nearest 15 minutes of
an hour like 1:15, 1:30,
1:45
E. Comprehension of
Division
1. Divide whole numbers
with dividends through
81 by 1-digit divisors
1.1 Show division as
repeated subtraction
1.2 Identify the parts of a
division sentence
namely dividend,
divisor and quotient
1.3 Illustrate 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
1.4 Transform a division
sentence into
multiplication
sentence and vice
versa
1.5 Divide 1- to 2-digit
numbers by 1-digit
numbers
1.6 Divide 2-digit numbers
with dividends through
81
2. Application of Division
2.1 Solve 1-step word
problems involving
division of whole
numbers with
dividends up to 81
2.1.1 Analyze the word
problem
1.1.1.3 Divide 2 to 3
digit numbers by
1 digit number with
remainder
1.2 Divide 2 to 3 digit
numbers by
multiples of 10 up to
90
1.3 Divide 2 to 3 digit
numbers by 1 to 2
digit numbers with
zero difficulty
1.4 Divide 3 to 4 digit
numbers by 1 to 2
digit numbers
without or with
remainder and with
zero difficulty
1.4.1 Divide 3 to 4 digit
numbers by
1 digit number
without remainder
1.4.2 Divide 3 to 4 digit
numbers by
1 to 2 digit numbers
with remainder
1.4.3 Divide 3 to 4 digit
numbers by
1 to 2 digit numbers
with zero difficulty
1.4.4 Divide whole
numbers by 5
1.4.5 Divide whole
numbers by 10 and
100
1.5 Divide mentally 2
digit numbers
through 99 by 1
digit numbers
without remainder
2. Application of Division
2.1 Solve 1 step word
problem involving
division of 2 to 4 digit
numbers by 1 to 2
digit numbers
including money
7.1.1 Analyze the word
problem
7.1.1.1 Tell:
- what is
used
- what is/are
given
- the word
clue/s the
hidden
question the
operation to
be used
7.1.2 Transform the
word problem into
a number
sentence
7.1.3 Use the correct
operation
7.1.4 State the complete
answer
8. Application of
Multiplication and Any
of Addition/Subtraction
8.1 Solve 2 step word
problems
involving
multiplication and
any of addition/
subtraction
E. Comprehension of
Division
1. Divide 5 or more digit
numbers by 3 or
more digit numbers
without or with
remainder and with
zero difficulty.
1.1 Divide 5 or more
digit number by
3 digit numbers
without
remainder
1.2 Divide 5 or more
decimals using models
1.2 Tenths by another tenths
1.3 Hundredths by tenths
and vice versa
2. Generalize the step in
multiplying decimals
3. Multiply mixed decimals
with tenths and hundredths
by whole numbers
4. Multiply mixed decimals
by mixed decimals with
tenths and hundredths
5. Multiply decimals by 10
and 100
6. Multiply decimals mentally
by 1, 01, and 001
7. Application of
Multiplication of Decimals
7.1 Solve word problems
involving multiplication of
decimals including money
I. Comprehension of
Division of Decimals
1. Divides decimals through
hundredths
1.1 Visualize division of
decimals using models
1.2 Divide decimals by whole
numbers
1.3 Divide decimals by
decimals through hundredths
2. Application of Division of
Decimals
2.1 Solve word problems
involving division of decimals
2.1.1 Analyze the word
problem
2.1.1.1 Tell:
- what is asked
- what is/are given
- the word clues
- the operation to be
used
2.1.2 Transform the word
problem into a
1.4 List the prime factors of
given numbers
1.5 Write the prime
factorization of a given
number
1.6 Determine the greatest
common factor (GCF) of 2 or
more numbers
1.7 Determine the least
common multiple (LCM) of 2
or more numbers
F. Comprehension of
Fractions
1. Write the factor described
involving regions, sets and
numberline
2. Rename fractions as
decimals and vice-versa
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
10
I II III IV V VI
3.1 Indicate time
such as 1:15, 1:30,
1:45 when the hand
is at 15 minutes
4. Read and write time
as shown on the clock
B. Comprehension of
Linear Measure
1. Make measurement
using non-standard
units of linear
measure.
2. Compare among the
non-standard units
of mass measure in
terms of consistency
and accuracy
C. Comprehension of Mass
Measure
1. Measure mass using
non-standard units of
linear 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
2.1.1.1 Tell:
• •• • what is asked
• •• • what is/are given
• •• • 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
3. Application of Division and
Any of the Three
Fundamental
Operations
3.1 Solve 2- to 3-step word
problem involving
whole numbers
including money
3.1.1 Analyze the word
problem
3.1.1.1 Tell:
• •• • what is asked
• •• • what is/are given
• •• • the word clue/s
• •• • the hidden
question
• •• • the operation to
be used
3.1.2 Transform the word
problems into a
number sentence
3.1.3 Use the correct
operation
3.1.4 State the complete
answer
II. Rational Numbers
A. Comprehension of
Fractions
3. Application of the Four
Fundamental
Operations
3.1 Solve 2 step word
problems involving
division and any one
of the fundamental
operations including
money
3.2 Solve 3 step word
problems involving
division and any two
of the other
fundamental
operations including
money
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 Order fractions less
than one
1.2.1 Tell the
relationship between
fractions less than one
1.3 Identify fractions
equal to one
1.4 Identify fractions
more than one
1.5 Order fractions less
than one/equal to
one/more than one
2. Change fractions to
lower forms
2.1 Tell the greatest
number by which
two given numbers
can exactly be
divided
2.1.1 Give the GCF
(Greatest Common
Factor) of 2 given
numbers
digit numbers by
4 or more digit
numbers without
or with
remainder
1.3 Divide whole
numbers by 10,
100 and 1,000
1.4 Divide 4 to 5
digit numbers by
2 to 3 digit
numbers with
zeros in the
middle or
continuous zero
in the dividend
2. Estimate the quotient
of 4 to 5 digit
dividends by 2-digit
numbers
3. Divide mentally 2-3
digit numbers by 1-
digit numbers without
remainder
4. Application of
Division
4.1 Solve 1- step
word problems
involving division
of 5 or more digit
numbers by 3 or
more digit
numbers
including money
4.1.1 Analyze
the word
problem
4.1.1.1 Tell:
- what is
asked
- what is/are
given
- the word
clue/s the
operation to
be used
number sentence
2.1.3 Use the correct
operation
2.1.4 State the complete
answer
J. Comprehension of
Percent
1. Relate fractions/ratios,
decimals and percent
1.1 Visualize the meaning of
percent (%)
1.2 Give the relationship
• •• • between
fractions/ratios and
percents (with visual
models)
• •• • between percent and
decimal (with visual
models)
• •• • among fractions/
ratios, decimals and
percents
III. Geometry
A. Comprehension of
Polygons
1. Draw 3- to 4-sided
polygons
1.1 Visualize polygons
1.2 Identify kinds of polygons
1.3 Describe polygons
2. Draw 5- or more-sided
polygons
e.g. pentagon, hexagon,
etc.
IV. Measurement
A. Comprehension of Area
1. Find the area of other
plane figures in square
meters/centimeters
9. Compare fractions and
mixed forms using different
methods
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 using different
methods
11. Solve mentally word
problems involving fractions
11.1 Reduce final answer
to lowest term
G. Comprehension 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 or subtract similar
fractions in simple or mixed
forms without regrouping
4. Add or subtract similar
fractions in simple or mixed
forms with regrouping
11
I II III IV V VI
2. Compare among the
non-standard units of
capacity measure in
terms and accuracy
of measurement
1. Identify
3
1
,
5
1
,
6
1
of a
given whole/group of
objects
1.1 Name the fractional parts
of a given whole/
group of objects
B. Read and write
3
1
,
5
1
,
6
1
in symbols and in
words
C. Compare unit fractions
using relation symbols
III. Geometry
A. Comprehension of
Shapes
1. Identify shapes
1.1 Name different shapes
common in the home
and in the school
2. Classify shapes according
to numbers of sides
and corners
2.1 Describe shapes
according to number
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 shapes
4. Discriminate
shapes/figures that
show symmetry
2.2 Reduce fractions to
lowest terms
3. Find the fractional part
of set/regions
e.g.
1
/3 of 12
1
/4 of 20
1
/2 of 8
III. Geometry
A. Comprehension of Line
and Line Segment
1. Draw perpendicular
parallel 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
3. Determine which motion
turn, flip or slide creates
a given tessellation
4. Form simple
symmetrical designs out
of given shapes
(triangles and squares)
IV. Measurement
A. Comprehension of Time
Measure
1. Convert time measure
from smaller to
larger units and vice-
versa
1.1 days to years years
to days
1.2 seconds to minutes
minutes to hours
hours to day
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
5. Application of the
Four Fundamental
Operations
5.1 Solve 2 to 3 step word
problems involving division
and any one or two of the
other fundamental
operations learned including
money
5.1.1 Analyze the
word problem
5.1.1.1 Tell:
- what is
asked
- what is/are
given
- the word
clue/s the
hidden
question the
operation to
be used
5.1.2 Transform the
word
problems into
a number
sentence
5.1.3 Use the
correct
operation
5.1.4 State the
complete
answer
- parallelograms
- trapezoids
- circles
2. Application of
Measurement of Area
2.1 Solve word problems
involving area of plane
figures
2.1.1 Analyze the word
problem
3. Draw congruent and
similar polygons
3.1 Visualize congruence/
similarity of polygons
3.2 Identify congruent/
similar polygons
B. Comprehension of
Circumference of a Circle
1. Find the circumference of
a circle in centimeter/
meter
1.1 Derive a formula for
finding the distance
around a circle
2. Application of the Concept
of Circumference
2.1 Solve word problems
involving circumference
measure
2.1.1 Analyze the word
problem
2.1.1.1 Tell:
- what is asked
- what is/are given
- the word clue
- 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
5. Add or subtract dissimilar
fractions in simple or mixed
forms without regrouping
6. Add or subtract dissimilar
fractions in simple or mixed
forms with regrouping
7. Add mentally similar and
dissimilar fractions using the
properties of addition
8. Application of addition and
subtraction of fractions
8.1 Write an equation to
solve word problems
8.2 Make drawings or
diagrams to better
understand the given
problem
8.3 Solve word problems
involving addition or
subtraction of fractions in
simple or mixed forms with
or without regrouping
8.3.1 Analyze the word
problem
8.3.1.1 Tell
- what is asked
- what is/are given
- the word clue/s
- the operation to
be used
8.3.2 Use the correct
operation
8.3.3 Describe the
answer in a complete
sentence with proper labels/
units
12
I II III IV V VI
IV. Measurement
A. Comprehension of Time
Measure
1. Use the calendar to tell
the number of:
1.1 week in a month
1.2 day in a month
1.3 month in a year
1.4 week in a year
1.5 days in a year
2. Determine the number of
days in a given number of
• •• • weeks
• •• • months
3. Name the days in a
week/months in a year
4. Tell the time using the
digital clock
5. Express the relationship
between the “hour hand” and
the “minute hand” of a clock
6. Indicate time to the
nearest 15 minutes of an
hour like 1:15, 1:30, 1:45
when the minute hand is at
the 15 minutes position
7. Read and write time as
shown on the clock
8. Application of time
measure
8.1 Solve simple word
problems involving time
without conversion of
standard units
B. Comprehension of
Linear Measure
1. Make measurement using
standard units of linear
measure
e.g. centimeter, metre
2. Find the exact time
between dates
3. Application of time
measure
3.1 Solve 1 step word
problems involving
time measure
following the steps
in problem solving
B. Comprehension of Area
1. Find the area of a figure in
square meters
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
1.3.1 Derive a formula
for finding the area
of a rectangle
1.3.2 Derive a formula
for finding the area
of a square
2. Application of concept
of area
2.1 Solve word problems
involving area of
2.1.1 rectangle
2.1.2 square
C. Comprehension of
Capacity
1. Find capacity using
standard units of
measure
e.g. small units-milliliter
2. Convert capacity
measure from smaller
to larger units and vice
versa
II. RATIONAL NUMBERS
A. Comprehension of
Decimals and money
1. Read and write common
fractions in decimal form
through hundredths
1.1 Visualize
common
fractions as
decimals
1.1.1 Use decimal
models
(blocks
grid,
money)
1.2 Write
common
fractions in
decimal form
1.3 Read and
write decimal
numbers
through
hundredths
1.4 Rename in
decimal form
fractions
whose
denominators
are powers of
10
1.5 Give the
place value of
each digit of a
given decimal
2. Express/write money
as pesos/centavos
3. Round decimal to the
nearest
tenths/hundredths/
thousandths
C. Comprehension of
Volume
1. Find the volume of a cube/
rectangular prism
1.1 Tell the unit of measure
used for measuring the
volume of cubes/
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/rectangular prism
2. Application of
Measurement of Volume
2.1 Solve word problem
involving measurement of
volume
2.1.1 Analyze the word
problem
2.1.1.1 Tell:
- what is asked
- what is/are given
- the word clue
- 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
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
8.4 Solve 2 to 3-step word
problems involving addition
and subtraction of fractions
in simple and mixed forms
without and with regrouping
8.4.1 Analyze the word
problem
8.4.1.1 Tell
- what is asked
- what is/are give
- the word clue/s
- the operation to
be used
8.4.2 Use the correct
operation
8.4.3 Describe the
answer in a complete
sentence with proper labels/
units
H. Comprehension of
Multiplication of
Fractions
1. Multiply a fraction by
another fraction (with
visual models)
2. Simplify factor by
cancellation method
before multiplying
3. Multiply fractions in simple
and mixed forms
3.1 Change mixed
numbers and whole
numbers to improper
fractions before
multiplying
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2. Approximate
measurement of length,
width, height and distance
C. Comprehension of Mass
Measure
1. Make measurement
using standard units of
mass measure
2. Convert standard units
of mass measure to
lower or higher units
3. Approximate
measurement of mass
4. Investigate accuracy in
measuring mass and
quantity of things bought
e.g. knowledge in using
the weighing scale
D. Comprehension of Area
1. Find the area of a given
figure using the square units
1.1 Visualize plane figures
and square units
1.2 Tell the number of
square units covering a
given area
1.3 Solve word problems
involving area
E. Comprehension of
Capacity
1. Make measurement using
standard units of capacity
measure e.g. litre
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. Read/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 legend
1.3 Read pictographs
2. Construct pictograph
2.1 Organize data
presented in a
pictograph
VI. Calculator
1. Identify the parts of a
calculator
2. Tell the function of each
part of a calculator
B. Comprehension of
Addition and
Subtraction of
Decimals
1. Add and subtract
decimals through
hundredths with
and without
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 including
money
3.1.1 Analyze the
word problem
2.1 Solve word problem
involving body/weather
temperature
V. Graphs
A. Comprehension of Line
Graph
1. Read/Interpret data
presented in a line graph
2. Read a line graph
3. Construct a line graph
3.1 Organize data presented
in a line graph
3.2 Find the average of data
presented in a line graph
4. Show that multiplying a
fraction by its reciprocal
is equal to 1
5. Application of
Multiplication of Fractions
5.1 Write an equation for
a word problem
5.2 Make drawings/
diagrams to better
understand the given
problem
5.3 Solve word problems
involving multiplication
of numbers in mixed
forms
5.4 Solve 2 to 3 step word
problems involving
addition, subtraction,
and multiplication of
numbers in mixed forms
5.5 Use correct order of
operations
5.6 Describe answer in a
complete sentence in
with proper labels/units
I. Comprehension of
Division of Fractions
1. Visualize division of a
whole number by a
fraction; a fraction by
another fraction
2. Divides a whole number
by a fraction; a fraction
by another fraction
3. Divide fractions in different
forms
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I II III IV V VI
3.1.1.1 Tell what is asked
what is/are given, the word
clue/s the operation 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
answer
3.2 Solve 1 to 2 step
word problems
involving addition
and subtraction of
decimals including
money
3.2.1 Analyze the
word problem
3.2.1.1 Tell:
- what is
asked
- what is/are
given the
word clues
- the hidden
question the
operation to
be used
3.2.2 Transform the
word problem
into a number
sentence
3.2.3 Use the
correct
operation
3.2.4 State the
complete
answer
4. Application of Division of
Fraction
4.1 Write an equation to
solve a word problem
4.2 Make drawings or
diagrams to better
understand the given
problem
4.3 Solve word problems
involving division of
fractions
4.4 Solve 2 to 3-step word
problems involving all
operations on
fractions
4.4.1 Use correct order
of operations
4.5 Describe answer in a
complete sentence with
proper labels/units
J. Comprehension of
Ratio and Proportion
1. Forms ratio and
proportion for groups of
objects/numbers
1.1 Use colon (:) and
fractions in writing
ratios and proportions
1.1.1 Reduces a ratio
to lowest terms
1.2 Find a missing term
in a proportion
2. Application of Ratio and
proportion
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I II III IV V VI
C. Comprehension of
Fractions
1. Visualize 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
involving
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
1.3 Rename decimals
and whole
numbers to
fractions from a
given set of
fractions
2. Order similar
fractions written in
different forms from
least to greatest and
vice-versa
2.1 Set up a proportion for
a given situation
2.2 Solve word problems
with:
2.2.1 Direct proportion
2.2.2 Partitive
proportion
2.2.3 Inverse proportion
2.3 Describe answer in a
complete sentence with
proper labels/units
K. Comprehension of
Percent
1. Gives the meaning of the
elements used in solving
percentage problems
1.1 Percentage
1.2 Ratio or Percent
1.3 Base
2. Determine the percentage
rate and base in a given
problem
3. Application of Percent
3.1 Set up an equation or
proportion to solve
problems
3.2 Solve the three types
of percentage
problems
3.2.1 Find the
percentage when the rate
and base are given
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I II III IV V VI
3. Order dissimilar
fractions written in
different forms from
least to greatest and
vice-versa
3.1 Change
improper
fraction to
mixed forms
and vice-versa
3.2 Change one (1)
to fraction
form and vice-
versa
D. Comprehension of
Addition and Subtraction
of Fraction
1. Add similar fractions
and whole numbers
without regrouping
1.1 Visualize addition
of similar
fractions
1.2 Add similar
fraction
1.3 Add fractions and
a whole number
1.4 Add mentally
similar fraction
2. Subtract similar
fractions without
regrouping
2.1 Subtract similar
fraction
2.2 Subtract a
fraction from a
whole number
2.3 Subtract mentally
similar fractions
3.2.2 Find the rate or
percent when the
% age and base
are given
3.2.3 Find the base
when the
percentage
or rate are given
3.3 Compute common
percentage mentally
3.4 Solve word problems
involving finding the
percentage/rate/base
3.4.1 Percent of
increase/decrease
- Discounts
- Original Price
- Rate of Discount
- Sale Price
- Mark-up Price
3.4.2 Commission
- Rate of
Commission
- Total Sales
- Total Income
3.4.3 Sales Tax
- Rate of Sales
- Tax
- Selling Price
3.4.4 Simple Interest
- Principal Rate
- Time
L. Simple Probability
1. Make simple predictions
2. Tell the number of
favorable outcomes/chances
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I II III IV V VI
3. Application of
Addition and
Subtraction of
fractions
3.1 Solve word
problems
involving addition
of similar
fractions without
regrouping
3.2 Solve word
problems
involving
subtraction of
similar fractions
without
regrouping
E. Comprehension of
Fractions
1. Multiply two fractions
1.1 Visualize
multiplication of
fraction
1.2 Find a fractional
part of a number
1.2.1 Translate
expressions
such as:
2
1
of
3
2
,
3
2
of
6
1
2. Multiply a fraction by
another fraction
3. Application of
Multiplication
3.1 Solve word
problems involving
multiplication of
fractions
3.1.1 Analyze the
word problem
3.1.1.1 Tell:
- what is
M. Comprehension of
Integers
1. Visualize integers in their
order on a number line
2. Compares integers
3. Order integers in
increasing/decreasing order
III. GEOMETRY
A. Comprehension of
Spatial Figures
1. Draw different spatial
figures
1.1 Visualize the different
spatial figures, cube,
rectangular prism,
cylinder, sphere,
pyramid, cone, etc.
1.2 Describes the
different spatial
figures
IV. Measurement
A. Comprehension of
Surface Area
1. Tell the surface area of
solids
2. Tell the unit of measure
used for measuring the
surface area of solids
3. Find the area formula of
the following plane
figures:
- parallelograms
- triangles
- trapezoids
- circles
18
I II III IV V VI
asked
- what is/are
given
- the word
clue/s the
operation to
be used
3.2 Transform the
word problem into a
number sentence
3.3 Use the correct
operation
3.4 State the complete
answer
III. GEOMETRY
A. Comprehension of
Plane Figures and
Angles
1. Draw plane figures
1.1 Identify the different
kinds of plane
figures
1.2 a. Identify the parts
of a triangle
1.2 b. quadrilateral
1.3 Describe plane
figures according to sides,
corners, shapes and their
functional use
1.3.1 Describe
plane
figures with 3
and 4 sides
and corners
- square
- rectangle
- different
types of
triangles
1.4 Construct plane
figures using a
ruler and
compass
2. Draw different kinds of
angles
4. Derive a formula for
finding the surface area of:
- cubes
- prisms
- cylinders
5. Application of
Measurement of Surface
Area
5.1 Write an equation or
formula to solve for the
surface area of solids
5.2 Solve the word
problems involving
measurement of surface
area
5.2.1 Analyze the word
problem
5.2.1.1 Tells:
- what is asked
- what is/are
given
- the word clue/s
the operation to
be used
5.2.2 Transform the
word problem into a
number sentence
5.2.3 Use the correct
operation
5.2.4 State the complete
answer
B. Comprehension of
Volume
1. Find the volume of a
solid
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I II III IV V VI
2.1 Identify parts of an
angle
2.2 Name different
kinds of angles such
as right angle, acute
angle and obtuse
angle
2.2.1 Visualize the different
kinds of angles as acute,
right obtuse
2.3 Classify angles as
right, acute or
obtuse
2.4 Identify congruent angles
IV. MEASUREMENT
A. Comprehension of
Perimeter
1. Find the perimeter of
polygons
1.1 triangle
1.2 quadrilateral
1.3 pentagon etc
2. Derive a formula for
finding the perimeter of
polygons
3. Application of Perimeter
3.1 Solve word
problems
involving
perimeter
measures
B. Comprehension of Area
1. Find the area of
polygons in square
metre/centimetre
a. triangle
b. parallelogram
1.1 Tell the unit of
measure used for measuring
the volume of solids,
rectangular prisms
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:
- prism
- cylinders
- pyramid
- cones
2. Application of
Measurement of Volume
2.1 Write an equation or
formula to solve for the
volume of solid
2.2 Solve word problems
involving measurement
of volume
2.1.1 Analyze the word
problem
2.1.1.1 Tell:
- what is asked
- what is/are given
- the word clue/s
- the operation to
be used
2.1.2 Transform the
word problems into a number
sentence
2.1.3 Use the correct
operation
2.1.4 State the complete
answer
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I II III IV V VI
1.1 Tell the unit of
measure used
for measuring
the area of
triangles and
parallelo-
grams
1.2 Tell the unit of
square
measures
used for
measuring the
area of a
triangle/
parallelogram
1.3 Derive a
formula for
finding the
area of a:
1.3.1 Triangle
1.3.2 Parallelogram
C. Comprehension of
Volume
1. Make measurement
using non-standard
units:
- cubes
- marbles
2. Compare among the
non-standard units of
measuring volume in
terms of consistency
and accuracy
3. Approximate
measurement of
volume
C. Comprehension of
Meter Reading
1. Read and interpret
readings from:
1.1 electric meter
1.2 water meter
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
presented in a
circle graph
2.2 Find the average of
data presented in a
circle graph
21
I II III IV V VI
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
presented in a
bar graph
2.2 Find the
average of
data
presented in a
bar graph