Bec-pelc 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.

shows mastery of

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 shows mastery of

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. shows mastery of

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.

shows appreciation

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. shows appreciation

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.

shows appreciation

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, 21

, 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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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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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, 21

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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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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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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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

2.1 Solve 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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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 31

, 51

, 61

of a given

whole/group of

objects

2. Read and write 31

,

51

, 61

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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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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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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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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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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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

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B. Expressions and

Equations

1. Give the meaning

of expression and

equation

2. Differentiate

expression from

equation

Documents

Bec-pelc 2010 - Mathematics