bec pelc 2010 mathematics
TRANSCRIPT
E:\CDD Files\BEC-PELC Finalized June 2010\COVER PELC - Math.docx Printed: 8/12/2010 11:30 AM [Anafel Bergado] 1
(Philippine Elementary Learning Competencies) BASIC EDUCATION CURRICULUM
MATHEMATICS
MATHEMATICS
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ELEMENTARY MATHEMATICS
INTRODUCTION All Filipino pupils need a high-quality mathematics curriculum that will prepare them to choose from among a broad range of career paths. A curriculum that is complete which provide pupils with the essentials of computational and procedural basic skills, conceptual understanding, and problem solving skills. This elementary mathematics curriculum was refined in consultation with curriculum development specialists, mathematics experts and teachers. Refinement was done based on the feedback from implementers especially teachers. Educators are faced with the challenge of raising the bar of pupil achievement through a more defined curriculum and instruction, and to provide the support necessary for all pupils to meet or surpass the mathematics standards set forth by the Department of Education. DESCRIPTION The 2010 Elementary Mathematics curriculum reflects recent developments and trends in mathematics education. With this refined curriculum, pupils will be given the opportunities to develop and enhance their mathematical knowledge and skills through creative thinking and critical reasoning; discover and apply new ways of solving problems and use various technologies available such as calculators and computer software tools. The standards defined in this curriculum identify what all pupils in the Philippine public schools should know and be able to do at each grade level. � Mathematics in Grades 1 and 2 includes the study of whole numbers, addition
and subtraction, basic facts of multiplication and division, basics of geometry, metric and local measurements, the use of money and their application to practical problems based on real life activities.
� Mathematics in 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 includes four fundamental operations of whole numbers for mastery, using series of operation, decimals and fractions, ratio and proportion, percent, polygons and spatial figures, measurement, graphs and simple probability, integers and simple algebra; and problem solving applications
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
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NOTES TO TEACHERS and SCHOOL ADMINISTRATORS: The following are important components in implementing the intended mathematics curriculum:
A. Assessment.
� Assessment should be the basis for instruction and utilization of different types of assessment is encouraged
� Pupils should be assessed regularly to determine whether or not they are progressing steadily, and results of assessment should be made basis for modifying curriculum and improving instruction
� Assessment can improve instruction when teachers use results to analyze how much and how well pupils learned
B. Instruction
The quality of instruction is the most important component in implementing the curriculum � Teachers should possess an in-depth understanding of the content
standards and the mathematics they are expected to teach and continually improve their knowledge of the content. If a teacher does not have a clear understanding of the content, he/she can seek the help of the school head, supervisor or master teachers in the learning area.
� Teachers should consider prerequisite skills in developing new Concept � Teachers using physical manipulative can assure better results � Teachers should use instructional strategies that are appropriate to the instructional objectives and to pupils’ needs � Teachers should introduce different strategies in solving routine and non-routine problems � Teachers should provide situations that will make children recognize and use connections among mathematical ideas and between mathematics and other learning areas � Teachers should use assessment results in planning for instruction
C. Instructional Time
Instructional time for mathematics should be free from all interruptions. � Teachers should observe strictly the time allocated for each grade level
and must be utilized solely for instruction. Whenever possible, additional instructional time should be allocated for pupils who are performing substantially below his/her grade level
� Learning time is extended through remedial instruction, homework for more practice and mastery, or for pupils to apply their previously learned knowledge and skills to new learning situations.. However, homework should be checked by the teachers for pupils to value its importance.
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D. Instructional Materials
All mathematics teachers need quality and adequate instructional resources and materials that are appropriate and aligned with the curriculum content. � Instructional materials should be accurate and address the learning
competency � Instructional materials should be adequate and appropriate in
developing a specific content � Instructional materials should provide pupils with the opportunities to
explain their thinking, verbally, and in writing � Instructional materials should provide ideas for addressing diverse
pupil performance � Instructional materials should promote interactivity between and among
pupils and teacher; develop independent learning; and simulate real-life situations
� Instructional materials should provide for remediation or re-teaching a concept, provide additional practice for low-performing pupils; or for reinforcement of concepts/skills for average-performing learners; or for enrichment for more able pupils or advancement to new material
� Instructional materials can be technology like calculators and computer software tools which are enablers for learning.
� Calculators enable pupils to concentrate on understanding and studying mathematical concepts instead of spending time on tedious computations. For the lower grades, use of calculators can be introduced after they have mastered their basic facts and can perform the four fundamental operations, even for large numbers using paper and pencil. Calculator can be used occasionally for special projects or when developing specific concepts; for some games/fun exercises or for checking homework and exercises.
� Online materials like mathematical games and exercises can reinforce basic skills and concepts.
� Using videos in teaching mathematics can enhance learning, provide a way to deliver new content, practice work or to reinforce learning. Pupils can use video to demonstrate their understanding, express ideas, and create authentic products.
E. Group Learning
Grouping is a tool that teachers can use to improve learning � Grouping pupils according to their instructional needs can improve
achievement � Cooperative learning is an effective strategy for learning mathematics
F. Classroom Management
The elementary mathematics curriculum is itself the primary tool for classroom management. Classroom management should actively engaged pupils and focus to learning mathematics at an acceptable performance.
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� Teacher should approach mathematics teaching with a positive attitude. Teacher’s enthusiasm for the subject matter can have greater effect to pupils’ perception about mathematics and achievement/performance.
� Classroom should be child-friendly. It serves a strong purpose both academic and social interaction. It should provide a space for group work or investigatory project.
� Classroom management should help pupils develop a deep understanding of mathematics, encouraging and motivating them to exert the effort necessary to learn, experience and master a difficult concept or skill with greater satisfaction.
� Rewards system can be in place temporarily to motivate pupils to perform and achieve at an acceptable level.
G. Professional Development
Mathematics teachers should have the necessary preparation in the learning area. They should have a continuous professional development program to keep them abreast with the current developments in mathematics education. � Teachers should form a group learning cell to learn together; work and
plan for mathematics instruction; review the curriculum, make the necessary adjustments to meet the needs of the pupils.
� Master teachers and other performing teachers who demonstrate effective instructional practices with the pupils should share these practices to new or struggling teachers.
H. Administrative Support
Administrative support for mathematics instruction can contribute to better achievement/ performance. � Administrative support can be provision for instructional
materials/resources � Assigning the best teachers in low-performing class � Provision of technical assistance � Provision for rewards to performing teachers and pupils
I. Community Involvement
Parents, community members and other stakeholders are great allies who can make valuable contributions in mathematics education. � Parents should be involved in education by assisting them support their
children in learning mathematics. They can be involved in planning for instruction by seeking their comments. Other stakeholders can provide resources for the improvement of mathematics education.
� Reporting to parents about the progress of their children can increase their awareness/participation to help the school achieve the goals of mathematics program.
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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/expressing 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI
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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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
II. RATIONAL NUMBERS
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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI write numbers from 0 to 10 in symbols
1.9 Tell the relationship of numbers from 0 to 10 using the expressions “less than”, “greater than”, “equal”
1.10 Associate numbers with sets 11-50 and identify the number of objects
1.11 Count by 1’s through 50
1.12 Skip count by 2’s, 5’s and 10’s through 50
1.13 Associate numbers with sets having 51 up to 100 objects and identify the number of objects in a set
2. Read and write numbers through 100 in symbols and in words 2.1 Read numbers
the pattern of naming ordinal numbers e.g. 21st, 22nd, 23rd, 24th, etc.
7. Read and write money value through 100 7.1 Read money in
symbols through 100
7.2 Express money as pesos and centavos through 100
7.3 Compare values of the different denominations of coins and paper bills through 100 using the relation symbol
B. Comprehension of
Addition 1. Add two to three-
digit numbers with sums up to 999 1.1 without
regrouping 1.2 with
regrouping 2. Add two to
three-digit numbers with zero in any of the addends without
value of the different denominations of coins and bills through 1000
5. Express Roman numbers through M in Hindu-Arabic symbols and vice versa 5.1 Read and
write the value of Roman numbers in Hindu-Arabic and vice versa 5.1.1 I to L 5.1.2 L to C 5.1.2 C to D 5.1.3 D to M
B. Comprehension of
Addition 1. Add four to five-
digit numbers up to four addends with sums up to 99 999 1.1 without
regrouping 1.2 with
regrouping in 1.2.1 tens and
hundreds places
1.2.2 thousands and ten
problems involving addition of whole numbers including money with sums through millions and billions without and with regrouping following the steps in problem solving
4.2 Solve mentally one-step word problems involving addition with sums up to 300 without regrouping
C. Comprehension of
Subtraction 1. Subtract five or
more digit numbers from six or more digit numbers without and with regrouping in any or all places and involving three or more zeros both in the minuend and subtrahend 1.1 Subtract five or
fractions to similar fractions 1.1 Visualize
changing dissimilar fractions to similar fractions
2. Identify equal fractions using regions and cross product method
3. Change fractions to lowest/higher term (LCM/GCF)
4. Order dissimilar fractions written in different forms from least to greatest and vice versa
5. Estimate fractions close to 0, 2
1, or 1
B. Comprehension of
Addition of Fractions
1. Add similar and dissimilar fractions 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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)without 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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
2.2 Multiply five or more digit factors by three- to five-digit factors with regrouping
2.3 Multiply five or more digit factors having one to three zeros in both factors without and with regrouping
2.4 Multiply five or 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 with zero difficulty 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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 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
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 (commutative/ 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 2. Multiply mentally
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 following the steps in solving problems
3.2 Solve two to three-step word problems involving addition, subtraction and multiplication of decimals including money following the steps in solving two-step
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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI problem
4.1.1.1 Tell: � what is
asked � what
is/are given
� the word clues
� the operation 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 operation 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
4. Multiply mentally 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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 Show that subtraction 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 with zero difficulty 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
II. RATIONAL NUMBERS 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 following 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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. Multiply decimals 1.1 Visualize
multiplication of decimals using models
1.2 Multiply tenths by another tenths
1.3 Multiply hundredths by tenths and vice versa
2. Multiply mixed decimals with tenths and hundredths by whole numbers
3. Multiply mixed decimals by mixed decimals
3. Form equivalent fractions
4. Solve for the missing terms in a pair of equivalent fractions
5. Reduce fractions to lowest terms
6. Change mixed numbers to improper fractions and vice versa
7. Estimate fractions close to 0, 2
1 or 1
8. Find the least common denominator (LCD) of a set of fraction
9. Compare fractions and mixed forms using 9.1 fraction sense,
visual reasoning, renaming to like forms
9.2 cross products method
9.3 LCD method 10. Order fractions
in simple and mixed forms in ascending or descending order
F. Comprehension of
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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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
21
and 41 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 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
to four-digit numbers by one to two-digit numbers with zero difficulty
2. Divide multiples of 5 by 5
3. Divide multiples of 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
4. Multiply decimals by 10 and 100
5. Multiply decimals 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 dissimilar fractions in simple or mixed forms without regrouping
6. Add and subtract dissimilar fractions in simple or mixed forms with regrouping
7. Add mentally similar fractions using the properties of addition
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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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 following 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 following the steps in solving two-step problems
G. Comprehension of
Multiplication of Fractions
1. Simplify factors by cancellation method before
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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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 2. Multiply fractions
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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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 following the steps in solving problems
7.2 Solve two to three-step word problems
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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI • what
is/are given
• the word clue/s
• the hidden question
• the operations 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
II. RATIONAL NUMBERS
A. Comprehension of
Unit Fractions 1. Identify 3
1
, 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. Multiply 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:
21
of 6 ,
32
of 61
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 following 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI 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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GRADE I GRADE II GRADE III GRADE IV GRADE V GRADE VI B. Expressions and
Equations 1. Give the meaning
of expression and equation
2. Differentiate expression from equation