(P h i li p p i n e Ele m e n ta ry Le a rn i n g Co m p e te n c i e s )

MATHEMATICS

MATHEMATICS
DESCRIPTION
Mathematics in Grades 1 and 2 includes the study of whole numbers, addition and subtraction, basic facts of multiplication and division, basics of geometry, fractions, metric and local measurements, the use of money and their application to practical problems based on real life activities. Grades 3 and 4 deals with the study of whole numbers, the four fundamental operations, fractions and decimals including money, angles, plane figures, measurement and graphs. In Grades 5 and 6 the child is expected to have mastered the four fundamental operations of whole numbers, performs skills in decimals and fractions, conceptualize the meaning of ratio and proportion, percent, integers, simple probability, polygons, spatial figures, measurement and graphs. Simple concepts in Algebra is also introduced to be articulated in the high school. Besides further development of the basic mathematical skills, the child is expected to solve problems related to business and industrial activities in the community.

TIME ALLOTMENT
Daily Weekly Grade 1 80 400 Grade 2 80 400 Grade 3 80 400 Grade 4 60 300 Grade 5 60 300 Grade 6 60 300

The 20-minute increase in the daily time allotment is given to ensure that all lessons are finished and there will be more activities that involve grouping practical investigations and problem solving. Pupils learn more if they have hands on or manipulative and interactive activities, learn on their own, explore, discover, generalize and apply what they learned in their daily life.

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EXPECTATIONS 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

At the end of Grade VI, the child is expected to have mastered the concepts and operations of whole numbers; demonstrate understanding of concepts and perform skills on decimals, fractions, ratio and proportion, percent, integers, simple probability, geometry, measurement, and graphs; integers; exact and estimated computation of the four fundamental operations involving decimals, money, fractions and measurement; and apply the concepts learned in solving problems. At the end of Grade V, the child is expected to have mastered the concepts and operations of whole numbers; demonstrate understanding of concepts and perform skills on fractions, decimals including money, ratio, percent, geometry, measurement and graphs; exact and estimated computation of the four fundamental operations on rational numbers including money and measurement and apply the concepts learned in solving problems. At the end of Grade IV, the child is expected to demonstrate understanding of concepts and perform skills of whole numbers up to millions and billions including money, decimals, fractions, geometry, graphs and scales; exact and estimated computation on the four fundamental operations; and apply the concepts learned to solve problems. At the end of Grade III, the child is expected to demonstrate understanding of concepts and skills on whole numbers up to one hundred thousand, fractions, measurement and graphs; perform the four fundamental operations of whole numbers and measurement; and apply the concepts learned in solving problems. At the end of Grade II, the child is expected to demonstrate understanding of concepts and skills on whole numbers up to one thousand including basics of geometry; perform addition and subtraction of 3 to 4-digit numbers, understand basic facts of multiplication and division; and apply the concepts learned to solve problems. At the end of Grade I, the child is expected to demonstrate understanding of basic concepts and skills on whole numbers up to one hundred including money and measurement; perform addition and subtraction of 1 to 3-digit numbers; and apply the concepts learned to solve problems.

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ELEMENTARY MATHEMATICS
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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 color size shape 1.2 Classify sets using common objects according to color, size shape 1.3 Order sets with 1 to 10 objects from least to greatest and vice-versa 1.4 Construct sets with objects 1 to 10 in 1.4.1 – the one more order 1.4.2 – the one less order 1.5 Compare 2 sets using the expressions “fewer than”, “more than”, and “as many as” 1.6 Associate numbers with sets having objects 0 to 10 1.7 Tell the number of objects in a given set of 10 or less

II
I. WHOLE NUMBERS A. Comprehension of Whole Numbers 1. Identify numbers from 101 through 1000 1.1 Associate numbers with sets having 101 up to 500 objects/ things 1.2 Associate numbers with sets having 501 up to 1000 objects/ sets 2. Read and write numbers from 101 through 1000 in symbols and in words 2.1 Give the place value of each digit in a 3-digit number 2.2 Read numbers through 1000 in symbols and in words 2.3 Write numbers through 1000 in symbols and in words 2.4 Write 3-digit numbers in expanded form 2.5 Compare numbers using >, < and = 3. Skip count numbers by 50s up to 1000 4. Read and write ordinal th numbers from 11 th through the 20 objects of given sets from a given point of reference th 4.1 Identify the 11 through th the 20 objects of given sets from a given point of reference 4.2 Identify ordinal numbers th up to the 20 5. Identify the pattern of naming ordinal numbers st nd rd th e.g. 21 , 22 , 23 , 24 ,

III
I. WHOLE NUMBERS A. Comprehension of Whole Numbers 1. Read and write the numbers through 100 000 in symbols and in words 1.1 Identify cardinal numbers 1.1.1 1000 through 10 000 1.1.2 10 001 though 100 000 1.2 Give the place value of each digit in 4 to 5 digit numbers 1.3 Read numbers through 100 000 in symbols and in words 1.4 Write numbers through 100 000 in symbols and in words 1.5 Express the relationship of numbers using expressions "less than" greater than and equal to (> < =) 1.6 Write 4 to 5 digit numbers in expanded form 2. Round number to the 2.1 Nearest tens and hundreds 2.2 Nearest thousands and ten thousands 3. Tell when a number is odd or even 4. Read and write money in symbols through 1000

IV
I. WHOLE NUMBERS A. Comprehension of Whole Numbers 1. Read and write numbers through millions in symbols and in words 1.1 Identify numbers from 100 001 through millions/ billions 1.2 Give the place value of each digit in a 6 or more digit numbers 1.3 Read and write numbers through millions/billions in symbols 1.4 Read and write numbers through millions/billions in words 2. Round off numbers to the nearest 2.1 tens 2.2 hundreds 2.3 thousands 2.4 ten thousands 2.5 hundred thousand 2.6 millions 2.7 billions B. Comprehension of Addition 1. Add 6 or more digit numbers with 4 or more addends with sums through billions 1.1 without regrouping

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I. WHOLE NUMBERS A. Comprehension of Whole Numbers REVIEW 1. Place Value 2. Properties of Whole Numbers • Addition • Multiplication 3. Rounding numbers 4. Operations of Whole Numbers: • Adding and Subtracting • Multiplying Whole Numbers • Dividing Whole Numbers 5. Problem Solving Involving Large Numbers: 1-step and 2- to 3-step 1. Subset of Whole Numbers 1.1 Differentiate odd from even numbers 1.2 Give the common factors of given numbers 1.3 Identify prime and composite numbers 1.4 Find prime factors of a number 1.5 Show multiples of a given number by 10, 100 1.6 Find the least common multiple of a set of numbers 1.7 Tell when a number is divisible by another number (Divisibility Rules)

VI I. WHOLE NUMBERS A. Comprehension of Whole Numbers 1. Comprehend the order of operations on whole numbers 1.1 Follow the correct order of operations (PEMDAS Rule) when solving expressions/equations having more than one operations 1.1.1 Give the meaning of - Expression - Equation - Exponent - Base 1.1.2 Evaluate an expression involving exponents 1.1.3 Evaluate an expression with two different operations with or without exponents and parenthesis/grouping symbols 1.1.4 Evaluate an expression with more than 2 operations with or without exponents and parenthesis/grouping symbols 1.2 Apply the order of operations in solving 2-3 step word problems

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1.8 Order numbers 1 to 10 including zero from least to greatest and vice-versa 1.9 Read and write numbers from 0 to 10 in symbols 1.10 Tell the relationship of numbers using the expressions “less than”, “greater than”, “equal” 1.11 Count by 1’s through 50 1.12 Identify numbers in sets having 11 to 50 objects 1.13 Skip count by 2’s, 5’s and 10 through 50 1.14 Associate numbers with sets having 51 up to 100 objects/things 2. Read and write numbers through 100 in symbols and in words 2.1 Give the place value of each digit in a 1to 2-digit numbers 2.2 Read numbers from 11 through 100 in symbols and in words 2.3 Write numbers from 11 through 100 in symbols and in words 2.4 Write numbers from 11 through 100 in expanded form 2.5 Regroup sets of ones into sets of tens and sets of tens into hundreds using objects

II etc. 6. Use the pattern of naming ordinal numbers beyond 20 7. Read and write money value through P100 7.1 Read money in symbols through P100 7.2 Express money as pesos and centavos through P100 7.3 Compare values of the different denominations of coins and paper bills through P100 using the relation symbol 8. Express Roman numbers in equivalent HinduArabic through L (50) 8.1 Read and write Roman numbers through L 8.2 Change Roman numbers in equivalent HinduArabic through L and vice-versa B. Comprehension of Addition 1. Add 2- to 3-digit numbers with sums up to 999 1.1 without regrouping in short form 1.2 with regrouping 2. Add 2- to 3-digit numbers with zero in any of the addends without regrouping with sums up to 999 3. Add 2- to 3-digit numbers with zero in any of the addends with regrouping with sums up to 999 4. Show properties of addition in adding numbers

III
4.1 Read money value in symbols through 1000 4.2 Write money value in symbols through 1000 4.3 Compare value of the different denominations of coins and bills through 1000 5. Express Roman numbers through M in Hindu-Arabic symbols and vice-versa 5.1 Read and write the value of Roman numbers in HinduArabic and vice-versa 5.1.1 L to C 5.1.2 C to D 5.1.3 D to M 1. Comprehension of Addition 1.1 Add 4 to 5 digit numbers up to four addends with sums up to 100 000 1.1.1 Without regrouping in short forms 1.1.2 With regrouping in 1.1.2.1 Tens and hundreds places 1.1.2.2 Thousands and ten thousands places 1.2 Estimate the sums of 3 to 5 digit addends 1.3 Add mentally 1 to 2 digit numbers with sums up to 100 without regrouping

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1.2 with regrouping in: - any two or more places - all places Show the properties of addition 2.1 Commutative Property 2.2 Associative Property 2.3 Identity Property Estimate the sum of 6 or more digit addends Add mentally 2 to 3 digit numbers with sums up to 300 without regrouping Application of Addition 5.1 Solve word problems involving addition of whole numbers including money with sums through millions and billions without and with regrouping 5.1.1 Analyze the word problem 5.1.1.1 Tell: - what is asked - what is/are given - the word clue/s - the operation to be used 5.1.2 Transform the word problem into a number sentence 5.1.3 Use the correct operation

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A. Comprehension of Fraction 1. Change dissimilar fractions to similar fractions 1.1 Visualize changing dissimilar fractions to similar fractions 1.2 Identify equal fractions 1.2.1 Use cross product to determine whether 2 fractions are equal 1.3 Change fractions to lower/higher term (LCM/GCF) 2. Estimate fractions close to 0,
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VI 1.2.1 Write an equation to solve multi-step word problems 1.2.2 Solve 2-3 step word problems involving whole numbers 1.3 Describe answer in a complete sentence with proper units/labels II. RATIONAL NUMBERS A. Comprehension of Decimals 1. Visualize ones, tenths, hundredths and thousandths 1.1 Name a decimal for a given model (region/blocks, money, number line) 1.2 Use different models to show a given decimal (region/block, money, number line) 2. Rename fractions whose denominators are power of 10 in decimal form 3. Read and write decimals through ten thousandths 3.1 Identify the value/place value of a digit in a given decimal 3.2 Read decimals through ten thousandths 3.3 Write decimals through ten thousandths in different notations

2.

3. 4. 5.

, or 1

B. Comprehension of Addition Fraction 1. Add numbers in mixed forms with similar and dissimilar fractions without and with regrouping 1.1 Add two to four similar fractions 1.2 Visualize addition of dissimilar fractions 1.3 Add dissimilar fractions 1.4 Add dissimilar fractions and whole numbers 1.5 Add whole numbers and mixed forms 1.6 Add mixed form and a dissimilar fraction 1.7 Add mixed forms 1.8 Estimate sum 1.9 Add mentally two fractional units with similar denominators 2. Application of Addition of Fractions

B.

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3, Read and write ordinal st nd rd numbers 1 , 2 , 3 up to th 10 in a given set st nd 3.1 Identify the 1 , 2 , rd th 3 up to the 10 object in a given set 4. Read and write money up to P 50.00 4.1 Read and write the symbol of c for centavo and P for pesos 4.2 Tell the value of a given set of coins and paper bills up to P50 4.3 Compare values of the different denominations of coins and paper bills through P50 using the relation symbols. 4.4 Skip count by P5s, P10s up to P50s B. Comprehension of Addition 1. Add two to three 1digit numbers with sums up to 18 horizontally and vertically 1.1 Join two sets with 1 to 9 objects 1.2 Show the relationship of joining sets to addition of whole numbers 1.3 Add two 1-digit numbers having sums of : - 6 and less - 7 through 10 (after concept of 1-10)

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4.1 Show the commutative property of addition in adding numbers 4.2 Show the associative property of addition in adding numbers 5. Add mentally 1- to 2-digit numbers with sum up to 50 6. Application of Addition 6.1 Solve word problems involving addition of whole numbers including money with sums up to 999 without and with regrouping 6.1.1 Analyzes word problem 6.1.1.1 Tell:

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2. Application of Addition 2.1 Solve word problems involving addition of whole numbers with sums up to 100 000 including money following the steps in problem solving 2.2 Solve mentally 1 step word problems involving addition with sums up to 100 without regrouping 5.1.4

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State the complete answer 5.2 Solve mentally 1 step word problems involving addition with sums up to 300 without regrouping C. Comprehension of Subtraction 1. Subtract 5 or more digit numbers from 6 or more digit numbers without and with regrouping in any or all places and involving three or more zeros in the minuend. 1.1 Subtract 5 or more digit numbers from 6 or more digit numbers without regrouping 1.2 Subtract 5 or more digit numbers from 6 or more digit numbers with regrouping 1.2.1 having zeros in the minuends and/or subtrahend 1.2.2 with three continuous or noncontinuous zeros in both minuends and subtrahend and with regrouping in any or all places

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2.1 Solve word problems involving addition of similar and dissimilar fractions without or with regrouping 2.1.1 Analyze the word problem 2.1.1.1 Tell: - what is asked - what is/are given - the word clue - the operation to be used 2.1.2 Transform word problem into a number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer C. Comprehension of Subtraction of Fractions 1. Subtract fractions and mixed forms with common denominators without and with regrouping 1.1 Visualize subtraction of fractions 1.2 Subtract whole numbers from mixed forms 1.3 Subtract mixed numbers from mixed numbers (with similar fractions) 1.4 Subtract fractions from whole numbers 1.5 Subtract fractions from mixed numbers 1.6 Subtract mixed numbers from whole numbers 2. Subtract Dissimilar Fractions 2.1 Visualize subtraction of dissimilar fractions 2.2 Subtract fractions from mixed numbers

VI - Standard Notation - Expanded Notation 4. Compare and order decimals through ten thousandths 5. Round decimals through ten thousandths B. Comprehension of Addition and Subtraction of Decimals 1. Estimate sums and differences of whole numbers and decimals 2. Add and subtract whole numbers and decimals 3. Add and subtract decimals through ten thousandths without and with regrouping (with concrete/visual models) 4. Add and subtract mixed decimals with regrouping 5. Apply the different properties of addition to compute sums mentally 5.1 Commutative property of addition 6. Application of addition and subtraction of decimals 6.1 Write an equation to solve word problems 6.2 Solve 1 to 3-step word problems involving addition and subtraction of decimals including money

be used 6.1.2 Transform the word problem into a number sentence 6.1.3 Use the correct operation 6.1.4 State the complete answer C. Comprehension of Subtraction

• what is asked • what is/are given • the word clues • the operation to

1. Subtract 2- to 3-digit numbers with minuends up to 999 without and with regrouping 1.1 Illustrate how subtraction is used when: 1.1.1 Taking away from the given set 1.1.2 Comparing two sets 1.1.3 Finding a missing addend

C. 1. Comprehension of Subtraction 1.1 Subtract 3 to 4 digit numbers from 4 to 5 digit numbers with minuends up to 100 000 without and with regrouping and with zero difficulty 1.1.1 Subtract 3 digit number from 4 to 5 digit numbers with minuends up to 100 000 without regrouping 1.1.2 Subtract 4 digit number from 4 to 5 digit numbers with minuends up to 100 000 without regrouping 1.1.3 Subtract 3 to 4 digit numbers from 4 to 5 digit numbers with regrouping 1.1.3.1 in the tens place 1.1.3.2 in the hundreds place 1.1.3.3 in the thousands place

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1.4 Illustrate that any given number plus zero is the same number 1.5 Show that changing the order of two addends does not affect the sum 1.6 Add three 1-digit numbers having sums up to 18 1.7 Show that changing the grouping of three or more addends helps make computation easy 2. Add mentally two to three 1-digit numbers with sums up to 18 3. Add 1-to 2-digit numbers with sum through 99 - without regrouping - with regrouping 4. Application of Addition 4.1 Solve 1-step word problems involving addition of whole numbers including money with sums up to 99 without and with regrouping 4.1.1. Analyze the word problem 4.1.1.1 Tell - what is asked - what is/are given - the word clues - the operation to be used

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1.2 Subtract 2- to 3-digit numbers with regrouping 1.2.1 in the tens place without or with zero 1.2.2 in the hundreds place value without or with zero difficulty 1.2.3 in the tens and hundreds place without or with zero difficulty 2. Use addition to check subtraction 3. Subtract mentally 1-digit number from 1 and 2 digit numbers with minuends up to 50 without regrouping 4. Application of Subtraction 4.1 Solve 1-step word problems involving subtraction of whole numbers including money with minuends up to 999 without and with regrouping 4.1.1 Analyze the word problem 4.1.1.1 Tell: what is asked what is/are given the word clue/s the operation to be used 4.1.2 Transform the word problem into a number sentence 4.1.3 Use the correct operation 4.1.4 State the complete answer 5. Application of Addition and Subtraction 5.1 Solve 2-step word problems involving addition and subtraction of 2- to 4-digit numbers

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1.1.3.4 in the ten thousand place 1.1.3.5 with zero difficulty in either tens or hundreds place 1.1.4 Estimate the difference of two numbers with 3 to 4 digits 1.2 Subtracts mentally 2 digit numbers with minuends up to 99 without regrouping 2. Application of Subtraction 2.1 Solve 1 step word problems involving subtraction of whole numbers including money with minuends up to 100 000 without and with regrouping following the steps in problem solving 2.2 Solve mentally 1 step word problems involving subtraction without regrouping 3. Application of Addition and Subtraction 3.1 Solve 2 step word problems involving addition and subtraction of whole numbers including money following the steps in problem solving 1. Comprehension of Multiplication 1.1 Multiply 2 to 4 digit numbers by 1 to 2 digit numbers

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1.3 Estimate the difference of two numbers with four to six digits 2. Subtract mentally numbers with minuends up to 300 without regrouping 3. Application of Subtraction 3.1 Solve 1-step word problems involving subtraction of whole numbers including money without and with regrouping 3.1.1 Analyze the word problem 3.1.1.1 Tell: - what is asked - what is/are given - the word clue/the operation to be used 3.1.2 Transform the word problem into a number sentence 3.1.3 Use the correct operation 3.1.4 State the complete answer 3.2 Solve mentally 1- step word problems involving subtraction without regrouping 4. Application of Addition and Subtraction 4.1 Solve 2-step word problems involving addition and subtraction including money

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2.3 Subtract mixed numbers from mixed numbers 3. Subtract mentally similar fractions 4. Application of Subtraction of Fractions 4.1 Solve word problems involving subtraction of fractions 4.1.1 Analyze word problems 4.1.1.1 Tell: what is asked what is/are given the word clue the operation to be used 4.1.2 Transform the word problem into a number sentence 4.1.3 Use the correct operation 4.1.4 State the complete answer 5. Application of Addition and Subtraction of Fractions 5.1 Solve 2-step word problems involving addition and subtraction of fraction D. Comprehension of Multiplication of Fractions 1. Multiply fractions by whole number, mixed form by a fraction 1.1 Visualize multiplication of fractions 1.2 Find a fractional part of a number 1.2.1 Translate expressions such as “ 2 of 3 1.3 Multiply 1.3.1 fraction by another fraction
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VI 6.3 Describe answer in a complete sentence with proper labels/units C. Comprehension of Multiplication of Decimals 1. Estimate products of whole numbers and decimals 2. Multiply up to 3 digit factors by 1 to 2 digit factors without and with regrouping and with zero difficulty 3. Multiply hundredths by hundredths 4. Multiply mixed decimals by mixed decimals with hundredths 5. Multiply mentally decimals by 10, 100 and 1,000 6. Multiply mentally decimals by .01, 0.01 and 0.001 7. Apply the properties of multiplication to compute products 7.1 Commutative property of multiplication 7.2 Associative property of multiplication 7.3 Distributive property of multiplication over addition 8. Application of multiplication of decimals

D.

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4.1.2 Transform the word problem into a number sentence Use the correct operation State the complete answer

II including money 5.1.1 Analyze the word problems 5.1.1.1 Tell: what is asked the word clue/s the hidden question the operation to be used 5.1.2 Transform the word problem into a number sentence 5.1.3 Use the correct operation 5.1.4 State the complete answer D. Comprehension of Multiplication 1. Multiply 1- to 2-digit numbers by a 1-digit number with products up to 81 1.1 Multiply 1-digit by 1-digit number with or without regrouping with products up to 45 1.1.1 Show the relationship of putting together 2 or more number of elements to repeated addition 1.1.2 Show multiplication of whole numbers as repeated addition on the number line or array, etc. 1.1.3 Transform an addition sentence into a multiplication sentence 1.1.4 Identify the parts of a multiplication sentence 1.1.5 Give the factors of a given number 1.1.6 Show that a number multiplied by 1 is the

III without and with regrouping in all places 1.1.1 Multiply 2 to 4 digit numbers without and with regrouping 1.1.1.1 Show that changing the order and/or regrouping in multiplication makes computation easy 1.1.1.2 Multiply 2 to 4 digit numbers by 1 to 2 digit numbers without regrouping 1.1.1.3 Multiply 2 to 4 digit numbers by 1 to 2 digit numbers with regrouping 1.1.1.4 Multiply 2 digit numbers by 1 digit number with zero in the multiplicand 1.1.1.5 Multiply 3 to 4 digit numbers by 1 digit numbers with zero in the multiplicand 1.1.1.6 Multiply 2 to 4 digit numbers by multiples of 10 1.1.1.7 Multiply 2 to 4 digit numbers by multiples of 100 1.1.2 Estimate the product of 2 to 3 digit factors by 1 to 2 digit factors 1.1.3 Estimate the product of 4 digit factors by 1 to 2 digit factors 1.1.4 Multiply mentally 2 digit numbers by 1 digit numbers 4.1.1

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Tell: - what is asked - what is/are given - the word clue/s - the hidden question - the operation to be used Transform the word problem into a number sentence Use the correct operation State the complete answer

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1.3.2 fraction by a whole number 1.3.3 mixed form by a fraction 1.3.4 mixed form by a mixed form 2. Multiply mentally fraction units 3. Application of multiplication of fractions 3.1 Solve word problems involving multiplication of fractions 3.1.1 Analyze the word problem 3.1.1.1 Tell: what is asked what is/are given the word clue the operation to be used 3.1.2 Transform the word problem into number sentence 3.1.3 Use the determined operations 3.1.4 State the complete answer 4. Application of Multiplication E. Comprehension of Ratio and Proportion Reducing ratios to lowest terms 1. Express the ratio of two numbers 1.1 Visualize the ratio of two given sets of objects 1.2 Express the ratio of two numbers by using either colon (:) or a fraction 2. Forms Proportion for Numbers

VI 8.1 Write an equation to solve word problems 8.2 Solve word problems involving multiplication of decimals including money 8.3 Solve 2 to 3 step word problems involving addition, subtraction and multiplication of decimals including money 8.4 Describe the answer in a complete sentence with proper labels/units D. Comprehension of Division of Decimals 1. Estimate problems of whole numbers and decimals 2. Divide 2.1 Whole numbers (2-5 digit dividends by decimals (1-2 digit divisions) 2.2 Recognize and differentiate between terminating and repeating from non-terminating decimal quotients 2.2.1 Recognize and differentiate between terminating and repeating from non-terminating decimal quotients 2.3 Mixed decimals by whole numbers 2.3.1 Visualize division using money as model

4.1.3 4.1.4

C. Comprehension of Subtraction 1. Subtract 1-to 2-digit numbers from 1-to2 digit numbers with minuends up to 99 without and with regrouping 1.1 Visualize situations when subtraction is used 1.1.1 Remove a subset from a given set of objects (taking away 1.1.1.1 Show the relationship of the removal of a group of objects from a given set to subtracting of whole numbers 1.1.1.2 Compare two given sets (more or less in number)

4.1.2

4.1.3 4.1.4

D. Comprehension of Multiplication 1. Multiply 5 or more factors by 3 to 5 digit factors without and with regrouping and with zero difficulty 1.1 Multiply 5 or more digit factors by 3 digit factors without and with regrouping 1.2 Multiply 5 or more digit factors by 4 to 5 digit factors without and with regrouping 1.3 Multiply 5 or more digit factors having one to three zeros in both factors without regrouping

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1.1.1.3 Find a missing addend 1.1.1.3.1 Show that subtraction is the inverse of addition 1.2 Subtract 1-digit nos. with minuends through 18 (basic facts) 1.3 Subtract 1-to 2-digit numbers with minuends up to 99 1.3.1 without regrouping 1.3.2 with regrouping 1.3.3 Subtract 2-digit without regrouping Subtract 21.3.4 digit with regrouping 2. Subtract mentally 1digit numbers from minuends up to 18 without regrouping 3. Application of Subtraction 3.1 Solve word problems involving subtraction of whole numbers including money with minuends up to 99 without and with regrouping 3.1.1 Analyze the word problems 3.1.1.1 Tell: - what is asked - what is/are given

II same number 1.1.7 Show that zero multiplied by a number is zero 1.2 Multiply 1- to 2-digit numbers by 1-digit number with products up to 81 1.3 Multiply mentally 1-digit numbers with products up to 81 without regrouping 2. Application of Multiplication 2.1 Solve 1-step word problems involving multiplication of whole numbers including money 2.1.1 Analyze the word problem 2.1.1.1 Tell:

III without regrouping with products up to 100 2. Application of Multiplication 2.1 Solve word problems involving multiplication of whole numbers including money following the steps in problem solving 3. Application of Multiplication and any one of Addition/ Subtraction 3.1 Solve 2-3 step word problems involving multiplication and any one of addition/ subtraction following the steps in problem solving E. 1. Comprehension of Division 1.1 Divide 2 to 4 digit numbers by 1 to 2 digit numbers without or with remainder and with zero difficulty 1.1.1 Divide 2 to 3 digit numbers by 1 digit number without/with remainder 1.1.1.1 Show that renaming 2 to 3 digit numbers help make computation easy 1.1.1.2 Divide 2 to 3 digit numbers by 1 digit number without remainder

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1.4 Multiply 5 or more digit factors having one to three zeros in both factors with regrouping in all places. 1.5 Multiply 5 digit or more factors by multiples of 10, 100 and 1,000 2. Show the properties of multiplication - Commutative - Associative - Zero Property - Identity Property - Distributive Property of Multiplication over Addition 3. Estimate the products of two factors with 5 or more digits by 2 to 3-digit numbers 4. Multiply mentally 2-digit numbers with products up to 200 without regrouping 5. Write numbers in exponent form 6. Write numbers in standard form to scientific notation and vice-versa 6.1 Write number in standard form to scientific notation 6.2 Write number in scientific notation to standard form 7. Application of Multiplication 7.1 Solve word problems involving multiplication of whole number including money

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F. Comprehension of Decimals 1. Read and write decimals through thousandths 1.1 Rename in decimal form fraction whose denominators are powers of 10 1.2 Give the place value of each digit of a given decimal 2. Round decimals to the nearest tenths/hundredths/ thousandths G. Comprehension of Addition and Subtraction of Decimals 1. Add and subtract decimals through thousandths without and with regrouping 2. Add and subtract mixed decimals with regrouping • Subtract mixed decimals with regrouping • Subtract mixed decimals from whole numbers 3. Application of addition and subtraction of decimals 3.1 Solve word problems involving either addition or subtraction of decimals including money 3.2 Solve 2-step word problems involving addition and subtraction of decimals including money H. Comprehension of Multiplication of Decimals 1. Multiply mixed decimals and whole numbers 1.1 Visualize multiplication of

VI 2.4 Whole numbers by decimals and mixed decimals 2.5 Mixed decimals by mixed decimals 3. Divide decimals by 10, 100, 1,000 mentally 4. Divide decimals by 0.1, 0.01, 0.001 mentally 5. Application of division of decimals 5.1 Write an equation to solve problems 5.2 Solve word problems involving division of decimals including money 5.3 Solve 2 to 3 step word problems involving decimals including money 5.4 Describe the answer in a complete sentence with proper labels/units E. Comprehension of Number Theory and Fractions 1. Comprehension of number theory and concepts 1.1 Generalize when a number is divisible by another number divisibility rules 1.2 Identify prime and composite numbers 1.3 Enumerate factors and multiples of given numbers

the operation to be used 2.1.2 Transform the word problem into a number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer 3. Application of Multiplication and Any of Addition/ Subtraction 3.1 Solve 2- to 3-step word problems involving multiplication of whole numbers including money

• • • •

what is asked what is/are given the word clue/s

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- the word clues - the operation to be used 3.1.2 Transform the word problem into a number sentence 3.1.3 Use the correct operation 3.1.4 State the complete answers II. Rational Numbers A. Comprehension of Fractions Recognize 1/ 2 and 1/ 4 of a whole 2. Separate a whole object into halves/fourths 3. Separate group of objects into halves/fourths IV. MEASUREMENT A. Comprehension of time measure 1. Tell the number of days in a week/months in a year using the calendar 2. Indicate time to the hour/half hour 2.1 Show that 60 minutes make an hour 2.2 Tell time using digital clock 3. Indicate time to the nearest 15 minutes of an hour like 1:15, 1:30, 1:45 1.

II
E. Comprehension of Division 1. Divide whole numbers with dividends through 81 by 1-digit divisors 1.1 Show division as repeated subtraction 1.2 Identify the parts of a division sentence namely dividend, divisor and quotient 1.3 Illustrate division By partition (including the equal parts of a number) By distribution (finding how many times a number is contained in a given number)

III
1.1.1.3 Divide 2 to 3 digit numbers by 1 digit number with remainder 1.2 Divide 2 to 3 digit numbers by multiples of 10 up to 90 1.3 Divide 2 to 3 digit numbers by 1 to 2 digit numbers with zero difficulty 1.4 Divide 3 to 4 digit numbers by 1 to 2 digit numbers without or with remainder and with zero difficulty 1.4.1 Divide 3 to 4 digit numbers by 1 digit number without remainder 1.4.2 Divide 3 to 4 digit numbers by 1 to 2 digit numbers with remainder 1.4.3 Divide 3 to 4 digit numbers by 1 to 2 digit numbers with zero difficulty 1.4.4 Divide whole numbers by 5 1.4.5 Divide whole numbers by 10 and 100 1.5 Divide mentally 2 digit numbers through 99 by 1 digit numbers without remainder 2. Application of Division 2.1 Solve 1 step word problem involving division of 2 to 4 digit numbers by 1 to 2 digit numbers including money

IV
7.1.1 Analyze the word problem 7.1.1.1 Tell: - what is used - what is/are given - the word clue/s the hidden question the operation to be used 7.1.2 Transform the word problem into a number sentence 7.1.3 Use the correct operation 7.1.4 State the complete answer 8. Application of Multiplication and Any of Addition/Subtraction 8.1 Solve 2 step word problems involving multiplication and any of addition/ subtraction E. Comprehension of Division 1. Divide 5 or more digit numbers by 3 or more digit numbers without or with remainder and with zero difficulty. 1.1 Divide 5 or more digit number by 3 digit numbers without remainder 1.2 Divide 5 or more

V decimals using models 1.2 Tenths by another tenths 1.3 Hundredths by tenths and vice versa 2. Generalize the step in multiplying decimals 3. Multiply mixed decimals with tenths and hundredths by whole numbers 4. Multiply mixed decimals by mixed decimals with tenths and hundredths 5. Multiply decimals by 10 and 100 6. Multiply decimals mentally by 1, 01, and 001 7. Application of Multiplication of Decimals 7.1 Solve word problems involving multiplication of decimals including money I. Comprehension of Division of Decimals 1. Divides decimals through hundredths 1.1 Visualize division of decimals using models 1.2 Divide decimals by whole numbers 1.3 Divide decimals by decimals through hundredths 2. Application of Division of Decimals 2.1 Solve word problems involving division of decimals 2.1.1 Analyze the word problem 2.1.1.1 Tell: - what is asked - what is/are given - the word clues - the operation to be used 2.1.2 Transform the word problem into a

VI 1.4 List the prime factors of given numbers 1.5 Write the prime factorization of a given number 1.6 Determine the greatest common factor (GCF) of 2 or more numbers 1.7 Determine the least common multiple (LCM) of 2 or more numbers F. Comprehension of Fractions 1. Write the factor described involving regions, sets and numberline 2. Rename fractions as decimals and vice-versa 3. Form equivalent fractions 4. Solve for the missing terms in a pair of equivalent fractions 5. Reduce fractions to lowest terms 6. Change mixed numbers to improper fractions and viceversa 7. Estimate fractions close to 0,
1 2

• •

• •

As repeated subtraction As inverse of multiplication 1.4 Transform a division sentence into multiplication sentence and vice versa 1.5 Divide 1- to 2-digit numbers by 1-digit numbers 1.6 Divide 2-digit numbers with dividends through 81 2. Application of Division 2.1 Solve 1-step word problems involving division of whole numbers with dividends up to 81 2.1.1 Analyze the word problem

or 1

8. Find the least common denominator (LCD) of a set of fraction

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3.1 Indicate time such as 1:15, 1:30, 1:45 when the hand is at 15 minutes 4. Read and write time as shown on the clock B. Comprehension of Linear Measure 1. Make measurement using non-standard units of linear measure. 2. Compare among the non-standard units of mass measure in terms of consistency and accuracy C. Comprehension of Mass Measure 1. 2. Measure mass using non-standard units of linear measures Compare among the non-standard units of mass measure in terms of consistency and accuracy 2.1.1.1 Tell:

II

III
3. Application of the Four Fundamental Operations 3.1 Solve 2 step word problems involving division and any one of the fundamental operations including money 3.2 Solve 3 step word problems involving division and any two of the other fundamental operations including money II. Rational Numbers A. Comprehension of Fractions 1. Order fractions less than one/equal to one/ more than one 1.1 Identify fractions less than one 1.2 Order fractions less than one 1.2.1 Tell the relationship between fractions less than one 1.3 Identify fractions equal to one 1.4 Identify fractions more than one 1.5 Order fractions less than one/equal to one/more than one 2. Change fractions to lower forms 2.1 Tell the greatest number by which two given numbers can exactly be divided 2.1.1 Give the GCF (Greatest Common Factor) of 2 given numbers

IV digit numbers by 4 or more digit numbers without or with remainder 1.3 Divide whole numbers by 10, 100 and 1,000 1.4 Divide 4 to 5 digit numbers by 2 to 3 digit numbers with zeros in the middle or continuous zero in the dividend Estimate the quotient of 4 to 5 digit dividends by 2-digit numbers Divide mentally 2-3 digit numbers by 1digit numbers without remainder Application of Division 4.1 Solve 1- step word problems involving division of 5 or more digit numbers by 3 or more digit numbers including money 4.1.1 Analyze the word problem 4.1.1.1 Tell: - what is asked - what is/are given - the word clue/s the operation to be used

V number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer J. Comprehension of Percent 1. Relate fractions/ratios, decimals and percent 1.1 Visualize the meaning of percent (%) 1.2 Give the relationship

the operation to be used 2.1.2 Transform the word problem into a number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer 3. Application of Division and Any of the Three Fundamental Operations 3.1 Solve 2- to 3-step word problem involving whole numbers including money 3.1.1 Analyze the word problem 3.1.1.1 Tell:

• • • •

what is asked what is/are given the word clue/s

VI 9. Compare fractions and mixed forms using different methods 9.1 fraction sense, visual reasoning, renaming to like forms 9.2 Cross products method 9.3 LCD method 10. Order fractions in simple and mixed forms in ascending or descending order using different methods 11. Solve mentally word problems involving fractions 11.1 Reduce final answer to lowest term G. Comprehension of Addition and Subtraction of Fractions 1. Visualize addition and subtraction of fractions (using concrete and visual/ pictorial models) 2. Estimate sums and differences of fractions in simple and mixed forms 3. Add or subtract similar fractions in simple or mixed forms without regrouping 4. Add or subtract similar fractions in simple or mixed forms with regrouping

•

2.

• •

between fractions/ratios and percents (with visual models) between percent and decimal (with visual models) among fractions/ ratios, decimals and percents

3.

4.

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

the hidden question • the operation to be used 3.1.2 Transform the word problems into a number sentence 3.1.3 Use the correct operation 3.1.4 State the complete answer II. Rational Numbers A. Comprehension of Fractions

• • • •

what is asked what is/are given the word clue/s

III. Geometry A. Comprehension of Polygons 1. Draw 3- to 4-sided polygons 1.1 Visualize polygons 1.2 Identify kinds of polygons 1.3 Describe polygons 2. Draw 5- or more-sided polygons e.g. pentagon, hexagon, etc. IV. Measurement A. Comprehension of Area 1. Find the area of other plane figures in square meters/centimeters

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2. Compare among the non-standard units of capacity measure in terms and accuracy of measurement
1 3

II
1. Identify , , of a given whole/group of objects 1.1 Name the fractional parts of a given whole/ group of objects B. Read and write
1 6 1 3 1 5 1 6

III
2.2 Reduce fractions to lowest terms 3. Find the fractional part of set/regions 1 e.g. /3 of 12 1 /4 of 20 1 /2 of 8 III. Geometry A. Comprehension of Line and Line Segment 1. Draw perpendicular parallel intersecting lines 1.1 Visualize perpendicular parallel and intersecting lines 1.2 Identify perpendicular parallel and intersecting lines 2. Draw congruent line segments 2.1 Visualize congruent line segments 2.2 Identify congruent line segments 3. Determine which motion turn, flip or slide creates a given tessellation 4. Form simple symmetrical designs out of given shapes (triangles and squares) IV. Measurement A. Comprehension of Time Measure 1. Convert time measure from smaller to larger units and viceversa 1.1 days to years years to days 1.2 seconds to minutes minutes to hours hours to day

IV
4.1.2 Transform the word problem into a number sentence. 4.1.3 Use the correct operation 4.1.4 State the complete answer 5. Application of the Four Fundamental Operations 5.1 Solve 2 to 3 step word problems involving division and any one or two of the other fundamental operations learned including money 5.1.1 Analyze the word problem 5.1.1.1 Tell: - what is asked - what is/are given - the word clue/s the hidden question the operation to be used 5.1.2 Transform the word problems into a number sentence 5.1.3 Use the correct operation 5.1.4 State the complete answer

V parallelograms trapezoids circles 2. Application of Measurement of Area 2.1 Solve word problems involving area of plane figures 2.1.1 Analyze the word problem 3. Draw congruent and similar polygons 3.1 Visualize congruence/ similarity of polygons 3.2 Identify congruent/ similar polygons B. Comprehension of Circumference of a Circle 1. Find the circumference of a circle in centimeter/ meter 1.1 Derive a formula for finding the distance around a circle 2. Application of the Concept of Circumference 2.1 Solve word problems involving circumference measure 2.1.1 Analyze the word problem 2.1.1.1 Tell: what is asked what is/are given the word clue the operation to be used 2.1.2 Transform the word problem into a number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer

VI 5. Add or subtract dissimilar fractions in simple or mixed forms without regrouping 6. Add or subtract dissimilar fractions in simple or mixed forms with regrouping 7. Add mentally similar and dissimilar fractions using the properties of addition 8. Application of addition and subtraction of fractions 8.1 Write an equation to solve word problems 8.2 Make drawings or diagrams to better understand the given problem 8.3 Solve word problems involving addition or subtraction of fractions in simple or mixed forms with or without regrouping 8.3.1 Analyze the word problem 8.3.1.1 Tell - what is asked - what is/are given - the word clue/s - the operation to be used 8.3.2 Use the correct operation 8.3.3 Describe the answer in a complete sentence with proper labels/ units

,

1 5

,

in symbols and in words C. Compare unit fractions using relation symbols III. Geometry A. Comprehension of Shapes 1. Identify shapes 1.1 Name different shapes common in the home and in the school 2. Classify shapes according to numbers of sides and corners 2.1 Describe shapes according to number sides 2.2 Describe shapes according to number of corners 2.3 Compare shapes according to number of sides and corners 3. Tessellate a surface using triangles and shapes 4. Discriminate shapes/figures that show symmetry

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IV. Measurement A. Comprehension of Time Measure 1. Use the calendar to tell the number of: 1.1 week in a month 1.2 day in a month 1.3 month in a year 1.4 week in a year 1.5 days in a year 2. Determine the number of days in a given number of

III
2. Find the exact time between dates 3. Application of time measure 3.1 Solve 1 step word problems involving time measure following the steps in problem solving B. Comprehension of Area 1. Find the area of a figure in square meters 1.1 Visualize the area of a rectangle 1.2 Visualize the area of a square 1.3 Derive a formula for finding the area of a rectangle/ square 1.3.1 Derive a formula for finding the area of a rectangle 1.3.2 Derive a formula for finding the area of a square 2. Application of concept of area 2.1 Solve word problems involving area of 2.1.1 rectangle 2.1.2 square C. Comprehension of Capacity 1. Find capacity using standard units of measure e.g. small units-milliliter 2. Convert capacity measure from smaller to larger units and vice versa A.

IV
II. RATIONAL NUMBERS Comprehension of Decimals and money

V
C. Comprehension of Volume 1. Find the volume of a cube/ rectangular prism 1.1 Tell the unit of measure used for measuring the volume of cubes/ rectangular prism 1.2 Convert one cubic unit of measure to a larger or smaller unit 1.3 Derive a formula for finding the volume of cube/rectangular prism 2. Application of Measurement of Volume 2.1 Solve word problem involving measurement of volume 2.1.1 Analyze the word problem 2.1.1.1 Tell: what is asked what is/are given the word clue the operation to be used 2.1.2 Transform the word problem into a number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer D. Comprehension of Temperature Measure 1. Give body/weather temperature using degree Celsius 1.1 Identify the parts of a thermometer 1.2 Read a thermometer 2. Application of Temperature Measure

1. Read and write common fractions in decimal form through hundredths 1.1 Visualize common fractions as decimals 1.1.1 Use decimal models (blocks grid, money) 1.2 Write common fractions in decimal form 1.3 Read and write decimal numbers through hundredths 1.4 Rename in decimal form fractions whose denominators are powers of 10 1.5 Give the place value of each digit of a given decimal 2. 3. Express/write money as pesos/centavos Round decimal to the nearest tenths/hundredths/ thousandths

VI 8.4 Solve 2 to 3-step word problems involving addition and subtraction of fractions in simple and mixed forms without and with regrouping 8.4.1 Analyze the word problem 8.4.1.1 Tell - what is asked - what is/are give - the word clue/s - the operation to be used 8.4.2 Use the correct operation 8.4.3 Describe the answer in a complete sentence with proper labels/ units H. Comprehension of Multiplication of Fractions 1. Multiply a fraction by another fraction (with visual models) 2. Simplify factor by cancellation method before multiplying 3. Multiply fractions in simple and mixed forms 3.1 Change mixed numbers and whole numbers to improper fractions before multiplying

• •

weeks months

3. Name the days in a week/months in a year 4. Tell the time using the digital clock 5. Express the relationship between the “hour hand” and the “minute hand” of a clock 6. Indicate time to the nearest 15 minutes of an hour like 1:15, 1:30, 1:45 when the minute hand is at the 15 minutes position 7. Read and write time as shown on the clock 8. Application of time measure 8.1 Solve simple word problems involving time without conversion of standard units B. Comprehension of Linear Measure 1. Make measurement using standard units of linear measure e.g. centimeter, metre

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2. Approximate measurement of length, width, height and distance C. Comprehension of Mass Measure 1. Make measurement using standard units of mass measure 2. Convert standard units of mass measure to lower or higher units 3. Approximate measurement of mass 4. Investigate accuracy in measuring mass and quantity of things bought e.g. knowledge in using the weighing scale D. Comprehension of Area 1. Find the area of a given figure using the square units 1.1 Visualize plane figures and square units 1.2 Tell the number of square units covering a given area 1.3 Solve word problems involving area E. Comprehension of Capacity 1. Make measurement using standard units of capacity measure e.g. litre

III
3. Application of measurement of capacity 3.1 Solve word problems involving capacity measure following the steps in problem solving V. Graphs A. Comprehension of Pictograph 1. Read/interpret data presented in a pictograph 1.1 Name the following parts of a pictograph a. title b. legend c. labels 1.2 Interpret the legend 1.3 Read pictographs 2. Construct pictograph 2.1 Organize data presented in a pictograph VI. Calculator 1. Identify the parts of a calculator 2. Tell the function of each part of a calculator

IV
B. Comprehension of Addition and Subtraction of Decimals 1. Add and subtract decimals through hundredths with and without regrouping 1.1 Add decimals through hundredths without and with regrouping 1.2 Subtract decimals through hundredths without or with regrouping 2. Add and subtract mixed decimals with regrouping 2.1 Add mixed decimals with regrouping 2.2 Subtract mixed decimals with regrouping 3. Application of addition and subtraction of decimals 3.1 Solve word problems involving either addition or subtraction of decimals including money 3.1.1 Analyze the word problem

V
2.1 Solve word problem involving body/weather temperature V. Graphs A. Comprehension of Line Graph 1. Read/Interpret data presented in a line graph 2. Read a line graph 3. Construct a line graph 3.1 Organize data presented in a line graph 3.2 Find the average of data presented in a line graph

VI 4. Show that multiplying a fraction by its reciprocal is equal to 1 5. Application of Multiplication of Fractions 5.1 Write an equation for a word problem 5.2 Make drawings/ diagrams to better understand the given problem 5.3 Solve word problems involving multiplication of numbers in mixed forms 5.4 Solve 2 to 3 step word problems involving addition, subtraction, and multiplication of numbers in mixed forms 5.5 Use correct order of operations 5.6 Describe answer in a complete sentence in with proper labels/units I. Comprehension of Division of Fractions 1. Visualize division of a whole number by a fraction; a fraction by another fraction 2. Divides a whole number by a fraction; a fraction by another fraction 3. Divide fractions in different forms

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IV
3.1.1.1 Tell what is asked what is/are given, the word clue/s the operation to be used 3.1.2 Transform the word problem into a number sentence 3.1.3 Use the correct operation 3.1.4 State the complete answer 3.2 Solve 1 to 2 step word problems involving addition and subtraction of decimals including money 3.2.1 Analyze the word problem 3.2.1.1 Tell: - what is asked - what is/are given the word clues - the hidden question the operation to be used 3.2.2 Transform the word problem into a number sentence 3.2.3 Use the correct operation 3.2.4 State the complete answer

V

VI 4. Application of Division of Fraction 4.1 Write an equation to solve a word problem 4.2 Make drawings or diagrams to better understand the given problem 4.3 Solve word problems involving division of fractions 4.4 Solve 2 to 3-step word problems involving all operations on fractions 4.4.1 Use correct order of operations 4.5 Describe answer in a complete sentence with proper labels/units J. Comprehension of Ratio and Proportion 1. Forms ratio and proportion for groups of objects/numbers 1.1 Use colon (:) and fractions in writing ratios and proportions 1.1.1 Reduces a ratio to lowest terms 1.2 Find a missing term in a proportion 2. Application of Ratio and proportion

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C. Comprehension of Fractions 1. Visualize fractions including those with denominators of 10 and 100 1.1 Identify proper fraction/ improper fraction/mixed forms from a given set of fractions including those with denominators of 10 and 100 1.1.1 Identify fractions involving regions, sets and number line 1.1.2 Use fraction to represent division 1.2 Identify similar and dissimilar fractions from a given set of fractions 1.3 Rename decimals and whole numbers to fractions from a given set of fractions 2. Order similar fractions written in different forms from least to greatest and vice-versa

V

VI 2.1 Set up a proportion for a given situation 2.2 Solve word problems with: 2.2.1 Direct proportion 2.2.2 Partitive proportion

2.2.3 Inverse proportion 2.3 Describe answer in a complete sentence with proper labels/units K. Comprehension of Percent 1. Gives the meaning of the elements used in solving percentage problems 1.1 Percentage 1.2 Ratio or Percent 1.3 Base 2. Determine the percentage rate and base in a given problem 3. Application of Percent 3.1 Set up an equation or proportion to solve problems 3.2 Solve the three types of percentage problems 3.2.1 Find the percentage when the rate and base are given

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3. Order dissimilar fractions written in different forms from least to greatest and vice-versa 3.1 Change improper fraction to mixed forms and vice-versa 3.2 Change one (1) to fraction form and viceversa D. Comprehension of Addition and Subtraction of Fraction 1. Add similar fractions and whole numbers without regrouping 1.1 Visualize addition of similar fractions 1.2 Add similar fraction 1.3 Add fractions and a whole number 1.4 Add mentally similar fraction 2. Subtract similar fractions without regrouping 2.1 Subtract similar fraction 2.2 Subtract a fraction from a whole number 2.3 Subtract mentally similar fractions

V

VI 3.2.2 Find the rate or percent when the % age and base are given 3.2.3 Find the base when the percentage or rate are given 3.3 Compute common percentage mentally 3.4 Solve word problems involving finding the percentage/rate/base 3.4.1 Percent of increase/decrease - Discounts - Original Price - Rate of Discount - Sale Price - Mark-up Price 3.4.2 Commission - Rate of Commission - Total Sales - Total Income 3.4.3 Sales Tax - Rate of Sales - Tax - Selling Price 3.4.4 Simple Interest - Principal Rate - Time L. Simple Probability 1. Make simple predictions 2. Tell the number of favorable outcomes/chances

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3.

IV
Application of Addition and Subtraction of fractions 3.1 Solve word problems involving addition of similar fractions without regrouping 3.2 Solve word problems involving subtraction of similar fractions without regrouping

V

VI M. Comprehension of Integers 1. Visualize integers in their order on a number line 2. Compares integers 3. Order integers in increasing/decreasing order III. GEOMETRY A. Comprehension of Spatial Figures 1. Draw different spatial figures 1.1 Visualize the different spatial figures, cube, rectangular prism, cylinder, sphere, pyramid, cone, etc. 1.2 Describes the different spatial figures IV. Measurement A. Comprehension of Surface Area 1. Tell the surface area of solids 2. Tell the unit of measure used for measuring the surface area of solids 3. Find the area formula of the following plane figures: - parallelograms - triangles - trapezoids - circles

E. Comprehension of Fractions 1. Multiply two fractions 1.1 Visualize multiplication of fraction 1.2 Find a fractional part of a number 1.2.1 Translate expressions such as: 1 of 2 ,
2 2 3

of 1
6

3

2. Multiply a fraction by another fraction 3. Application of Multiplication 3.1 Solve word problems involving multiplication of fractions 3.1.1 Analyze the word problem 3.1.1.1 Tell: - what is

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IV asked - what is/are given - the word clue/s the operation to be used 3.2 Transform the word problem into a number sentence 3.3 Use the correct operation 3.4 State the complete answer III. GEOMETRY Comprehension of Plane Figures and Angles 1. Draw plane figures 1.1 Identify the different kinds of plane figures 1.2 a. Identify the parts of a triangle 1.2 b. quadrilateral 1.3 Describe plane figures according to sides, corners, shapes and their functional use 1.3.1 Describe plane figures with 3 and 4 sides and corners square rectangle different types of triangles 1.4 Construct plane figures using a ruler and compass 2. Draw different kinds of angles A.

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VI 4. Derive a formula for finding the surface area of: - cubes - prisms - cylinders 5. Application of Measurement of Surface Area 5.1 Write an equation or formula to solve for the surface area of solids 5.2 Solve the word problems involving measurement of surface area 5.2.1 Analyze the word problem 5.2.1.1 Tells: - what is asked - what is/are given - the word clue/s the operation to be used 5.2.2 Transform the word problem into a number sentence 5.2.3 Use the correct operation 5.2.4 State the complete answer B. Comprehension of Volume 1. Find the volume of a solid

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2.1 Identify parts of an angle 2.2 Name different kinds of angles such as right angle, acute angle and obtuse angle 2.2.1 Visualize the different kinds of angles as acute, right obtuse 2.3 Classify angles as right, acute or obtuse 2.4 Identify congruent angles IV. MEASUREMENT A. Comprehension of Perimeter 1. Find the perimeter of polygons 1.1 triangle 1.2 quadrilateral 1.3 pentagon etc 2. Derive a formula for finding the perimeter of polygons 3. Application of Perimeter 3.1 Solve word problems involving perimeter measures B. Comprehension of Area 1. Find the area of polygons in square metre/centimetre a. triangle b. parallelogram

V

VI 1.1 Tell the unit of measure used for measuring the volume of solids, rectangular prisms 1.2 Convert one cubic unit of measure to a larger or smaller unit 1.3 Derive a formula for finding the volume of solids like: - prism - cylinders - pyramid - cones 2. Application of Measurement of Volume 2.1 Write an equation or formula to solve for the volume of solid 2.2 Solve word problems involving measurement of volume 2.1.1 Analyze the word problem 2.1.1.1 Tell: - what is asked - what is/are given - the word clue/s - the operation to be used 2.1.2 Transform the word problems into a number sentence 2.1.3 Use the correct operation 2.1.4 State the complete answer

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1.1 Tell the unit of measure used for measuring the area of triangles and parallelograms 1.2 Tell the unit of square measures used for measuring the area of a triangle/ parallelogram 1.3 Derive a formula for finding the area of a: 1.3.1 Triangle 1.3.2 Parallelogram C. Comprehension of Volume 1. Make measurement using non-standard units: - cubes - marbles Compare among the non-standard units of measuring volume in terms of consistency and accuracy Approximate measurement of volume

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VI C. Comprehension of Meter Reading 1. Read and interpret readings from: 1.1 electric meter 1.2 water meter V. Graphs A. Comprehension of Circle Graph 1. Read and interpret data presented in a circle graph 2. Construct a circle graph 2.1 Organize data presented in a circle graph 2.2 Find the average of data presented in a circle graph

2.

3.

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IV. Graphs A.

IV
Comprehension of Bar Graph 1. Read and interpret data presented in a bar graph 1.1 Read the following parts of a bar graph a. title b. legend c. labels 1.2 Interpret bar graphs 2. Construct bar graphs 2.1 Organize data presented in a bar graph 2.2 Find the average of data presented in a bar graph

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