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Lesson Guides in Elementary Mathematics Grade IV Copyright © 2003 All rights reserved. No part of these lesson guides shall be reproduced in any form without a written permission from the Bureau of Elementary Education, Department of Education.
The Mathematics Writing Committee
GRADE 4
Region 3
Evelyn H. Magpayo – Pampanga Myrna Vicente – Nueva Ecija Ester Ramones – Tarlac Virgie Costales  Zambales
Region 4
Flordeliza D. Yamo – Laguna Araceli C. Montoya – San Pablo City Estelita Q. del Rosario – Cavite City
National Capital Region (NCR)
Remylinda T. Soriano – Manila Maria Brucal – Makati Lina Seña – Taguig/Pateros Analee Pacaña – Pasig/San Juan
Bureau of Elementary Education (BEE)
Leony M. Achacoso Zosima C. Ventura
Ateneo de Manila University
Eva Marie Guevarra
Suppo rt Staff
Ferdinand S. Bergado Ma. Cristina C. Capellan Emilene Judith S. Sison Julius Peter M. Samulde Roy L. Concepcion Myrna D. Latoza Eric S. de Guia – Illustrator
Consultants
Fr. Bienvenido F. Nebres, SJ – President, Ateneo de Manila University Ms. Carmela C. Oracion – Principal,
Ateneo de Manila University High School
Project Staff
Teresita G. Inciong – Director IV
Merlita A. Nolido – Chief, Curriculum Development Division Mirla R. Olores – Asst. Chief, Curriculum Development Division
Virginia T. Fernandez – Project Coordinator
EXECUTIVE COMMITTEE
Edilberto C. de Jesus – Secretary, Department of Education Juan Miguel M. Luz – Undersecretary for Finance and Administration
Fe A. Hidalgo – Undersecretary for Programs and Projects
Printed in the Philippines ISBN – 971927753x
iii
TABLE OF CONTENTS Introduction............................................................................................................................. vii Matrix .................................................................................................................................. viii I. WHOLE NUMBERS
A. Comprehension o f Whole Numbers
Numbers from 100 001 through Millions/Billions.......................................................... 1 Place Value ............................................................................................................... 4 Reading and Writing Numbers through Millions/Billions in Words ............................... 7 Rounding Off Numbers to the Nearest Tens .............................................................. 9 Rounding Off Numbers through Hundred Thousands ................................................. 13 Rounding Off Numbers to the Nearest Millions and Billions ........................................ 15
B. Comprehension o f Addition Adding Numbers through Billions without Regrouping ................................................ 18 Adding Numbers through Billions with Regrouping ..................................................... 20 Commutative Property of Addition .............................................................................. 24 Associative Property of Addition ................................................................................ 27 Identity Property of Addition ....................................................................................... 29 Estimating the Sum .................................................................................................... 32 Adding Mentally 2 to 3Digit Numbers with Sums up to 300 ...................................... 34 Analyzing Problems ................................................................................................... 36 Solving Problems involving Addition ........................................................................... 39 Solving Mentally 1Step Word Problems .................................................................... 43
C. Comprehension o f Subtraction Subtracting without Regrouping ................................................................................. 45 Subtracting with Regrouping ...................................................................................... 48 Subtracting Large Numbers with Zero Difficulty .......................................................... 52 Estimating the Difference of Two Numbers ................................................................. 54 Subtracting Mentally Numbers without Regrouping .................................................... 57 Analyzing Problems involving Subtraction .................................................................. 59 Solving Mentally 1Step Word Problems involving Subtraction without Regrouping........................................................................................ 62 Solving Problems involving Subtraction ...................................................................... 64 Analyzing 2Step Problems involving Addition and Subtraction including Money ......... 67 Solving 2Step Problems involving Addition and Subtraction including Money............. 69
D. Comprehension o f Multiplication Multiplying 5 or More Digit Factors by 3 Digit Factors with and without Regrouping .......................................................................... 72 Multiplying 5 or More Digit Factors by 4 to 5Digit Factors with and without Regrouping .......................................................................... 74 Multiplying Numbers having Zeros in both factors without Regrouping ........................ 77 Multiplying Numbers having Zeros with Regrouping.................................................... 80 Multiplying by Multiples of 10, 100 and 1000 .............................................................. 82 Properties of Multiplication ......................................................................................... 85 Distributive Property of Multiplication over Addition .................................................... 88 Estimating Products ................................................................................................... 92 Multiplying Mentally without Regrouping ..................................................................... 94
iv
Numbers in Exponential Form ................................................................................... 97 Numbers from Standard Form to Scientific Notation ................................................... 100 Numbers in Scientific Notation to Standard Form ....................................................... 103 Analyzing Problems.................................................................................................... 106 Solving Problems ....................................................................................................... 109 TwoStep Word Problems .......................................................................................... 111
E. Comprehension o f Division Dividing Numbers by 3 Digit Numbers without Remainder ........................................................................................ 114 Dividing Numbers by 4 or More Digit Numbers without or with Remainder ............................................................................. 117 Dividing Whole Numbers by 10, 100 and 1000 ........................................................... 120 Dividing Numbers with Zeros in the Dividend ............................................................. 123 Estimating the Quotients ............................................................................................ 126 Dividing Mentally without Remainder .......................................................................... 129 Analyzing Word Problems involving Division............................................................... 131 Solving 1Step Problems involving Division................................................................. 136 Analyzing 2 to 3Step Word Problems ....................................................................... 139 Solving 2 to 3Step Word Problems involving Division ............................................... 141
II. RATIONAL NUMBERS
A. Comprehension of Decimals and Money Reading and Writing Decimal Numbers ...................................................................... 144 Renaming Fractions to Decimals ................................................................................ 147 Place Value of Decimal Numbers ............................................................................... 152 Expressing/Writing Money as Pesos and Centavos ................................................... 154 Rounding Decimals .................................................................................................... 157
B. Comprehension o f Addition and Subtraction o f Decimals Adding Decimal Numbers ........................................................................................... 160 Subtracting Decimal Numbers .................................................................................... 163 Adding Mixed Decimals .............................................................................................. 167 Subtracting Mixed Decimals ....................................................................................... 170 Analyzing 1Step Word Problems involving either Addition or Subtraction of Decimals ................................................................................. 173 Solving Word Problems ............................................................................................. 176 Analyzing 1 to 2Step Word Problems involving Addition and Subtraction of Decimals including Money ....................................................... 179 Solving 1 to 2Step Word Problems .......................................................................... 182
C. Comprehension o f Fractions Identifying Proper Fractions/Improper Fractions/Mixed Form ...................................... 186 Fractions involving Regions, Sets and Number Line .................................................. 190 Similar and Dissimilar Fractions in a given Set of Fractions......................................... 194 Renaming Decimals and Whole Numbers to Fractions................................................ 198 Ordering Similar Fractions .......................................................................................... 203 Changing Improper Fractions to Mixed Forms and Vice Versa ................................... 207 Changing One (1) to Fraction Form and Vice Versa ................................................... 211
v
D. Comprehension o f Addition and Subtraction o f Fraction Adding Similar Fractions ............................................................................................ 215 Adding a Fraction and a Whole Number .................................................................... 220 Adding Similar Fractions Mentally .............................................................................. 224 Subtracting Similar Fractions ..................................................................................... 227 Subtracting Fractions from Whole Numbers ............................................................... 232 Subtracting Mentally Similar Fractions ....................................................................... 235 Solving Word Problems involving Addition of Similar Fractions without Regrouping ....................................................................................... 239 Solving Word Problems involving Subtraction of Similar Fractions without Regrouping ....................................................................................... 243
E. Comprehension o f Multiplication o f Fraction Visualizing Multiplication of Fractions ......................................................................... 246 Fractional Part of a Number ....................................................................................... 250 Translating Expressions ............................................................................................ 254 Analyzing Word Problems .......................................................................................... 260 Solving Word Problems.............................................................................................. 265
III. GEOMETRY
A. Comprehension o f Plane Figures and Ang les Kinds of Plane Figures .............................................................................................. 268 Triangles ................................................................................................................... 274 Parts of a Quadrilateral .............................................................................................. 277 Parts of a Circle ......................................................................................................... 282 Describing and Constructing Plane Figures ............................................................... 286 Parts of an Angle ....................................................................................................... 289 Different Kinds of Angles ............................................................................................ 292 Classifying Angles ...................................................................................................... 295 Congruent Angles ...................................................................................................... 298 Perimeter of a Triangle .............................................................................................. 300 Perimeter of a Polygon .............................................................................................. 303 Solving Problems on Perimeter................................................................................... 307
IV. MEASUREMENT
A. Comprehension o f Area Unit of Measures used in Measuring the Area of a Triangle/Parallelogram ........................................................................... 309 Formula for Finding the Area of Parallelograms ......................................................... 312 Area of a Parallelogram ............................................................................................. 314 Formula for Finding the Area of a Triangle ................................................................. 318 Area of a Triangle ...................................................................................................... 321
B. Comprehension o f Volume Measuring Volume using NonStandard Units of Measure ......................................... 324
vi
V. GRAPH
A. Comprehension o f Graphs Bar Graph ................................................................................................................. 328 Constructing Bar Graph ............................................................................................. 332
vii
I N T R O D U C T I O N
The Lesson Guides in Elementary Mathematics were
developed by the Department of Education through the Bureau of
Elementary Education in coordination with the Ateneo de Manila
University. These resource materials have been purposely
prepared to help improve the mathematics instruction in the
elementary grades. These provide integration of values and life
skills using different teaching strategies for an interactive
teaching/learning process. Multiple intelligences techniques like
games, puzzles, songs, etc. are also integrated in each lesson;
hence, learning Mathematics becomes fun and enjoyable.
The skills are consistent with the Basic Education
Curriculum (BEC)/Philippine Elementary Learning Competencies
(PELC). These should be used by the teachers as a guide in their
daytoday teaching plans.
viii
MATRIX IN ELEMENTARY MATHEMATICS Grade IV
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
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
Carefulness
Group and check Concept development
Number writing, Manipulative, Handson activities
1.2 Give the place value of each digit in a 6 or more digit numbers
Active participation Cooperation
Concept development Looking for pattern Educated guess
Handson activities, Manipulative, Writing, Charting
1.3 Read and write numbers through millions/billions in symbols
Honesty Concept development Educated guess Cooperative learning
Reading, Writing, Speaking, Charting, Handson activities, Cooperative learning, Manipulative
1.4 Read and write numbers through millions/billions in words
Cooperation Concept development Reading, Writing, Handson activities, Manipulative
2. Round off numbers to the nearest 2.1 tens
Cooperation
Concept development Educated guess Looking for pattern
Completing tables, Drawing, Writing
2.2 hundreds 2.3 thousands 2.4 ten thousands 2.5 hundred thousands
Cooperation Friendliness
Concept development Educated guess
Speaking, Completing tables, Reading, Charting
2.6 millions 2.7 billions
Thriftiness Concept development Guess and check
Selfawareness, Handson activities, Cooperative learning, Graph, Reading
B. Comprehension of Addition
1. Add 6 or more digit numbers with 4 or more addends with sums through billions
1.1 without regrouping Accuracy Diligence
Educated guess Concept development Write equation
Logic, Writing, Charting, Cooperative learning, Handson activities
1.2 with regrouping in:  any two or more places  all places
Helpfulness Concept development Write equation Guess and check Working backward Cooperative learning
Logic, Diagram, Handson activities, Manipulative
ix
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
2. Show the properties of addition
2.1 Commutative Property
Thoughtfulness Concept development Use equation Use logical reasoning
Drawing, Illustration, Handson activities, Cooperative groups
2.2 Associative Property
Cooperation Active participation
Concept development Looking for patterns Write equation Working back Cooperative learning
Scientific method, Reading, Speaking, Music appreciation, Drawing,
2.3 Identity Property Sportsmanship Educated guess Looking for patterns
Cooperative learning, Handson activities, Independent study
3. Estimate the sum of 6 or more digit addends
Hardwork Perseverance
Determine reasonable answers Concept development Estimate the answers
Cooperative groups, Independent study, Reading
4. Add mentally 2 to 3 digit numbers with sums up to 300 without regrouping
Appreciation of nature Guess and check Concept development
Logic, Diagram, Reading, Speaking, Independent study
5. Application of Addition
5.1 Solve word problems involving addition of whole numbers including money with sums through millions and billions without and with regrouping
5.1.1 Analyze the word problem 5.1.1.1 Tell:
 what is asked  what is/are given  the word clue/s  the operation to be used
Generosity
Mental math Concept development Acting out the problem Develop formula and write equation Working back
Reading, Writing, Manipulative, Cooperative groups, Handson activities
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
Proper behavior during programs
Concept development Simplifying problems Guess and check Working back Cooperative learning
Cooperative learning, Handson activities, Speaking
5.2 Solve mentally 1step word
problems involving addition with sums up to 300 without regrouping
Love for nature
Concept development Drawing pictures Listing
Cooperative groups, Number, Logic, Speaking, Charting, Simulation
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.
x
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
1.1 Subtract 5 or more digit
numbers from 6 or more digit numbers without regrouping
Helpfulness
Mental math Concept development Use of data resources from a story
Numbers, Logic, Handson activities, Writing
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
Cooperation Thoughtfulness Cooperation
Concept development Looking for pattern Write equation Working back Cooperative learning Concept development Writing equation Guess and check Working back Cooperative learning Concept development Looking for pattern Write equation Working back Cooperative Learning
Reading, Diagram Drawing, Speaking, Logic, Reading, Speaking Reading, Diagram Drawing, Speaking
1.3 Estimate the difference of two numbers with four to six digits
Thoughtfulness Concept development Guess and check
Logic, Speaking, Charting, Cooperative learning
2. Subtract mentally numbers with minuends up to 300 without regrouping
Helpfulness Guess and check Simplifying problem Concept development Cooperative learning
Logic, Puzzle, Speaking, Game
3. Application of Subtraction 3.1 Solve 1step word problems
involving subtraction of whole numbers including money without and with regrouping
Intelligent decision in voting
Concept development Guess and check Simplifying problem Write Equation Cooperative learning
Logic, Reading, Handson activities, Manipulative
3.1.1 Analyze the word problem
3.1.1.1 Tell:  what is asked  what is/are given  the word clue/s the
operation to be used
Helpfulness
Concept development Drawing picture Write equation Simplifying the problem
Logic, Speaking, Cooperative learning, Handson activities
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 2step word problems involving addition and subtraction including money
4.1.1 Tell:  what is asked  what is/are given
Hardwork
Write equation
Cooperative Groups
xi
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
 the word clue/s  the hidden question  the operation to be
used 4.1.2 Transform the word
problem into a number sentence
4.1.3 Use the correct operation
4.1.4 State the complete answer
Love for books
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
Conservation of trees Concept development Mental math Looking for pattern
Numbers, Logic, Cooperative groups, Handson activities, Manipulative, Reading, Writing
1.2 Multiply 5 or more digit factors by 4 to 5 digit factors without and with regrouping
Nationalism Mental computation Concept development Use logical reasoning
Cooperative group, Independent study
1.3 Multiply 5or more digit factors having one to three zeros in both factors without regrouping
Carefulness Mental math Concept development Looking for pattern
Cooperative groups, Reading, Writing, Handson activities, Manipulative
1.4 Multiply 5 or more digit factors having one to three zeros in both factors with regrouping in all places.
Cooperation Concept development Guess and check
Cooperative learning, Reading, Handson activities, Independent study
1.5 Multiply 5 digit or more factors by multiples of 10, 100 and 1 000
Health consciousness Looking for pattern Concept development Write equation
Graphing, Charting, Speaking, Handson activities
2. Show the properties of multiplication
 Commutative  Associative  Zero Property  Identity Property  Distributive Property of Multiplication over Addition
Love for reading Concept development Discovery approach Write equation
Cooperative groups, Handson activities, Reading; Logic, Writing
3. Estimate the products of two factors with 5 or more digits
by 2 to 3 digit numbers
Love of nature Concept development Working back Guess and check Cooperative learning
Charting, Nature Manipulative
4. Multiply mentally 2 digit numbers with products up to
200 without regrouping
Health consciousness Concept development Mental math Using estimation Guess and check Completing tables
Cooperative groups, Independent study, Reading, Logic, Number, Speaking, Puzzle
5. Write numbers in exponent form
Cooperation Concept development Use equation Looking for pattern
Independent activity
6. Write numbers in standard form to scientific notation and viceversa
Cooperation Use tables
xii
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
6.1 Write number in standard form to scientific notation
Accuracy Concept development Guess and check Looking for pattern Write equation Cooperative learning
Independent activity, Diagram, Handson activities
6.2 Write number in scientific notation to standard form
Cooperation Concept development Develop formula Write equation Cooperative Learning
Independent activity, Diagram, Handson activities
7. Application of Multiplication
7.1 Solve word problems involving
multiplication of whole number including money
Cooperation
Concept development Develop formula Write equation
Writing, Reading, Handson activities, Manipulative
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
Hardwork Resourcefulness
Concept development Working back Write equation
Game, Number, Manipulative, Handson activities, Cooperative groups
8. Application of Multiplication and any of Addition/Subtraction
8.1 Solve 2 step word problem
involving multiplication and any of addition/subtraction
Cooperation
Simplifying the problem Modeling Cooperative learning
Reading, Speaking, Handson activities
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 4 to 5 digit numbers
by 2 to 3 digit numbers with zero in middle or continuous zero in the dividend
Helpfulness
Concept development Guess and check Looking for pattern Working back Simplify the problem Cooperative learning
Nature, Manipulative, Handon activities, Number, Logic
1.2 Divide 5 or more digit numbers by 4 or more digit numbers without or with remainder
Helpfulness Concept development Working back Looking for pattern
Games, Reading, Speaking, Writing, Handson activities, Manipulative
1.3 Divide whole numbers by 10, 100 and 1 000
Willingness Concept development Mental math Completing the table
Games, Reading, Handson activities, Writing, Manipulative
xiii
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
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
Helpfulness Concept development Working back Looking for pattern
Games, Cooperative groups, Number, Reading, Writing, Manipulative, Logic, Handson activities
2. Estimate the quotient of 4 to 5 digit dividends by 2digit numbers
3. Divide mentally 23 digit numbers by 1digit numbers without remainder
4. Application of Division
4.1 Solve 1 step word problems involving division of 5 or more digit numbers by 3 or more digit numbers including money
Neatness Simplifying the problem Group activity Concept development Develop formula and write equation
Games, Independent study, Puzzle, Cooperative learning, Manipulative, Diagrams, Handson activities
4.1.1 Analyzes the word problem
4.1.1.1 Tell:  what is asked  what is/are given  the word clue/s the
operation to be used
Cooperation Modeling Simplifying the problem Acting out the problem
Games, Puzzle, Handson activities, Manipulative, Cooperative learning, Skit, Number, Logic, Self awareness activities
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
Fairness Sharing Kindness
Concept development Guess and check Working back Simplifying the problem
Cooperative learning, Handson activities, Manipulative, Diagram, Speaking
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
Kindness Concept development Use of data resources from a story Write equation
Numbers, Logic, Reading, Writing, Handson activities
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
xiv
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
II. RATIONAL NUMBERS
A. Comprehension of Decimals and money 1. Read and write common
fractions in decimal form through hundredths 1.1 Visualize common
fractions as decimals
1.1.1 Use decimal models (blocks
grid, money) 1.2 Write common fraction in
decimal form
Listening attentively
Drawing/illustrating Modeling Concept development
Manipulative, Drawing, Reading, Completing tables
1.3 Read and write decimal numbers through hundredths
Hospitality Concept development Looking for pattern Making an educated guess
Reading, Writing, Logic
1.4 Rename in decimal form fractions whose denominators are powers of 10.
Cooperation Concept development Looking for pattern Logical reasoning Cooperative learning
Manipulative, Reading, Games, Diagrams
1.5 Give the place value of each digit of a given decimal
Sportsmanship
2. Express/write money as pesos/centavos
Thrift and economy
Concept development Acting out Linguistic
Skit, Handson activities
3. Round decimal to the nearest tenths/hundredths/ thousandths
Preciseness and speed
Educated guess Looking for pattern Drawing tables
Reading, Logic Completing tables
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
Thoughtfulness
Mental computation Concept development Constructing tables
Completing tables, Puzzles
1.2 Subtract decimals through hundredths without or with regrouping
Health consciousness Mental computation Listing Modeling
Puzzles, Making illustrations
2. Add and subtract mixed decimals with regrouping
2.1 Add and subtract mixed decimals with regrouping
2.2 Subtract mixed decimals with regrouping
xv
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
3. Application of Addition and subtraction of decimals
3.1 Solve word problems
involving either addition or subtraction of decimals including money
Accuracy and cooperation
Completing tables Polya’s strategy
Cooperative groups, Independent study, Reading
3.1.1 Analyze the word problem 3.1.1.1 Tell what is
asked what is/are given, the word clue/s the operation to be used
Spending money wisely
Concept development Acting out Simplifying the problem
Reading, Cooperative groups, Handson activities, Charting, Illustrating, Drawing, Writing
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
Industry and thoughtfulness
Acting out Looking back Polya’s strategy Write equation
Cooperative groups, Skit, Reading, Writing
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
Thrift Concept development Polya’s strategy Following directions
Puzzle, Number, Logic, Reading, Writing, Cooperative groups
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
C. Comprehension o f Fractions
1. Visualize fractions including those with denominators of 10 and 100.
Enjoyment in one’s work
Drawing pictures Looking for pattern Modeling
Geometry, Diagrams, Handson activities
1.1 Identify proper fraction/improper fraction/mixed forms from a given set of fractions
Carefulness Drawing pictures Concept development
Diagrams, Speaking, Handson activities, Writing, Reading
xvi
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
including those with denominations of 10 and 100 1.1.1 Identify fractions
involving regions, sets and number line
1.1.2 Use fraction to represent division
Enjoyment in one’s work
Concept development Looking for pattern Following direction
Handson activities, Logic, Drawing, Illustrating
1.2 Identify similar and dissimilar fractions from a given set of fractions
Cooperation Concept development Drawing pictures Looking for pattern
Handson activities, Numbers, Logic, Writing, Illustrating diagrams
1.3 Rename decimals and whole numbers to fractions from a given set of fractions
Wise use of leisure time Speed and accuracy
2. Order similar fractions written in different forms from least to greatest and viceversa
Sharing Looking for pattern Concept development
Diagrams, Charts
3. Order dissimilar fractions written in different forms from least to greatest and viceversa
Health consciousness Drawing pictures Concept development
3.1 Change improper fraction to
mixed forms and viceversa
Cooperation Concept development Looking for pattern
Diagrams, Handson activities, Logic, Writing, Number
3.2 Change one (1) to fraction
form and viceversa
Love and kindness
Concept development Write equation Looking for pattern
Manipulative, Diagrams, Handson activities
D. Comprehension o f 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
Helpfulness
Guess and check Work backward Concept development
Manipulative, Games, Diagrams, Writing, Cooperative Groups
1.3 Add fractions and a whole
number
Gratitude Use data resources from a story Work backward Drawing pictures Concept development
Cooperative groups, Reading, Handson activities, Games
1.4 Add mentally similar fraction
Attentiveness Use data resources Mental math Guess and check using objects
Games, Speaking, Handson activities
2. Subtract similar fractions without regrouping
2.1 Subtract similar fraction
Thoughtfulness
Concept development Guess and check Completing tables
Games, Diagrams, Handson activities
2.2 Subtract a fraction from a whole number
Taking care of things Use data resources from a story Illustrations
Diagrams, Reading
xvii
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
2.3 Subtract mentally similar Fractions
Helpfulness Concept development Use of data resources
Games, Speaking, Handson activities
3. Application of Addition and Subtraction of fraction
3.1 Solve word problems involving addition of similar fractions without regrouping
Cooperation
Use data resources from a story Drawing pictures Concept development Working back
Diagrams, Writing, Cooperative groups, Story telling, Handson activities
3.2 Solve word problems involving subtraction of similar fractions without regrouping
E. Comprehension of Fractions 1. Multiply two fractions
1.1 Visualize multiplication of fraction
Generosity Concept development Modeling
Acting out, Reading, Writing, Handson activities
1.2 Find a fractional part of a number
Cooperation Simplifying the problem Use data resources from a story
Manipulative, Imagery
1.2.1 Translate expressions such as: 1/ 2 of 2 /3 2 /3 of 1/ 6
Resourcefulness Use data resources from story and a chart
Manipulative, Completing tables
2. Multiply a fraction by another fraction
Generosity Concept development Following direction Drawing pictures Looking for pattern
Games, Speaking, Cooperative groups, Handson activities, Illustrating
3. Application of Multiplication 3.1 Solve word problems
involving multiplication of fraction
Cooperation and Sportsmanship
Concept development Use of data resources from a story Looking back Drawing pictures
Contest, Handson activities, Logic, Reading, Number, Cooperative groups
3.1.1 Analyze the word problem
3.1.1.1 Tell:  what is asked  what is/are
given  the word clue/s
the operation to be used
Active participation and cooperation
Concept development Guess and check Write equation Acting out Simplifying problems
Puzzle, Reading, Writing, Speaking, Cooperative groups, Handson activities
3.1.2 Transform the word problem into a number sentence
Active participation And cooperation
Concept development Guess and check Write equation Acting out Simplifying problems
Puzzle, Reading, Writing, Speaking, Cooperative groups, Handson activities
3.1.3 Use the correct operation
3.1.4 State the complete answer
III GEOMETRY A. Comprehension of Plane
Figures and Angles 1. Draw plane figures
1.1 Identify the different kinds
Carefulness and awareness to the
Concept development Drawing picture
Numbers, Singing, Drawing, Cooperative
xviii
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
of plane figures
things around us Modeling Acting out Simplify problem
learning, Manipulative, Ecology
1.2.a Identify the parts of triangle
Orderliness Concept development Modeling
Handson activities, Diagrams, Manipulative, Logic, Drawing
1.2.b quadrilateral Sportsmanship Concept development Modeling Drawing picture
Chart, Drawing, Cooperative learning
1.3 Describe plane figures according to sides, corners, shapes and their functional use
Cooperation and self confidence
Concept development Working back Simplifying the problem Looking for pattern
Speaking, Reading, Diagrams, Cooperative learning, Handson activities
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 ruler and compass
2. Draw different kinds of angels
2.1 Identify parts of an angle
Cooperation
Modeling Drawing picture Concept development Simplifying problem
Drawing, Cooperative learning, Handson activities, Manipulative, Speaking
2.2 Name different kinds of angles such as right angle, acute angle and obtuse angle
2.2.1 Visualize the different
kinds of angels as acute, right obtuse
Sportsmanship Modeling Drawing picture Concept development Guess and check
Speaking, Drawing, Diagram, Cooperative learning, Manipulative, Handson activities
2.3 Classify angles as right, acute, or obtuse
Cooperation Concept development Drawing a picture Acting out the problem Guess and check
Handson activities, Manipulative, Drawing, Cooperative learning, Diagram
2.4 Identify congruent angels Cooperation Concept developing Modeling Drawing a picture Simplifying the problem Acting out the problem
Handson activities Manipulative, Cooperative learning, Drawing, Diagram, Speaking
IV. MEASUREMENT A. Comprehension of Perimeter
1. Find the perimeter of polygons
1.1 triangle 1.2 quadrilateral 1.3 pentagon, etc.
Conservation of trees Accuracy Accuracy
Concept development Write equation Using estimation Develop formula
Handson activities, Manipulative, Reading, Writing, Completing tables, Illustration, Diagram,
xix
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
Cooperative groups, Nature
2. Derive a formula for finding the perimeter of polygon
Accuracy Concept development Write equation Develop formula
Drawing, Reading, Diagram, Handson activities, Cooperative groups, Manipulative
3. Application of Perimeter 3.1 Solve word problems involving perimeter
measures
Cooperation and accuracy
Concept development Write equation Polya’s strategy
Diagram, Geometry, Illustrating, Independent study
B. Comprehension of Area
1. Find the area of parallelograms in square meter/centimeter a. triangle
Cooperation and sharing one’s ideas
Drawing picture Concept development Modeling Acting out the problem Simplifying the problem
Speaking, Puzzle, Drawing, Cooperative learning, Logic, Handson activities, Manipulative
b. parallelogram Sharing one’s ideas Concept development Guess and check Develop formula Write equation Simplifying problem
Manipulative, Puzzle, Handson activities, Diagram, Drawing, Logic, Cooperative groups
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
Accuracy Concept development Handson activities, Movement, Cooperative groups, Nature, Diagrams
1.3 Derive a formula for finding the area of triangle/parallelogram
1.3.1 Triangle
Cooperation Concept development Educated guess Simplifying problem Develop formula
Handson activities, Diagram, Drawing, Speaking
1.3.2 Parallelogram Sharing one’s idea and active participation
Writing equation Manipulative
C. Comprehension of Volume
1. Make measurement using non
standard units  cubes
 marbles 2. Compare among the non
standard units of measuring volume in terms of consistency and accuracy
3. Approximate measurement of volume
Helpfulness and sharing one’s idea
Concept development Looking for a pattern Modeling Acting out Listing
Logic, Puzzle, Speaking, Manipulative, Hands on activities, Cooperative groups, Reading, Writing, Speaking
V. Graphs A. Comprehension of Graphs
1. Read and interpret data presented in a bar graph. 1.1 Read the following parts of
a bar graph a. title
Helping one another with a cause
Concept development Guess and check Listing Acting out
Games, Manipulative, Handson activities, Movements, Self awareness,
xx
Competencies Values Integrated Strategies used Multiple Intelligence Techniques
b. legend c. labels
Cooperative groups, Graphing, Charting, Speaking, Reading, Writing
1.2 Interpret bar graph
2. Construct bar graph
2.1 Organize data presented in a bar graph
Good study habit Hardwork Cooperation
Concept development Drawing picture Listing
Game, Puzzle, Manipulative, Hands on activities, Cooperative groups, Charting, Graphing, Speaking, Reading, Writing
2.2 Find the average of data
presented
Perseverance and alertness
Concept development Guess and check Listing Drawing pictures
Music appreciation, Cooperative groups, Manipulative, Handson activities,
1
Numbers from 100 001 through Milli ons/Billi ons I. Learning Objectives
Cognitive: Identify numbers from 100 001 through millions/billions Psyc homotor: Write numbers from 100 001 through millions/billions Affective: Practice carefulness in writing numbers through millions/billions
II. Learning Content
Skill s: 1. Identifying numbers from 100 001 through millions/billions 2. Writing numbers from 100 001 through millions/billions References : BEC – PELC I.A.1.1
textbooks in Math 4 Materials: flash cards, chart, place value chart, set of numbers written on
cards with cord Value: Carefulness
III. Learning Experiences
A. Preparatory Activities 1. Drill
Ask for 10 volunteers. Give each a number tag. Have them wear the cord with numbers
from 0 to 9. Guide the pupils to form 3 to 6digit numbers. Ask the pupils who are sitting to read the numbers orally.
Example: a)
b)
c) d) e)
2. Review Pick out the numbers less than 100 001 from the set of numbers posted on the houses.
3. Motivation
Start by playing “Guess What Number”. The teacher places the following statements on the board: a. My telephone number is “III II II  II III IIII”.
7 3 2 4 1
7 4 2
5 8 6 9 0
8 2 7 5 9
5 4 6 2 3 1
8 432 10 100
6 789 436 132
7 634 99 999
100 000 436 849
138 472 24 382
89 432 94 389
45 489 634 312 123 421
2
b. The space capsule is circling the earth every “> > > IIIIII” c. I traveled “CDLXXIV” kilometres by motorcycle.
Do you think the sentences are easy to read and understand? Why? What number do you think the numeral represents? Do you think the symbols can be represented in our numeration system?
B. Developmental Activities
1. Presentation
a. Read the data.
Traffic in Metro Manila is heavy because nearly onehalf of the
2 904 487 vehicles in the country are registered here.
1) What is the given number? (2 904 487) 2) How do we read it? (2 million, 904 thousand, 487) 3) How do we write it in words? (Two million, nine hundred four thousand, four hundred
eightyseven) 4) Is the number easy to read and understand? Why? (Yes, because it is written in
standard form.) b. Present the number in the place value chart.
MILLIONS THOUSANDS UNITS hundreds tens ones hundreds tens ones hundreds tens ones 2 9 0 4 4 8 7
2
millions 9 hundred thousands
0 ten
thousands
4 thousands
4 hundreds
8 tens 7 ones
1) Ask them to give the digit in the one millions place, in hundred thousands place, ten
thousands place and so on. 2) Ask them to give the expanded form then give the value of each digit. 3) Repeat the activity on billion numbers.
Example: 15 086 912 403 357 296 324 081 How many periods are there in millions? How many digits are found in billions?
c. Present the lesson using an abacus with 12 rods. An improvised abacus may be made
using bottle caps, pieces of wood or balls for the beads, a piece of wooden board for the stand and a thick wire or banana cue stick for the post. Let the pupils show the number 487 293 465 on the abacus. Then ask them what digit is represented by the beads on each rod? Present also numbers in billions place.
2. Guided Practice
Activity 1 Put a check (9) if the number is in millions and a cross (x) if it is in billions.
___a) 6 386 798 ___b) 76 998 289 584 ___c) 17 633 549
3
Activity 2 Write M if the number is in millions and B if it is in billions.
___a) 89 679 289 548 ___b) 3 386 798 ___c) 456 126 834
Activity 3 Write a number on your paper that has 11 digits.
1) 7 in the ten billions place. 2) A digit that is 5 less than 8 in the one thousands place. 3) 4 in the hundred millions place.
3. Generali zation How do you identify a number in million or in billion?
Million has three periods. It contains 7, 8 or 9 digits. Billion has four periods. It contains 10, 11 or 12 digits.
C. App lication
Read the data. Write the number words in figures. 1. One drop of blood contains about five million red blood cells. 2. The human eye can see more than seven million, five hundred thousand color differences. 3. During an average lifetime, the human heart beats about two billion, five hundred million
times.
IV. Evaluation
A. Write T if the number is in thousands, M if it is in millions and B if it is in billions.
___1) 6 034 597
___2) 145 793 000
___3) 206 000 371 148
___4) 52 758 137
___5) 425 010
B. Arrange the following set of numbers starting from the thousands, millions and billions place.
Rewrite them on your paper. 1) 4 759 248 804; 541 298; 532 689 012
2) 205 946 101; 423 543 103 811; 988 415
3) 726 054; 7 685 004 208; 8 684 452
4) 29 673 000; 127 683; 1 542 678 725
5) 75 942 376 055; 24 673 503; 898 145
C. Examine the given numbers below. Write them in the proper place where they should belong. Be
sure that the numbers in each column are written from the smallest to the greatest.
15 086 912 305 674 981 643 212 002
17 196 741 014 357 296 324 899 120 741 019
185 451 9 273 050 357 296 234 8 095 403 002
4
BILLIONS MILLIONS THOUSANDS
V. Assignment
Study the given numbers. Copy the number which does not belong to the group.
1) 718 345 210 340; 151 968 254; 219 742 036
2) 50 307 501; 500 897 621 543; 15 718 260 345
3) 258 154; 508 476; 8 696 425
4) 3 274 503; 310 608; 2 830 458
5) 450 187 402; 897 500 126; 2 247 364 869
Place Value I. Learning Objectives
Cognitive: Give the place value/value of each digit in a 6 or more digit number Psyc homotor: Read and write numerals up to the hundred billions place Affective: Participate actively
II. Learning Content
Skill s: 1. Identifying the place value and value of each digit in a 6 or more digit number 2. Reading and writing numerals up to the hundred billions
References: BEC – PELC I.A.1.2 textbooks in Math 4
Materials: place value chart, number cards, number words, flash cards Values: Active participation and being considerate
III. Learning Experiences
A. Preparatory Activities
1. Drill Have a drill in the form of a game. “ Number Tag Game” a. Each group will have a set of numbers from 0 to 9. b. Pupils will form the number given by the teacher.
The number must be less than 6 digits. Example: 79 384 c. First group to form the digit will be the winner.
2. Review
Reading and writing numerals in the standard form using different ways.
5
“ Matching Game” Mechanics: Divide the class into 2 groups. A representative from each group takes turn in answering or matching the numeral with its number name or word name.
A B 37 1 thousand 3 hundreds 5 tens
6 ones 145 Thirtyseven
1 356 Eight hundred twentysix thousand, one hundred fortyone
24 295 1 hundred 4 tens 5 ones 826 141 20 000 + 4 000 + 200 + 90 + 5
3. Motivation
Ask the pupils why smaller pupils are seated in front while the bigger pupils are seated at
the back. Help the pupils realize that people must be considerate to get along well with others.
B. Developmental Activities
1. Presentation
a. Tell the pupils that numbers are like people. They can be grouped in many ways. b. Discuss the three ways in representing numbers in standard form.
3 765 1) word form: three thousand, seven hundred sixtyfive 2) number and abbreviation form: 3th 7h 6t 5 ones 3) number and word: 3 thousands 7 hundreds 6 tens 5 ones
c. Show a place value chart which is up to the hundred billions place. Tell the pupils that our system of numeration has digits grouped in threes, we call them PERIODS.
Bil lions Millions Thousands Units
Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones
2 0 6 4 3 7 6 1 2 9 7 5
2. Group Activity
a. Groups will be given activity sheets with the data below written on it. b. Tell them to follow the directions in answering the data.
Directions: Give the place value and the value of the underlined digits 2 3 7 9 8 7 4 3 2 1 4 2
Digit Place Value Value
c. Show more exercises in identifying the place value and value of each digit in a 6 or more
digit numeral using number cards. (This will be done orally.)
6
Give the place value and the value of the digit 6 in each numeral: a) 864 439 b) 826 453 c) 682 975
d) 86 451 197 e) 126 468 300 f) 26 974 431 100
d. Have a game on the different skills learned for the day.
Do blackboard relay. Divide the class in columns. Each pupil takes turn in writing the correct answer on
the board. The column with the most number of correct points wins. Questions: 1) What is the value of 6 in 64 395? 2) What is the value of 4 in 1 462 587? 3) In the numeral 45 376 192, what digit is in the one millions place? 4) What is the standard form of sixtyfive billion, one hundred four million, two hundred
thirtyseven thousand, eightysix? 5) What is the standard form for 9m 6hth 3tth 8h 7ones?
3. Generali zation
How do you tell the value of each digit in a given number? Valuing: �� Did you participate in the activities today?
Rate yourself: 5highest and 1lowest
C. App lication Write each digit of the given number in the place value chart. 1) 144 785 2) 27 436 192
Bil lions Millions Thousands Units H T O H T O H T O H T O 1 2
IV. Evaluation
A. Give the value of each digit in the number 27 436 198.
1) 2 _____ 5) 6 _____ 2) 7 _____ 6) 1 _____ 3) 4 _____ 7) 9 _____ 4) 3 _____ 8) 8 _____
B. Answer the following:
1.
a. Form the smallest number using all the digits above. b. Form the smallest odd/even number using all the digits above. c. Form the largest odd/even number using all the digits above.
2. Show, using drawing, that 235 has 23 tens. Explain further in words. 3. Who am I?
My tens digit is 2 times my hundreds digit. My hundreds digit is 4. My ones digit is a factor of my tens and hundreds digit.
2 6 4 7 5
7
4. Use each digit once: 1 Æ 8 a. Write the greatest number possible with 5 in the hundred thousands place b. Write the least number possible with 8 in the one millions place.
V. Assignment
Write ten numbers up to millions/billions in the standard form.
Reading and Writing Numbers through Milli ons/Billi ons in Words I. Learning Objectives
Cognitive: Read and write numbers through millions/billions in words Psyc homotor: Write numbers in words correctly Affective: Participate actively in different activities
II. Learning Content
Skill : Reading and writing numbers through millions/billions in words References: BEC–PELC I.A.1.4
textbooks in Math 4 Materials: flash cards, charts Value: Cooperation
III. Learning Experiences
A. Preparatory Activities 1. Drill
Reading of numbers.
242 186 246 386 187 623 305 160 65 187
2. Review Teacher will dictate these numbers and pupils will write them in their showmecards.
682 468 23 694 3 743 7 218 946 569
3. Motivation How many digits has 723 964 157 368? Can you write the number in words?
B. Developmental Activities
1. Presentation
The land surface of the earth is 148 892 864 square kilometres and the water surface is 362 011 332 square kilometres.
8
a. Discuss 1) How many square kilometres is the land surface? Write it on the board. 2) How many square kilometres has the water surface? Write it on the board. 3) How many digits has the land surface area? How about the water surface area? 4) Read the numbers. 5) Write the numbers in words.
b. Read and write the word name for each numeral. 1) 389 152 247 2) 2 714 683 389 3) 1 186 792 053 4) 9 544 416 936 5) 7 110 313 425
2. Group Activities
Let’s have a contest. “Groups 1 and 2 form your line. 5 members each group.” (Infuse the value of active participation.) Get a number card in the box and match it with the word names in the pocket chart. Those who finish first should be commended. a) 85 312 914 677 b) 18 000 777 283 c) 109 067 214 511 d) 87 782 570 308 e) 5 112 914 000
3. Fixing Skill s/Practice
Read and answer the following: a. The Bureau of Forest Development donated three seedlings each for school children all
over the country. The total number of seedlings was 15 223 564 821. Write this figure in words.
b. Mrs. Luna’s shell craft factory used five hundred eightysix million, three hundred twentyfour thousand, three hundred eightytwo shells in one year. Write the number of shells in symbol.
c. Zero has no value. Can we just leave the space for zero vacant? Why? d. Is zero important in writing numbers? e. How would you write 204 000 785 083 in words? Valuing: • Did you participate in the activity? How? What did you share with your group? Do you
also practice this at home? How?
4. Generali zation
How are numbers written in words?
The numbers are written in words in the same way that they are read.
IV. Evaluation
A. Match the figures with the correct words
1) 3 411 789 a) Sixteen million, three hundred eightythree thousand, one hundred five
9
2) 16 383 105 b) Four billion, five hundred sixtyeight thousand, one hundred
seventytwo 3) 205 168 347 c) Three million, four hundred eleven thousand, seven hundred
eightynine 4) 3 521 681 d) Three million, five hundred twentyone thousand, six hundred
eightyone 5) 4 000 568 172 e) Two hundred five million, one hundred sixtyeight thousand,
three hundred fortyseven
B. Write the figure in words. 1. Increase by 5 the numeral 6 478 921 720 in the billions place to form a new number 2. Write the standard form in words of this numeral
6 000 000 + 400 000 + 70 000 + 8 000 + 500 + 20 + 3
C. Write in figures. 1. One billion, five million, five hundred twenty thousand, twentyeight 2. Nine billion, six hundred two million, five hundred fortyone thousand, two hundred ninety
eight V. Assignment
Write the number in words. a. 6 463 342 264 b. 520 175 786 c. 23 596 384 103 d. 501 000 176 330 e. 43 781 648 134
Rounding Off Numbers to the Nearest Tens I. Learning Objectives
Cognitive: 1. Round off numbers to the nearest tens
2. Identify the place value of the digit in a given numeral Psyc homotor: 1. Make use of a number line to show rounded off numbers 2. Give the place value/value of the digit in a given numeral Affective: Cooperate during group activities
II. Learning Content
Skill s: 1. Rounding off numbers to the nearest tens 2. Identifying place value/value of a digit in a numeral
References: BEC–PELC I.A.2.1 textbooks in Math 4 Materials: charts, activity cards, number lines Value: Cooperation
10
III. Learning Experiences
A. Preparatory Activities 1. Drill
“ Guessing Game”
Divide the class into 2 groups. Any pupil in the group takes turn in solving the given problem. The first pupil who gives the correct answer wins. They should answer correctly as fast as they can. a. My ones digit is 2. My tens digit is thrice the first digit. My hundreds digit is four times the
first digit and my thousands digit is the sum of the ones and the tens digit. What number am I?
b. My thousands digit is 9. My ten millions digit is 3. My hundreds digit is 6. The other digits are 0. What number am I?
2. Review
Write the place value and value of the underlined digit in the following numbers.
35 492 73 985 1 591 635 469 789 143 785 19 432 156 000
3. Motivation
Ask a pupil to read a news item that shows estimation. Examples: Last week, a company manager called for a meeting. Almost 50 employees
came. • Did the actual number of employees attend the meeting? • What word was used which expressed an estimate? (almost)
The population in our school is about 2 000 pupils. What word in the sentence expresses an estimate? (about)
B. Developmental Activities
1. Presentation
a. Read the problem carefully then answer the questions briefly.
Rica, a Grade 4 pupil needs 27 for her school project. She did not ask money from her parents because she has saved 30 from her daily allowance. What kind of a girl is Rica?
1) Who is Rica? What does Rica need? 2) How much money did she need for the school project? 3) Where did she get the money? 4) How much is her savings? 5) What kind of a girl is Rica?
b. Present a number line showing numbers from 20 to 30.
Draw a ring around 27. Ask: Is 27 closer to 20 or 30? 20 21 22 23 24 25 26 27 28 29 30
11
2. Analysis/Abstraction
Looking back at the number line, is 27 nearer to 20 or 30? Number 27 is nearer to 30 than 20. So, if we round 27 to the nearest tens, it will become 30.
Valuing: • How did you find the activity? • What kind of a girl is Rica? • How much did Rica need for her school project? • How much is her savings? • Are you like Rica? Do you also save a certain amount from your daily allowance?
3. Fixing Skill s
Let the pupils group themselves into 4 and perform the activities in the activity sheet. Emphasize the value of cooperation. Let them relate how they cooperate with other members of their group. Group 1
Original Number Rounded to the nearest tens 15 Æ 43 Æ 79 Æ 32 Æ 64 Æ 87 Æ
Group 2
Original Number Rounded to the nearest tens 126 Æ 342 Æ 568Æ 269Æ 644Æ 853Æ
Group 3
Original Number Rounded to the nearest tens 1 349 Æ 4 784Æ 8 632Æ 3 786Æ 7 755Æ
Group 4
Original Number Rounded to the nearest tens 16 277Æ 28 163 Æ 56 788Æ 33 154Æ 17 416 Æ 10 112Æ
12
4. Generali zation How do we round off numbers to the nearest tens?
In rounding numbers to the nearest tens, look at the digit at the right of the tens digit. If the number is 5 or more, add 1 to the tens place, if the digit is less than 5, retain the tens digit. Change the ones digit to zero
C. App lication
Round the following to the tens place. a. 342 b. 4 638 c. 5 419 d. 28 326 e. 49 749
IV. Evaluation
Study the number line below. Answer the following questions.
1.
20 21 22 23 24 25 26 27 28 29 30 31
a. Draw a ring around 26. Is 26 closer to 20 or 30? 26 will become ____. b. Draw a square around 24. Is 24 closer to 20 or 30? What will happen to 24? c. Cross out (X) 28. Is 28 closer to 20 or 30? 28 will become ____. d. Check (9) 21. Is 21 closer to 20 or 30? How will 21 be rounded to the nearest tens?
2. Do what is asked for each problem stated below.
a. Lydia has 37 rubber bands. Around how many rubber bands does Lydia have? b. Mother bought 43 bananas. Around how many bananas did mother buy? c. When 83 is rounded off to the nearest tens, 83 will become___. d. Mang Tony gathered 94 eggs in the poultry farm. About how many eggs did Mang Tony
gather? e. If 769 is rounded off to the nearest tens 769 becomes ___.
V. Assignment
Round off the following numbers to the nearest tens. a. 362 b. 837 c. 5 742 d. 6 424 e. 9 654
13
Rounding Off Numbers through Hundred Thousands I. Learning Objectives
Cognitive: Round off numbers to the nearest hundreds, thousands, ten thousands and
hundred thousands Psyc homotor: State the rules in rounding numbers correctly Affective: Find joy in working with others and doing something for others
II. Learning Content
Skill : Rounding off numbers to the nearest hundreds, thousands, ten thousands and hundred thousands
References: BEC–PELC I.A.2.42.5 textbooks in Math 4
Materials: chart, number cards Values: Cooperation and friendliness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Teacher picks out any number from a box. The task of each pupil is to round these numbers to the nearest tens.
Example: 37 rounds to 40 21 rounds to 20
2. Review
How do we round off numbers to the nearest tens? Show examples on the board. Elicit
from the pupils the rule in rounding off numbers to the nearest tens.
3. Motivation
Which of the following numbers can be rounded to 400? 600? 385 349 562 515 571
B. Developmental Activities
1. Presentation
There are 371 582 residents in the city of Makati and 256 454 residents in
Pasay City who are benefiting from the Clean and Green Program of the government.
Look at the table below and examine how are the numbers 371 582 and 256 454 have been rounded.
Number Nearest Hundreds
Nearest Thousands
Nearest Ten thousands
Nearest Hund red Thousands
371 582 371 600 372 000 370 000 400 000 256 454 256 500 256 000 260 000 300 000
37
21
14
2. Analysis/Abstraction Discuss the given problem. a. What cities benefited from the Clean and Green Program of the government? b. How many residents were benefited in the city of Makati? Pasay City? c. Round off 371 582 to the nearest hundreds, thousands, hundred thousands. d. Round off 256 454 to the nearest thousands, ten thousands, hundred thousands.
Let us try rounding off numbers to the nearest: hundreds, thousands, ten thousands, hundred thousands. (Group the pupils according to their ability.) Stress the value of cooperative learning and friendliness. 1. Round off the numbers to the nearest hundreds, thousands. 2. Round off the numbers to the nearest ten thousands, hundred thousands.
a) 831 732 b) 925 501 c) 655 321 100 d) 531 841 215 e) 736 386 133
3. Group Activities
Let each group report to class the answer in the activity sheet assigned to them.
Encourage pupils to state the rule in their own words. Example: Pupil 1: Round off 456 837 to the nearest ten thousands.
Pupil 2:The answer is 460 000. Round off 329 465 to the nearest hundred thousands.
Pupil 3: 300 000, etc.
4. Generali zation
How do we round off numbers to the nearest hundreds, thousands, ten thousands and hundred thousands?
Round up if the digit to the right of the digit to be rounded is 5, 6, 7, 8 and 9. Round down if the digit to the right of the digit to be rounded is 0, 1, 2, 3 and 4.
C. App lication
1. Round the following numbers to the nearest ten thousands then answer the questions that
follow. a. 25 743 = _____ Did you round up or down? b. 15 652 = _____ Is your answer 20 000? How did you get the answer? c. 34 730 = _____ How will you round to the nearest thousands? d. 76 348 = _____ Did you round up? Why? e. 89 192 = _____ Is the answer 80 000? Why? State the rule.
2. Read the following situations below. Tell whether the number has an exact value or an
estimated value. a. Mrs. Reyes lives at 10 Monte de Piedad Street. b. There were 1 275 people at the auditorium. c. Karen’s student number is 15 031. d. In school there were about 150 seats at the cafeteria.
15
IV. Evaluation
Round off the following to its nearest specific place value. Numbers Ten Thousands Hundred Thousands 1) 127 563 2) 486 170 3) 816 342 4) 374 139 5) 732 256
V. Assignment
Round off the underlined digits to the nearest specific place value. a. 238 789 d. 793 948 b. 394 634 e. 943 431 c. 545 381
Rounding Off Numbers to the Nearest Mill ions and Billi ons I. Learning Objectives
Cognitive: Round off numbers to the nearest millions and billions Psyc homotor: Tell numbers rounded off to the nearest millions and billions Affective: Appreciate the importance of being thrifty
II. Learning Content
Skill s: 1. Rounding off numbers to the nearest millions and billions 2. Identifying numbers rounded off to the nearest millions and billions
References: BEC–PELC I.A.2.62.7 textbooks in Math 4
Materials: flash cards, activity cards Value: Thriftiness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Reading numbers through millions/billions
2. Review
How do we round off numbers to the nearest hundred thousands? Recall the steps in rounding numbers to its nearest specific place value.
3. Motivation
Have you been to a cement factory? What did you see there? Do you have an idea about
the number of bags of cement that can be manufactured in a month?
16
Read and understand the story on the activity card carefully.
Mary’s Cement is a big factory. It supplies cements to the whole country. Last year, Mary’s Cement delivered a total of 64 768 117 bags to Visayas and Mindanao. About how many bags of cement were delivered in all?
B. Developmental Activities
1. Presentation
a. What product does Mary’s Cement Factory have? b. Is cement manufacturing a good business? Why? c. Why do most people buy cement? d. What was the actual number of cement delivered to Visayas and Mindanao? e. How did you get 60 000 000? f. Which of these rules do you use?
Round up if the digit on the millions place to be rounded is 5, 6, 7, and 8. Round down if the digit to the right of the millions place to be rounded is 0, 1, 2, 3, 4.
Show and discuss another problem in class.
One of the wealthiest man in Asia opened a savings account in a Philippine bank with an initial deposit of 25,643,914,377.00. About how much is his deposit in the bank? a. Who opened a savings account in a bank? b. Why do you think he keeps his money in the bank? c. About how many billions was his initial deposit? Valuing: � If you have plenty of money, what will you do? Will you save some of it? If you have little
money, will you still save? Why? � How would your savings affect your life in the future? How much money did the man
deposit?
Let the pupils show their work on activity 1 & 2 on the board. Activity 1
Number 64 768 117
Nearest Millions 65 000 000
Activity 2
Number 25,643,914,377.00
Nearest Billions 26,000,000,000.00
2. Guided Practice
Let us play a game. Divide the pupils into 2 groups, the yellow group and the red group.
The group who can round off the numbers first to the nearest millions wins. Are you ready now? The numbers are inside the boxes in front of your group. a) 8 856 000 b) 23 431 785 c) 4 180 374 d) 42 683 360
17
e) 9 793 205 f) 75 413 000 g) 6 316 348 h) 17 938 172 i) 2 630 539 j) 136 715 340
Do the same in billions. Call on the pupils who did not participate in the first game then
give them the same directions stated in the first activity. The numbers are inside the box. Play blackboard relay. a) 2 942 628 241 b) 23 592 176 302 c) 5 341 707 333 d) 47 234 346 532 e) 14 603 100 784 f) 92 739 316 035 g) 6 421 125 000 h) 16 484 148 703 i) 17 725 823 421 j) 345 800 000 145
Winners should be commended.
3. Generali zation
How do we round off numbers to the nearest millions/billions?
Round up if the digit to the right of the millions/billions place is 5, 6, 7, 8, and 9. Round down if the digit to the right of the place to be rounded is 0, 1, 2, 3 and 4.
C. App lication Round off to the nearest millions/billions.
Number Nearest Mil lions Nearest Bill ions
6 831 462 126 a. f. 2 124 549 314 b. g. 8 314 183 512 c. h. 27 573 976 249 d. i. 15 439 873 831 e. j.
IV. Evaluation
A. Choose the letter of the correct answer.
1. During the Christmas season, a hotdog company delivered 3 745 000 bags of hotdogs to 3 986 rolling stores all over Metro Manila. Round 3 745 000 to the nearest millions. a. 4 000 b. 3 000 000 c. 4 000 250 d. 4 000 000
2. A certain tire supplier disposed different sizes of tires all over the country. If they supplied
236 435 677 tires, how will you write it in the nearest hundred millions? a. 236 000 000 b. 200 000 000 c. 240 000 000 d. 300 000 000
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B. Name the place value in which the following numbers are rounded. 1) 287 455 rounded to 290 000 ____________ 2) 27 643 189 rounded to 28 000 000 ___________ 3) 458 096 245 rounded to 500 000 000 ____________ 4) 35 613 827 549 rounded to 35 610 000 000 __________ 5) 57 924 603 285 rounded to 58 000 000 000 __________
V. Assignment
The table gives the distance of the five planets from the sun. Round the figures to the nearest hundred millions and nearest billions.
Planet Distance from the sun in kilometres
Nearest Hund red Millions Nearest Bill ions
1. Jupiter 778 300 000 2. Saturn 1 427 000 000 3. Uranus 2 869 600 000 4. Neptune 4 496 700 000 5. Pluto 5 900 000 000
Adding Numbers through Billi ons wi thout Regrouping I. Learning Objectives
Cognitive: Add 6 or more digit numbers with 4 or more addends with sums through billions without regrouping
Psyc homotor: Write large numbers in column and add them correctly Affective: Show accuracy with numbers
II. Learning Content
Skill s: 1. Adding 6 or more digit numbers with 4 or more digit addends without regrouping 2. Writing large numbers in column References: BEC–PELC I.B.1.1
textbooks in Math 4 Materials: chart with exercises, drill cards, picture of vegetable garden Values: Accuracy and diligence
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic addition facts Administer A1 card. Record pupils’ errors.
2. Review
a. Review or have a game on identifying the terms used in addition. (sum, addends, plus,
put together, more, more than, combine, total, add, added to) b. Solve this math problem.
What is the sum of 450 712 and 113 210? Discuss the steps in adding large numbers.
19
3. Motivation
Show a picture of vegetable garden. What vegetables are planted in the garden? Do you want to read a short story about this?
B. Developmental Activities
1. Presentation
Problem Opener
Mt. Province is home for what we call Baguio vegetables. Everyday it produces 230 212 kilograms of potatoes, 120 413 kilograms of beans, 111 201 kilograms of cabbage and 110 142 kilograms of carrots. How many kilograms of vegetables does the province produce daily?
How will you find the answer? Guide the pupils in stating the mathematical sentence 230 212 + 120 413 + 111 201 + 110 142 = n, where n is the total number of kilograms of vegetables. Ask the pupils to write the numbers in column.
Add the ones
Add the tens
Add the hundreds
Add the thousands
Add the ten thousands
Add the hundred
thousands 230 212 230 212 230 212 230 212 230 212 230 212 120 413 120 413 120 413 120 413 120 413 120 413 111 201 111 201 111 201 111 201 111 201 111 201 110 142 110 142 110 142 110 142 110 142 110 142
8 68 968 1 968 71 968 571 968 Check by adding upward. 230 212 120 413 111 201 110 142 571 968
Valuing: � Stress the value of accuracy and diligence when writing each digit in their proper column.
2. Guided Practice
Group yourselves into 4 groups. Add the addends to get the sum. Do it as fast as you can with accuracy. The first group to finish the exercise will do the “bomb clap.”
a. 1 041 002 b. 2 152 101
2 301 025 1 304 024 3 113 210 4 101 641 + 2 120 241 +1 012 033 c. 3 612 111 d. 3 215 210 1 024 125 1 030 024 2 152 021 2 410 153 + 3 201 532 + 1 234 502
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Give more exercises. Write in column then add. a. 410 320 + 102 123 + 201 021 + 104 213 b. 240 120 + 211 103 + 213 132 + 104 213 c. 102 022 011 + 301 531 120 + 421 013 104 + 103 213 453
3. Generali zation
How do we add large numbers?
In adding large numbers, write the addends in column, add the digits in the ones first, then the tens, the hundreds and so on. Continue up to the last digit. Write the sum under each column.
C. App lication Solve this problem.
A progressive farmer kept an accurate record of his sales in his vegetable garden for five years. His yearly sales amounted to 156 572, 400 203, 10 102,
211 001 and 121 121. What was the total amount of his sales for the last five years?
IV. Evaluation
Find the sum. Check your answers by adding upward.
a. 3 421 000 b. 2 121 031 4 252 341 21 032 213 1 102 123 32 422 612 + 1 214 225 + 44 302 141 c. 3 221 112 d. 4 350 245 1 112 322 1 012 104 4 302 130 2 403 050 + 1 062 423 + 1 220 300
V. Assignment Write in column then add. a. 313 112 + 201 003 + 241 301 + 1 203 021 b. 4 321 263 + 1 034 120 + 2 512 504 + 2 021 012
Solve for the following. a. Putting together 8 256 115, 987 140 and 12 721 234 gives a result of n. b. A number added to 87 463 gives a result of 298 685. What is the number?
Adding Numbers through Billi ons wi th Regrouping I. Learning Objectives
Cognitive: Add 6 or more digit numbers with 4 or more addends with sums through billions
with regrouping Psyc homotor: Give the sum of 6 or more digit numbers with 4 addends with sums through
billions with regrouping Affective: Help the community in the “clean and green” project
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II. Learning Content
Skill s: 1. Adding 6 or more digit numbers with 4 or more addends with sum through billions with regrouping
2. Giving the sum of 6 or more digit numbers with 4 addends with sums through billions with regrouping
References: BEC–PELC I.B.1.2 textbooks in Math 4 Materials: flash cards, chart with problems Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic Add ition Facts a. Do the relay game. b. Divide the class in groups of 10. Each pupil in the group will take turn in answering the
flash cards with addition facts on the board. The group who finishes first with the most number of correct points wins.
2. Review
Add the following:
1 203 121 023 2 102 312 112 2 351 213 312 + 3 121 000 121
3. Motivation
Have you experienced staying in the field harvesting fruits? What things did you see
around? What did you feel when staying in the place with fresh air and plenty of fruits? Valuing: � What should you do to keep your community clean and green?
B. Developmental Activities
1. Presentation
Read the problem silently. Answer the questions that follow.
Farmers in the 4 towns of Quezon harvested a big number of coconuts. Farmers in the first town harvested 434 136 724 coconuts, the second 158 122 386, the third 3 150 924 and the fourth 1 425 260. They celebrated for they had a big harvest. Find the total number of coconuts harvested by the farmers in the 4 towns.
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Questions: a. How many towns harvested a big number of coconuts? b. How many coconuts were harvested by the farmers in the first town, second, third and
fourth? c. What is asked in the problem? d. What are we going to do to solve the problem? e. What will you add? f. What is the answer to the problem? g. What is the label for the final answer? Discussion: Present the table to the pupils. Ask them to write the numbers in column and illustrate the process in adding the numbers.
Add the
ones
Add the
tens
Add the hundreds
Add the thousands
Add the hundred
thousands
Add the one
mil lions
Add the ten
mil lions
Add the hundred mil lions
a. What happened to the group? b. What answer did you get? How did you get it? c. What did you do? d. What are the given facts? e. What can you say about the farmers of the 4 towns? (industrious, hardworking)
2. Guided Practice (Group Activities)
Find the sum.
You and your partners will add in two ways. One going down and the other going up. As
soon as you have finished, say the word “yes!”
a. 132 416 430 b. 186 433 840 329 854 932 249 678 432 461 503 006 123 456 789 + 892 756 834 + 148 385 108 c. 400 600 500 d. 302 120 612 700 300 899 674 531 421 456 832 627 61 478 523 + 863 442 816 + 527 347 618
e. If the addends are 87 463 129, 458 645 and 35 185 687. What is the sum? f. What is 275 146 the added to and gives a result of 3 798 347?
23
3. Generali zation How do we add large numbers with regrouping?
In adding large numbers with regrouping, add the ones first, the tens, then hundreds, and continue up to the millions and billions. Regroup in all places if there is a need to regroup the numbers.
C. App lication
Find the answer.
As a Christmas project for the needy, the government spent 223,300 for rice, 121,000 for sugar, 524,050 for sardines and 405,270 for milk. What was the
total expenses of the government for its Christmas project? IV. Evaluation
Add the following numbers.
1) 853 836 643 2) 902 268 586 103 382 672 488 164 812 41 924 417 173 184 896 58 065 721 400 758 560 + 414 124 028 + 102 963 843
3) 746 257 853 4) 136 031 647 5) 583 236 205 844 758 560 330 141 445 123 841 523 348 369 102 341 319 303 481 325 108 561 567 134 134 638 072 248 248 316 278 754 956 103 411 981 106 523 410 + 371 184 869 + 642 345 012 + 919 303 124
V. Assignment
Solve this problem.
A big warehouse has stocks of canned goods. There are 623 405 234 cans of sardines, 731 065 823 cans of milk, 136 291 629 cans of corned beef, 786 341 098 cans of green peas, and 600 493 587 cans of meatloaf. If you were the stockman, how will you know the total number of canned goods?
1. What are the canned goods stated in the problem? 2. What canned good has the biggest number? 3. Which of these do you like most? 4. Write the number sentence. 5. Solve for the sum.
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Commutative Property of Add ition I. Learning Objectives
Cognitive: Identify the commutative property of addition used in an equation Psyc homotor: 1. Write commutative property in two ways 2. Supply the missing number in a given equation Affective: Manifest thoughtfulness during special occasions
II. Learning Content
Skill : Comprehension of the commutative/order property of addition References: BECPELC I.B.2.1
textbooks in Math 4 Materials: bean seeds, corn seeds, stones, dried leaves, marbles, bottle
caps, straw, popsicle sticks, rubber bands Value: Thoughtfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Warm up Exercises (Number game involving addition) “I am thinking of a number” Example: I am thinking of a number, my first number is 5 and the second is 6, what number am I?
2. Review
Addition facts using flash cards
3. Motivation
Ana gave her teacher 9 white roses and 8 red roses because it’s her birthday. How many roses did she give her? What did Ana give? If somebody ask you about the total number of roses, what should you do?
B. Developmental Activities
1. Presentation
1) How many red roses were given? How about the white roses? What is the total number
of roses? 2) Write the number sentence.
a. (red + white) b. (white + red)
3 +4
4 +3
6 +2
2 +6
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3) Does the sum change? Why? Let’s find out.
2. Group Activity
Divide the pupils into 3 groups.
Group 1 Illustrate the given facts in the problem by following these directions. 1) Draw the given data.
Write the number sentence for the given data. 2) Change the positions of the given data, does the sum change? Why?
Group 2 1) Express the mathematical sentence using the mathematical sticks. 2) Change the order of the data, tell if the sum changes also. 3) Explain why the sum did not change.
Group 3 1) Use the bean seeds to express the mathematical phrase for the problem. 2) Change the order of the given data. 3) Tell if the sum changes.
3. Analysis/Abstraction How did you write the given data?
How did you draw it? Can you change the position of the data or the given facts?
What happens to the sum if you change the order of the numbers?
+
4. Practice Exercises
Write the reverse method. 1. IIIII + III = _____ + _____ 2. 00000000 + 00000 = _____ + _____ 3. _____ + _____ = 10 + 12 4. _____ + 10 = 15 + ? 5. Mario gathered 25 blue marbles and 18 yellow marbles. How many marbles were
gathered? Express/give the mathematical sentence in two ways.
9 + 8 = 17 8 + 9 = 17
9 8 +8 +9 17 17
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5. Generali zation
What is commutative property of addition?
Commutative property – Changing the order of the addends does not change the sum.
C. App lication
Give the missing numbers. 1) 17 + _____ = 9 + 17 2) 20 + 45 = _____ + 20 3) _____ + 19 = 19 + 18 4) 23 + _____ = 17 + 23 5) 68 + 49 = 49 + _____ 6) Jose gathered 48 big bamboos and 28 small bamboos for his poultry house. How many
bamboos did he gather? Show the addition sentence in two ways.
IV. Evaluation
Give the missing numbers. 1) 46 + _____ = 93 + 46 2) 60 + 80 = 80 + _____ 3) 23 + _____ = 17 + 23 4) 60 + 94 = 94 + _____ 5) Fred mixed 28 kilograms of corn grits and 25 kilograms of soya beans. How many kilograms of
feeds did he mix?
V. Assignment
Give/express the given figures in addition sentence in 2 ways. 1)
+
2) +
Give the missing numbers. 3) 7 + 10 = _____ + 7 4) 17 + _____ = 10 + 17 5) Ben harvested 73 eggplants and 94 pieces of okra. How many pieces of vegetables were
harvested? (Show your solutions in two ways)
27
Associative Property of Add ition I. Learning Objectives
Cognitive: Show the associative property of addition Psyc homotor: Supply for the missing number Affective: Participate actively in any group activity
II. Learning Content
Skill s: 1. Showing the associative property of addition 2. Supplying the missing number
References: BECPELC I.B.2 textbooks in Math 4
Materials: chart, activity sheet, drill cards, cutout of shapes Values: Cooperation and active participation
III. Learning Experiences
A. Preparatory Activities
1. Drill/ Review Mental Activity
Supply the missing number (asking one another).
a. 9 + __ = 16 d. 24 + __ = 30 __ + 9 = 16 __ + 24 = 30 b. __ + 6 = 15 e. __ + 23 = 48
6 + __ = 15 23 + __ = 48 c. 18 + __ = 35 f. 32 + 40 = ___ __ + 18 = 35 40 + 32 = ___
What property of addition did you do? State the rule.
2. Motivation
How will you learn better? (Help the pupils realize that grouping helps them learn group work.) This is a group work. How can your group perform well in the activity? What does each member of the group need?
B. Developmental Activities
1. Presentation
Activity Sheet Read carefully and do as instructed. a. Inside the envelope are cutout materials which you are going to use in the activity. b. Make a group of three green shapes, plus 4 red shapes plus 7 yellow shapes. What is
the sum? Write the addition sentence for this.
28
c. Make another group, 7 green shapes + 3 yellow shapes, then add 4 red shapes. What is the sum? Write the addition sentence.
d. What can you say about the addition sentence? e. What is the difference between the two problems? f. Can you write the two addition sentences into one?
2. Discussion/Abstraction
(Each group present and explain their work.)
( 3 + 4 ) + 7 = (7 + 3) + 4 15 + ( 10 + 3 ) = (15 + 10) + 3 7 + 7 = 10 + 4 15 + 13 = 25 + 3 14 = 14 28 = 28
In the given addition sentences, which are the same? What are different? When you change the way in which the addends are grouped, does the sum change? Why?
3. Guided Practice
a. Give the missing number.
Example:
3 + ( 4 + 6 ) = 6 + ( 4 + 3 ) = 13
3 + 10 = 6 + 7 = 13
a. ( 8 + 3 ) + 5 = ( 5 + ___ ) + 3 = ___ ___ + 5 = 13 + ___ = 16
b. 4 + ( 9 + 7 ) = ( 4 + 9 ) + ___ = ____
4 + _____ = ____ + 7 = ____
c. ( 12 + 3 ) + ___ = 3 + ( 12 + 8 ) = ___ 15 + ___ = 3 + 20 = ___
b. Use the associative property for the following:
1) Use the addends 9, 8 and 5. Write two different addition sentences then solve each. 2) Use 35 as your sum. The first addend is 17. What are the two addends, if the second
is 2 more than the first addend. Solve it in two ways.
4. Generali zation What is the associative property of addition?
Changing the grouping of the addends does not affect the sum.
29
C. App lication Write the missing number. a. ___ + (3 + 4) = 12 (___ + 3) + 4 = 12 d. (___ + 6) + 2 = 15 2 + (6 + ___) = 15
b. 6 + (___ + 4) = 20 (4 + 6) + ___ = 20 e. (6 + 9) + ___ = 25 ___ + (6 + 9) = 25
c. 7 + (9 + ___) = 21 (7 + 9) + ___ = 21
IV. Evaluation
A. Write the missing number. a. 7 + (5 + 6) = (7 + 5) + 6 7 + ___ = ___ + 6 ___ = ___ c. (9 + 7) + 20 = 9 + (7 + 20) ___ + 9 = 9 + ___ ___ = ___ e. (13 + 6) + 9 = (9 + 13) + 6 ___ + 9 = ___ + 6 ___ = ___ g. (10 + 7) + 3 = (7 + 3) + 10 ___ + 3 = ___ + 10 ___ = ___
b. (7 + 3) + 12 = 7 + (3 + 12) ___ + 12 = 7 + ___ ___ = ___ d. What is the other addend if one group
is 9 + 8 and the sum is 45. Write the number sentence and solve it.
f. Solve these numbers in two ways. 33, 27 and 18. Give the number sentence and find the sum.
B. Find the sum using the associative property.
a. 8 + 9 + 6 = c. 7 + 3 + 10 = e. 8 + 7 + 12 =
b. 9 + 4 + 13 = d. 15 + 8 + 5 =
V. Assignment
Identify the property of addition used in each equation. Write your answer on the blank provided for. a. 3 + 4 = 4 + 3 ____ c. 9 + ( 8 + 7 ) = ( 9 + 8 ) + 7 ____ e. 20 + 47 = 60 = 47 + 20 ____
b. 35 + 18 = 53 = (17 + (18 + 18) ____ d. 76 + (30 + 70) = 176 = (76 + 30) + 70
Identity Property of Add ition I. Learning Objectives
Cognitive: Identify the identity property of addition used in an equation Psyc homotor: 1. Write the addition sentences showing the identity property of addition
2. Supply the missing number in a given equation Affective: Show sportsmanship during games/activities
II. Learning Content
Skill s: 1. Identifying the identity property of addition 2. Supplying the missing number
Reference: BECPELC I.B.2.5 Materials: flash cards, written exercises on a cartolina Value: Sportsmanship
30
III. Learning Experiences
A. Preparatory Activities
1. Drill (Emphasize sportsmanship during the game)
Do the following exercises in the form of a race. Have the pupils form two lines. Teacher shows the flash cards. Pupils give the answers orally. Pupils make one step forward for every correct answer.
a. 26 54 43 35 46 51 24 +53 +33 +24 +44 +42 +28 +63
b. 55 28 37 31 62 35 63
+33 +41 +30 +57 +27 +57 +34
2. Review Give the property of addition shown in each equation below. Write your answer on the blank provided for. a. 23 + 68 = 68 + 23 _____ b. 13 + (10 + 30) = (13 + 10) + 30 _____ c. 96 + 22 = 22 + 96 _____ d. 38 + 19 = 19 + 38 _____ e. (50 + 12) + 6 = 50 + (12 + 6) _____
3. Motivation
Ask what happens if a number is added to zero. Elicit answers from the class. Leads
them to the next property of addition. Which is zero property? Show the equations on the board.
I II 10 + 0 = ___ 0 + 70 = ___ 192 + 0 = ___ 0 + 66 = ___ 35 + 0 = ___ 0 + 37 = ___ 62 + 0 = ___ 0 + 88 = ___
B. Developmental Activities
1. Presentation
a. Call on a pupil to read the exercises written on a cartolina or in the blackboard. b. Let them answer the exercises as fast as they can. c. Ask: What do you observe about the equations under column I? What can you say about
the equations in column II? d. Focus the children’s attention on the numeral 0. Ask: What is the sum when zero (0) is
added to a number? What about when a number is added to zero? e. Introduce the term zero or identity property of addition.
2. Group Activities a. Fill in the correct answers.
1) 6 + 0 = ___ 2) 3 + ___ = 3 3) 12 + ___ = 12 4) ___ + 69 = 69 5) 80 + ___ = 80
31
b. Put a check (3) on the blank provided for if the equation shows the identity property of addition and a cross (x) if it does not show. _____ 1) (36 + 21) + 5 = 36 + (21 + 5) _____ 2) (13 + 19) + (65 + 25) = (65 + 25) + (13 + 19) _____ 3) 1888 + 0 = 1888 _____ 4) (67 + 93) + 16 = 16 + (67 + 93) _____ 5) 0 + 820 = 820
c. Supply the missing number then write the property of addition shown on the blank before
each number. _____ 1) 88 + 0 = ___ _____ 2) (86 + 39) + 7 = ___ + (39 + 7) _____ 3) ___ + 270 = 270 _____ 4) 78 + ___ = 78 _____ 5) 3000 + 0 = ____
3. Generali zation What is identity property of addition?
Zero is the identity property of addition. When zero is added to any number the sum is also the number.
C. App lication
Fill in the correct answer. 1) 8 + __ = 8 2) 5 + 0 = __ 3) 45 + 0 = 45 4) 36 + 0 = __ 5) __ + 21 = 21
IV. Evaluation
A. Supply the missing number that will make each equation correct.
1) 628 + 0 = ___ 2) ___ + 711 = 711 3) 564 + ___ = 564 4) ___ + 128 = 128 5) 323 + 0 = ___
B. Encircle the number of the equation showing the identity property of addition.
1) 420 + 0 = 420 2) 926 + 24 = 24 + 926 3) 372 + (35 + 63) = (372 + 35) + 63 4) 0 + 306 = 306 5) 821 + 0 = 821
C. Complete each equation. Write IPA on the blank if the equation shows the identity property of
addition. _____ 1) 150 + 0 = ___ _____ 2) 370 + ___ = 370 _____ 3) 26 + 800 = 26 + ___ _____ 4) (85 + ___) + 90 = 85 + (20 + 90) _____ 5) ___ + 922 =922
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V. Assignment A. Write the number that will make each equation correct.
1) 62 + 0 = ___ 2) ___ + 1250 = 1250 3) 121 + ___ = 121 4) 728 + ___ = 728 5) 550 + 0 = ___ 6) 230 + ___ = 230 7) 236 + ___ =236 8) ___ + 552 = 552 9) ___ + 801 =801 10) 525 + ___ = 525
B. Write 10 equations showing the identity property of addition.
Estimating the Sum I. Learning Objectives
Cognitive: Estimate the sum of 6 or more digit addends Psyc homotor: Illustrate how to find the estimated sum of 6 digit addends Affective: Appreciate the importance of working hard
II. Learning Content
Skill : Estimating the sum of 6 or more digit addends References: BECPELC I.B.3
textbooks in Math 4 Materials: pictures, pocket chart, colored chalk, showmecard or drill board Values: Hard work, perseverance
III. Learning Experiences
A. Preparatory Activities
1. Drill Basic addition facts using flash cards.
9 + 7 9 + 4 4 + 7 9 + 6 8 + 3 8 + 6 6 + 5 8 + 8 7 + 5 7 + 9 8 + 5 7 + 9 2. Review
“ Rounding o ff numbers to the nearest 10 000 to 100 000”
Play “Pass the Paper Game.” Each pupil in the column takes turns in rounding numbers as fast and correctly as they can. Check answers in class.
3. Motivation
Show picture of farmers working in a farm or coconut plantation. What do you see in the
picture? What does the farmer do to have a good quality harvest? Can you tell the number of coconuts seen in the drawing?
33
B. Developmental Activities 1. Presentation
Mang Mario has a coconut plantation. He usually works in his farm the whole day. He
harvested 11 389 coconuts on the first month and 14 481 coconuts on the second month. About how many coconuts did he harvest in two months? Help pupils analyze and solve the given problem. Ask the following questions: a. What is asked in the problem? b. What are the given facts? c. What is the operation needed? d. What is the number sentence? e. What kind of a farmer is Mang Mario? What benefits could we get if we work hard?
If you’re given a task, do you work on it? 1) 11 389 Æ10 000 First round the addends to the nearest +14 481Æ14 000 ten thousand then add the rounded 24 000 numbers to get the estimated sum. 2) Using the front end technique front end 11,389 Æ10 000 1 000 Round the first addends to the first digit +14,481 Æ10 000 4 000 then to the second digit and find the sum. 20 000 5 000 Combine the sum of the 2 rounded numerals.
2. Group Activities
a. Work with a partner. One will get the exact sum and the other will estimate the sum. (Use your drill board.)
a) 594 b) 3 978 c) 5 928 d) 783 e) 1 397 +678 +5 697 +1 436 +492 +1 280
b. Estimate the sum of each to the highest place value.
a) 25 635 b) 36 403 c) 43 321 d) 18 476 e) 611 175 +46 780 +53 296 +52 085 +20 581 + 258 806
c. Below are the prices of some school supplies. Use your estimation skills to answer each of the questions without using paper and pencil. ballpen 4.50 glue 18.50
pad paper 19.00 pencil case 21.25 ruler 10.50 math notebook 21.25 pentel pen 35.25 pencil 5.25 crayons 28.25
1) About how much will a box of crayons and a pencil case cost? 2) Randy has 50.00. Has he enough money to buy one pad paper, crayons and a
math notebook? 3) You have 50.00. What 3 things can you buy? 4) What can you buy if you have 20.00 bill? 5) You have 100.00. How many math notebooks and pad paper can you buy?
3. Generali zation
What are the steps involved in estimating sums of 6 or more digit addends? How do
you estimate? How would you come up with a good estimate?
34
Round off the addends to the nearest highest place value then add.
A good estimate is a little less or more than the exact answer. C. App lication
Solve the problem.
Mrs. Dayo’s poultry farm produced 236 378 eggs in 1997 and 147 932 eggs in 1998. About
how many thousands of eggs were produced in two years?
IV. Evaluation
A. Round each addend to the highest place value. Then add.
1) 713 156 2) 138 819 3) 514 912 4) 614 346 5) 192 143 + 291 724 + 861 412 + 813 125 + 201 223 + 361 414
B. Using the frontend technique, find the estimated sum of the following. 1) 762 304 2) 631 918 3) 154 128 4) 521 146 5) 178 675 + 134 503 + 167 214 + 318 125 + 319 272 + 369 512 V. Assignment
A. Estimate then find the exact sum.
1) 56 435 2) 456 412 3) 74 825 4) 21 165 5) 63 729 + 90 845 + 141 708 + 9 567 + 3 270 + 23 878
B. Arrange each item in column then estimate the sum. 1) 156 435 + 290 845 2) 829 456 + 246 723 3) 871 702 + 249 581 4) 379 405 + 845 563
Adding Mentally 2 to 3Digit Numbers wi th Sums Up to 300 I. Learning Objectives
Cognitive: Add 2 to 3digit numbers mentally with sums up to 300 without regrouping Psyc homotor: Solve for the sum of 2 to 3digit numbers mentally Affective: Appreciate the value of trees and other plants around us
II. Learning Content
Skill : Adding mentally 3 digit numbers with sums up to 300 References: BECPELC I.B.4
textbooks in Math 4 Materials: flash cards, number cards, window cards Value: Appreciation of nature
35
III. Learning Experiences
A. Preparatory Activities
1. Drill
“ Game on Basic Add ition Facts Using Flashcards” Relay game by pairs.
2. Review
Estimate the sum of each item orally.
312 143 163 192 676 780 816 136 376 762 + 291 + 414 + 681 + 271 + 215 + 342 + 415 + 861 + 213 + 134
3. Motivation Are trees and other plants important to us? Why? What do trees and other plants give
us? Do you take care of our trees and plants? In what way?
B. Developmental Activities
1. Presentation
Problem Opener
In an orchard, there are 125 avocados, 175 mango and santol trees. How many trees are there in all?
2. Group Activities
a. Activity 1
1) What kind of trees are found in the orchard? 2) Can you name them? 3) How would you get the total number of trees in the orchard? 4) Do you need to use paper and pencil? 5) Can you solve for the final answers mentally? How?
b. Activity 2
Let us help the baby go up and down the stairs by adding the equations mentally
as fast as you can.
136+174=
111+189= 186+113=
140+140= 100+200= 124+186=
158+36= 152+36= 165+123= 116+170=
276+241= 127+178= 117+132= 156+130= 128+182=
190+110= 137+60= 129+170= 134+64= 153+37= 141+26=
36
3. Generali zation
What is the fastest way in solving for the sum mentally? Recall once again the steps.
C. App lication Add the following numbers mentally.
1) 248 2) 275 3) 153 4) 150 5) 134 + 52 + 25 + 137 + 150 + 45
1) 278 2) 189 3) 167 4) 123 5) 265 + 10 + 100 + 133 + 86 + 34
Use window cards with 2 to 3digit numbers with sum up to 300.
IV. Evaluation
Teacher will flash a card one at a time in class. The task of each pupil is to write the sum on their paper.
a. 135 b. 213 c. 241 d. 196 e. 153 f. 148 + 174 + 182 + 50 + 111 + 146 + 151 g. 175 h. 102 i. 237 j. 286 k. 160 + 124 + 191 + 22 + 11 + 134 l. 178 m. 283 n. 195 o. 152 p. 266 +121 + 12 +101 +143 + 43 V. Assignment
Find the sum by adding mentally. Write the answers in your notebook.
a. 131 b. 160 c. 125 d. 208 e. 121 + 128 + 46 + 175 + 92 + 77 f. 163 g. 211 h. 138 i. 112 j. 240 + 122 + 87 + 141 + 145 + 49 k. 146 l. 213 m. 123 n. 221 o. 121 + 121 + 74 + 145 + 85 + 178
Analyzing Word Prob lems involving Add ition I. Learning Objectives
Cognitive: Analyze word problems involving addition Psyc homotor: Tell what is asked, what is/are given, the word clues and the operation to be
used in solving story problems Affective: Show proper behavior during programs
37
II. Learning Content
Skill : Analyzing word problems involving addition References: BECPELC I.B.5.1.1 5.1.4
textbooks in Math 4 Materials: story problem, flash cards, pocket charts, strips of cartolina Value: Proper behavior during programs
III. Learning Experiences
A. Preparatory Activities
1. Drill
Have a game using basic addition facts. (Use flash cards)
2. Review
Adding mentally without regrouping (work in pairs) to be given orally by the teacher. Example: 65 green apples and 31 yellow red apples
35 boys and 73 girls
3. Motivation
Who is your favorite artist? How about singers? Why do you like him/her? Whenever you watch programs and performances, how are you supposed to behave?
B. Developmental Activities
1. Presentation
During the concert of Regine Velasquez in Araneta Coliseum, there were 3 120
girls and 1 512 boys who watched the concert. How many persons watched the concert?
Activity 1 a. Who had a concert? b. Where was the concert held? c. Who watched the concert? Valuing:
• How would you behave while watching such program or other art performances?
Activity 2 Questions should be written in activity cards to be distributed to each group. a. What is asked for in the problem? b. What are given in the problem? c. What operation will help you solve the problem? d. What number sentence can you make from the given facts?
38
Activity 3 Match the steps used in solving problem found in column A with the given facts written in column B.
Column A Column B
1. What is/are given in the problem? a. 3 120 + 1 512 =n 2. What is the operation to be used? b. The total number of people
who watched the concert. 3. What is asked for in the problem? c. 3 120 girls and 1 512 boys 4. What is the number sentence? d. addition
2. Practice/ Fixing Skills
Read and analyze each problem carefully (group activity). a. During the week, 2 basketball games were played in the stadium. There were 9 948
people who came to watch the first game and 9 865 people who came to watch the second game. How many people in all watched the two games? 1. What is asked in the problem? 2. What are given in the problem? 3. What operation will help us solve the problem? 4. What is the number sentence?
b. Mr. and Mrs. De la Rosa sold their lot in Tagaytay for 759,635.00 and their car for
435,126.00. How much did they get in all? 3. Generali zation
What have you learned today? How do you solve story problems? What are the steps
involved?
C. App lication Read and analyze each problem carefully. 1. Mrs. Lilia Gomez earned 144,670.00 in year 2003 while Mr. Sam Gomez earned
142,000.00 for the same year. How much did they earn altogether? 2. Mrs. Araneta exported prawns worth 24,000.00 and milkfish worth 15,000.00. What
was the total cost of the seafoods exported by Mrs. Araneta? 3. During the Palarong Pambansa, 3 125 people watched the first day, 1 420 on the second day
and 3 146 on the third day. How many people watched the Palaro in 3 days?
IV. Evaluation
A. Analyze each problem carefully. Encircle the letter of the correct answer.
Mr. de Jesus owns a big piece of land planted with rice, corn and coconuts. This year, he harvested rice worth 58,570.00; coconut and corn worth 52,435.00. How much did he earn in all?
1. What are given in the problem? a. 58,570.00 b. 52,435.00 c. 58,570.00 and 52,435.00
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2. What is asked in the problem? a. The total rice harvested b. The total amount earned from coconut and corn c. The total amount earned from rice, coconut, and corn
3. What operation is needed to solve the problem?
a. Addition b. Subtraction c. Multiplication
4. What is the number sentence? a. 58,570.00 + 52,435.00 = n b. 58,570.00  52,435.00 = n c. 58,570.00 x 52,435.00 = n
5. What clues tell you that you are going to add?
a. money b. in all c. and
B. Read and analyze each problem carefully then solve. Label your final answer.
1. A poultry farm exported 18 654 chickens last year and 25 172 this year. How many chickens
were raised in two years? 2. Mang Jose gathered 2 365 eggs on the first week 1 875 eggs on the second week and 2 174
on the third week. How many eggs did he gather in 3 weeks? V. Assignment
Read and analyze each problem carefully. 1. Monica bought a pair of shoes for 1,495.00 and a bag for 599.00. How much did she pay
the cashier? 2. The district property custodian distributed 7 981 English books and 5 172 Math books for Grades
I to VI pupils. What is the total number of books distributed in all the grades? 3. Angelica has two volumes of encyclopedia. One encyclopedia has 2 594 pages. The other
has 2 678 pages. What is the total number of pages of the two volumes of encyclopedia?
Solving Word Prob lems involving Add ition I. Learning Objectives
Cognitive: Solve word problems involving addition of whole numbers including money with
sums through millions and billions Psyc homotor: Analyze and solve word problems accurately Affective: Share one’s ideas and materials with others
II. Learning Content
Skill : Analyzing and solving word problems involving addition of whole numbers References: BECPELC I.B.5.1
textbooks in Math 4 Materials: story problems, charts, pictures, strips of cartolina Value: Sharing
40
III. Learning Experiences
A. Preparatory Activities
1. Drill
Post addition equations on the board. Each pupil should solve the sum mentally as fast and as correct as he can.
32 45 16 44 64 35 42 25 66 + 2 + 11 + 43 + 23 + 33 + 12 + 26 + 32 + 11
2. Review
Match the appropriate phrase suited to the given facts and statements below. Write the
letter of the correct answer on the blank provided for. _____ 1) The total population for both schools. _____ 2) 13,486 + 23,465 = n _____ 3) addition _____ 4) 13 486 + 23 465 = 36 951
3. Motivation
Song (Sing to the tune of “Planting Rice.”) Learning math is really fun I am glad you are glad New ideas every time For your answers are all right There is joy for everyone We all feel that we are bright Problem solving satisfies Solving problems makes us wise a. What words are underlined once? b. What words are underlined twice? c. Is it true that solving problems makes us wise? How?
B. Developmental Activities
1. Presentation
Materials: drawing of trees with figures shown on the trunk of each tree as mentioned in the problem
The Estrada’s and Cruzado’s are 2 generous families. They donated tree seedlings to the different barangays of the country. The Estrada family donated 126 896 acacia and ipilipil trees. The Cruzado family donated 315 724 molave and narra trees. How many trees were donated by the 2 families?
2. Group Work Activity 1 A representative will act as a facilitator to discuss the questions presented by the teacher. a. Who are the families mentioned in the problem?
a. operation needed c. number sentence e. asked in the b. given facts d. solution and answer problem
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b. What kind of families are they? c. What did they donate? d. How many trees were donated by the Estrada family? e. What kind of trees were donated by Cruzado family? Estrada family? Valuing: � At your age, do you share things with others? What things do you share with others?
What did you feel? (Share experiences in class.)
Activity 2 Call another representative in class to ask and discuss the following questions. a. What is being asked in the problem? b. What are the given facts? c. What operation will you use to solve the problem? Why? Explain your answer. d. Give the number sentence that will help you solve the problem. e. Show the solution to the problem on the board.
Example: 126 896 acacia and ipilipil trees + 315 724 molave and narra trees 442 620 total trees donated by the 2 families
Activity 3 Materials: chalk, miniboards The group will give the answer to the problem by supplying the information below. a. The given facts are _____ b. The process to be used _____ c. The answer is _____
3. Fixing Skill s/Practice Read the problem carefully then answer the following questions briefly. a. There was a benefit show for the orphans. On the first day, 512,761.00 was earned.
On the second day, 726,895.00 was the proceed. How much was generated by the show in 2 days?
b. The math Club of Barrio Obrero Elementary School started a newspaper drive to raise funds for the poor children of Sapang Palay. If one group brought 434 253 old newspapers and the other group brought 625 250 old newspapers. How many old newspapers would there be in all?
c. Last year, Manny deposited 1,276,718.00 in a bank. This year, he deposited 991,221.00. How much did he deposit in 2 years?
3. Generali zation
How do you solve problems? What are the steps involved in solving story problems?
Elicit the steps.
In solving word problems involving addition of numbers with sums up to millions and billions, the following steps are to be followed: a) Read and understand the problem. b) Plan on what to do c) Solve d) Look back to check if the answer to the problem is correct
42
C. App lication Read and solve each problem carefully. 1) During the best of seven series in the basketball game, there were 1 211 125 tickets sold in
the fifth game while 2 179 600 in the sixth game. How many tickets were sold in the two games?
2) Mr. Domingo Sy earned 1,224,663.00 in the year 2001 while Mrs. Ellen Sy earned 926,175.00 for the same year. How much did they earn altogether?
3) Look at the earnings of a certain food company. Then answer the questions that follow: Milk Products 378,584.00 Fruit Juices 198,475.00 Meat Products 326,421.00 Other products 178,623.00
a) What is the total earnings for meat products and fruit juices? b) What is the total earnings for meat and dairy products?
IV. Evaluation
Read and solve the problems carefully. 1. It was reported that the total population in Benguet is 541 817 and in Kalinga is 154 145. What
was the total population of Benguet and Kalinga? 2. Quezon City has a population of 8 424 262 while Manila has 11 189 296 people. What is the
combined population of the two cities? 3. The Marcela Cooperative Farms earned 17,342,262.00 while Barangay Bayambang
Cooperative earned 48,159,926.00. Altogether, how much money did the two cooperatives earn?
V. Assignment
Solve the following problems carefully. 1. Mr. Reyes purchased a pair of shoes worth 4,179.45 and a jacket which costs 725.95 at
SM Megamall. How much did he pay the cashier? 2. There are 2 big central schools in Mindanao. In the first school, population was 4 486 while
3 654 in the second school. What is the total population of the 2 schools? 3. A car dealer had this sales summary for the last quarter of 2000.
October – 653,410.00 November – 585,688.00 December – 890,462.00
What was his total sales in 3 months?
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Solving Mentally 1Step Word Prob lems I. Learning Objectives
Cognitive: Solve mentally 1step word problems involving addition with sums up to 300
without regrouping Psyc homotor: Tell the answer to the problems accurately Affective: Appreciate the beauty of nature
II. Learning Content
Skill : Solving 1step word problems mentally References: BECPELC I.B.5.2
textbooks in Math 4 Materials: flash cards, pocket chart, set of numbers Value: Love for nature
III. Learning Experiences
A. Preparatory Activities
1. Drill
Complete the addition wheel.
2. Review
Solve for the following math sentences. a. What is the sum of 78 and 71? b. What is 74 more than 24? c. What is the result when 87 is added to 23? d. What is 18 more than the sum of 35 and 47? e. Add 35 to the sum of 43 and 69
3. Motivation Who is your favorite newscaster? Why did you choose him/her? If given a chance,
would you like to be like him/her? Why?
B. Developmental Activities
1. Presentation a. Call a pupil to report the problem in class.
+11
2 5
7 6
3 1
9
+12 3
5
2 1 7
9
8 6
+13 5
4
7 1 8
9
6 3
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One sunny day, Mrs. Almonte and her pupils went to the park. They enjoyed
looking at the different flowers. On their way home, they decided to count all the flowers they saw. A group of boys reported that there were 71 roses and daisies while the girls reported 128 gumamela, camia and yellow bells. How many flowers were there in all? This is (name of student) reporting.
Discussion: 1) Who went to the park? 2) What did they do there? 3) If you were to visit a park, will you do what they did? Explain. 4) What are the flowers mentioned in the problem? 5) How many flowers were counted by the boys? 6) How many flowers were counted by the girls? 7) How many flowers are there in all? 8) How did you get the answer? 9) What is the fastest way of solving the given problem? 10) How will you solve the problem mentally? Draw out the steps.
b. Solve mentally 1) A crowd of 162 people watched the first day of the football game. The next day, 138
attended the game. How many people watched the games? 2) Ramon had 175.00. His father gave him 123.00. How much does he have
now? 2. Fixing Skill s/Practice
Divide the class into groups. Assign a leader to act as the facilitator in the discussion of the problem. Group 1
Jeff collected 145 stamps while Alvin collected 153 stamps. How many stamps did they collect altogether? Group 2
Sheila used 147 bond paper. Irene used 132 bond paper. How many sheets of bond paper did Sheila and Irene used altogether? Group 3
At Basilan Elementary School, there are 110 members of Science Club and 181 members of Math Club. How many members are there altogether?
3. Generali zation
What have you learned today? What are the steps involved in solving story problems mentally?
In solving word problems mentally, give the answers to the problems accurately without using paper and pencil.
C. App lication You can do these orally. Try them. 1. Kevin picked 135 santols. Marie picked 161 santols. How many santols were picked in all? 2. Lyn has 137 stamps in her album. Alma has 151. How many stamps do they have in all? 3. Marlyn walked 138 metres north and 160 metres south. How far did she walk in all?
45
4. Father drove 162 km from their home. After an hour, he drove 45 kilometres more. How far away is he from his starting point?
5. Mang Igme accepted an order of 175 baskets. After 5 days, there was an order of 124 baskets more. How many orders did he accept in all?
IV. Evaluation
A. Study the table then answer the following questions below.
1. How many pupils are enrolled in Grades 1 and 2 altogether? 2. The total number of pupils enrolled in Grades 4 and 5 is _____ 3. What is the sum of the enrollment of Grades 5 and 1? 4. The combined enrollment of Grades 3 and 4 is_____
B. Think and solve mentally.
1. Kalawaan Elementary School has 35 classes. Pasig Elementary School has 24 more classes than Kalawaan Elementary School. How many classes does Pasig Elementary School have in all?
2. Jenny is 35 years old now. Her mother is 41 years older. How old is her mother now? 3. The weight of Benjie is 74 pounds. His friend is 22 pounds heavier than him. What is the total
weight of Benjie’s friend?
V. Assignment
1. Read and answer. a. Rosa sells fruits in the market. She earned 275.00 for her mangoes and 126.00 for the
papayas. How much did she earn from the fruits she sold? b. My aunt went shopping last Saturday. She bought a blouse for 280.00 and an umbrella for
125.00. How much did my aunt spend in shopping?
Subtracting wi thout Regrouping I. Learning Objectives
Cognitive: Subtract 5 or more digit numbers from 6 or more digit numbers without
regrouping Psyc homotor: Find the difference of 5 or more digit numbers from 6 or more digit numbers
without regrouping Affective: Show concern in the cleaning and greening of the community
Dr. Sixto Elementary Schoo l Grade 1 – 140 Grade 4 – 120 Grade 2 – 115 Grade 5 – 144 Grade 3  152
46
II. Learning Content
Skill : Subtracting 5 or more digit numbers from 6 or more digit numbers without regrouping
References: BECPELC I.C.1.1 textbooks in Math 4
Materials: flash cards, pocket charts Value: Environmental concern
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic addition facts using flash cards
2. Review/Mental Computation
a. What is 45 more than the sum of 12 and 13? b. Tony picked 35 apples. He gave 11 to his friends. How many apples were left?
3. Motivation
What do children of your age do to help the barangay officials in their campaign for the
clean and green program? What activities would you suggest to promote the clean and green program of your barangay?
B. Developmental Activities
1. Presentation
a. Activity 1
In support of the clean and green campaign of our government, the officials and
constituents of barangay Kalawaan decided to raise a total amount of 685,976.00 to buy ornamental plants, flowering plants, grass and some garden materials. During the recent fund drive they conducted, they were able to raise a net amount of
234,802.00. How much more should they raise in order to meet the target amount for their beautification project?
1) What is asked in the problem? 2) What are the given facts? 3) What operation is to be used? 4) What is the number sentence? 5) Solution (help the pupils solve the problem)
Strategy 1
Subtract the ones Subtract the tens Subtract the hundreds
685 976 685 976 685 976  234 802  234 802  234 802 4 74 174
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Subtract the Subtract the Subtract the thousands. ten thousands. hundred thousands.
685 976 685 976 685 976
 234 802  234 802  234 802 1 174 51 174 451 174
Let us familiarize ourselves with the terms we used in subtraction. 685,976 (minuend)  234,802 (subtrahend) 451,174 (difference)
How do we check if our answer is correct? Do this by adding the difference and the
subtrahend. If the minuend and the sum are the same, then our difference is correct. 451,174 (difference) + 234,802 (subtrahend) 685,976 (minuend)
Strategy 2 Use of expanded notation
685 976 = 600 000 + 80 000 + 5 000 + 900 + 70 + 6 234 802 = 200 000 + 30 000 + 4 000 + 800 + 0 + 2
400 000 + 50 000 + 1 000 + 100 + 70 + 4 = 451 174 b. Activity 2
1) Use your drill board to find the difference of each. a) 62 716 b) 78 914 c) 386 112 d) 297 564 e) 687 312  41 302 12 513 125 011 126 231  574 211
2) Answer and check with the class.
a) Subtract 633 420 from 955 420 b) Take away 59 104 from 89 102 c) What is 475 634 minus 243 522? d) What is the difference between 878 945 and 25 714? e) What is 215 847 less than a number gives a result of 772 122? f) 961 837 g) 457 791
351 425 231 661
2. Generali zation
How would you find the difference of 5 or more digit numbers from 6 or more digit numbers without regrouping?
In subtracting 5 or more digits from 6 or more digits without regrouping, subtract from the ones until the last given digit.
48
C. App lication Subtract. a) 27 892 b) 287 196 c) 279 124 d) 78 465 e) 754 683
16 574  163 164  59 113 52 431  310 521
Find the missing numbers. a) 85 421 b) 75 436 c) 495 837 d) 787 251 e) 893 526  _ _ _ _1  _ _ _ 12  _7_ 2_ _  _1_ _3_  _7_ 1_ _ . . . . .
42 310 52 3_4 1_4 _24 345 121 621 412 IV. Evaluation
Find the difference. Choose the letter of the correct answer.
1) 67 071 a. 475 071 p. 52 010 15 061 b. 465 072 l. 56 572
2) 70 184 l. 40 010 n. 40 210 30 174 m. 40 111 o. 40258
3) 871 976 a. 530 701 c. 530 702
341 275 b. 531 714 d. 531 711
4) 987 726 k. 222 731 m. 221 611 765 115 l. 222 511 n. 222 611
5) 876 752 s. 335 421 u. 351 214 561 331 t. 315 421 v. 315 241
What word is formed out of your answer? What do plants do to our surroundings?
V. Assignment
Find the difference. Check your answer. 8 184 21 748 95 614 72 114 65 718 6 153 11 136 34 512 31 002 23 416
Solve for n. a. 38 415 – 27 304 = n b. n – 24 923 = 53 024 c. 17 556 – (2 475 + 625) = n d. 875 122 – 764 111 = n e. 693 952 – 512 841 = n
Subtracting wi th Regrouping I. Learning Objectives
Cognitive: Subtract 5 or more digit numbers from 6 or more digit numbers having zeros in
the minuend or subtrahend Psyc homotor: Illustrate how to subtract numbers from 6 or more digit numbers having zeros in
the minuend/or subtrahend Affective: Show concern for others
49
II. Learning Content
Skill : Subtracting 5 or more digit numbers by 6 or more digit number References: BECPELC I.C.1 textbooks in Math 4 Materials: flash cards, drill board Value: Thoughtfulness
III. Learning Experiences
A. Preparatory Activities 1. Drill
Follow the clue to find the final answer.
() (=) (+) (=) () (=) (+) (=) () 40 Final Answer
2. Review
Find the difference. 684 1 284 7 486 5 764 3 241 298  196 5 162 3 624 2 632
3. Motivation
Who among you spend your vacation in the province? What will you do so that you will have money to spend during your stay there?
B. Developmental Activities
1. Presentation
Mang Lauro wanted to visit his father in the province. He was planning to give a
colored TV to his father which costs 14,525.00. If he has saved 35,200.00, how much will be left in his bank account?
a. Who wanted to go to the province? b. How much is his savings? c. What will be his gift to his father? Valuing: � Even if you are still young can you also save money to buy a gift for your father?
How? What good character trait does Mang Lauro possess?
37 12 ? 33 ?
13 ? ? 66 ?
50
Discussion a. What does the problem want you to find? b. What are the given facts? c. What word clues tell you what to do in the problem? d. What number sentence can you make out of the given information? e. What is the answer?
Steps in Subtracting Numbers:
1. The digits in the subtrahend is bigger than the digits in the minuend so you have to
regroup. Rename 5 thousands first as 4 thousands and 10 hundreds.
2. Regroup 10 hundreds with 2 hundreds. 10H + 2H = 12H
Rename 1 hundred as 10 tens. 12H – 1H = 11H
3. Regroup 1 tens as 10 ones.
10T – 1T = 9T
4. Now you can subtract the subtrahend from the minuend. Subtract the ones. Subtract the tens. Subtract the hundreds. Subtract the thousands. Subtract the ten thousands.
11 9 . 4 12 10 10 3 5 2 0 0  1 4 5 2 5 2 0 6 7 5
2. Practice/Group Activities Regroup each minuend so that you can begin subtracting. a) 4 053 b) 6 309 c) 51 623 d) 26 000 1 206 2 134 15 535 14 327 e) 40 681 f) 6 010 g) 57 360 h) 80 000 12 530 3 040 29 435 24 561 i) 31 896 j) 70 000 k) 64 710 l) 405 679 22 458 25 564 39 256 256 495
11 9 . 4 12 1010.
35 200 14 525 20 675
11 . 4 12 10 .
35 200 14 525
4 12 .
35 200 14 525
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3. Generali zation
How will you subtract numbers with regrouping?
C. App lication
Follow the rule. Find the missing numbers. 1. Rule: Subtract 2 000.
Input Output 9 635 7 406 8 000 8 153 9 401
2. Rule: Subtract 12 914.
Input Output 63 842 35 001 28 602 79 800 89 716
IV. Evaluation
Subtract. Write your answers on your paper.
a) 14 362 b) 52 090 c) 8 040 321  2 784  19 816  901 007 d) 15 134 e) 803 020 f) 600 720 13 750  114 040  425 408 g) 82 751 h) 682 700 i) 710 002 61 903  299 438  190 059
V. Assignment
Find the difference and check.
a) 780 004 b) 508 200 c) 208 050  36 842  42 860  98 463 d) 901 060 346 e) 81 502 360 f) 129 103 719  9 345 678  1 234 567  12 428 151
Solve the following problems.
1. What is 376 459 subtracted from 90 000 000? 2. What is the difference between 82 104 612 and 1 321 476? 3. What is 834 500 less than the sum of 235 875 and 2 146 290?
52
Subtracting Large Numbers wi th Zero Difficulty I. Learning Objectives
Cognitive: Subtract 5 or more digit numbers from 6 or more digit numbers with 3
continuous or noncontinuous zeros in both the minuend and subtrahend with regrouping
Psyc homotor: Solve for the difference of 6 or more digit numbers with zero difficulty Affective: Support organizations that help poor people
II. Learning Content
Skill : Subtracting large numbers with zero difficulty References: BECPELC I.C.1.2.2
textbooks in Math 4 Materials: flash cards, charts, pocket charts Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Subtract.
17 18 21 17 23 35 41 19 10 11 16 12 19 11 21 19
2. Review
Find the difference.
3. Motivation
What government organizations help poor people? Have you experienced asking help
from some organizations?
 1 968
74 814
 3 876  47 765
 58 437  59 732
=
=
=
=
=
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B. Developmental Activities
1. Presentation
Red Cross is an organization which helps the poor people. During the Red Cross Week, Garita Elementary School was given 12 000 tickets to sell for a benefit show. The school was able to sell 9 032 tickets. How many tickets were not sold? a. Who sells tickets? b. Why do they sell tickets? Valuing: • As a student, how will you help this organization? • Is it right to help them? Why?
Discussion a. What is asked in the story problem? b. What is/are given? c. What is the word clue to determine the operation needed in the problem. What
operation are we going to use? d. What is the number sentence for the problem? e. What is the answer?
When there are continuous zeros in the minuend, we rename and regroup, starting at the left most digit.
9 9 1 10 10 10 1 101010 12 000 1 2 0 0 0 1 2 0 0 0  9 032 9 0 3 2  9 0 3 2
2 9 6 8
2. Group Activity
Find the difference. a.
b.  = 
 =  = =
800 120
400 050
621 000
70 625
711 000
500 200
93 150 000 13 281 600
176 105 79 092 200
93 100

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3. Generali zation
How can you subtract numbers with 3 continuous or noncontinuous zeros in both minuends and subtrahends and with regrouping in any places?
When there are continuous zeros or noncontinuous zeros, we regroup first in places that
need regrouping, starting at the leftmost digit, then proceed to subtraction.
C. App lication Find the difference.
1) 780 004 2) 2 357 000 3) 9 856 000 4) 900 603  36 842  26 453  500 032  590 407 5) 700 080 6) 7 800 000 7) 97 000 136 8) 160 080 000 345 000 1 156 000  6 002 179  42 165 000
IV. Evaluation
Find the difference. 1) 900 034 2) 867 000 3) 320 400  720 004  123 000  10 009 4) 98 000 000 5) 65 000 000 6) 261 976 000  15 900 050  9 261 000  105 000 834
7) 6 000 537  1 485 000 =  153 000  290 007 =  =
V. Assignment
Write in column and subtract. 1) 901 060 006 – 9 300 518 = n 3) 80 000 000 – 1 234 567 = n 5) 726 140 009 – 402 124 000 = n
2) 100 000 000 – 85 643 214 = n 4) 421 300 048 – 216 321 832 = n
Estimating the Difference of Two Numbers I. Learning Objectives
Cognitive: Estimate the difference of two numbers with four to six digits Psyc homotor: Solve for the difference mentally Affective: Show love and concern for parents
II. Learning Content
Skill : Estimating the difference of two numbers with four to six digits References: BEC – PELC I C 1.3
textbooks in Math 4 Materials: flash cards, chart Value: Thoughtfulness
55
III. Learning Experiences
A. Preparatory Activities
1. Drill
Find the difference. 65 – 22 = 10 – 6 = 9 – 5 = 17 – 10 = 127 – 105 = 7 – 3 = 12 – 6 = 18 – 11 = 396 – 254 = 17 – 9 = 11 – 8 = 12 – 7 =
2. Review
Round the following numbers to the nearest tens and thousands. Nearest Tens Nearest Thousands a. 74 325 ____________ ______________ b. 25 936 ____________ ______________ c. 127 547 ____________ ______________ d. 31 247 ____________ ______________ e. 743 426 ____________ ______________
3. Motivation
What would you do if you cannot afford to buy a greeting card or gifts for your loved
ones? What do you feel? B. Developmental Activities
1. Presentation
The grade 4 pupils of Maybunga Elementary School made 2 568 greeting cards for their parents while the grade 3 pupils made 1 756 cards. About how many greeting cards did the grade 4 pupils make than grade 3?
a. Who made greeting cards? b. Why did they make the cards? c. Who among them made more cards? Valuing:
• To whom will they give the cards? • Do you also give cards to your parents? When? Why?
Activity 1 a. What is asked in the problem? b. What are the given facts? c. What operation is to be used? d. What is the number sentence?
To estimate the difference, round off the minuend and subtrahend to the highest place value then subtract. 2 568 3 000 2 568  1 756  2 000  1 756 1 000 812  estimated difference  actual difference
56
Activity 2 Estimate to the highest place value then find the difference. a) 54 798 b) 95 895 c) 349 258
 42 991 72 521  121 123
d) 4 912 e) 6 861 f) 5 762 g) 25 376  3 165  4 136  3 223 14 213
h) 265 i) 4 632 j) 5 134 k) 72 571  142  1 482 1 675  61 933
2. Generali zation
How do you estimate the difference of two numbers with four to six digits?
C. App lication
1. Round each minuend and subtrahend to the nearest a) tens b) hundreds c) thousands and d)
ten thousands then find its estimated difference. 78 528 78 530 43 187 43 190
2. Estimate the difference to its highest possible place value. a) 6 348 b) 8 888 c) 13 429 d) 52 634 e) 73 287  3 344  2 929 12 363 19 584  48 896
IV. Evaluation
A. Estimate the difference by rounding to the nearest ten thousands. 1) 85 946 2) 34 879 3) 59 679  52 346  16 843  37 051
B. Write the reasonable estimate for each problem.
1) 595.75 2) 863.05 3) 785.40  243.85  592.95  126.30
C. Round number to the nearest a) tens b) hundreds c) thousands and d) ten thousands and find the
difference. 67 595
 49 172 V. Assignment
1. Ask the actual income of the family. Estimate the difference of their monthly expenses from their actual income.
2. Estimate the difference by rounding to the nearest a) tens b) hundreds c) thousands d) ten thousands.
194 385 168 651
57
3. Estimate the difference by rounding to the highest possible place value. 5 672 67 935 84 764  5 219  61 398  84 159
Subtracting Mentally Numbers wi thout Regrouping I. Learning Objectives
Cognitive: Subtract mentally numbers with minuends up to 300 without regrouping Psyc homotor: Give the correct answer mentally and orally Affective: Show the value of helpfulness when given a task
II. Learning Content
Skill : Subtracting mentally with minuends up to 300 without regrouping References: BECPELC I.C.2
textbooks in Math 4 Materials: flash cards, chart, window card, pocket chart Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Basic subtraction facts. Each pupil takes turns in answering the basic subtraction facts written on each strip of manila paper. Check the answers in the class.
2. Review
This may be done in form of a game. Let a pupil pick one petal of the flowers (one at a time) and have him/her answer the equation.
10  2
10  9
10  9
12  8
16  7
15  6
10  7
47 16
87 64
45 20
53 32 37
26
83 23
67 33
75 21
66 12 99
11
78 24
99 83
58
3. Motivation
During weekends, what do you do to help your parents earn extra income? • Guide the pupils to see the value of helpfulness.
B. Developmental Activities
1. Presentation o f Lesson
During weekends, Leah helps her mother sell mangoes in the market. One
morning, she had 275 mangoes. At the end of the day, she had 55 mangoes left. How many mangoes were sold?
2. Discussion
a. How many mangoes did Leah have in the morning? b. How many mangoes did she have at the end of the day? c. How many mangoes were sold? c. What will you do to get the answer? d. What is the fastest way of solving for the final answers?
3. Fixing Skill s/Practice
a. Relay Game
Mechanics: Group the pupils into 5. Let them form a line outside or inside the room. Teacher
writes all the exercises in a rolled paper and pastes it on the board. When the teacher says “go”, pupils take turns in going to the board. The first group who correctly answers the questions wins.
Group 1 Group 2 Group 3 Group 4 Group 5
1) 276 2) 239 3) 179 4) 264 5) 148  132  135  146  153  46
b. Supply the missing numbers orally.
1) _____ 2) _____ 3) _____ 4) 171 5) 247
 102  132 275  _____  _____ 104 141 33 210 102
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c. Find the missing number to complete the puzzle.
1) 2)
274 ____ 142
____ 21 ____
131 ____ 20
____ 248 44
143 112 ____
149 ____ 13 4. Generali zation
How can you subtract mentally? Give the steps.
C. App lication
1. Subtract mentally. a. 284 – 174 = n b. 300 – 130 = n c. 182 – 130 = n d. 488 – 242 = n e. 575 – 273 = n
2. Subtract mentally the following numbers.
a) 299 b) 299 c) 266 d) 278 e) 265 183 153 155 178 152
IV. Evaluation
Give the difference orally.
1) 300 2) 239 3) 270 4) 290 5) 239  200 105 120 190 133 6) 284 7) 281 8) 248 9) 205 10) 211
 221 141  137  204 101 V. Assignment
Subtract mentally. 1) 712 2) 838 3) 174 4) 174 5) 294  249  712  100  74  258 6) 120 7) 150 8) 150 9) 249 10) 678  110  140  147  123  423
Analyzing Word Prob lems involving Subtraction
I. Learning Objectives
Cognitive: Analyze word problems involving subtraction Psyc homotor: Write the correct answers to the questions Affective: Help one another during class activities
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II. Learning Content
Skill : Analyzing word problems References: BECPELC I.C.3.1.13.1.4
textbooks in Math 4 Materials: word problems on chart Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Basic facts on subtraction Example:
2. Review
Do black board exercises.
85 38 67 987 574  43 12 35  452  242
3. Motivation
What can you say about the prizes of commodities nowadays? How can you help your
parents in making both ends meet? Ana, a Grade 4 pupil, helps her mother in their fruit stand. One Saturday, they sold 1 950
green and yellow mangoes. If they sold 957 green mangoes, how many yellow mangoes did they sell?
B. Developmental Activities
1. Presentation
What is asked in the problem? What are the given facts? What is the word clue? What operation will you use? Illustrate the problem.

Valuing: � How did Ana help her mother? What kind of daughter is Ana? Who among you helps in
the family? Aside from selling mangoes, what else can you do to help your parents?
8  1 9  2 7  3 9  5 8  3
1 950 957
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2. Group Work Activity Group the pupils into 4. Let each group get one problem in the box and answer the
questions below each problem. a. Mang Pedro exports native bags. He produced 2 780 bags in 2001 and 4 093 bags in
2002. How many more bags did his family produced in 2002 than in 2001?  What is asked for in the problem?  What are the given facts?  What are the word clues?  What is the operation to be used in solving the problem?
b. A municipality has a population of 14 276. After 2 years, it became 14 858. How many people were added to the previous population?
 What is asked for in the problem?  What are the given facts?  What are the word clues?  What is the operation to be used in solving the problem?
c. Philip bought 4 629 kilograms of garlic and sold 2 348 kilograms. How many kilograms of garlic were left?
 What is asked for in the problem?  What are the given facts?  What are the word clues?  What is the operation to be used in solving the problem?
d. There were 1 415 children vaccinated at the health center. Six hundred ninetyfive were boys. How many were girls?
 What is asked for in the problem?  What are the given facts?  What are the word clues?  What is the operation to be used in solving the problem?
3. Generali zation
How do we analyze word problems?
In analyzing word problems, follow these guide questions:  What is asked for in the problem?  What are the given facts?  What are the word clues?  What is the operation to be used in solving the problem?
C. App lication
Read the problem carefully and answer the questions that follow.
During the mango season, Mr. Andres Marquez sold 32 192 pieces of ripe mangoes. He also sold 16 514 pieces of green mangoes. How many more ripe mangoes did Mr. Marquez sell than green mangoes? a. What is asked in the problem? b. What are the given facts? c. What is/are the word clue/s? d. Write the mathematical sentence for the problem e. What is the correct answer?
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IV. Evaluation Read each problem carefully. Identify the given facts and operation to be used to solve each problem. 1. Luis sold empty bottles on Saturday and received 18.50. He bought half a kilo of rice for
10.50. How much money was left? 2. Mang Tomas caught 165 kilos of fish in the morning and 178 kilos of fish in the afternoon. How
many more kilos of fish did he catch in the afternoon than in the morning? 3. Rafael Palma Elementary School has 3 573 pupils last year. This year, it has 4 745, how many
pupils were added this year? 4. Arturo has 1 879 rubber bands. He lost 728 in the game. How many rubber bands were left with
him? 5. There were 6 278 people at the Rizal Memorial Stadium in the morning and 4 561 people in the
afternoon who watch the ball game. How many more people came in the morning than in the afternoon?
V. Assignment
Read and analyze the problems. 1. Bong’s round trip plane ticket from Manila to Zamboanga costs 6,860.00. His other trip to
Davao costs 6,930.00. How much more did he spend in his travel to Zamboanga than in Davao?
2. Ric traveled to Baguio and bought woodcarvings worth 2,345.00. He also bought bottled sweets and fresh vegetables costing 598.00. How much more did he spend in woodcarvings than in sweets or fresh vegetables? Complete the statements: a. The problem asks_____ b. The given facts are_____ c. The number sentence is _____
d. The word clue is _____ e. The answer is _____
Solving Mentally 1Step Word Prob lems involving Subtraction wi thout Regrouping I. Learning Objectives
Cognitive: Solve mentally 1step word problems involving subtraction without regrouping Psyc homotor: Solve problems mentally Affective: Show appreciation for God’s creation
II. Learning Content
Skill : Solving mentally 1step word problems involving subtraction without regrouping References: BECPELC I.C.3.2
textbooks in Math 4 Materials: flash cards, picture, chart, activity sheets, paper, crayons Value: Appreciation of God’s creation
III. Learning Experiences
A. Preparatory Activities
1. Drill
Mental Computation Let the pupils solve for the difference mentally as fast and as correct as they can in their math notebook.
96 85 874 305 4 248  54  61  523  202 2 125
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2. Review
Answer orally. Jose sold 120 sampaguita garlands. Rosa sold 135 sampaguita garlands. How many
more sampaguita garlands did Rosa sell than Jose?
3. Motivation
Show pictures of trees, skies, land, fish, people, etc. Valuing: � Who created these things? Can we be like God? Why or why not?
B. Developmental Activities
1. Presentation
Marc has 78 fishes in his aquarium. His mother transferred 25 fishes into another
aquarium. How many fishes were left?
2. Discussion Guide the pupils in the discussion of the problem by answering the following questions. a. What is asked in the problem? b. What are given? c. What operation is needed to solve the problem? d. What is the fastest way of solving for the final answer? e. What is the final answer?
Group the pupils by pairs. Distribute activity sheets to each pair. Their task is to help
each other solve the problems carefully. a. Edgar helps his father in the farm. There were 150 coffee seedlings. If 90 seedlings have
been planted, how many more does he need to plant? b. Aling Norma has 12 children. Ten of her children went to America. How many children
still lives with Aling Norma? c. If Carlo accidentally broke 12 of his 24 crayons, how many crayons were not broken? d. Loren has 15 guavas. She gave 12 guavas to her sister. How many has she left? e. Mother baked 28 cookies. Lita ate 12 of the cookies. How many cookies were left?
3. Generali zation
How do we solve problems involving subtraction mentally? What are the rules to
remember in solving problems mentally?
In solving word problems involving subtraction mentally, follow the following steps: understand, think, plan, solve and look back to check your answer then subtract without using pencil and paper.
C. App lication
Solve mentally. Write the answers on your paper. 1. Danny planted 54 upo seedlings. Ernie planted 65 ampalaya seedlings. Who planted more?
How many more? 2. Nancy planted 39 patani seeds. If 13 of them did not grow, how many seeds grew?
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IV. Evaluation
Solve the problems mentally. 1. Nilo bought 15 candies. On his way home, he ate 5 of the candies. How many candies did he
bring home? 2. Mother gave Niko 14.75 for his allowance. He spent 12.50 for a pad paper and a pencil.
How much money was left for Niko? 3. Jose and Rose sell sampaguita garlands. Yesterday, Jose sold 110 garlands while Rose sold 235
garlands. How many more sampaguita garlands did Rose sell than Niko? 4. Jose’s Earnings
Monday – 110.00 Wednesday – 120.00 Friday – 154.00 Sunday – 264.00
Answer the following questions below: On which day did Jose earn more – Monday or Wednesday, by how much? How much more did he earn on Sunday than Friday? How much more did he earn on Friday than Wednesday?
V. Assignment
Create your own story problem involving subtraction. You may exchange problems with your partners then try to solve it accurately. Discuss solutions in class.
Word Prob lems involving Subtraction I. Learning Objectives
Cognitive: Solve word problems involving subtraction of numbers including money, with and without regrouping
Psyc homotor: Write the number sentence for a given story problem Affective: Practice wise decisionmaking
II. Learning Content
Skill s: 1. Writing number sentences for story problems 2. Solving word problems involving subtraction of whole numbers including money with and without regrouping
References: BECPELC I.C.3.1 textbooks in Math 4
Materials: flash cards, chart on problem solving Value: Intelligent decision in voting
III. Learning Experiences
A. Preparatory Activities 1. Drill
Have a short drill on selected subtraction facts.
35 18 16 31 34  5  7  8  9  6
65
2. Review
Find the difference. 7 367 6 380 7 125 2 375 9 245  2 314  2 629  5 443  1 142  6 730
3. Motivation
Purok Masagana has 7 206 registered voters. If 3 271 are male voters, how many are female voters?
How many registered voters are there?
How many male voters are there? How many are female?
Valuing: � If you are to vote in an election, how are you going to select a good leader? Why?
B. Developmental Activities
1. Presentation
a. What is asked in the problem? b. What is/are given in the problem? c. What operation will you use? Is there a clue word? d. What is the number sentence for the problem? e. How is the solution done?
2. Group Activity
Group the pupils into 4 groups. Have each group solve the problems then present their work to the class. Group 1
1) The pineapple planters of Laguna gathered 4 276 pineapples last month. This month, they harvested 6 278 pineapples. How many more pineapples did they harvest this month than last month?
2) Mrs. Posadas wants to buy a washing machine worth 5,785.00. She has 2,356.00 cash on hand. How much more money does she need in order to buy
the washing machine? Group 2
1) A fish dealer sold 232 152 kg of assorted fish in one week. If 156 218 kg were sold in 4 days, how many kg of fish were sold in 3 days?
2) Mr. Perez bought a car that costs 356 826.00. After five years, she decided to sell the old car for 186 738.00. How much is the cost difference?
Group 3
1) A farmer harvested a total of 10 404 watermelons last year. This year, he was able to harvest 22 098 watermelons. What is the difference between the watermelons harvested this year and last year?
2) A big library has 38 459 books in the shelves. There are 7 079 Science books. How many books are not Science books?
Group 4 1) There were 450 computers St. Mary’s school. After the school year, it was discovered
that 86 were not functioning. How many computers were in good condition? 2) Aling Precy sold fruit at a public market. She had 2 056 mangoes. At the end of the
day, she had only 94 left. How many mangoes were sold on that day?
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Provide provisions for word clues leading to the solutions of the word problems, specifically for the slow groups.
3. Generali zation
What are the steps to follow in problem solving? What clues are needed to solve word problems involving subtraction?
C. App lication
Solve the following word problems.
1. In a week, Mang Carlos earned 4,265.00 for catching fish. He gave 1,500.00 to his wife and deposited the rest in the bank. How much did he deposit in the bank?
2. Mrs. Malvar and her eldest daughter watched the songfest. There were 10 206 who watched the said competition. If 6 259 were females, how many were males?
3. Mariano’s cottage industry exported a total of 250 756 native slippers and bags. Of these products, 75 903 were native bags, how many bags were exported?
4. Mr. Cortez has 527,968.00 in a savings bank. He withdrew 35,500.00 for his children’s school expenses. How much money is left in the bank?
IV. Evaluation
Read and solve the following word problems.
A. 1. Virgie collected 1 280 local and international stamps. If the local stamps are 452, how many
are international? 2. The school property custodian distributed 4 758 English and Math books for grade IV pupils.
If 2 307 are English books, how many are Math books? B.
1. Emmy bought 60 sacks of corn that costs 15,940.00. If she had 32,075.00 in her wallet, how much more was left?
2. During the local election for Mayor, Atty. Roxas received 32 078 votes while Mr. Reyes received 21 926 votes. How many more votes did Atty. Roxas receive than Mr. Reyes?
C. 1. A garment factory earned 858,928.00. The workers were paid 28,968.00. How much
was left for the factory’s other expenses? 2. Mr. Gomez plans to buy a car for 55,726.00. He already have 48,905.00. How much
more does he need to be able to buy the car?
V. Assignment
Read and solve the following word problems. 1. To sustain and maintain the Clean and Green Project, the city hired 315 new workers. If they
need 1 210 new workers, how many more should be hired? 2. The Junior Red Cross members of Bagong Silang Elementary School collected old newspapers
and bottles. They sold the old newspapers for 1,090.00 and the bottles for 2,115.00. How much more did the Junior Red Cross earn from selling bottles than newspapers?
3. The Bantayog Ladies Circle invited several women to participate in the beautification project. The women were able to raise 100,000.00 for the improvement of the town park. They spent
46,000.00 for making a flower garden and the rest they spent for playground apparatus. How much was spent for the playground apparatus?
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4. Parañaque City had a Clean and Green Project. All the barangays planted a total of 32 500 seedlings of fruit trees. The school children planted about 25 000 ornamental plants in their homes and schoolyards. How many more were fruit trees than ornamental plants?
5. The food committee ordered 15 000 doughnuts. Only 13 269 were sold. How many doughnuts were left?
Analyzing Word Prob lems involving Add ition and Subtraction including Money I. Learning Objectives
Cognitive: Analyze word problems involving addition and subtraction including money Psyc homotor: Solve problems involving addition and subtraction including money Affective: Appreciate the value of hardwork
II. Learning Content
Skill s: 1. Analyzing word problems 2. Telling what is asked, what are given, the word clues, the hidden question
and the operation to be used 3. Transforming the word problem into a number sentence 4. Using the correct operation 5. Solving for the final answer with the necessary label References: BECPELC I.C.4.1.1 – 4.1.4
textbooks in Math 4 Materials: charts, strips of cartolina, manila paper, markers Value: Value of hardwork
III. Learning Experiences
A. Preparatory Activities 1. Drill
Do merrygoround. Divide the class into groups of 5. Each pupil takes turn in solving for
the sum/difference mentally to be written in an activity sheet. Check answers in class. 25 37 74 65 46 98 64 37 +86 +43 +28 +13 33 75 49 18
2. Review
Tell something about the following:
a. 26 mangoes, 30 bananas b. 26 + 30 = n c. 56 fruits d. number of fruits e. addition
3. Motivation
Rica’s father earns 2,500.00 a week. Her mother earns 1,800.00. They set aside 3,500.00 for their weekly expenses. How much money was left for their savings?
What do you know about the word earnings, savings and expenses? Valuing: • Why do people work? Do you spend all your earnings? • Why do you have to save?
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B. Developmental Activities 1. Presentation
Guide the students in analyzing and solving the problem in class. Refer to the questions below. a. What is asked in the problem?
The total savings for the week. b. What are given?
2,500.00 1,800.00 3,500.00 c. What is the hidden question?
How much do they earn altogether? d. What words were used to help solve the problem?
Money left as savings e. What operations will you use?
Addition and subtraction f. What is the number sentence?
(2 500 + 1 800) – 3 500 = n g. What is the answer?
800.00 in a week Give more problems to be discussed in class.
Adrian bought a bag for 500.00 and a raincoat for 250.00. Maria bought an umbrella for 230.00. How much more did Adrian spend than Maria?
2. Group Activity
Divide the class into groups of 3s. Distribute a sheet with problems on it. The task of each
student is to help each other solve the problems. Assign a representative/leader to report and discuss solutions made by their group in class.
a. Mr. Nicolas bought a house for 350,000.00. He spent 120,000.00 for its repair.
Then, he sold the house for 670,000.00. How much did he gain? b. In November, Mrs. Rizon spent 8,200.00 for household expenses and 1,750.00 for
her children’s allowance. In October, she spent 8,550.00 for the same expenses. How much more does she spend in November than in October?
c. On the first day, there were 1 415 children vaccinated at the Health Center and 1 054 on the second day. Of these, 1 459 were boys. How many were girls?
3. Practice Exercises
Solve the following problems using the steps in problem solving. a. Some pupils donated seedlings for their plantatree project. The girls donated 2 518
seedlings while the boys donated 1 736 seedlings. Of these seedlings, 1 385 withered. How many plants did not wither?
b. Jay watched two movies and paid 60.00 each as admission fee. Then, he ate at a restaurant and paid 120.00 for a pizza and a glass of juice. If he spent 10.00 for transportation, how much money was left if he had 400.00 at the start?
4. Generali zation
How do we solve word problems? What are the steps involved?
69
C. App lication Read each problem and solve on your paper. 1. In a town’s fundraising drive, several organizations raised the following amounts. Knights of
Rizal, 18,176.00; Daughters of Isabela 12,735.00 and the Women’s Club 10,487.00. How much did they raise altogether?
2. In 1990, the number of overseas workers in the country was 417 301. It went up to 782 297 in 1995. What was the increase in the number of overseas workers from 1990 to 1995?
IV. Evaluation
Solve the problems by following the steps in problem solving. 1. Precy went shopping. She wants to buy a pair of pants which cost 395.75 and a blouse which
costs 250.00. How much would be her change if she gave the cashier 1,000.00? 2. The school auditorium can hold 5 000 people. Of the school population, 3 246 boys and 1 362
girls went to see the basketball game. How many more students can the auditorium accommodate?
V. Assignment
Write your analysis of these problems by answering the seven questions. 1. Mrs. Reyes collected 8 345 seashells from Luzon, Visayas and Mindanao. She collected 3 420
from Luzon and 3 058 from Mindanao. How many seashells did Mrs. Reyes collect from the Visayas?
2. You have 200.00. How much change would you receive if you paid for all the items below. Ballpens and pencils 48.35 Notebooks 75.75 Crayons 24.20 Pad paper 20.00 Art papers 31.00
Solving 2Step Word Problems involving Add ition and Subtraction including Money I. Learning Objectives
Cognitive: Solve 2step word problems involving addition and subtraction including money Psyc homotor: Solve problems accurately Affective: Show love for books
II. Learning Content
Skill : Solving 2step word problems involving addition and subtraction including money References: BECPELC I.C.4.1
textbooks in Math 4 Materials: flash cards, charts Value: Love for books
70
III. Learning Experiences
A. Preparatory Activities
1. Drill Use flash cards for the basic addition and subtraction facts.
3 9 5 6 9 4 8 + 8 + 2 + 7 + 4 + 8 + 7 + 8 12 11 6 15 18 17  5  8  2  7  8  9
2. Review
Find the sum. Write the answers in your math notebooks.
238 277 364 811 675 + 215 + 124 + 125 + 278 + 324 128 248 899 278 367  114  231  176  72  56
3. Motivation
Have you gone to the library? What do you see in the library?
B. Developmental Activities 1. Presentation
Glenda and Girlie love to read books. They always go to the library to read books.
Glenda has read 238 books and Girlie read another 215 books. If their library has 10 000 books, how many books do they still need to read?
Let 2 or 3 pupils show the solution on the board. Discuss the solutions on the board.
10 000 – (238 + 215) = n 10 000 – 435 = n n = 9 547 books
Valuing: • What kind of girls are Glenda and Girlie? • Do you also enjoy reading books? • What kind of books do you love to read? • Is reading books a good hobby? Why?
2. Group Activity
a. Activity 1
Divide the class into groups/columns. Let the pupils help each other solve the
problem. Solve for the answer. Show the solution. 1) Aling Naty picked 25 tomatoes from her vegetable garden on Monday and 43
tomatoes on Tuesday. She used 12 of these for cooking. How many tomatoes were left?
71
2) Nita needs 100.00 for her project. Father gave her 25.00 and mother gave her 55.00. How much more does she need?
3) Janice collected 300 shells and Riza collected 250 shells on the beach. On their way home, they lost 120 shells. How many shells were they able to bring home?
b. Activity 2
Divide the pupils into 3 groups. The first group to give the correct answer will get the
points. 1) For the month of January, a department store received 4 838 denim pants and 3 746
slacks. If 6 220 pants were sold, how many were left? 2) Mother baked 365 cookies in the morning and 273 cookies in the afternoon. She sold
526 cookies to her neighbors. How many cookies were left? 3) Lani deposited 1,350.00 in November and 3,175.00 in December. She
withdrew 2,000.00 in January. How much money is left in the bank?
3. Generali zation What do we have to do before we can solve a problem?
Follow the steps in analyzing and solving a problem. a. Think b. Plan
c. Solve d. Look back
C. App lication
Group the pupils. The leader of each group will pick a problem using the “Wheel of Fortune”.
They will be given 2 minutes to solve the problem. If the answer is correct, they will be given points. 1. Mr. and Mrs. Ignacio planned to buy a house and lot worth 31,486,875.00 and a car worth
1,755,930.00. If they have 25,950,395.00, how much more money do they have to raise to be able to buy the house and lot and the car?
2. In 1998, the population of barangay San Antonio was 5 786. In 1999, there were 1 296 newborns and 325 deaths. What is the population of barangay San Antonio in 1999?
3. Portland Industries earned 17,836,109.00 in the year 2001 and 21,350,865.00 in 2002. Because of fire, they spent 16,650,370.00 to rebuild their factory. How much of their earnings were left?
IV. Evaluation
Solve the following problems. 1. Lino sold empty bottles on Saturday and received 18.50. On Sunday, he received 21.50.
He spent 15.00 for food. How much money was left? 2. Rafael earned 45.00 for washing cars and 55.00 for running errands. He bought a box of
crayon for 24.00. How much money was left? 3. Mandy caught 148 fishes in the morning and 216 in the afternoon. He gave 56 of these to her
mother for dinner. How many fishes were left to be sold in the market? 4. Mrs. Cruz bought canned goods worth 375.00 and garments worth 950.00. She gave the
cashier 1,500.00. How much change did she get? 5. Bonifacio Elementary School had 3 568 Grade 1 pupils in 2001 and 3 756 in Grade 2. If the
enrolment is 17 324, how many pupils are in Grade 1?
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6. Mr. Del Rosario’s monthly income is 20,150.00 while his wife’s monthly income is 16,720.00. If their monthly expenses are 26,450.00, how much is their monthly savings?
V. Assignment
Solve the problem. Show your solution. 1. A mineral water company bottled 15 476 bottles of mineral water for the month of June and 21
658 for the month of July. They were able to sell 33 274 bottles of mineral water. How many bottles were unsold?
2. A soft drink factory was able to manufacture 48 357 bottles for January and 55 219 for February. The factory was able to sell 84 379 bottles. How many were not sold?
Multiplying o f 5 or More Digit Factors by 3digit Factors wi thout and with Regrouping I. Learning Objectives
Cognitive: Multiply 5 or more digit factors without and with regrouping Psyc homotor: Illustrate multiplying by 5 or more digit factors using partial product method Affective: Appreciate the importance of trees
II. Learning Content
Skill : Multiplying of 5 or more digit factors by 3digit factors with and without regrouping
References: BECPELC I.D.1.1 textbooks in Math 4
Materials: drill cards, picture, manila paper, markers Value: Conservation of trees
III. Learning Experiences
A. Preparatory Activities
1. Drill Basic multiplication facts using drill cards
2. Review
Let the pupils solve for the product mentally as fast and correct as they can.
12 23 17 13 42 x 5 x 3 x 4 x 7 x 8
3. Motivation
Show a picture of a mango orchard. Elicit from the children the answer to the following
questions: • What can you see in the picture?
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• Do you have fruit trees in your farm/backyard? • Is it good to plant trees? Why?
B. Developmental Activities
1. Presentation
Mang Ambo and his coworkers can deliver 12 234 coconuts in a day. How
many coconuts can they deliver in 123 days?
Analyze the problem. a. How many mangoes did Mang Ambo and his coworkers gather in one day? b. What is asked in the problem? c. How can we solve the problem? d. Show the solution by using the sum of partial products.
12 234 12 234 12 234 12 234 x 123 x 123 x 123 x 123 36 702 36702 36702 36702 24468 24468 24468 12234 + 12234 1504782
Step 1 Step 2 Step 3 Step 4 Multiply 12 234 by 3
Multiply 12 234 by 2
Multiply 12 234 by 1
Add the partial products
More Practice
Show the solution.
a. 14 213 b. 16 821 c. 23 568 x 132 x 424 x 238
Study the multiplication algorithm.
625 543 x 352
1251086 3127715 + 1876629__
220191136
Let the children have more practice. a) 68 214 b) 52 183 c) 821 145 d) 21 963 e) 72 584 x 327 x 172 x 634 x 453 x 921
2. Group Activity
Each group will be given activity sheets/cards containing 3 items. Each group that finishes the work will display them on the board. The group with the most number of correct answers will be given a prize.
65 218 21 465 392 146 24 693 24 986 x 456 x 382 x 781 x 423 x 142
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421 826 95 218 76 542 621 483 x 321 x 523 x 352 x 218
3. Generali zation
How do we multiply 5 or more digit factors by 3digit factors without and with regrouping?
We multiply 5 or more digit factors by 3digit factors without and with regrouping by multiplying all the digits in the multiplier by the ones digit of the multiplicand to get the first partial product. Then by the tens digit to get the second partial product and the hundreds digit to get the third partial product. Then add the partial products to get the final product.
C. App lication
Mr. Mendoza can gather 12 350 eggs in a week from his poultry farm. How many eggs can
he gather in 12 weeks?
IV. Evaluation
Solve for the products. 1) 32 512 2) 29 786 3) 69 214 4) 35 683 5) 21 463
x 312 x 521 x 382 x 748 x 121
6) If the factors are 32 416 and 145, what is the product? 7) A number times 6 equals 2 712. What is the number?
V. Assignment
Give the products. 1) 85 354 2) 82 806 3) 49 236 4) 421 832 5) 678 322 x 978 x 814 x 314 x 175 x 387
6) What is the product of 2 876 and 489? 7) What is 27 654 added to the product of 32 145 and 237?
Multiplying 5 or More Digit Factors by 4 to 5Digit Factors wi thout and with Regrouping I. Learning Objectives
Cognitive: Find the product of 5 or more digit factors by 4 to 5digit factors without and with
regrouping Psyc homotor: Multiply 5 or more digit factors by 4to5 digit factors with and without regrouping Affective: Show nationalism by patronizing Philippine products.
II. Learning Content
Skill : Multiply 5 or more digit factors by 4 to 5digit factors with and without regrouping
References: BECPELC I.D.1.2 Materials: pictures, strips of cartolina, chart, illustrations Value: Patronizing Philippine products
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III. Learning Experiences
A. Preparatory Activities
1. Drill (Mental Computation)
33 92 80 91 81 64 x 3 x 4 x 6 x 5 x 7 x 3
2. Review
Solve for the answer.
69 432 32 184 98 521 x 413 x 215 x 762
(This is in the form of a contest. The first one to give the correct answer will receive a reward.)
3. Motivation
Show the pictures of different Philippine fruits. What is your favorite fruit? Why? Point out
to the children that Philippine fruits are comparable if not better than foreign fruits. In buying Philippine fruits, we can help our economy. Valuing: • What character trait do we show if we buy our own products?
B. Developmental Activities
1. Presentation
a. Present the problem
The Bureau of Plant Industry needs chico seedlings for tree planting
throughout the country. If 1 538 schools will participate giving 15 120 seeds each, how many seeds can be collected by the Bureau?
b. Analyze the problem
How many schools will participate in giving chico seeds to the bureau? How many
seeds will each school give to the bureau? What will you do to solve the problem? Show the solution on the board using the algorithm method.
1) 15 120 15 120 15 120 15 120 x 1 538 x 1 538 x 1 538 x 1 538
120960 120960 120960 120960 45360 45360 45360 75600 + 75600 15120 23254560
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c. Introduce another way of multiplying using the Lattice Multiplication.
Answer: 23,254,560
How to do the Latt ice Multipli cation
Each square is divided diagonally. The multiplicand is written on top and the multiplier on the right sides outside the box.
Every entry in a square is the product of a digit in one factor and a digit of the other factor. The entry maybe a onedigit product or a 2digit product. In case of a 2digit product, the digit in the upper half of the square is to be regrouped to the next higher place value. The entries in each row are the partial products of one factor. Adding the numbers in the diagonals is the same as adding the partial products column by column. Example:
To multiply: 345 x 162
Solution: 345 x 162 = 55 890
2. Practice Exercise
a. Group Activity
Each group will perform the exercise. It will be done using cooperative learning and using the Lattice multiplication.
23 564 x 2 135
0 1
0 5
0 1
0 2
0 0
0
5
2 5
0 5
1 0
0 0
0
3
1 5
0 3
0 6
0 0
0
8
4 0
0 8
1 6
0 0
5
1 5 1 2 0
3
1
X
5
8
3
2
2
0 4 5 6
0 3
0 4
0 5
1
8
2 4
3 0
0
6
0 8
1 0
8
5 4 3
2
1
X
6 5
0
5
9 0
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b. Individual Exercise Find the product. 64 325 21 832 36 842 14 683 56 943 x 256 x 464 x 218 x 123 x 416
3. Generali zation
How do we multiply 5 or more digit factors by 4 to 5digit factors with and without regrouping?
C. App lication
The marble factory can produce 55 683 marbles a day. How many marbles can be produced in 2 365 days?
IV. Evaluation
1. Solve using the algorithm method. 42 183 331 247 294 375 329 457 x 1 358 x 7 265 x 2 153 x 11 263
2. Solve using the lattice multiplication method. 34 928 163 432 273 516 375 168
x 1 673 x 2 514 x 3 425 x 21 341
3. Solve using the algorithm and lattice method. 46 935 216 395 325 176 173 212 x 1 564 x 1 632 x 3 482 x 45 326
V. Assignment
A. Solve the following using the two methods.
46 935 x 2 564
B. Solve the following.
1. If the factors are 35 and 476, what is the product? 2. Add 2 754 to the product of 134 and 52 gives a result of n. What is n? 3. What is 1 876 subtracted from the product of 74 and 36?
Multiplying Numbers having Zeros in both Factors wi thout Regrouping I. Learning Objectives
Cognitive: Multiply 5 or more digit factors having 1 to 3 zeros in both factors without
regrouping Psyc homotor: Find the product using the process of long multiplication with ease Affective: Show carefulness in doing other activities
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II. Learning Content
Skill : Multiplying 5 or more digit factors having 1 to 3 zeros in both factors without regrouping
References: BECPELC I.D.1.3 textbooks in Math 4
Materials: M1 window cards Value: Carefulness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Drill on basic multiplication facts using window cards. Give the exact time (number of minutes) to finish the drill card.
2. Mental Computation
Answer the following in your notebook.
213 842 524 400 523 x 3 x 2 x 3 x 7 x 10
3. Review
Show how to solve for the product using the long method on the board. Elicit the steps,
be sure that the pupils follow correctly and carefully the steps in multiplying using the long method. Valuing: • Are you also careful in doing other things aside from our activities in Math? How?
Find the product.
65 432 x 765
What did you do to get the correct product?
4. Motivation
Sing the song (tune: Are you sleeping).
Mathematics! Mathematics! How it thrills, how it thrills Addition, Subtraction Multiplication, Division Mental Math! Mental Math! (Repeat)
B. Developmental Activities
1. Presentation
The Zoom Rice Milling Company delivered 30 trucks of rice in Metro Manila. If each truck contains 400 sacks, how many sacks did the company deliver in all?
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a. Analyze the problem • How many trucks of rice did the company deliver? • How many sacks are in each truck? • What is asked? • What is the operation to be used? • Show the solution
b. Write on the board.
400 x 30
12 000 sacks of rice
c. Written exercises 10 411 20 011 20 500 80 003 x 200 x 60 x 101 x 300 40 004 95 000 70 100
x 2 000 x 100 x 300
How did you come up with the answers? Is there a faster way to solve for the product? Elicit the patterns.
2. Group activity Divide the class into two groups.
Give them activity sheets where the exercises are written. Each group will report their
answers. 60 002 30 052 21 220 23 001 x 300 x 1001 x 40 x 200 11 000 21 200 30 022 x 500 x 400 x 30
Dyad Pair the children. Each pair will work on these exercises.
32 000 10 052 50 012 52 003 3 002 x 300 x 201 x 400 x 100 x 303
3. Generali zation
How do we multiply 5 or more digit factors having 1 to 3 zeros in both factors without
regrouping?
Any number multiplied by zero equals zero. If the zeros in both factors are found in the end, multiply the given numbers then count the number of zeros found at the end of the factors and write them in the answer.
C. App lication
There are 12 300 members of Barangay Masikap. If each member contributed 30 packs of
noodles for the Lutong Bayan Project, how many pack of noodles were collected?
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IV. Evaluation A. Find the product.
44 000 60 021 32 011 34 000 x 20 x 200 x 101 x 403 43 002 2 340 x 300 x 20
B. Answer the following:
1. Multiply 7 400 and 200, what is the product? 2. What is 23 100 repeated 40 times? 3. If the factors are 4 500 and 90, what is the product? 4. What is 61 002 multiplied to 400?
V. Assignment
Find the product.
a. 30 002 b. 42 102 c. 21 004 d. 60 002 e. 32 102 x 300 x 40 x 100 x 50 x 400 Multiplying Numbers having Zeros in both Factors wi th Regrouping I. Learning Objectives
Cognitive: Find the product of 5 or more digit factors having 1 to 3 zeros in both factors with regrouping
Psyc homotor: Multiply 5 or more digit factors having 1 to 3 zeros in both factors with regrouping in all places
Affective: Show cooperation during class activities
II. Learning Content
Skill : Multiplying 5 or more digit factors having 1 to 3 zeros in both factors with regrouping in all places
References: BECPELC I.D.1.4 textbooks in Math 4 Materials: window cards Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill a. Basic multiplication facts using window drill cards
(Record each pupil’s time.)
b. Mental Math 2 004 30 100 80 020 7 001 70 200 600 x 2 x 4 x 3 x 5 x 50 x 20 x 400
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2. Review Find the product.
80 100 93 002 72 000 80 100 61 003 x 50 x 30 x 40 x 50 x 30
3. Motivation
Game: Roll the Dice
A player rolls the dice. The player will multiply the two numbers that appeared on the
dice. Each number corresponds to an exercise like the following: 61 001 81 012 61 001 70 200 31 100 x 400 x 60 x 200 x 40 x 60
B. Developmental Activities
1. Presentation
A shoe factory pays each laborer 31,200.00 annually. How much does the owner pay for its 50 laborers?
a. Analyze the problem. • How many laborers are there in the shoe factory? • What is the salary per year of each laborer? • What is asked in the problem? • What is the operation to be used? • How will the problem be solved?
b. Show the solution of the problem.
31,200.00 x 50
1,560,000.00
2. Group Activities
Cooperative Exercise Complete the table.
x 40 50 60 70 80
86 000 4 300 000 90 042 7 203 360 809 051 56 633 570 700 800
Divide the class into three groups. Give each group an activity card/sheet. Each member
in the group will help each other answer the following exercises shown below.
64 000 70 800 80 700 90 050 80 007 x 30 x 40 x 150 x 203 x 701
460 010 391 021 3 620 400 1 210 055 x 50 x 100 x 720 x 302
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How did you find the exercise? Does the work make easier if members work cooperatively? Why?
3. Generali zation
How do we multiply 5 or more digit factors having 1 to 3 zeros in both factors with
regrouping in all places? Remember:
1. Use the same steps in multiplying. 2. Regroup whenever necessary. 3. Write zero in the product when multiplied by any number or bring down the
terminal zeros of the factors and proceed with multiplying.
C. App lication
Ralph is a salesman of electrical appliances. His average sales for a month is 23,005. What is his sales for 105 months?
IV. Evaluation
Find the product. 40 056 30 108 46 003 30 050 92 005 x 40 x 50 x 203 x 700 x 300
200 052 460 005 200 024 2 100 306 5 708 251 x 60 x 102 x 50 x 310 x 305 V. Assignment
Find the product. 61 002 370 501 462 003 1 874 002 20 621 000 x 40 x 50 x 800 x 108 x 306
Solve the following math problems. 1. What is 37 100 times 50? 2. Multiply 700 to the difference of 2 100 and 355. 3. If the factors are 20 710 and 40, what is the product?
Multiplying Numbers by Multiples of 10, 100 and 1 000 I. Learning Objectives
Cognitive: Multiply 5 or more digit factors by multiples of 10,100 and 1 000 Psyc homotor: Write the product of factors of 5 or more digit by multiples of 10,100 and 1 000 Affective: Show kindness to other people in times of need
II. Learning Content
Skill : Multiplying 5 or more digit factors by multiples of 10,100 and 1 000 References: BECPELC I.D.1.5
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Materials: flash cards, charts, number wheel Value: Kindness and helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic multiplication facts using flash cards
2. Mental Computation
4 x 10 8 x 10 9 x 1000 16 x 10 25 x 100 7 x 10 36 x 100 4 x 1000 11 x 10 35 x 1000
3. Review
Have the class count together by tens up to 100, and by hundreds up to 1 000.
4. Motivation
Show pictures of people or families hit by calamities like typhoon or earthquake. Valuing:
• How does our government help the people during typhoon or earthquake? How about you, how do you help others during heavy typhoon, fire and the like?
B. Developmental Activities
1. Presentation
Barrio San Agustin was hit by typhoon Lucing last October. The president promised to
give each family 12,250.00. If there were 100 families in the barrio, how much will be given to the families in Barrio San Agustin?
Analyze the problem. a. What calamity hit Barrio San Agustin last October? b. What did the president promise each family in the barrio? c. How many families are there in the barrio? d. What is asked in the problem? e. What operations will help solve the problem? f. What is the answer? Show and discuss the solution on the board.
Challenge the class to find the pattern for the following:
A. 52 163 x 4 = 208 652 B. 21 846 x 3 = 65 538 52 163 x 40 = 2 086 520 21 846 x 30 = 655 380
52 163 x 400 = 20 865 200 21 846 x 300 = 6 553 800 52 163 x 4 000 = 208 652 000 21 846 x 3 000 = 65 538 000
Ask: What pattern did you observe? How do we multiply numbers by multiples of 10? 100? 1 000?
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2. Group Activities
1) Answer the following. Bring down the zeros before multiplying. a. 21 882 b. 23 635 c. 21 245 d. 53 421 e. 38 456
x 40 x 30 x 500 x 200 x 3 000 f. 32 185 g. 24 683 h. 12 832 i. 32 145 j. 18 321 x 10 x 100 x 1 000 x 500 x 7 000
2) Solve for n.
a. 31 142 x 500 = n d. 22 135 x 1 000 = n b. 72 416 x 900 = n e. 34 312 x 400 = n
c. 82 214 x 7 000 = n
3. Fixing Skill s/Practice Complete the table.
X 60 400 2 000 a. 24 345 b. 21 632 c. 25 998 d. 32 529 e. 37 292
4. Generali zation
How do we multiply numbers by multiples of 10? 100? 1 000?
Multiply the nonzero digits first, then annex to the product as many zeros as there are in the factors.
C. App lication Solve this problem.
Miss Lim receives a monthly salary of 10,625.00. How much can she earn in 10 months?
IV. Evaluation
Find the product. a. 32 561 x 20 = g. 46 214 x 10 = b. 46 128 x 300 = h. 12 836 x 100 = c. 15 212 x 40 = i. 45 681 x 1 000 = d. 62 183 x 100 = j. 21 468 x 300 = e. 21 421 x 5 000 = k. 42 612 x 50 = f. 52 183 x 200 = l. 69 421 x 80 =
V. Assignment
Complete the table. X 60 1 200 6 000
a. 21 345 b. 53 466 c. 25 364 d. 51 528 e. 85 432
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Solve the following math problems. 1. Multiply 80 to the sum of 320 and 180. 2. What is the product of 2 145 and 50? 3. What is 319 000 minus the product of 376 and 800?
Properties of Multiplication I. Learning Objectives
Cognitive: Show the different properties of multiplication • Commutative property • Associative property • Zero property • One/Identity property
Psyc homotor: 1. Solve for the product mentally 2. Supply for the missing numbers in a given equation
Affective: Show love for reading II. Learning Content
Skill : Identifying the properties of multiplication References: BECPELC I.D.2 Materials: counters, cartolina strips, chart Value: Love for reading
III. Learning Experiences
A. Preparatory Activities 1. Drill
Answer as fast as you can. (number sentences written on cartolina strips) 9 + 6 4 + 7 5 + (3 + 6) 7 + 4 6 + 9 (2 + 5) + 6 (5 + 3) + 6 9 + (4 + 2)
2. Review
What are the pairs of factors of the following numbers? 18 = 6X3 3x6 9x2 2x9 1x18 20 =
32 = 25 = 42 = 3. Motivation
Miss Daisy has 25 pupils. She required each pupil to read two books for home reading per month. How many books will the children read in 10 months?
Valuing: • What do you think will be developed among the pupils of Miss Daisy?
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• What do you think shall we get from reading many books?
B. Developmental Activities
1. Presentation 25 x 2 = 50
What are the factors? Do you think that if we interchange the factors, the product will still
be the same? Let us see. 25 x 2 = 2 x 25 50 = 50
Materials: counters Group size: pairs Procedure: • Distribute 40 counters to each pair. • Say 2 multiplication problems using the same factors (e.g. 3 x 6, 6 x 3). • Each pupil in pair shows and solves one of the problems using counter. • Pupils compare the products and discuss. • Repeat activity (510 mins.). a. Distribute cards to all the pupils. Each card contains a different multiplication fact such as
4 x 2 = 8 and 2 x 4 =8. Each child will look for his/her partner. Include in the multiplication facts 0 and 1, factors like 0 x 1=0, 1 x 0=0, 3 x 1=3, 1 x 3=3
b. Based on the activities done, present the following:
A B C 9X4 = 36 7X0 = 0 2X1 = 2 4X9 = 36 0X7 = 0 1X2 = 2 8X3 = 24 9X0 = 0 6X1 = 6 3X8 = 24 0X9 = 0 1X6 = 6 7X9 = 63 15X0 = 0 12X1 = 12 9X7 = 63 0X15 = 0 1X12 = 12
What have you observed in Group A?If the order of the factors are changed,
does the product also change or remain the same? (Then present the commutative Property of multiplication) Does addition also have this property? How about column B? What have you observed?
(Introduce the zero property.) How about column C? What can you say about the numbers multiplied by 1? (Introduce
the identity property.)
c. Present 2 cartolina strips showing. (4x2) x 5 = 4 x (2x5)
8 x 5 = 4 x 10 40 = 40 6 x (4x3) = (6x4) x 3
6 x 12 = 24 x 3 72 = 72
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What have you observed? Do the groupings of the factors affect the product? (Introduce the associative property)
2. Group Activity
Distribute activity cards.
Each group will answer the exercises in the activity card and report. (Identify what property is illustrated.)
a) 3 x 6 = 6 x 3 c) (8 x 4) x 5 = 8 x (4 x 5) e) 6 x 0 = 0
b) 1 x 12 = 12 d) 18 x 9 = 18 x 9 f) 12 x (2 x 5) = (12 x 2) x 5
3. Generali zation
What are the properties of multiplication? Define each.
Commutative Property – changing the order of the factors does not change the product.
Associative Property – changing the grouping of the factors does not change the product.
Zero Property – any number multiplied by zero equals zero. Identity Property – any number multiplied by 1 equals the number.
C. App lication
Mang Tonyo prepares his harvest to be brought to the market. He has 5 kaings of tomatoes. If each kaing contains 300 tomatoes, how many tomatoes are there in all? (Prove your answer by showing the commutative property) Solution: 5 x 300 = 300 x 5
1 500 = 1 500 IV. Evaluation
A. Use multiplication properties to solve the following.
1) 3 X 4 = 12 2) 9 X 2 = 18 3) 0 X 5 =_____ 4 X 3 = ____ 2 X 9 = _____ 9 X 1 =_____
4) (3 X 3) X 5 = 3 X (3 X 5) 5) (2 X 4) X 6 = 2 X (4 X 6) 9 X 5 = 3 X 15 ___ X 6 = 2 X ___ ___=___ ___=___
B. What property of multiplication is indicated?
1) 6 x 4 = 4 x 6 2) (3 x 9) x 6 = 3 x (9 x 6) 3) 4 x 0 4) 11 x 1 5) 92 x 3 = 3 x 92
C. Solve for the answer and indicate the property of multiplication.
1) 7 x 8 = 8 x 7 2) (4 x 8) x 3 = 4 X (8 x 3) 3) 120 x 0
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4) 29 x 1 5) (14 x 5) x 8 = 14 x (5 x 8)
V. Assignment
Solve for the answer.
1) 5 + 8 = 8 + 5 2) (2 x 3) X 6 = 2 x (3 x 6) ___=___ ___ x 6 = 2 x ___ 3) 9 + 4 = 4 + 9 ___=___
___=___ 4) 14 x 1 = ___ 5) 6 x 0 =___ 6) 100 x 0 =___ 7) 80 x 1 =___ 8) 4 + 9 = ___+___ 9) (3 x 8) x 4 = 3 X (8 x 4) 10) 7 x 3 = 3 x 7 ___x 4 = 3 x ___ ___=___ ___=___
The Distributive Property of Multiplication over Add ition I. Learning Objectives
Cognitive: Identify the distributive property of multiplication over addition Psyc homotor: 1. Supply the missing number 2. Solve for the product mentally Affective: Demonstrate love for work
II. Learning Content
Skill : Showing the distributive property of multiplication over addition References: BECPELC I.D.2.b
textbooks in Math 4 Materials: flash cards, chart, picture, counters, activity cards Value: Dignity of labor
III. Learning Experiences
A. Preparatory Activities
1. Drill
a. Flash the cards and drill the pupils orally on multiplication facts. b. Mental Computation
Identify the property of multiplication. 6 x 2 = 2 x 6 (6 x 0) x 5 = 6 x (0 x 5) (4 x 8) x 2 = (4 x 1) x 9 = 4 x (1 x 9) 9 x 0 = 4 x 12 = 12 x 4 1 x 25 = 36 x 1 = 1 x 36
2. Review
Identify the property of multiplication.
7 x 6 = 6 x 7 4 x 10 = 10 x 4 9 x 0 = 300 x 0 =
89
75 x 1 = 95 x 1 = (3 x 9) x 6 = 3 x (9 x 6) (1 x 7) x 8 = 1 x (7 x 8)
3. Motivation
Rene works every afternoon after his classes as a dishwasher in Chefoo restaurant. He is able to wash 74 dishes in one day. How many dishes can he wash in 5 days?
Valuing: • What kind of person is Rene? • How many dishes is he able to wash? • How many days does he work? • Would you want to be like Rene? Stress the value of one’s work.
B. Developmental Activities
1. Presentation
a. Present the following illustrations. Write the number sentence below the illustration. 3 x 9 =
3 x (4 + 5) 3 x 9 = (3 x 4) + (3 x 5) 27 = 12 + 15 27 = 27
Ask: Did the answers change in the two illustrations?
What was done in the second illustration? (the stars were grouped apart)
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b. Study the next illustration. What is the number sentence?
4 x 7 = 28 4 x (4+3)
4 x 7 = 4 x (4 + 3) 28 = (4 x 4) + (4 x 3) 28 = 16 + 12 28 = 28 Explain why the answers are the same.
2. Group Activity a. Divide the class into 3 groups. Give them counters. Distribute the activity cards. Show by
means of counters the following combination facts showing the distributive property of multiplication over addition.
A = 2 x 12 B = 5 x 14 C = 4 x 15
b. Draw in your manila paper your work and explain it to the class. (advise the pupils to use crayons to make their work nice and presentable)
3. Practice Exercises
Do your work as fast as you can. The example is given to you.
(3 + 4) x 8 = (3 x 8) + (4 x 8) = 24 + 32 = 56
a. 6 x (3 + 3) b. 4 x (5 + 4) c. (6 + 3) x 7 d. (2 x 7) x 8 e. (3 + 2) x 4 f. (3 + 6) x 9 g. (2 + 5) x 7 h. 9 x (4 + 4) i. 8 x (3 + 3) j. 3 x (2 + 7)
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4. Generali zation What is the distributive property of multiplication?
Another property of multiplication is the distributive property over addition. “Breaking apart” a factor does not affect the product or renaming either factor as two addends does not change the product.
C. App lication
Liza and Marie have 3 dolls and 4 stuffed toys each. How many toys do they have in all?
IV. Evaluation
A. Give the missing numbers.
1) 3 x (7 + 4) = ( ___ x 7) + (3 x 4) = _____ 2) 9 x (3 + 4) = (9 x 3) + (9 x ___) = _____ 3) 5 x (10 + 3) = (___ x 10) + (5 x 3) = _____ 4) 6 x (4 +4) = (6 x 4) + (___ x 4) = _____ 5) (3 + 4) x 5 = (3 x 5) + (___ x 5) = _____
B. Rename the second factor as two addends and find the product.
1) 6 x 12 2) 8 x 25 3) 5 x 14 4) 3 x 13 5) 7 x 9
C. Solve these problems. Write the necessary label for the final answer
1. Jojo, Grace and Len have 5 ribbons and 3 headbands each. How many ribbons and headbands do they have?
2. Each of the 7 pupils in a class has 3 storybooks and 4 coloring books. How many books do they have?
3. Eight farmers were given 2 cows and 3 hogs to take care. How many animals were given to them?
V. Assignment
1. Show the distributive property of multiplication over addition then solve for the product.
Example: 6 x 7 = 6 x (4+3) = (6 x 4) + (6 x 3) = 24 + 18 = 42
a. 9 x 15 b. 3 x 21 c. 2 x 9 d. 8 x 18 e. 4 x 10
2. Solve the problem. Write the number sentence.
a. There were 8 pupils who helped the science teacher. Each of them carried 3 beakers and 2 alcohol lamps. How many things did the pupils carry?
b. Each of the 9 families in our street has 4 fruit trees and 2 shade trees. How many trees are there in our street?
c. Jojo and his 4 friends were given 4 guavas and 3 chicos each by their Uncle Bert. How many fruits did they get?
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Estimating Products I. Learning Objectives
Cognitive: Estimate the products of two factors with 5 or more digits by 2 to 3digit numbers
Psyc homotor: 1. Tell the importance of caring for our environment 2. Find the estimated product of two factors with 5 or more digits by 2 to 3 digit numbers
Affective: Show love for nature
II. Learning Content
Skill : Estimating the products of two factors with 5 or more digits by 2 to 3digit numbers
References: BECPELC I.D.3 textbooks in Math 4
Materials: cutouts, chart, activity cards, number wheel, pictures Value: Love for nature
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic Multipli cation Facts Game: ” Pick ing Guavas”
A pupil picks a guava with a multiplication fact. He/she answers as fast as he/she can. A
correct answer gets a candy.
2. Review
Review rounding off numbers. Round off to the nearest:
10 100 1 000 10 000 100 000
213 685 172 294 36 428 69 123
3. Motivation
a. Show the picture of three baskets full of mangoes. About how many mangoes do you
think are contained in the baskets? (Pupils are expected to give different numbers.) b. Explain that what they give are just estimates. They give an estimation on the number of
mangoes in the baskets. They are not sure and did not actually count the number of mangoes in the baskets.
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B. Developmental Activities
1. Presentation The garden club is selling orchid plants at 12,323.00 a pot to collect funds. If 123 pots
were sold, about how much money did the club get? a. How much is a pot of orchid plant? b. How many pots were sold? c. What phrase in the problem indicates that what is asked is an estimated product?
Let us study how to estimate products.
1. 12,323 12,000 2. 12,000 x 123 x 100 x 100 1,200,000
How do we estimate products? What did we do first? Valuing: • Orchids are beautiful flowers. What do they do to our surroundings? Are they important to
us? Why? 2. Group Activity
Distribute the activity cards. Let each group solve the problem. Estimate the products. a. The Girl Scouts of Cavite is engaged in rose gardening. They gather 55 125 roses a day
and sell them. How many flowers can they gather in 24 days? b. An environmentalist distributed gift envelopes to 24 565 school children. If each envelope
contained 17 plantatree bookmarks, how many bookmarks were distributed? c. The Sangley Nursery grows 33 284 santan every month. How many santan will it
produce in 212 months? Analyze and discuss the answers of each group. Ask the children why do we need to grow plants?
3. Guided Practice Solve for the estimated product by rounding each factor to the nearest tens.
a. 14 325 b. 21 178 c. 56 683 d. 47 928 x 42 x 43 x 62 x 37
e. 34 625 f. 51 321 g. 32 182 h. 52 146 x 63 x 28 x 33 x 45 i. 45 682 j. 21 456 x 78 x 81
Target Game
Prepare a wheel with numbers. At the back of each number is a corresponding exercise to be solved. The greatest estimated product will be the winner and will receive a reward.
The pupil who is called will make a target on the wheel and answer the corresponding exercise at the back.
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4. Generali zation How do you estimate the product of 2 factors?
To estimate the products, round the factors to the highest/greatest place value then multiply the rounded factors.
C. App lication
Solve each problem. 1. A nursery sells 34 296 seedlings a day. About how many seedlings can be sold in 23 days? 2. A town has an average of 81 989 number of trees. Give the estimated total number of trees
of 12 towns.
IV. Evaluation Estimate the products.
a. 34 231 b. 184 599 c. 265 463 x 62 x 586 x 371
d. 43 960 e. 98 521 f. 48 214 x 42 x 241 x 34
V. Assignment
Estimate then multiply.
a. 631 236 b. 184 599 c. 265 463 x 143 x 586 x 371 d. 572 169 e. 491 641 x 39 x 334 Multiplying Mentally wi thout Regrouping I. Learning Objectives
Cognitive: Multiply mentally 2 digit numbers with products up to 200 without regrouping Psyc homotor: Practice speed and accuracy Affective: Tell the importance of fruits in our body
II. Learning Content
Skill : Multiplying mentally 2digit numbers with products up to 200 without regrouping Reference: BECPELC I.D.4 Materials: textbook, flash cards, activity cards Value: Health consciousness
III. Learning Experience
A. Preparatory Activities
1. Drill
Basic multiplication facts using flash cards
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2. Mental Computation
13 24 12 16 22 11 x 3 x 2 x 4 x 1 x 4 x 7
3. Review
Estimate the products.
32 465 12 365 72 146 31 654 46 123 x 28 x 47 x 52 x 32 x 81
4. Motivation Do you like fruits? What is your favorite fruit? What food nutrients do we get from fruits? Which do you prefer to eat, chocolate candies or fruits? Why? Why do we have to eat fruits everyday?
B. Developmental Activities
1. Presentation
a. Present this word problem.
A kilo of mango costs 80.00. How much will you pay for 2 kilos? • How much is a kilo of mango? • What is the cost of 2 kilos? • What did you do to solve the problem? • Can you solve it without using paper and pencil?
b. Give the products orally.
42 54 62 72 83 92 54 x 3 x 2 x 4 x 4 x 3 x 3 x 2
c. Copy and complete the table.
Factor 14 22 41 21 32 40 Factor 2 3 2 4 2 2 Product ? ? ? ? ? ?
2. Group Activity
Give each group an Activity Card like the one below. Record which group answered first,
the second and the third. Answers will be written on the other square.
22 63 52 43 32 72 21 41 30 44 126 104 129 96 216 84 164 120
2 X 3 X
4 X
Answers
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3. Generali zation
How do you multiply mentally 2digit numbers by 1digit number without regrouping?
In multiplying mentally, multiply first the ones and then the tens, without using paper and pencil.
C. App lication
Solve mentally. 1. There are four rows of chairs in Miss Luna’s class. If there are 10 chairs in each row, how
many chairs are there in all? 2. Rizal Primary School has three sections in Grade 4. Each section has 42 pupils. How many
Grade 4 pupils are there in Rizal Primary School?
IV. Evaluation
A. Multiply mentally.
41 86 42 31 44 40 30 41 x 2 x 2 x 3 x 3 x 2 x 2 x 5 x 5
B. Solve for n by multiplying mentally. 23 x 3 = n 21 x 4 = n 3 x 62 = n 2 x 50 = n 21 x 9 = n 4 x 50 = n
C. Prepare 5 exercises about the skill. Include the answers. IV. Assignment
A. Multiply mentally. 61 20 43 64 72 x 3 x 10 x 3 x 2 x 2 24 36 73 54 82 x 2 x 1 x 2 x 2 x 2
B. Oral drill. Test your speed in multiplying each number mentally.
12 22 23 11 12 x 2 x 3 x 1 x 4 x 3 32 11 43 33 50 x 3 x 7 x 2 x 3 x 2
C. Create two word problems involving multiplying numbers mentally.
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Numbers in Exponential Form I. Learning Objectives
Cognitive: Write numbers in exponential form Psyc homotor: Express numbers in exponential form Affective: Practice cooperation in group activities
II. Learning Content
Skill : Writing numbers in exponential form References: BECPELC I.D.5
textbooks in Math 4 Materials: flash cards, activity sheet Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill
Use flash cards in conducting this drill. Select two to three volunteers/pupils to act as contestants. Whoever answers first will be given points until the time limit has been consumed.
Example: 25 36 22 81 18 50 x 2 x 4 x 3 x 2 x 5 x 4
2. Review
Write the missing number.
a. 6 b. 12 c. 30 d. 48 2 3 4 10 3 6 2 2 2
3. Motivation Look at the given data below. Notice how the numbers are written.
Standard Form Product of Factors Exponent Form 2 = 2 21 4 = 2 x 2 22 8 = 2 x 2 x 2 23 16 = 2 x 2 x 2 x 2 24 32 = 2 x 2 x 2 x 2 x 2 25 64 = 2 x 2 x 2 x 2 x 2 x 2 26
What did you observe on how the numbers are written?
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B. Developmental Activities
I. Presentation
Group 1 1. Study the table. 2. Write your observations on the chart.
Given Data Observation/s a. 2 b. 4 c. 8 d. 16 e. 32 f. 64
Group 2 a. Tell something about this illustration. b. How many times is number 2 being written?
2
2 x 2
2 x 2 x 2
2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 x 2
Group 3 a. What did you observe about the way 2 is written? b. Observe from the first to the sixth number. Group 4 a. Compare this data to that of the power of 2. Does it show a pattern? How? b. Write your observations below.
3 = 3 9 = 3 x 3 27 = 3 x 3 x 3 81 = 3 x 3 x 3 x 3 243 = 3 x 3 x 3 x 3 x 3 729 = 3 x 3 x 3 x 3 x 3 x 3
Observations: __________________________________________
1
2
3
4
5
6
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2. Analysis and Discussion
Ask the pupils the following questions: a. What happens to 2 when multiplied by another 2? By another 2? b. What did you observe about the numbers from 2 up to 64? How about the factors?
Illustrations: 2 Æ 4 Æ 8 Æ 16 Æ 32 Æ 64
What is the relation of the first number to the second number? What happens when you double 2, 4 and so on? Does it form a pattern?
Do you know that these numbers could also be expressed as exponents? How are we going to do this?
20 = A number to the zero power is always 1. 21 = 2 The first power is always itself. 22 = The number to the second power is always squared. exponent 22 = 4 (standard form) = 2 x 2 (product of factor) base
Based on the work of group 4, 3 to the third power is cubed, it is equal to 33. Valuing: • How did you work with the other members in your group? • Is it important to cooperate with each other while working on something? Why?
3. Group Activity
a. Write the answer using exponents. 1) 7 x 7 3) 9 x 9 x 9 x 9 2) 8 x 8 x 8
b. Write as a product of factors. Then write in standard form. 1) 62 2) 105
4. Generali zation
The exponent tells how many times the base is used as a factor. A number to the zero power is always 1. A number to the first power is always itself, the second power is squared and so on.
Exponent (tells how many times the base 4 = 2 x 2 = 22 is multiplied by itself)
Base (the factor to be multiplied) factors
C. App lication 1. Write in standard form.
a. 24 b. 43 c. 74
d. 85 e. 94
2. Write in exponential form.
a. 2 x 2 x 2 x 2 d. 7 x 7 x 7 x 7 x 7 x 7 b. 3 x 3 x 3 x 3 e. 9 x 9 x 9 x 9 x 9 x 9 x 9 c. 4 x 4 x 4
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IV. Evaluation A. Match column A with column B.
A B 1) 53 a. three cubed 2) 45 b. five cubed 3) 22 c. five to the seventh power 4) 57 d. two squared 5) 33 e. four to the fifth power
B. Write the standard form.
1) 35
3) 54 5) 63
2) 143 4) 95
V. Assignment
Select the letter of the correct answer. 1) 7 x 7 x 7 x 7 x 7 =
a. 77 b. 75 c. 57 2) 9 x 9 x 9 x 9 =
a. 49 b. 94 c. 99 3) 10 =
a. 100 b. 101 c. 102
4) 43 = a. 12 b. 16 c. 64
5) 64 =
a. 82 b. 28 c. 88
Numbers from Standard Form to Scientific Notation
I. Learning Objectives
Cognitive: Write numbers from standard form to scientific notation Psyc homotor: Compute accurately the power of a number Affective: Show accuracy in giving answers
II. Learning Content
Skill s: 1. Writing numbers in scientific notation 2. Computing the power of a number References: BECPELC I.D.6.1
textbook in Math 4 Materials: flash cards, chart, learning activity sheets Value: Accuracy
III. Learning Experiences
A. Preparatory Activities
1. Drill
Find each product.
a. 10 x 10 = 10 x 10 x 10 = 10 x 10 x 10 x 10 =
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b. 1) 1 x 10 = n 10 x 10 = n 2) 3 x 200 = n 30 x 200 = n 3) n x 40 = 20 x 80 30 x 100 = n x 50
2. Review
Write the standard form for the following:
a. 23 b. 34 c. 42 d. 53 e. 65 3. Motivation
The teacher shows a picture of the solar system and asks the following questions: a. What is the composition of a solar system? b. What is the closest planet to the sun? c. How far is this planet from the sun? Do you know what planet is this? It is Mercury. Problem:
Mercury is the planet closest to the sun. It is about 60 000 000 kilometres from the sun. How far is it from the sun?
Valuing: • How are you going to answer the different exercises? Why? • How do you feel if you get a correct answer?
B. Developmental Activities
1. Presentation
Introduce the lesson through illustration/drawing.
Mercury is 60 000 000 km away from the sun. Look at this illustration:
60 000 000 6 x 107
Standard Form Scientific Notation
In what form is 60 000 000 km written? • Is it in standard form? • How many zeros are there? There are 7 zeros.
Where can we find 6? • Is it the 8th digit of the number? • Is it a number greater than 1 but less than
10? • The scientific notation consists of two factors,
the first factor is number 1 or greater but less than 10.
• So, 6 is the first factor. The second factor is a power of 10.
• What is the power of 10?
60 000 000 = 6 x 107 exponent 7 zeros (shows the number of zeros)
Sun
Mercury
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Example # 2 Standard Form Scientific Notation
500 5 x 102 How many zeros are there? Why is it raised to the 4th power? 40 000 4 x 104
Example # 3 360 Think: 360 is between 300 and 400. 300 = 3 x 102 400 = 4 x 102
Shortcut method: 3. 6. 0. = 3.6 x 102 move the decimal point 2 places
to the left. (you have to move the decimal point 2 places to the left
Need a number greater than so the first factor is more than 1 or equal to one but less than but less than 10.)
ten 2. Practice Exercises
Dyad Grouping Write in scientific notation. a) 30 b) 600 c) 7 400
3. Generali zation
How do we write numbers from standard form to scientific notation?
Standard numerals are written in scientific notation as a product of 2 factors. First factor is greater than or equal to 1 but less than 10 and the second factor is a power of 10.
C. App lication
Triad Grouping Write in scientific notation. 1) 300 2) 6 000 3) 40 000 4) 800 000 5) 700 000 000
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IV. Evaluation
1. Fill in the missing number. a. 600 = ___ x 102 b. 7 000 = 7 x 10__ c. 160 000 = 16 x 10__ d. 12 000 000 = ___ x 106 e. 250 000 000 = 25 x 10__
2. Write in scientific notation.
a. 80 b. 500 c. 240 d. 6 700 e. 31 000
V. Assignment
Express in scientific notation. 1) 564 000 2) 3 120 000 3) 6 400 000 000
Numbers in Scientific Notation to Standard Form I. Learning Objectives
Cognitive: Write numbers in scientific notation to standard form Psyc homotor: Use powers of 10 to write numbers in exponential form Affective: Show cooperation in group activities
II. Learning Content
Skill s: 1. Writing numbers in scientific notation 2. Using powers of 10 to write numbers in exponential form References: BECPELC I.D.6.2
textbooks in Math 4 Materials: flash cards, chart, learning activity sheets Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill Mental computation using multiplication facts Materials: pocket chart, set of numbers (cut individually)
pocket for the product
pocket for pocket for the multiplier numbers
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The numbers can be changed.
2. Review
Write the numbers in exponential form. a. 6 000 b. 7 000 000 c. 80 000 000 d. 860 000 e. 3 800 000
3. Motivation
Mercury is the planet closest to the sun. It is about 60 000 000 km from the sun. a. How far is Mercury from the sun? b. What did we study yesterday? c. What did we do with the number?
B. Developmental Activities
1. Presentation
60 000 000 is in what form of the number? 6 x 107, what is this form? How did we express the numbers?
Suppose, we do it this way:
6 x 107 Æ 60 000 000 How did I write the given number? Do you know how to do it?
2. Group Activity a. Present this number.
6 x 107 Æ 60 000 000
What is the exponent? Based on previous lesson, the exponent shows the number of zeros 6 has. 6 x 107 What is this form?  Scientific Notation
60 000 000 How about this?  Standard Form
Pupils’ Activity: Dyad Example: 4 x 10 7 Æ 40 000 000 7 x 10 6 Æ 7 000 000 b. Show the changing of exponential form to standard form. 1.2 x 104 = 1. 2 000 Æ 12 000
105
1. The exponent is 4. Move the decimal point 4 places to the right. 2. What happened to the number when the decimal point is moved to the right using the
exponent? 3. Give other examples for dyad activity
3.1 x 106 Æ 3. 1 00000 Æ 3 100 000 7.31 x 106 Æ 7. 3 1 0000000 Æ 7 310 000 000
3. Practice Exercises
Write in standard form (group activity) a. 3 x 103
b. 4 x 106 c. 6 x 108 d. 6.1 x 103 e. 9.3 x 106
4. Generali zation
How do we write numbers in scientific notation to standard form?
To change scientific notation to standard numerals, move the decimal point to the right
depending on the exponent. It makes it a whole number. C. App lication
Write in standard numerals:
8 x 104 9 x 102 1.2 x 105 2.81 x 103
IV. Evaluation 1. Match column A with column B.
A B 1. 6 x 102 a. 6 000 2. 6 x 104 b. 60 000 3. 6 x 103 c. 600 4. 6 x 105 d. 6 000 000 5. 6 x 106 e. 600 000
2. Write in standard form. a. 8 x 102
b. 8.1 x 102
c. 2.16 x 105
d. 3.49 x 108
e. 6.11 x 107
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V. Assignment Write in standard form. 1) 3 x 103
2) 4 x 104 3) 9.3 x 106 4) 12 x 103 5) The earth is about 1.5 x 108 km from the sun.
Analyzing Prob lems I. Learning Objectives
Cognitive: Analyze word problem involving multiplication by telling what is asked, what are
given, the word clue/s, the hidden question and the operation to be used Psyc homotor: Transform the word problem into a number sentence Affective: Strengthen family ties through annual reunion
II. Learning Content
Skill : Analyzing word problems involving multiplication References: BECPELC I.D.7.1.1 – 1.4
textbooks in Math 4 Materials: flash cards, charts, learning activity sheets, strips of cartolina with steps in
analyzing word problems Value: Strengthening family ties
III. Learning Experiences
A. Preparatory Activities
1. Drill Multiplication facts in flash cards Solve mentally.
123 x 3 = _____ 23 x 3 = _____ 50 x 7 = _____ 124 x 2 = _____ 45 x 4 = _____ 800 x 70 = _____ 60 x 40 = _____ 7 000 x 9 = _____
2. Review
Game Power: Ordering of steps Each group will be given strips of cartolina with steps in analyzing word problems written on it. The group who places the strips in correct order first will be the winner.
3. Motivation
Mr. Jamison’s family holds a reunion once a year. Fifteen of the grandchildren invited 3 friends each. How many of their friends are expected to attend the reunion? a. What did Mr. Jamison’s family do every year? b. Are you doing it too?
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c. If Mr. Jamison’s family holds a reunion once a year, what do you think he should do so that there will be no problem financially?
B. Developmental Activities 1. Presentation
The teacher groups the pupils into 4. Each group is given a card with a problem written
on it. Read and answer the questions that follow.
2. Group Activity Group 1
Rose bought 4 ribbons at 86.50 each. She gave a 500peso bill. How much
change did she get?
a. What is asked in the problem? b. What are given? c. Find the word clues. d. What are the operations to be used? Group 2
Rose bought 4 ribbons at 86.50 each. She gave a 500peso bill. How much
change did she get?
a. What is the hidden question? Write the number phrase.
b. What is the mathematical sentence? c. What is the answer? d. Does your answer make sense? Group 3
Ana brought home 3 baskets of papaya with 8 pieces in each basket. Susan brought home 12 mangoes. How many fruits did Ana and Susan brought home altogether?
a. What is asked in the problem? b. What are given? c. What are the word clue/s? d. What are the operations to be used? Group 4
Ana brought home 3 baskets of papaya with 3 pieces in each basket. Susan
brought home 12 mangoes. How many fruits did Ana and Susan brought home altogether?
3. Analysis/Abstraction
a. What is the hidden question?
Write the number phrase b. What is the mathematical sentence?
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c. What is the answer? d. Does your answer make sense?
4. Oral Exercises
Teacher reads the problem and asks the pupils to answer the questions orally.
There were 12 packages with 24 paper plates in each package. If 142 of the
plates were used, how many plates were not used?
a. What is asked in the problem? b. What are given in the problem? c. Is there a hidden question in the problem? d. What is/are the word clue/s in the problem? e. What operation is to be used to solve the problem? f. What is the correct answer?
Alan and Andy have one garden plot each. Alan has 4 rows of 12 pechay plants
in each row. Andy has 5 rows of 10 pechay plants in each row. How many pechay plants do they have altogether?
a. What is asked in the problem? b. What are given in the problem? c. Is there a hidden question in the problem? d. What is/are the word clue/s in the problem? e. What operation is to be used to solve the problem? f. What is the correct answer?
5. Generali zation
How do we analyze and solve word problems involving multiplication? Review the questions to be answered in analyzing word problems.
In analyzing word problems, take note of the following: a. What is asked b. The given facts c. The word clue/s d. The operation/s to be used e. The hidden question/s
f. The mathematical sentence g. Solve for the answer h. Write the label i. Look back if answer make sense
IV. Evaluation
The teacher will present problems and asks the pupils to answer the questions that follow. 1. In the canteen’s refrigerator, there were 4 trays of eggs. Each tray had 12 eggs. The cook used
15 eggs. How many eggs were left in the refrigerator? a. What is asked in the problem? b. What are given? c. What is/are the word clue/s in the problem? d. What operation/s to be used? e. Transform the word problem into a number sentence. f. What is the answer?
2. Ben bought 6 Tshirts. His brother also bought 6 Tshirts. Each Tshirt costs 285.00. How
much did all the TShirts cost?
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a. What is asked in the problem? b. What are given? c. What is/are the word clue/s in the problem? d. What operation/s to be used? e. Transform the word problem into a number sentence. f. What is the answer?
V. Assignment
Read and analyze the problem. Answer the questions correctly.
Lita bought 5 kilograms of lapulapu which costs 150.00 per kilogram and 3 kilograms of bangus which costs 110.00. How much did she pay for the lapulapu? How much did she pay for the bangus? How much did she pay in all? a. What is asked in the problem? b. What are given? c. What operation is to be used? d. Write the mathematical sentence. e. What is the word clue in the problem? f. What is the correct answer?
Solving Prob lems I. Learning Objectives
Cognitive: Solve word problems involving multiplication of whole numbers including money Psyc homotor: Follow correctly the steps in solving word problems Affective: Realize the importance of backyard gardening for the family
II. Learning Content
Skill : Solving word problems involving multiplication of whole numbers including money
References: BECPELC I.D.7.1 textbooks in Math 4
Materials: flash cards, chart, learning activity sheet Value: Industry
III. Learning Experiences
A. Preparatory Activities
1. Drill
a. Basic multiplication facts using window cards. b. Solve for the product of factors with multiples of 10 and 100.
Examples: 40 x 9 = _____ 400 x 30 = _____
50 x 30 = _____ 20 x 90 = _____ 20 x 700 = _____ 500 x 8 = _____ 600 x 8 = _____ 60 x 20 = _____
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2. Review
What are the steps in solving a problem? a. Have a game on rearranging the steps in analyzing word problems that are written on
strips of cartolina. b. The group who finishes ahead of the others is declared the winner.
3. Motivation
How many of you have gardens at home? What are planted in your garden? Are they in
rows? How do farmers plant seedlings in a farm? Valuing: • Is it important to have gardens at home? Why?
B. Developmental Activities
1. Presentation
An orchard contains 8 rows of trees. There are 10 trees in a row, how many trees are there?
The teacher specifies that to solve a word problem, we must always think of the steps in
solving a word problem. Let us use these guide to solve word problems. a. What is asked? b. What are given? c. What operations to be used? d. Write the number sentence. e. Do the operation. f. What is the answer?
2. Group Activity
Remind the pupils the importance of analyzing the problems first before solving for the
answer. a. Group the pupils. b. Each group is given an activity sheet with a problem written on it. c. They will solve the problems using the steps in problem solving.
Activity 1
Supply the missing information below. a. The given facts are ______. b. The process to be used is _____. c. What is the answer _____?
Activity 2
Illustrate the problem.
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Activity 3
Write the given data and solve for the answer.
Given _____ Solution _____
3. Practice Exercises
The teacher gives problems and lets the pupils solve for the answer by following the steps. a. Mang Julio’s jeepney uses 175 litres of gasoline in a week. How many litres of gasoline
can it consume in 15 weeks? b. A basket of lanzones costs 1,285.00. How much do 25 baskets of lanzones cost? c. There are 1 648 shoppers who go to Mabuhay Department Store everyday. How many
shoppers go to the store in 59 days? d. There are 953 names listed in each guest book of the National Museum. How many
names are listed in 52 guest books?
4. Generali zation What are the steps in solving word problems?
C. App lication
Read and solve on your paper. 1. Mrs. Dizon, the school nurse examined 48 pupils per day. How many pupils did she examine
in 5 days? 2. Alissa and her classmates used 5 packs of cornstarch for their maja blanca recipe. Each
pack costs them 19.00. How much did they spend for cornstarch?
IV. Evaluation Read the problems carefully. Solve and label your answer. 1. Mr. Fuentes ordered 45 boxes of baseball gloves. Each box contains 12 gloves. How many
baseball gloves will Mr. Garcia receive? 2. Jose earns 48.00 a day. How much will he earn in one week? 3. Mark planted 16 plots of pechay plant in the garden. Each plot contains 26 pechay plants. How
many pechay plants are there in all? V. Assignment
Solve. 1. Aling Rosa sells flowers. She can sell 12 dozens of roses a day. How many roses can she sell in
two weeks? 2. It was Lara’s seventh birthday. Her mother bought 15 kilos of pork. If each kilo costs 120.00,
how much will her mother spend for pork?
TwoStep Word Prob lems
I. Learning Objectives
Cognitive: Solves 2step word problems involving multiplication and any of addition/subtraction
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Psyc homotor: Write the solution to the problem accurately Affective: Work cooperatively with the group
II. Learning Content
Skill : Solving 2step word problems involving multiplication and any
addition/subtraction Reference: BECPELC I.D.8.1
textbooks in Math 4 Materials: textbook, flash cards, chart, learning activity sheet Value: Cooperation
III. Learning Experiences
A. Preparatory Activities 1. Drill
Write the numeral mentioned in the blank provided. Story:
The statue of Liberty is one hundred fiftyone (_____) feet tall. The tip of the torch is three hundred five (_____) feet above the ground. It is made with over three hundred (_____) thin sheets of copper. To climb the top of the statue, there are one hundred sixtyeight (_____) steps. a. The largest number in the story is _____. b. The smallest number in the story is _____. c. The numbers in the story that are less than 186 are _____ and _____. d. The numbers in the story that are greater than 200 are _____ and _____.
2. Review
Ask pupils about the different steps in solving word problems.
3. Motivation
Do you know what a mailman is? What is his work? What do you notice on the mail envelope? Is this important? Why? Here is a problem about stamps. Let us find what it is all about. Problem:
Marie has 153 pages in her stamp album. There are 12 stamps in each page. She gave 63 stamps to her friend. How many stamps were left with her?
B. Developmental Activities
1. Presentation
Children, if you are to solve the problem, what are you going to do? If I will let you work in groups, what are you going to do? Why?
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Activities – Discovery Approach Group 1 Acting out the problems Materials: magazines, pieces of art paper
The pupils are to present the problem by acting it out. One member will act as Marie and others will help in answering the problem using improvised album and stamps. Group 2 Solving the problem (Computation) Materials: chalk, miniboards The group is allowed to have a direct computation based on their understanding about the problem. The problem will come out with only one common answer. Group 3 Picture illustrations about the problem. Materials: manila paper, mini board, chalk, crayons, marker pen The group is to give the answer to the problem by illustrating it through pictures. They should indicate the given data. Report their answer. Group 4 Solve the problem by answering the guide questions. a. What are given? b. What is asked? c. What are the operations to be used? d. Write the number sentence? e. How will you do the operations? f. What is the answer?
2. Analysis/Abstraction
Teacher will use the data presented by the pupil. a. Who collects stamps? b. What did she do with her stamps? c. Did she give all her stamp? How many stamps were given? d. Do you know the number of stamps? What do you think you will do? e. Is the final answer correct? Why?
3. Practice Exercises – Dyad
Solve the problems carefully. a. Manny had boxes of paper plates. Each box contains 36 plates. He used 73 paper plates
for the birthday party of his son. How many paper plates were left? b. There were 27 children who went to the library in the morning and 16 children in the
afternoon. Each child read 7 books. How many books were read by them?
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4. Generali zation
In solving 2step word problems involving multiplication and addition/ subtraction, follow the following steps:
a. Read b. Understand c. Plan d. Solve e. Look back to check the answer
C. App lication
Solve and give the correct answer. 1. Naty has a vegetable garden. Last week, she sold 65 pieces of papaya for 10.00 each
and 90 pieces of ampalaya for 5.00 each. How much was her total sales last week? 2. Pacita bought 6 kilograms of rice at 24.00 a kilogram and 4 bars of laundry soap at
19.00 each. How much did she pay in all? IV. Evaluation
Solve and give the correct answer. 1. Rey bought 3 boxes of apples. Each box contained 321 apples. He gave 480 apples to his
brothers and sisters. How many were left with Rey? 2. Letty bought 15 kilos of rice at 25.00 per kilo. How much should be her change if she gave
500.00? 3. A preschool teacher charges 125.00 per tutorial classes for one hour per person. The teacher
pays 35.00 per hour for the rental of her place. How much does she earn for a 12hour tutorial class?
4. Rica sold 785.00 worth of beauty products. The products she sold were makeup kits and lipsticks. She was able to sell 6 makeup kits at 95.00. How much was her sales for the lipstick?
5. Marie and Peping bought the following good for their picnic. Two cakes at 15.00 each. 4 bags of potato chips at 14.00 each. 3 boxes of chocolate candies at 25.00 per box. How much did they pay for the goods? Is 150.00 enough?
V. Assignment Solve the following word problems and label your answers. 1. Jubal packed 12 pillowcases in a box. Each pillowcase costs 25.00. How much would 3
boxes of pillowcase cost? 2. A group of balikbayan rented 3 cottages at 1,275.00 each. They also rented 2 extra beds at
475.00 each. How much did the group pay for the cottages and the extra beds?
Dividing Numbers by 3Digit Numbers wi thout Remainder I. Learning Objectives
Cognitive: Divide 5 or more digit numbers by 3digit numbers without remainder Psyc homotor: Solve problems with ease and accuracy Affective: Practice helpfulness and cooperation
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II. Learning Content
Skill : Dividing 5 or more digit numbers by 3digit numbers without remainder References: BECPELC I.E.1.1 Materials: window cards, butterfly cutouts Value: Helpfulness and cooperation
III. Learning Experiences
A. Preparatory Objectives 1. Drill
Game – Catching the Butterflies (butterfly cutout from a garden of flowers and answer the combination at the back) Each pupil will get one butterfly cutout.
20 ÷ 5 24 ÷ 4 35 ÷ 7 15 ÷ 3 10 ÷ 2 36 ÷ 6 21 ÷ 3 28 ÷ 7 42 ÷ 6 18 ÷ 6
2. Review
“Mix and Match” Teacher prepares several pairs of number sentences. Example:
707 ÷ 7 = 101
303 ÷ 3 = 101
6006 ÷ 6 = 1001
1269 ÷ 9 = 141
9660 ÷ 3 = 3220
Pupils will get one card each. Teacher announces, “mix” and the pupils will mix around with their classmates. Teacher calls, “Pair” and the pupils will find a partner to match their cards.
3. Motivation
A while ago, we used cutouts of butterflies. Where do butterflies stay? Why is it that they
love to stay in the garden? What do we find in this place? Present the lesson through this problem:
Ruben helped his father in gathering tomatoes in their vegetable farm. If he gathered 671 875 tomatoes and placed 215 in each bag, how many bags did Ruben use? Valuing: � What kind of a boy is Ruben? Are you like Ruben? Are you also helpful at home? What
do you do?
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B. Developmental Activities 1. Presentation
a. The pupils are going to answer the following:
• Who helped father in gathering tomatoes? • How many tomatoes did he gather? • What did he do to the tomatoes? • How many bags were used?
b. The teacher may answer the problem with the whole class or let the pupils work in dyads. Let the pupils present their work and have them explain how they arrived at the answer.
c. Teacher will follow the same steps in gathering data but this time he will concentrate on how to answer the problem.
d. The teacher will illustrate to further enhance the pupils’ understanding. divisor 215 671 875 dividend (number to be divided) (number to divide) 1) What are you going to do? 2) What is the number that you are going to divide?
3 125 215 671 875
 645 268 215 537  430 1075  1075 0
e. How many 215s are there in 645?
Use: 215 215 (trial and error) x 2 x 3 430 645 or repeated addition 215 +215 430 +215 645 1) Which is the correct answer? 2 or 3? Why? 2) Where did I write 3? Why? 3) What do you call 3? 4) What will you do to 3 and 215? 5) How about 671 and 645? 6) How do we know if the answer is correct? 7) Follow the same questions until the time the answer is given
f. Solve individually.
162 519 ÷ 213
2. Practice Exercises Solve: “Quad Group” a) 52 216 ÷ 122 b) 266 299 ÷ 473
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c) Mr. Francisco subdivided his coconut farm in Cavite whose area is 37 800 square metres. It will be used as a resettlement area for 120 landless families in a squatters area in Metro Manila. How many square metres will each family get?
3. Generali zation
In dividing 5 digit numbers by 3digit numbers, take the first 3 digits at the left then divide,
multiply, subtract and bring down. Check the answer by multiplying the quotient by the divisor. The answer is correct if the product is equal to the dividend.
C. App lication
Find the quotient. 1. 76 622 ÷ 421 2. 57 024 ÷ 132 3. A furniture factory delivered 42 875 chairs to 175 schools. Each school got an equal number
of chairs. How many chairs did each receive?
IV. Evaluation 1. Divide the following:
a. 39 751 ÷ 127 = c. 50 924 ÷ 116 = e. 167 072 ÷ 368 =
b. 237 744 ÷ 312 = d. 240 264 ÷ 422 =
2. Read and solve.
1. What number will you get if you divide 91 372 by 431? 2. If you divide 66 248 by 292 what quotient will you get? 3. 223 136 divided by 608 equals ___ 4. 188 020 divided by the sum of 345 and 250 = ___
V. Assignment
Find the quotient.
1) 213 564 ÷ 926 2) 663 552 ÷ 864 3) 554 552 ÷ 673
Dividing Numbers by 4 or More Digit Numbers wi thout or with Remainder I. Learning Objectives
Cognitive: Divide 5 or more digit numbers by 4 or more digit numbers without and with
remainder Psyc homotor: Solve for the quotient accurately Affective: Help one another in group activities
II. Learning Content
Skill s: Dividing 5 or more digit numbers by 4 or more digit numbers without or with remainder
Reference: BECPELC I.E.1.2 textbooks in Math 4
Materials: flash cards, charts, activity sheets Value: Helpfulness
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III. Learning Experience
A. Preparatory Activities
1. Drill
Game: “Mix and Match”
Teacher prepares several pairs of division equations. Distribute these to each pupil in class. When teacher announces “mix,” each pupil in the class will mix with the others. When the teacher says “match,” each pupil will look for their partner which will match the card that they are holding. Discuss solutions in class.
2. Review
a. 68373213 b. 34882107 c. 32256512
3. Motivation
Have you received an invitation? What kind of invitation did you receive? I have here a
story of a class who prepared some invitation cards.
B. Developmental Activities
1. Presentation
Problems: a. A big school with 2 134 pupils made 53 350 invitations for their program. If each pupil
made an equal number of cards, how many invitations did each pupil make? b. The Matulungin Foundation donated 424 625 bags of commodities to the typhoon victims
in Eastern Visayas. If 1 075 bags were given to each barangay, how many barangays were able to receive the donation?
2. Analysis/Discussion
Problem a a. Who made the invitations? b. Why did they make the invitations? c. How many invitations did they make? d. What does the problem ask for? e. Who can give the number sentence for the problem? f. Which is the dividend? divisor? g. Why do you think the teachers helped the principal send the letters of invitation? h. What good character trait did the teachers show? (The same procedure will be followed in working with problem b.)
33 91 212
109 71 132
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3. Practice Exercises
Divide the class into four groups. Give each group activity sheet. Let them answer the division exercises in the activity sheet. Let them clap their hands if they have finished.
Group I and III Group II and IV
a. 601381542 a. 638051823
b. 658282351 b. 2773232291
c. 392542781 c. 3109543173
d. 8746732513 d. 9124875322
e. 4263941512 e. 7924041462
4. Generali zation
How do we divide 5 or more digit numbers by 4digit divisors?
a. Divide the first partial dividend by the divisor. b. Multiply the partial quotient by the divisor then write the answer below the first
partial dividend. c. Subtract the partial product from the first partial dividend. d. Bring down the next digit. e. Repeat steps 1 – 4 to the last digit of the dividend.
C. App lication
Solve for this problem.
A baker can bake 75 550 pieces of pandesal in 60 days. What is the average number of pandesal he bakes in one day?
IV. Evaluation
1. Solve for the quotients.
a. 2594922237 b. 3868281118 c. 5749231679
d. 29713562563 e. 47464221719
2. Answer the following:
a. How many digits will there be in the quotient of 726 418 ÷ 1 246? b. In the mathematical sentence 725 834 ÷ 4 123, what do we call 4 123? c. How many 1 304 are there in 100 408? d. Divide 5 440 596 by 1 673 and write your quotient in exponential notation. e. What quotient will you get if you divide 382 166 by the sum of 630 and 511?
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V. Assignment
Divide and check.
1) 834 726 ÷ 4 213 = n 2) 797 436 ÷ 5 314 = n 3) If the divisor is 235 and the dividend is 87 954, what is quotient? 4) What is 32 615 divided by 24? 5) A number divided by 23 equals 398 r 6. Solve for the missing number.
Dividing Whole Numbers by 10,100 and 1 000 I. Learning Objectives
Cognitive: Divide whole numbers by 10,100 and 1 000 Psyc homotor: Solve or compute with speed and accuracy Affective: Show willingness in performing group activities
II. Learning Content
Skill : Dividing whole numbers by 10,100 and 1 000 References: BECPELC I.E.1.3 Textbooks in Math 4 Materials: flash cards, activity sheets Value: Willingness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic division facts Boysgirls contest or do the relay game.
12 ÷ 3 = _____ 56 ÷ 8 = _____ 64 ÷ 8 = _____ 24 ÷ 8 = _____ 12 ÷ 6 = _____ 30 ÷ 6 = _____ 21 ÷ 7 = _____ 42 ÷ 6 = _____ 15 ÷ 5 = _____ 40 ÷ 5 = _____
2. Review
Round off the following numbers to the nearest tens, hundreds and thousands. Game: Distribute the activity sheet with the table on rounding numbers written on it per column. When the teacher says “go” each pupil takes turn in rounding numbers to its specific place value as fast and as correct as they can. The pupil who finishes first with the most number of correct points wins. Did everybody join the activity willingly? As a member of the group, what attitude should you show so everybody would participate? Why?
Number Nearest Tens Nearest Hund reds Nearest Thousands a. 344 b. 563 c. 4 275 d. 5 948 e. 6 225
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3. Motivation
The Bureau of Plant Industry will distribute 13 000 mango seedlings to 10 provinces. How many seedlings will each province receive?
a. What did the Bureau of Plant Industry do? b. What will you do to solve the problem?
B. Developmental Activities
1. Presentation
a. Is it possible to divide any number by zero? Explain your answer. b. Suppose there are 100 barangays? How about 1 000 provinces?
1) 1300 2) 130 3) 13
1300010 13000100 130001000
10 100 1000 30 300 3000 30 300 3000 0 0 0 0 0
0 0 0
0 so,
13 000 ÷ 10 = 1 300 13 000 ÷ 100 = 130 13 000 ÷ 1 000 = 13
2. Analysis/Discussion
a. Who distributed the mango seedlings? How many seedlings did they distribute? Why do you think the BPI distributed these seedlings?
b. What is the dividend? What is the divisor? c. In example 1) how many zeros were cancelled both in the dividend and in the divisor?
What digits were left? In example 2) how many zeros were cancelled in both the dividend and the divisor? What digits were left?
d. What will be done with the digits not cancelled?
3. Exercises a. Using activity sheets
Divide the class into 5 groups. Give each group activity sheets. Exercise sheet: Find the quotient. Cancel the number of zeros. 1) 400 ÷10 = 2) 400 ÷100 = _____ 3) 29 000 ÷ 1 000 = _____ 4) 6 200 ÷ 10 = _____ 5) 110 000 ÷ 1 000 = _____
b. Using “Mix and Match” There are number phrases and numbers in flash cards. As the teacher says “mix”
pupils holding the flashcards will mix with their classmates. When the teacher says “match” the pupils will look for their partners to pair the flash cards.
670 ÷ 10 = 67
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c. Solve for the quotient mentally.
1) 420 000 ÷ 600 = _____ 2) 51 000 ÷ 500 = _____ 3) 56 000 ÷ 700 = _____ 4) 270 900 ÷ 900 = _____ 5) 6 650 ÷ 70 = _____
4. Generali zation
How do we divide whole numbers by 10, 100 and 1 000? Elicit the pattern.
When dividing numbers that are multiples of 10 100 and 1 000, cancel as many
zeros in the dividend as there are in the divisor before dividing. This means dividing the dividend and divisor by the same power of 10. Then divide the remaining digits.
C. App lication
Solve the following problems:
1. The pencil factory has rush orders from 10 stores. The factory has a stock of 55 000 pencils. If the stores were given an equal number of pencils, how many would each store get? Were all the pencils given out?
2. A sack of cement costs 100.00. How many sacks can one buy with 600.00? IV. Evaluation
1. Solve for the quotient. Write your answer on the blank provided for.
a. 670 ÷ 10 = _____ b. 3 500 ÷ 100 = _____ c. 78 000 ÷ 100 = _____ d. 5 000 ÷ 1 000 = _____ e. 9 300 ÷ 100 = _____ f. 83 000 ÷ 100 = _____ g. 3 120 ÷ 40 = _____ h. 315 000 ÷ 7 000 = _____ i. 13 500 ÷ 300 = _____ j. 84 000 ÷ 6 000 = _____
2. Solve each problem.
a. How many pesos are there in 32 000 centavos? b. How many 200 mL bottles are there in a 43 000 mL can of vinegar? c. There are 100 cm in a metre. If a road is 742 000 cm long, how many metres long is it? d. How many metres long is a ribbon that is 2 500 cm long?
7 800 ÷ 100 =
2 000 ÷ 20 =
3 900 ÷ 130 =
36 000 ÷ 1 000 =
100
30
36
78
123
e. Suppose you had 1,000,000.00 in 100.00bills. If you could give away one 100.00bill in a minute, how long would it take you to give away all the money?
V. Assignment
Complete the table. Divide by 10 100 and 1 000.
Divisor Dividend 10 100 1 000
1) 63 000 2) 800 000 3) 2 500 000 4) 130 000 5) 75 000
Dividing Numbers wi th Zeros in the Dividend I. Learning Objectives
Cognitive: Divide 4 to 5digit numbers by 2 to 3digit numbers with zeros in the middle and
continuous zeros in the dividend Psyc homotor: Solve 4 to 5digit numbers by 2 to 3digit divisors accurately Affective: Help others who are in need
II. Learning Content
Skill : Dividing 4 to 5digit numbers by 2 to 3digit numbers with zeros in the middle or continuous zeros in the dividend
Reference: BECPELC I.E.1.2 textbooks in Math 4
Materials: charts, flash cards, learning activity sheets Value: Cooperation and helpfulness
III. Learning Experience
A. Preparatory Activities
1. Drill Game: Picking mangoes Pick mangoes (mango cutouts) from the tree and answer the combinations at the back.
90 ÷ 5 = 60 ÷ 15 = 28 ÷ 14 = 70 ÷ 15 = 80 ÷ 20 =
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2. Review
Group activity Divide the class into four groups. Each group will be given cutouts with division
combinations at the back. The first group to finish will clap their hands. Discuss and write the solutions on the board.
a. b. c. d. e.
2700180 63030 32004 3000060 36015
3. Motivation
Who among you are members of the boy and girl scouts? Valuing: � What are the activities that you do to help other people? How about at home?
B. Developmental Activities
1. Presentation
a. Problem 1
The Girl Scouts collected 1 308 canned goods to be given to 25 poor families. How many pieces of canned goods should each family receive? 1) Analysis/Discussion
a) Why did the Girl Scouts collected canned goods? b) What can you say about the Girl Scouts? c) How do you feel when helping other people? d) What are the given facts? e) What is asked in the problem? f) What operation is needed to solve the problem? g) What is the number sentence for the problem? h) How do we divide 1 308 by 25?
2) Show the stepbystep process using long division on the board.
52
130825 Æ 130 ÷ 25 = 5
125 Æ 5 x 25 = 125 58 Æ 58 ÷ 25 = 2 50 Æ 2 x 25 = 50 8  remainder
3) Check the answer by multiplication.
b. Problem 2
The San Jose Elementary School ordered 10 200 school ID’s for the pupils of 85
teachers. How many ID’s will each teacher receive? 1) Analysis/Discussion
a) Why do you think the school ordered ID’s? b) What can you say about the school who ordered ID’s for its pupils?
125
c) What are the given in the problem? d) What does the problem ask for? e) What is the number sentence for the problem? f) How do we divide 10 200 by 85?
2) Show the stepbystep process using long division on the board.
1020085
85 Æ 102 x 85 = 1 170 Æ 170 ÷ 85 = 2
170 0 Æ 0 ÷ 85 = 0 0 0
3) Check the answer by multiplication.
2. Fixing Skill s
Divide the class into 5 groups. Have each group pick out a problem written on a rolled paper. Ask them to solve the problems by group. Afterwards, ask them to report in class their answer, solution and checking. a. b. c. d. e.
331027 600528 8398038 9492084 8750025
3. Generali zation
How do you divide 4 to 5digit numbers by 2 to 3digit numbers with zeros in the
dividend? In dividing dividends with zeros, use the same step: divide, multiply, subtract and
bring down. Zero is used as a place holder in the quotient.
C. App lication Read and solve the following problems. 1. The Grade 4 classes will go on a field trip. There should be one teacher for every 25 pupils.
There are 1 025 pupils. How many teachers are needed? 2. There are 50 026 mangoes. One basket can hold 46 mangoes. How many baskets are
needed to put the mangoes in?
IV. Evaluation 1. Copy and divide the following on your paper. a. b. c. d. e.
40804 550825 2016024 7003535 5405427
2. Find the missing number that will make the division statement correct.
a. 11 035 ÷ _____ = 175 r 10 b. _____ ÷ 45 = 137 r 4 c. _____ ÷ 634 = 305 r 630 d. 1 005 ÷ 14 = _____
120
126
e. 30 070 ÷ _____ = 85 r 320
V. Assignment Answer the following then check by multiplying the quotient by the divisor. a. b. c. d. e
409563 236024 2807035 60400156 28060411
Estimating Quotients I. Learning Objectives
Cognitive: Estimate the quotient of 4 to 5digit dividends by 2digit numbers Psyc homotor: Give the rounded number to the nearest tens, hundreds, thousands and ten
thousands Affective: Being helpful and cooperative
II. Learning Content
Skill s: 1. Estimating the quotients of 4 to 5digit dividends by 2digit numbers 2. Giving the rounded numbers to the nearest 10,100 and 1 000
Reference: BECPELC I.E.2 textbooks in Math 4
Materials: flash cards, charts, drill boards Value: Helpfulness and cooperation
III. Learning Experience
A. Preparatory Activities
1. Drill
Mental Computation Give the quotient as fast as you can. a. 3 000 ÷ 30 = b. 6 000 ÷ 20 = c. 24 000 ÷ 80 = d. 81 000 ÷ 90 = e. 14 000 ÷ 70 =
2. Review
(Stress the value of cooperation.)
Students will be grouped in dyads, player A and B. Each player takes turn in answering the questions. The group who finishes first wins the contest. Round off the following numbers to the nearest thousands or ten thousands.
a. 1 879 b. 31 187 c. 2 638 d. 45 616 e. 3 448 f. 44 594 g. 8 649 h. 72 634 i. 9 338 j. 85 111
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3. Motivation
What do we usually do before entering a movie house? If you don’t pay for the tickets, do you think you can watch the movie? We are going to read a problem regarding pupils who work for a cause.
A group of students collected 1,290.00 from the tickets sold for their stage
play. Each ticket costs 15.00. How many tickets were sold?
B. Developmental Activities
1. Presentation If you are a member of that group, how are you going to answer the problem? We are going to group together and find out some ways to answer the problem.
Activity Exercises – Discovery Approach
Group 1: Guess and check s trategy (Answers of pupils must be an educated guess.) a. What is the answer? Write it down. b. Solve and find if your answer is correct. Write your solution. c. Check if the answer makes sense.
Group 2: Simplifying problem approach Pupils will follow the 4 steps in problem solving. a. Understand/think b. Plan for the operation, mathematical sentence, equation c. Solve d. Looking back – Check your answers by multiplying the quotient and divisor
Group 3 The members of the group will give the answer through dyads.
Group 4 All members of this group will answer individually and afterwards they will come up with a common answer.
2. Analysis/Abstraction
(The teacher should use data from the pupils for the analysis and discussion of the problems.) a. Who collected the amount of money from the tickets sold? b. How much money have they collected? c. How much is the cost of ticket? d. How many tickets were released?
20.00 15.00 1,290.00 1,000.00
20 1 000
Followup Questions: 1. What happened to the 1,290.00? _____
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2. How about 15.00? _____ Did it change? 3. What did you do to the given numbers? Did you round the given numbers? 4. How did you divide the given numbers? 5. What did you do to the numbers before dividing it?
Important reminder: Rounding off numbers is needed in estimating the numbers.
4. Practice Exercises
Estimate and divide. a. 5 136 ÷ 21 = b. 1 501 ÷ 69 = c. 8 445 ÷ 92 = d. 62 926 ÷ 47 = e. 34 108 ÷ 82 =
5. Generali zation
In estimating quotients, first round off the dividend and the divisor to the highest place value then divide.
C. App lication
Estimate the following: 1) How many 23s are there in 4 323? 2) How many 52s are there in 1 322? 3) How many dozens are there in 105 pieces? 4) How many minutes are there in 3 578 seconds? 5) 58 389 ÷ 26 =
IV. Evaluation
A. Write the reasonable estimate for each of the problem. 1) 98.95 ÷ 48 = _____ 2) 41 872 ÷ 19 = _____ 3) 17 399 ÷ 34 = _____ 4) 19 457 ÷ 23 = _____ 5) 69 673 ÷ 68 = _____
B. Estimate. Then choose the correct answer.
1) 11 4432 a. 400 b. 40 c. 4 d. 4 000
2) 13 6347 a. 6 b. 60 c. 600 d. 6 000
3) 17 48497 a. 250 b. 20 c. 25 d. 2 500
4) 21 51346 a. 250 b. 25 c. 2 500 d. 25 000
5) 47 67389 a. 1 400 b. 140 c. 14 d. 400
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V. Assignment
Round both numbers then estimate the quotient. 1) 62.95 ÷ 56 = 2) 43 209 ÷ 18 = 3) 44 867 ÷ 93 = 4) 27 431 ÷ 34 = 5) 9 536 ÷ 16 =
Dividing Mentally wi thout Remainder I. Learning Objectives
Cognitive: Divide mentally 2to 3digit numbers by 1digit number without remainder Psyc homotor: Practice speed and accuracy in dividing mentally Affective: Tell the importance of fruits to our body
II. Learning Content
Skill : Dividing mentally 2 to 3digit numbers by 1digit number without remainder References: BECPELC I.E.3
textbooks in Math 4 Materials: flash cards, chart, picture of fruits, show board Value: Health consciousness
III. Learning Experiences
A. Preparatory Activities
1. Drill Contest “ A Step for Victory”
Teacher tells the pupils, that they’re going to have a contest. It will be called “ A Step
for Victory”. Pupils will be grouped by 5. A participant from each group will be called. The teacher will flash the cards. Two numbers written on the cards: the first number gives the product and the second number gives the quotient of the number pair the contestant will say. The first one to give the correct answer will make a step until he or she reaches the vase. Upon reaching the vase, he/she will be given a flower to be placed in their flower vase. The group with the most number of flowers in the vase will be declared as winner.
Product Quotient 24, ___, ___, 6
18, ___, ___, 2 25, ___, ___, 1 16, ___, ___, 4 20, ___, ___, 5
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2. Review Riddles a. I’m thinking of a number, when you divide it by 9, the quotient is 8. What is the number? b. The dividend is 54, the quotient is 6, what is the divisor? c. The divisor is 9, the quotient is 7, what is the dividend? d. The divisor is 7, the quotient is 21 what is the dividend? e. The dividend is 279, the divisor is 9, what is the quotient?
3. Motivation
What is your favorite fruit? Why? Valuing � Why are fruits important to our body? What do they do to our body? to our health? � What vitamins can we get from mangoes?
B. Developmental Activities
1. Presentation
Read the problem carefully and give the answer without using your pencil and paper.
Kent and his three friends picked 124 mangoes from the farm. They divided the
mangoes equally among themselves. How many mangoes did each boy receive?
a. Group the pupils into 4. b. Each pupil in the group must participate in giving answers. c. Conduct a game of numbers. d. Comprehension checkup will be asked after the answer is given.
1) Who picked mangoes from the farm? 2) How many mangoes did they pick? 3) What did they do with the mangoes? 4) What are the given facts? 5) What is the process to be used? 6) What is the correct number sentence for the word problem? 7) Can you get the quotient without using your pencil and paper? How?
Solution: Divide 12 by 4 mentally, then give the quotient. e. The teacher will also give additional exercises.
36 ÷ 3 = 60 ÷ 3 = 72 ÷ 8 = 105 ÷ 5 = 213 ÷ 3 =
2. Analysis and Discussion • How do we get the answer? • How many digits are there in the dividends? the divisor? • Can we get the answer without using our paper and pencil? How?
3. Practice Exercises
Pupils may answer the exercises through dyads. Divide the following numbers mentally.
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a. Using flash cards with division facts (2 digits by 1 digit combination) b. Divide.
39 ÷ 3 84 ÷ 4 50 ÷ 5 848 ÷ 4 846 ÷ 6 The teacher may provide more combinations to enhance speed and accuracy in dividing mentally.
4. Generali zation
How do we divide numbers mentally?
When we divide numbers mentally, we think first of one or two dividends at a time, then divide without using paper and pencil. Do the same with the remaining digits.
C. App lication 1. Miss Roxas has 44 pupils. She grouped her pupils into 4 groups for their Science experiment.
How many members are there in each group? Can you solve the problem mentally? Is dividing mentally important? Why?
2. 88 ÷ 4 = 96 ÷ 3 = 255 ÷ 5 = 497 ÷ 7 = IV. Evaluation
Solve for n mentally. 1) 66 ÷ 6 = n 2) 99 ÷ 3 = n 3) 110 ÷ 5 = n
4) 884 ÷ 4 = n 5) 819 ÷ 9 = n
V. Assignment
Divide mentally. 1) 49 ÷ 7 = ___ 2) 63 ÷ 9 = ___ 3) 120 ÷ 6 = ___
4) 550 ÷ 5 = ___ 5) 442 ÷ 2 = ___
Analyzing Word Prob lems involving Division I. Learning Objectives
Cognitive: Analyze the word problems involving division of 5 or more digit numbers by 3 or
more digit numbers including money by telling what is asked, what is/are given, the word clue/s, the operation/s to be used and transform the problem into a number sentence
Psyc homotor: Tell the steps in analyzing word problems Affective: Work cooperatively in group activities Tell the importance of forest conservation
II. Learning Content
Skill : Analyzing word problems involving division of 5 or more digit numbers by 2 to 3digit numbers including money
References: BECPELC I.E.4.1.1 – 4.1.4
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Materials: activity sheet, chart, flash cards Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill Group Work The group that finishes first is declared the winner. Do the operations. Follow the paths.
Start here End Here
Start here End Here
2. Review
Mental Division Game: Mix and Match Teacher prepares several pairs of cards like:
Pupils get one card each. Teacher announces “mix” and the pupils will mix with each other. Teacher calls “pair” and the pupils will find a partner to match their cards.
3. Motivation
Show a picture of a forest. Ask: Have you been to the forest? What did you do there?
Share some of your experiences. Valuing: � Is it necessary for us to conserve our forest? Why? How can you help conserve our
forest?
18
+18
÷3 21
x 4
+ 2 ÷ 5
?
?
x 3
12 ÷ 7
660 ÷ 6
639 ÷ 3 484 ÷ 2
648 ÷ 8 110
242
6
81
213
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B. Developmental Activities
1. Presentation (Group Activity)
a. Problem Situation A total of 93 184 pupils in Cavite will join the tree planting program. If there were 256
pupils in each barangay, how many barangays joined the tree planting program? 1) What is asked in the problem? 2) What are the given facts? 3) What word clue would help you solve the problem? 4) What question is to be used? 5) Why do you think many pupils join the tree planting program? 6) What can you say about the barangays that joined the treeplanting program? What
can you say about those who did not join?
b. Role Playing Some pupils will act out the given situation. The rest of the class will listen carefully
and write important facts given in the short presentation. Scout master: Boys, get all the newspaper and bottles and put them in the truck Ruben: Sir, they were already packed. Arjay: Our troop is ready to put them in the truck, sir. Scout master: Very well done boys! Now, let me check the other troop. After 3 days in a BSP meeting Scout master: Boys, we were able to raise P12,584.00 from selling the empty bottles and old newspapers last week. Boy scouts: (shouting) Yehey! Scout master: Thanks for your full support, cooperation and hard work.
You have shown a sense of responsibility in your own little ways. Very well done, boys!
Boy scouts: (shouting some BSP yells) Ruben: Sir, if 32 of us joined the project, how much did each of us raise? Scout master: Oh! Very good question! Okay, let’s solve it.
2. Analysis and Discussion
After the presentation of each group, the teacher will give her/his comment. Other
questions will be asked. a. Problem Situation
• Why are trees important? Support your answer. • How can we protect and save our forest? • If you were one of the pupils, will you join the treeplanting program? Why? • Do we need to support this program? Why? • What did you discover as you analyze the word problem? • What is the first step in solving word problems? Second? Third? Etc. • Are word clues important in solving word problems? Why?
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b. Role Playing • Who were the characters in the short presentation? • What did the boy scouts do? Describe them? • What character traits do they possess? • Do you want to be a BSP or GSP member? Why? • Why do we need to collect empty bottles and old newspaper? • Why do we need to recycle these materials? • How can we make them useful? Teacher shows different recycled materials. Now, let us analyze the word problem carefully.
The Boy Scouts were able to raise 12,584.00 from selling empty bottles and old newspapers. If there were 32 scouts who joined the project, how much did each scout raise?
• What is asked in the problem? • What are the given facts? • What operation is to be used? • Transform this problem into a number sentence.
3. Practice Exercises/Fixing Skill s
a. Using the showmedrillboard
Read the problem carefully and answer the questions that follow.
There are 63 360 textbooks to be shipped to Cebu City. If there are 165 boxes, how many books are there in each box? • What is asked in the problem? • What are the given facts? • What operation is to be used? • Transform this problem into a number sentence.
b. Small group Technique
The class will be divided into groups. Each group will choose a leader and a recorder. The leader will get an activity sheet and they will answer it as a group. The group who has finished will clap their hands.
Activity Sheet Read the problem carefully and answer the questions below.
Mr. Reyes prepares a weekly payroll of 96,250.00 for 110 workers in the shipyard. What is the average weekly pay of each worker? • What is asked in the problem? • What are the given facts? • What operation is to be used? • Transform this problem into a number sentence.
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4. Generalization How do we analyze word problems?
To analyze word problems, read the problem carefully. Tell what is asked, what are given, what is/are the word clue/s, what operation to be used and transform the problem into a number sentence.
C. App lication
1. Mrs. Garcia, the librarian, asked the Grade 4 pupils to place the 43 632 textbooks in 202
boxes. How many books will each box have? 2. Mother buys 2 000 grams of fish. If she cooks 250 grams for each meal, how many meals will
it take to consume the fish? IV. Evaluation
A. Read the problems carefully and answer the questions that follow.
A farmer wants to ship 11 088 potatoes. A crate holds 144 potatoes, how many crates are needed? 1. What is asked in the problem? 2. What are the given facts? 3. What operation is to be used? 4. Transform this problem into a number sentence.
B. Study the problems carefully. Determine the operation to be used, then transform each word problem into a number sentence. 1. There are 21 550 coconut trees to be distributed to 345 barangays in Laguna. How many
coconut trees will be given to each barangay? Operation to be used_________ Number sentence _________
2. A Christmas tree costs 950.00. How many Christmas trees can be bought from
34,200.00? Operation to be used_________ Number sentence _________
3. Carlos gathered 17 040 oranges. He packed them in boxes which each can hold 284
oranges. How many boxes did he use? Operation to be used_________ Number sentence _________
4. A medical team brought 12 500 boxes of assorted medicines to be distributed equally among
25 barangays. How many boxes of assorted medicines will each barangay receive? Operation to be used_________ Number sentence _________
5. A television set is sold for 19,180.00 to be paid in equal monthly installment for one year.
How much will be the monthly payment? Operation to be used_________ Number sentence _________
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V. Assignment
A. Construct word problems on the following data:
1) 65,340.00 ÷ 235 = 2) 73,342.00 ÷ 176 =
B. Ben has 3,000.00 in 100.00 bills. How many pieces of hundredpeso bills does he have?
Solving OneStep Prob lems involving Division I. Learning Objectives
Cognitive: Solve 1step word problems involving division of 5 or more digit numbers by 3 or more digit numbers including money
Psyc homotor: Divide 5 or more digit numbers by 3 or more digit numbers with or without remainder
Affective: Show neatness and orderliness in any written work
II. Learning Content
Skill s: 1. Solving 1step word problems involving division of 5 or more digit numbers by 3 or more digit numbers including money
2. Dividing 5 or more digit numbers by 3 or more digit numbers with and without remainder
References: BECPELC I.E.4.1 textbooks in Math 4
Materials: charts, flash cards, activity sheets Values: Neatness and orderliness
III. Learning Experiences
A. Preparatory Activities 1. Drill
Wheel of Fortune Pupils will use the Wheel of Fortune and answer it.
÷4
36
40
32 48 20
12
44
28
÷6
60
36
96 66 48
42
54
18
÷5
60
15
35 45 55
25
30
50
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2. Review Solve for the answer. Use your showmecards.
7 420 10 528 9 4 518 10 4 261 15 3 459
3. Motivation
a. Sing the song “Happy in Math” b. Who among you have a father or mother who works in the factory? What kind of factory
is it?
B. Development Activities
1. Presentation The class will be divided into 3 groups with a leader and a recorder. Each group will be given an activity sheet with a problem situation. Read the problem carefully and analyze it.
Mr. Cruz, a factory owner has 156 workers. The weekly pay of the workers amounts to
185,328.00. How much does each worker get weekly? a. What is asked in the problem? b. What are the facts given? c. What operation is to be used? d. Transform the word problem into a number sentence. e. Solve for the correct answer. f. Label your answer.
The first group to finish will be the one to present their work.
2. Analysis and Discussion a. Who owns the factory? b. Do you think it is better to own a factory? Why? c. How much does Mr. Cruz spend a week for his workers? d. Does the factory help the people in the community? How? e. Do you want to work in a factory? Why?
Analyze the answer of the other groups to see if their answers are correct. Pupils will read the questions in the activity sheet. What should you do before solving a word problem? Remember also to label your answer.
The Red Cross distributed 11 214 packs of noodles to the typhoon and flood victims in
Central Luzon. They are distributed equally among 623 families. How many packs of noodles did each family get? a. What is asked in the problem? b. What are the given facts? c. What operation is to be used? d. What is the mathematical sentence suited for the problem? e. What is the correct answer? f. Check your answer.
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Valuing: • How do you write your answers to the problem? Why do you think you should write your
answer neatly and orderly? Do you also practice neatness and orderliness at home? How?
3. Practice Exercises
Read the problems carefully and solve for the answer. Label your answers. a. There were 25 200 bars of soap at the wholesale counter. If these were distributed
equally among 101 retailers, how many bars of soap will each retailer get? b. Mr. Perez spent 1,883,222.50 for the bangus fingerlings he placed in his 122
fishponds. How much did he spend for each fishpond? c. One summer, 13 720 students signed up for a leadership training. If 245 students were in
each group, how many groups were formed? d. In 105 days, a large bakery sold 10,185.00 worth of loaves of bread. On the average,
how much loaves of bread were sold each day?
4. Generali zation What are the steps in solving word problems?
The steps in solving 1step word problems are: a. Read – Know what is asked, what are given. b. Plan – Draw the problem. Know the operation. Write the number sentence. c. Solve – Write the correct units/label your answer. d. Look back – Review and check your answers.
C. App lication
There are 21 550 coconut seedlings to be distributed to 345 barangays in Laguna. How many coconut seedlings will each barangay receive?
IV. Evaluation
Read the problems carefully, then solve for the answer. Label your answers. 1. A factory can manufacture 125 fish nets using 156 250 metres of nylon thread. How many metres
of nylon thread is used for each net? 2. An orchard owner harvested 17 040 oranges. He packed them in boxes which each can hold 284
oranges. How many boxes did he use? 3. A Christmas tree costs 950.00. How many Christmas trees can be bought from 34,200.00? 4. A delivery truck unloaded 600 boxes of canned milk at a supermarket. There were 14 400 cans of
milk in all the boxes. How many cans were in each box? V. Assignment
Solve for the answer. 1. Mr. Sison had 69 965 kilograms of apples available for sale. Two hundred sixtythree vendors
bought equal weights of apples. How many kilograms did each vendor get? 2. There are 22 190 cookies to be packed in a plastic container. One hundred thirtyfive cookies are
in each pack. About how many plastic containers are needed to pack all the cookies? 3. Mangoes are sold by the “kaing”. If one “kaing” costs 1,025.00, how many “kaings” of mango
can you buy in 142,475.00?
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Analyzing 2 to 3Step Word Problems I. Learning Objectives
Cognitive: Analyze 2 to 3step word problems involving division and any of the other fundamental operations
Psyc homotor: 1. Choose the correct operation 2. Write the problem into a number sentence
3. Solve for the final answer with the necessary label accurately Affective: Show kindness to others
II. Learning Content
Skill s: Analyzing 2 to 3step word problems involving division and any of the other fundamental operations
References: BECPELC I.E.5.1.1 – 1.4 Mastering Math IV TX pp. 9094 Growing with Math IV Workbook pp. 108110
Materials: problem solving chart, flash cards Value: Kindness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Drill on dividing 3 to 4digit numbers by 1digit number. You may use flash cards or have a relay game to be done by columns.
235 ÷ 5 = 824 ÷ 4 = 650 ÷ 2 = 328 ÷ 8 = 738 ÷ 6 = 248 ÷ 8 =
2. Review
Dividing money values. Show and discuss the solutions on the board.
654 ÷ 2 = 928 ÷ 8 = 606 ÷ 6 = 455 ÷ 5 = 729 ÷ 9 = 920 ÷ 4 =
3. Motivation
Katrina has 20.00. Anne has 25.00 and Christine has 30.00. They give the
money to the 3 school janitors. If the janitors divide the money equally among themselves, how much will each of them get?
B. Developmental Activities
1. Presentation
a. Activity 1
1) Call one pupil to read the problem aloud.
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2) Have the pupils analyze the given problem. Then show and discuss the solutions on the board. a) What is asked in the problem? b) What are the given facts? c) What operations are to be used? d) What is the hidden question? e) What is the mathematical sentence for the problem? f) If you have a classmate without food for recess, are you willing to share your
baon? Why?
3) Give other examples for the pupils to analyze. Divide the class according to their abilities (slow, fast, average).
4) Analyze the following word problems using the different steps learned in class.
SLOW LEARNERS a) Mr. Velez gave his two daughters 35.00 each. If the two girls will buy a pack
of candies at 50.00 and divide the remaining amount equally among themselves, how much money will each girl have?
b) Anita had 232 red and white roses. If 64 of these roses were red, how many white roses can be made into bouquets, if each bouquet will have 12 white roses?
FAST LEARNERS a) During the school year, the pupils harvested 3 250 baskets of fruits and 1 225
baskets of vegetables. They were sold equally to 25 stalls in the market. How many baskets of fruits and vegetables did each get?
b) Roy intends to buy a pair of shoes that costs 1,500.00. He has 850.00 at present and plans to save 50.00 every week. How many weeks will it take him to be able to buy the shoes?
AVERAGE LEARNERS a) A beach resort had 48 cottages. A cottage has three rooms. Each room can
only be occupied by two persons. If 250 tourists came, how many cottage should they rent?
b) Mang Luis earned 9,463.00 from the cabbage harvested. He set aside 3,502.00 for his expenses and divided the rest among his 3 workers. How
much money did each worker get?
2. Generali zation
What are the steps needed in solving 2step word problems?
To solve 2step word problems involving division and any of the other operations, follow the following steps: read, understand, plan and solve.
C. App lication
Read and solve.
The Farmer’s Association of Nueva Ecija planted rice, corn, mongo, peanuts and other crops in their fields. By the end of the year, they harvested about 3,250.00 worth of rice,
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76,500.00 worth of corn and 2,300.00 worth of other crops. If there are 45 members in the association, how much will each farmer earn?
IV. Evaluation
Read the problem. Don’t forget to write the necessary label for the given problem. (Keep in mind the different steps in solving the problems.)
The Grade 1 class in Sta. Monica Elementary has a population of 245 pupils. Grade 2 has 230,
Grade 3 has 340, Grade 4 has 500, Grade 5 has 501 and the Grade 6 classes have 620. What is the average enrolment of the grades?
V. Assignment
Analyze the following word problems using the different steps learned in the class. Then solve for the final answer with the necessary label.
1) Last month, John and Jun worked in Mr. Castro’s farm. They earned 4,276.00 but spent
800.00 for their food. If they divided what was left equally between them, how much did each get?
2) Mr. Santos used his jeep to transport 1 629 kilograms of bananas. He delivered 649 kilograms to his customers in Divisoria and the rest to his 4 customers in Quiapo. How many bananas did each customer in Quiapo receive?
Solving 2 to 3Step Word Prob lems involving Division I. Learning Objectives
Cognitive: Solve 2 to 3step word problems involving division and any one or two of the
other fundamental operations learned including money Psyc homotor: Write the solution in solving 2 to 3step word problems Affective: Show the value of fairness and sharing
II. Learning Content
Skill : Solving 2 to 3step word problems involving division and any one or two of the other fundamental operations learned including money
References: BECPELC I.E.5.1 textbooks in Math 4
Materials: flash cards, charts Values: Fairness, sharing, kindness
III. Learning Experiences
A. Preparatory Activities 1. Drill
Using flash cards Solve for the correct answer. a. (5 + 9) ÷ 7 = _____ b. (15 ÷ 3) + 8 = _____ c. (25 ÷ 5) – 4 = _____ d. (81 ÷ 9) + 3 = _____ e. (36 + 4) ÷ 10 = _____
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2. Review a. Have a review on the steps in problem solving and how to analyze a word problem. b. Read this problem carefully and answer the questions that follow.
The national library has 28 470 books. 130 books can fill one shelf. How many
shelves can be filled? • What is asked? • What is/are given? • What operation is to be used? • What is the number sentence? • What is the correct answer? • Check the answer if it makes sense.
3. Motivation
Read this news item. There was a big fire that happened last night in San Simon, Pampanga. Hundreds of families were left homeless. The governor allowed them to use the schools as their temporary shelters. Mr. Ed Reyes, a farmer from San Simon harvested 890 sacks of rice. He donated 185 sacks to the fire victims and sold the remaining sacks to 5 rice dealers. How many sacks did each rice dealer receive?
• What happened in San Simon, Pampanga? • What did Mr. Ed Reyes do? • How many sacks of rice did he harvest? • How many did he donate to the fire victims? • What did he do with the remaining sacks? • How will you solve the problem? • What is the answer?
Valuing: � What kind of a person is Mr. Ed Reyes? Why? � Do you think you can do what Mr. Reyes has done in another way? How?
B. Developmental Activities
1. Presentation
Read the problem and let the pupils answer the questions below. a. Mang Celso can collect 540 eggs in a week from his poultry farm. If he will collect in 6
weeks and will deliver these to 8 egg dealers, how many eggs will each receive? 1) What is asked? 2) What is/are given? 3) What operation will be used? 4) What is the hidden question? 5) What is the number sentence? 6) What is the correct answer? 7) Check the answer if it make sense.
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b. Mang Goyong shipped 25,286.00 worth of garlic to Mindanao and 31,484.00 worth of pepper to Visayas for sale. The two shipments cost him 1,510.00. He divided the profit among his 3 sons. How much did each one receive? 1) What is asked? 2) What is/are given? 3) What operation will be used? 4) What is the first hidden question? 5) What is the second hidden question? 6) What is the number sentence? 7) What is the correct answer? 8) Check the answer if it makes sense.
2. Fixing Skill s
Group Activity
Group the pupils into 3 groups. Give each group an Activity Sheet. Each activity sheet contains a problem and the eight questions above.
Activity Sheet 1
A store bought 428 black pens and 356 blue pens for P940.80. How much does each pen cost?
Activity Sheet 2 A storekeeper put 720 cans of milk in packages with 3 cans each. She sold each package for 37.50. How much did she receive?
Activity Sheet 3 The Romblon Marble Factory manufactured 580 marble tiles in one week. After manufacturing for 15 weeks 2 200 marble tiles were sold in Bohol. The remaining tiles were delivered to 5 provinces. How many marble tiles did each province receive?
3. Generali zation
How do you solve 2 to 3step word problems?
To solve 2 to 3step word problems, analyze the problem correctly; then follow the steps in problem solving.
C. App lication Solve the following. 1. Mang Ito gathered 350 mangoes which he equally shared among his 13 cousins and 12
neighbors. How many mangoes will each of his friends and relatives receive? 2. Bea has collected 260 stamps. She placed them in albums. The first 15 pages have 8 stamps
each and the next pages have 7 stamps each. How many pages were with 7 stamps each?
IV. Evaluation
Solve the following problems. 1. Four people shared a room in a hotel. The cost of room rental is 3,576.00. They paid a down
payment of 1,000.00 and shared equally the cost of the remaining balance. How much did each of them share?
2. Mr. Miranda collected 1,250.00, 1,350.00 and 1,550.00 as rentals for their 3door apartment. If he were to divide the total amount collected among his 5 children, how much would each child get?
3. Agnes harvested 1 776 chicos. She gave 120 chicos to her mother and put the remaining chicos in 12 baskets. How many chicos were placed in each basket?
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4. Mr. Avila used a jeep to transport 1 629 kg of bananas. He delivered 645 kg to his customer in Divisoria and the rest to his 3 customers in Quiapo. How many kg of bananas did each customer in Quiapo receive?
5. Kenneth sold 1 296 roses. He gave 120 pieces to the church and tied the rest in bunches of 12 pieces each. How many bunches did he make in all?
V. Assignment
Solve the following problems. 1. Last month, Rico and Jojo worked in Mrs. Agsaway’s farm. They earned 5,150.00 but spent
750.00 for their food. If the remaining amount was divided equally between them, how much did each of them get?
2. Noli had 9 850 mangoes. He placed 1 100 small mangoes in a sack and put the big ones in baskets which could hold 50 pieces each. How many baskets did he use?
3. Mr. Cruz bought a new TV set worth 28,575.00 in an appliance center and availed of its “zerointerest plan” promo. If he paid a down payment of 8,000.00 and he will pay the balance equally in 5 months, how much will be his monthly amortization?
Reading and Writing Decimal Numbers I. Learning Objectives
Cognitive: Read decimal numbers through hundredths Psyc homotor: Write decimal numbers through hundredths Affective: Show hospitality to visitors
II. Learning Content
Skill : Reading and writing decimal numbers through hundredths References: BECPELC II.A.1.3 Materials: flash cards, chart, place value chart Value: Hospitality
III. Learning Experiences
A. Preparatory Activities
1. Drill Show illustrations of figures divided into 10 or 100 equal parts. Let children identify the fractional parts of the whole.
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2. Review Based on the drill, let the children write the decimal form of the above fractions.
3. Motivation
There were 100 boys and girls who welcomed the vicepresident of USA at the Airport. Of the 100 pupils, 60 were girls and the rest were boys. Valuing: � Do we have to welcome foreign visitors in that manner? Why? � What character trait of Filipinos did the children demonstrate?
B. Developmental Activities
1. Presentation
a. Analyze the situation given.
• How many pupils welcomed the vicepresident of USA? • How many were girls? • What is the number of girls in fraction form? In decimal form? • How many were boys? • What is the number of boys in fraction form? In decimal form?
b. Present the place value chart below.
Ones . Tenths Hundredths . 6 0 . 4 0
Let volunteers place the decimal numbers on the chart.
Explain to the children that a hundredths decimal has two decimal place values. Let the children read the decimals. Emphasize to them the correct spelling of hundredths.
c. The basketball court is divided equally into 100 parts for the mass demonstration. The
Grade 4 children are occupying 41 out of the 100. What decimal part of the big square are
the children occupying?
(At this point, if the children still do not know that 41 of 100 is 25, they have to discover or
make an educated guess as to the decimal part occupied by the children. They have to get a graphing paper or draw lines to get the correct answer.)
d. Emphasize how decimal numbers are read.
1) 0.60 is read as sixty hundredths 2) 0.40 is read as forty hundredths 3) 0.4 is read as four tenths 4) 0.6 is read as six tenths
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2. Fixing Skill s
a. Read the following:
0.15 0.16 0.56 0.24 0.05 0.18 0.35 0.02 0.59 0.05
b. Write the following in decimals.
1) ten hundredths 2) twentyfive hundredths 3) three hundredths 4) six hundredths 5) twelve hundredths
c. Complete the series.
1) 0.25, _____, 0.27, _____ 2) 0.15, _____, _____, 0.12 3) 31 , _____, _____, 34 100 100 4) 0.38, _____, 0.40, _____ 5) 5 , _____, 7 , _____ 100 100
3. Generali zation What should you remember in reading and writing decimals?
a. Read the number after the decimal point as a whole number and then name the place value position of the last digit.
b. If a decimal number is in hundreths, there are two decimal places to the right of the decimal point.
C. App lication
Noli picked 100 oranges from the orchard. He gave his friend 25 oranges. Give the decimal
number for the oranges Noli gave to his friend. Read it.
IV. Evaluation 1. Write the following decimals.
a. Seven hundredths b. Eightytwo hundredths c. Sixtyfive hundredths d. Two tenths
2. Read the following decimals orally.
a. 0.3 b. 0.8 c. 0.28 d. 0.09 e. 0.15 f. 0.04
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V. Assignment
1. Read orally. a. 0.33 b. 0.15 c. 0.75 d. 0.13 e. 0.05 f. 0.46 g. 0.83 h. 0.02
2. Write as decimals.
a. Three tenths c. Five hundredths e. Four tenths
b. Twentysix hundredths d. Thirtyfive hundredths
Renaming Fractions to Decimals I. Learning Objectives
Cognitive: Rename in decimal form fractions whose denominators are powers of 10 Psyc homotor: Write fractions as decimals Affective: Show cooperation with the group
II. Learning Content
Skill s: 1. Renaming in decimal form fractions whose denominators are powers of 10 2. Writing fractions as decimals
References: BECPELC II.A.1.4 Materials: illustrations, counters, cartolina strips, activity sheets Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill Let the pupils read the following decimals using flash cards.
0.43 0.9 2.5 4.46 0.7 0.25 3.65 9.2
2. Review
Ask the pupils to write the common fraction and decimal number for each of the shaded parts below:
a) b) c)
d) e)
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3. Motivation
Distribute strips of cartolina to the pupils with the following information.
Four tenths 0.36 Two and five tenths 12.3 Twelve and three tenths 0.4 Two and five hundredths 2.05 Thirtysix hundredths 2.5 The first pair of pupils with the correct decimals in figures and in words will come to the
front and get the stick with the word “first”. The other pairs will do the same. B. Developmental Activities
1. Presentation
a. Activity 1
Let the pupils get 10 counters. Ask them to set aside 4 counters. What fractional part of the whole set is your 4 counters?
Write the answer on the board. (10
4)
Repeat the process with other numbers: 3, 6, 9 (10
3 , 10
6 , 10
9 )
b. Activity 2
Show the pupils a bundle of 100 sticks. Ask a pupil to get 7 of the sticks. What part of the sticks did you get? Write the
answer on the board. (100
7 )
c. Activity 3
Study the number line.
1 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
What does the short line segment show? (10
7 )
What does the long line segment show? (10
16 )
d. Activity 4
Present the place value chart.
Tens Ones Tenths Hundredths 0 . 4 0 . 0 7 0 . 7 1 . 6
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Put all the answers from Activity 13 on the place value chart.
What do you notice about 104
and 0.4? 100
7 and 0.07?
What replaced the denominator 10? What replaced the denominator 100? How many digits are there after the decimal point in tenths? In hundredths? How about if it is in thousandths? If it is in ten thousandths?
e. Activity 5
Divide the class into three groups Give each group an Activity Card. Emphasize that each member of the group has to cooperate with each other in answering the exercises to be sure that the answers are correct? What good will this do?
Activity Sheet #1
Write the following fractions as decimals.
9 5 35 . 6 . 34 . 32. 12 . 7 . 153 . 10 10 10 000 10 1 000 10 100 10 100
Activity Sheet #2
Put a check (9) if the pair is correct and a cross (x) if it is wrong.
1) 103 = 0.3 2)
1004 = 0.40 3)
1005 = 0.50
4) 10074 = 0.74 5)
100016 = 0.016 6)
10013 = 0.13
Activity Sheet #3
Write the missing numbers.
a. 0.07 = ___ b. 0.7 = ___ c. 0.32 = ___ 100 10 100
d. 0.3 = 3 . e. 0.47 = 47 . f. ____ = 95 . ___ ___ 100
2. Analysis and Discussion
Call a member from each group to read their answers. Valuing: � After all the groups have given their answers, ask: “How did you work as a group? Did all
the members cooperate in working on the answers? Was there any member of your group who did not cooperate? Why is cooperation important in any group work?”
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3. Generali zation
How do we rename fractions whose denominators are powers of 10 in decimals? To rename fractions whose denominations are powers of 10 we must remember that:
a. a denominator of ten means tenths in decimal. Write the numerator with a decimal point
at the left. b. a denominator of 100 means hundredths in decimal. It has 2 places to the right of the
decimal point. c. a denominator of 1 000 means thousandths in decimal. It has 3 places to the right of the
decimal point.
C. App lication Write each number as a decimal.
1. Barbara rode her bicycle 108
of a kilometre to school.
2. The winner of the race was 10024
of a second faster than the person who finished next.
IV. Evaluation
A. Match Column A with column B.
A B 1) 7 10
a. 0.68
2) 2 100
b. 0.02
3) 68 100
c. 0.9
4) 9 10
d. 0.40
5) 40 100
e. 0.7
B. Write a decimal for each fraction.
1) 8 2) 16 10 100 3) 24 4) 5
100 10 5) 9 100
C. Write a fraction for each decimal.
1) 0.8 2) 0.213 3) 0.01 4) 0.12 5) 0.85
V. Assignment
Write the decimal for each number.
1. The taxi traveled 104
1 kilometres from St. Mark’s Square to the glass factory.
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2. Mang Ramon made a pitcher out of clay in the shape of a swan. The pitcher holds 10075
1 litres of
water.
3. The tour of Rizal Park takes 10025
3 hours.
4. Joan walked 103
4 blocks to see the San Agustin Church.
4. The length of my room is 103
2 metres.
Place Value of Decimal Numbers I. Learning Objectives
Cognitive: Name the place value of each digit of a given decimal number Psyc homotor: 1. Give the place value of the digits of a given decimal number
2. Place the digits in its proper place in the place value chart Affective: Show sportsmanship during games or competition
II. Learning Content
Skill : Naming the place value/value of the digits in a given decimal number References: BECPELC II.A.1.5 Materials: place value chart (on manila paper or cartolina), money, flash cards, showme
cards Value: Cooperation
III. Learning Experiences
A. Preparatory Activities 1. Drill
a. Show decimals written on flash cards.
Pupils will read these orally. b. Show decimals in words.
Pupils will write them in standard form using the showmecards.
2. Review Review the place value chart of whole numbers.
3. Motivation
Present this problem opener.
Marc has 25centavo coins in his pocket. The coins totaled to 3.50. How many 25centavo coins does Marc have?
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B. Developmental Activities 1. Presentation
a. Using play or real money, have pupils discover how many 25centavo coins are there in
1.00, 5.00 and 0.50. b. From these, they will discover a pattern and will be able to find out if their answer in the
problem opener is correct. c. Use this strategy as a spring board for the lesson of the day.
1.00 = 1 whole 0.50 = hundredths
d. Present the place value chart for decimals. Place the 1.00 and the 0.50 in the chart. 1 . 5 0
e. At this point, explain to the pupils the place value of decimal numbers. Explain too the “value” of each place.
f. Give some decimal numbers and place each digit to its specific place in the place value
chart. 93.9 49.368 412.246 386.03 20.107 0.0053 52.123
g. From the place value chart, elicit from the pupils the value of each digit in 52.123. 5 means 5 tens
2 = 2 ones 1 = 1 tenth 2 = 2 hundredths 3 = 3 thousandths
2. Fixing Skill s
a) “Quiz Bee”
Divide the class into five groups. Give several questions to be answered. The team with the highest number of points wins. Sample Questions:
1) How many tenths are there in 6.09? 2) In the decimal 80.30, what digit is in the tenths place? 3) What is the value of 8?
b) Cooperative Learning (stress the value of cooperation) 1) Pupils will be grouped in dyads, player A and B. Each player takes turn in
answering the questions dictated by the teacher.
Hun
dred
s
Ten
s
One
s/U
nits
Dec
imal
Poi
nt
Ten
ths
Hun
dred
ths
Tho
usan
dths
Ten
T
hous
andt
hs
Hun
dred
T
hous
andt
hs
Mill
iont
hs
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2) Work with a learning partner Pupils will be paired. (a slow learner with a fast learner) Working as a team, each pair will answer the questions posted by the teacher.
Valuing:
� How did you work with your group? � How about with your partner?
3. Generali zation
Just like whole numbers, decimal numbers have place values. The value of each digit of
a decimal number depends on its place or position. The decimal point separates the whole numbers from the decimal numbers.
C. App lication Estela earned 92.75 from the sale of her banana fritters. She gave this amount to her mother for their daily expenses. 1. What is the value of 9? 2. What is the value of 2? 3. What is the value of 7? 4. What is the value of 5?
IV. Evaluation
A. Identify the place value of the underlined digit in each given numeral.
21.614 428.095 37.59 78.0069 113.015
B. In the numeral 389.756, write the place value of the following digits.
9 _____________ 8 _____________ 7 _____________ 3 _____________ 5 _____________ 6 _____________
C. Give the missing word and corresponding number.
861.085 The 5 in the (thousandths) place means (1000
5)
31.52 The 2 in the ___________ place means _______ 18.653 The 6 in the ___________ place means _______ 6.54893 The 3 in the ___________ place means _______ 36.0543 The 4 in the ___________ place means _______
V. Assignment
A. Give the place value of each underlined digit. 1. 215.05 2. 9.13 3. 14.165
4. 5.0052 5. 18.709
B. Identify the digit of the number 168.324 according to the place value indicated below.
1. Tenths _____________ 2. Thousandths _____________
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3. Hundreds _____________ 4. Hundredths _____________ 5. ones _____________
Express ing/Writing Money as Pesos and Centavos I. Learning Objectives
Cognitive: Express money as pesos and centavos Psyc homotor: 1. Write money as pesos and centavos
2. Use the peso sign ( ) in writing money Affective: Spend money wisely
II. Learning Content
Skill : Writing money as pesos and centavos References: BECPELC II.A.2 Materials: play money, flash cards, charts Value: Thrift and economy
III. Learning Experiences
A. Preparatory Activities
1. Drill
Using flash cards, give the value of the following a) b)
c) d)
e) f)
20
20
1,000
100
5
50¢
500
500
20
25¢
500
100
50
20
50 10
100
100
155
g) h)
i) j)
2. Review
Review the place value chart for decimal.
3. Motivation
Have you gone shopping? What did you buy? Did you buy everything that you like? Why? Valuing: � If you buy only what you need, what does that show? Is it important to be thrifty? Why?
Therefore, what should you practice?
B. Developmental Activities
1. Presentation
a. Activity 1 1) Put up a mini fruit stand in a pocket chart or on your table. Each fruit should have a
tag price. 2) The pupils will buy from the fruit stand.
Example: Jose wanted to buy a bunch of bananas. 3) The seller would say the cost of the fruits bought.
Example: Bananas cost 35.00 per kilo 4) Using the play money, ask the pupil to give 1 20.00, 1 10.00 and 1 5.00. 5) Write the amount of money as 35.00.
• What symbol was used? • How is it written?
b. Activity 2
1) Group the class into four groups. Using the mini fruit store, the leader will act as the
seller and the members will act as the buyers. Pupils will list down the items they bought from the mini fruit stand. Then they will write the amount of each item using symbols.
2) Write each amount using the peso sign. a. ten pesos b. eight pesos and fifty centavos c. ninety centavos d. sixty pesos and eight centavos e. one hundred twenty pesos and thirtyfive centavos
100 500
10 10
5
5 25¢
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2. Fixing Skill s Michael deposited his savings from his allowance. Write the amount of his daily deposit:
Week 1 – 2 tenpeso bills and 6 onepeso coins Week 2 – 1 fiftypeso bill and 3 tencentavo coins Week 3 – 3 tenpeso coins and 1 fivepeso coin Week 4 – 5 fivepeso coins and 2 twentyfivecentavo coins
3. Generali zation
How do you write money?
Remember, the peso sign ( ) is used in writing pesos and centavos. The decimal point, which is read as “and”, separates the pesos from the centavos.
C. App lication
1) Match the amount in words with the amount in figures. I II ___1) Thirtysix pesos a. 9.15 ___2) Two hundred pesos b. 1,020.00 ___3) Fortyfive centavos c. 36.00 ___4) Nine pesos and fifteen centavos d. 200.00 ___5) One thousand twenty pesos e. 0.45 f. 3.60
2) Every lunch time, Olivia eats at the cafeteria since the food there is cheaper compared to the
food sold in the store outside the school. Below are the prices of the food.
Rice – four pesos and fifty centavos per cup Menudo – twentyfive pesos and fifty centavos per plate Soup – two pesos and seventyfive centavos per bowl Leche Flan – six pesos and ninetyfive centavos per slice Write the prices of the food in figures on the blank.
Rice _____ Menudo _____ Soup _____ Leche Flan ____ • How much is the cheapest food item? • If you want to save, which will you buy during meal time? • How much does it cost you? • How much can you save?
IV. Evaluation
A. Write each amount of money. Use the peso sign. a. 3 pesos and 20 centavos b. 9 centavos c. 89 centavos d. fifteen pesos and five centavos e. nine hundred pesos and seventyfive centavos
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B. Write the total amount for each in your paper.
a.
b.
c.
d.
C. Write the price of each article using the peso sign. Article Amount in Words Figures Tshirt one hundred pesos and fifty centavos ________________ Dress two hundred pesos and ninetyfive centavos ________________ Shoes five hundred pesos and ninetyfive centavos ________________ V. Assignment
Write the amount using the peso sign. 1) 720 centavos 2) 20 999 centavos 3) 1 334 centavos 4) 5 871 000 centavos 5) 17 000 centavos
Rounding Decimals I. Learning Objectives
Cognitive: Round decimals to the nearest tenths/hundredths/thousandths Psyc homotor: Write the rounded form of decimals to the nearest tenths, hundredths,
thousandths Affective: Develop speed in rounding decimals through thousandths
5
5¢ 100
25¢
5 10 10¢
1 5¢
500
500
10
50 5
100
50 10¢ 5¢
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II. Learning Content
Skill : Rounding decimals to the nearest tenths/hundredths/thousandths References: BECPELC II.A.3 Materials: flash cards, chart Value: Preciseness and speed
III. Learning Experiences
A. Preparatory Activities
1. Drill Round off the whole number to the indicated place value.
6 754 (hundreds) 58 495 (thousands) 37 638 (tens) 38 754 (ten thousands) 76 850 000 (millions)
2. Review
Choose the rounded numbers from the given numbers.
Rounded Numbers Given Numbers a. 800 748 854 775 b. 1 000 1 565 1 040 1 605 c. 20 000 20 218 18 999 20 841 d. 95 000 95 500 94 806 95 132 e. 8 000 000 8 900 000 8 525 000 8 300 000
3. Motivation
Guessing game
The teacher will dictate a number. The pupils will guess the number being referred to like: “this number is close to 50. It is between 45 and 47. What is the number?” Pupils will mention the number. Another example: “this number is 3 more than 40. What is the number?” (continue this activity until the pupils master the game)
B. Developmental Activities
1. Presentation
Use a problem opener using a number line.
During the Palaro ng Bayan, Aris ran the 100metre dash for 11.843 seconds. Mike ran the same event for 11.861 seconds. Who is faster between the two runners?
Let us look at the number line.
11.800 11.820 11.840 11.860 11.880 11.900
11.810 11.830 11.850 11.870 11.890
a. How many seconds did it take Aris to run the 100metre dash? (11.843 seconds) b. Locate this in the number line. c. Let us round the number 11.843 to the nearest tenths.
159
d. To where is it closer ? 11.800 or 11.900? e. How many seconds did it take Mike to run the 100metre dash? (11.861 seconds) f. Locate this in the number line g. To where is it closer? to 11.800 or 11.900?
Therefore, 11.843 rounded off to the nearest tenths is 11.8 and 11.861 rounded off to the nearest tenths is 11.9.
h. Who ran faster? Who won the race? Valuing: � Why do we have to work quickly and properly in doing our lesson? (We have to work
quickly and properly in doing the lessons so that we can save time.) Do you do this also at home? Why? (Have pupils cite examples.)
Discovering a pattern. Study how the decimals are rounded.
0.3168 tenths 0.3 hundredths 0.32 thousandths 0.317 1.2871 tenths 1.3 hundredths 1.29 thousandths 1.287
a. What is your point of reference when rounding decimals? (the place value to be rounded
and the number to its right). b. What happens to the digit of the number that you are rounding if the number to the right
of it is 5 or higher? If it is lower than 5? 2. Fixing Skill s
Round the following to the nearest place as indicated. Tenths Hundredths Thousandths 8.7256
12.6321 87.0568 22.0054 35.1069
3. Generali zation
How do we round decimals to the nearest tenths? nearest hundredths? nearest
thousandths?
C. App lication Rex finished cycling about 18.8216 km in 3 hours. Around how many km did he finish to
the nearest tenths? nearest hundredths? nearest thousandths? IV. Evaluation
1. Round the following as indicated.
a. 0.6542 (nearest tenths) b. 0.9568 (nearest thousandths) c. 10.2346 (nearest hundredths) d. 73.6834 (nearest thousandths) e. 25.1934 (nearest tenths)
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2. Complete the table. Round each number to the given place value. Tenths Hundredths Thousandths 89.6273 0.8495 5.0637
347.9641 93.4672
V. Assignment
Round off the underlined digit.
a. 0.653 b. 0.467 c. 6.8321 d 2.4623 e. 2.1832
Adding Decimal Numbers I. Learning Objectives
Cognitive: Add decimals through hundredths without and with regrouping Psyc homotor: Place the decimal points in a column Affective: Show thoughtfulness during special occasions
II. Learning Content
Skill : Adding decimals through hundredths without and with regrouping References: BECPELC II.B.1 textbooks in Math 4 Materials: flash cards, chart Value: Thoughtfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Put the sum on the outer spaces of the box.
+40
15 26
83 71 38
64
47 52
+122
832 651
373 706 440
625
714 326
+318
453 639
453 928 736
686
754 622
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2. Review a. Read these decimals and amount.
0.06 0.2 0.17 5.06 24.95 0.9 0.07 0.28 12.50 6.15 b. Write in decimals.
nineteen hundredths four tenths five tenths sixtyfive hundredths three hundredths
3. Motivation
Have you wrapped a gift? What are the things we need in wrapping a gift? When do we give gifts?
B. Developmental Activities
1. Presentation
Elaine used 0.5 metre of red ribbon and 0.8 metre of white ribbon on the gift that she will give her mother. How many metres of ribbon did she use? a. How many metre of red ribbon was used? (0.5)
How many metre of white ribbon was used? (0.8) Valuing: � Why did Elaine give her mother a gift? What kind of a girl is Elaine? Do you also do what
Elaine is doing? Why?
b. Let us illustrate using a number line. 0 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
0.5 + 0.8 = 1.3
c. Using the shortcut method: 1
0.5 + 0.8 1.3 Find the missing number. a. 0.5 . b. 0.45 c. 0.93 d. 0.36 e. 0.49 f. 0.86 +0.25 +0.37 +0.25 +0.87 +0.53 +0.75
2. Analysis/Abstraction a. How do we add decimal numbers? b. Why do we write the numbers in column?
162
3. Fixing Skill s a. Find the sum. 1) 0.3 2) 0.12 3) 0.15 4) 0.26 5) 0.82
+ 0.5 + 0.25 + 0.04 + 0.42 + 0.23 b. Arrange in column then add.
1) 0.12 + 0.15 = 2) 0.25 + 0.38 = 3) 0.34 + 0.99 = 4) 0.68 + 0.36 = 5) 0.75 + 0.49 =
c. Copy and complete each table by adding the decimal down and across.
0.13 0.05 0.08 0.57
0.26 0.78 0.42 0.69
4. Generali zation
How do we add decimals?
Adding decimals is like adding whole numbers. Remember to place the decimal points in one column.
C. App lication Add.
1) 0.5_ 2) 0.63 3) 0.39 4) 0.79 5) 0.92 +0.14 +0.27 +0.93 +0.78 +0.73
IV. Evaluation A. Find the sum of the following:
1) 0.3_ 2) 0.53 3) 0.41 4) 0.92 5) 0.74 + 0.04 + 0.25 + 0.9_ + 0.50 + 0.28
B. Arrange in column then add. 1) 0.53 + 0.46 = 3) 0.27 + 0.83 = 5) 0.65 + 0.93 =
2) 0.09 + 0.38 = 4) 0.95 + 0.67 =
C. Answer the following:
1) What is the sum of 0.72 and 0.49? 2) Increase 0.57 by 0.38. 3) Add 0.46 to 0.78 then add 0.16 4) Find n. 0.47 + 0.36 + 0.12 = n 5) Add 0.69 to the sum of 0.37 and 0.79
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V. Assignment Find the sum of each.
1) 0.85 2) 0.62 3) 0.23 4) 0.96 5) 0.15 +0.66 +0.78 +0.57 +0.02 +0.98
Arrange in column and give the sum. 1) 0.63 + 0.78 + 0.7 = 3) 0.92 + 0.9 + 0.76 = 5) 0.36 + 0.08 + 0.86 =
2) 0.62 + 0.34 + 0.57 = 4) 0.93 + 0.84 + 0.8 + 0.42 =
Give your answer to each of the following:
1) 0.89 more than 0.8 is ____ 2) 0.06 added to 0.79 gives ____ 3) Increase 0.47 by 0.07 ____ 4) When 0.19 and 0.62 are put together, the result is ____ 5) 0.63 more than the sum of 0.06 and 0.85 is ____
Subtracting Decimal Numbers I. Learning Objectives
Cognitive: Subtract decimals through hundredths without and with regrouping Psyc homotor: Write decimal numbers in column Affective: Appreciate the importance of exercise to one’s health
II. Learning Content
Skill : Subtracting decimals through hundredths without and with regrouping References: BECPELC II.B.1 Materials: counters, charts, flash cards Value: Health consciousness
III. Learning Experiences
A. Preparatory Activities
1. Drill Light each bulb mentally every time you get an exact difference by subtracting the outer number from the middle number.
100
59
48
77 25
68 69
25 32 17
56 41
52
351
263
118
125 234
143
164
2. Review Review place value in tenths and hundredths. Give the place value of the underlined digits.
0.42 0.38 1.03 5.48 7.65 12.5 15.72 10.18
3. Motivation How many of you are Boy scouts or Girl scouts? What activities do you have in scouting? Have you ever done some hiking? Did you enjoy the activity? Valuing: � What is the importance of doing this kind of activity? What other activities are good for
our body?
B. Developmental Activities
1. Presentation
a. Read this problem.
The Boy Scouts hiked a distance of 0.75 kilometre in the morning and 0.43 kilometre in the afternoon. How much farther did they hike in the morning than in the afternoon?
b. Analyze the problem then answer the questions below. 1) How far did the boy scouts hike in the morning? (0.75 km) 2) How far did the boy scouts hike in the afternoon? (0.43 km) 3) How much farther did they hike in the morning than in the afternoon? 4) Illustrate the problem.
c. Present the decimals in a place value chart.
Ones . Tenths Hundredths 0 . 7 5 0 . 4 3 0 . 3 2
Ask: What do you notice about the decimal point? (in column)
Show how subtraction is done. Emphasize that decimal points should be kept in column. Show how the answer may be checked by addition.
d. Present another problem.
In a long jump competition, Emma recorded 0.85 metre while Lina has a record of 0.48 metre. How much farther did Emma jump than Lina?
Analyze the problem. 1) What are the facts given? (0.85, 0.48) 2) What is asked in the problem? 3) What shall we do to find the answer? 4) How do we subtract decimal numbers? 5) Present the solution step by step.
Difference Æ
165
Step 1 – Write the decimal numbers in column. 0.85 0.48
Step 2 – Regroup and subtract the hundredths. 7 1
0. 8 5 0. 4 8 7
Step 3 – Subtract the tenths. 7
0. 8 5 0. 4 8
3 Step 4 – Write the decimal point in the answer in column. 0.85 0.48 0.37
a. Show how to check the answer by adding. • Add the subtrahend and the difference. • The sum should be the same with the minuend.
0.48 +0.37 0.85
b. Give two more decimals for them to subtract. 0.87 0.93  0.23  0.76
2. Guided Practice
a. Copy each item on your paper then subtract. 1) 0.73 2) 0.83 3) 0.45 4) 0.76 5) 0.52  0.42  0.51  0.28  0.59  0.28
b. Write the decimals in column, then subtract.
1) 0.65 – 0.40 = 2) 0.12 – 0.05 = 3) 0.79 – 0.32 = 4) 0.22 – 0.16 = 5) 0.67 – 0.43 =
c. Align the decimals and then subtract.
1) 0.56 – 0.39 = 2) 0.63 – 0.27 = 3) 0.82 – 0.58 = 4) 0.74 – 0.36 = 5) 0.59 – 0.32 =
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3. Generali zation How do we subtract decimals?
When subtracting decimals, a. Write the decimal numbers with the decimal point in column. b. Start subtracting. c. Regroup, if needed. d. Place the decimal point aligned it in the answer.
C. App lication
Read and solve the problem.
A whole squash weighed 0.95 kg while a whole upo weighed 0.75 kg. Which is heavier? By how many kilograms?
IV. Evaluation A. Find the difference.
1) 0.92 2) 0.84 3) 0.88 4) 0.63 4) 0.56  0.61  0.27  0.79  0.47  0.29
B. Write the decimals in column then subtract. 1) 0.98 – 0.37 = 2) 0.57 – 0.32 = 3) 0.75 – 0.28 = 4) 0.65 – 0.39 = 5) 0.87 – 0.48 =
C. Find the difference by subtracting horizontally and vertically.
0.78 0.57 0.39 0.26
0.82 0.34 0.54 0.19
V. Assignment
Answer the following: 1. Subtract 0.38 from 0.51 2. Find the difference between 0.63 and 0.92 3. Take away 0.52 from 0.70 4. What is 0.54 less than 0.91? 5. What is the value of n in 0.81 – 0.56 = n?
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Adding Mixed Decimals I. Learning Objectives
Cognitive: Add mixed decimals with or without regrouping Psyc homotor: Read and write mixed decimals properly Affective: Show helpfulness and cooperation Internalize the importance of being thrifty
II. Learning Content
Skill : Adding mixed decimals with or without regrouping References: BECPELC II.B.2.1
textbooks in Math 4 Materials: different kinds of vegetables (real vegetables), bamboo sticks, tape measure,
basket, flash cards, drill boards, money, canteen sales, ruler Values: Industry, thriftiness, helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Wheel of Number Give the sum of the combination of numbers orally.
2. Review
Find the sum by adding diagonally and horizontally.
0.3 0.36 0.8 0.9 0.7 0.22
0.11 0.4 0.1
3. Motivation Mother wants to prepare “pinakbet” for lunch. Can you help her get or buy the vegetables
for the menu?
+9
9
6
8
4 3
7
2
1
+12
10
8
3
11 7
6
4
9
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B. Developmental Activities
1. Presentation Study the list of vegetables sold in a vegetable stand.
Vegetable Stand eggplant 15.00/kilo squash 22.50/kilo sayote 15.50/kilo string beans 10.50/bundle carrots 12.00/kilo kangkong 5.00/bundle tomatoes 20.00/kilo okra 5.00/bundle
What are the vegetables needed in cooking “pinakbet”? About how many kilograms of each vegetable does mother need? About how much will she pay for the vegetables?
2. Group Activity Group 1: Amount of money in mother’s wallet a. List down the amount of money according to denominations. b. Determine the process to be used and solve.
Group 2: Finding the exact distance of the house to the market a. Determine the exact distance of the house to the market and vice versa. b. Determine the process to be used and solve.
1.25km
Group 3: Pinakbet preparation Materials: Different kinds of vegetables with a tag price, basket, money a. Get the vegetables to be included in the preparation of pinakbet. b. Make a list of the vegetables and their specific price. c. Plan for the process to be used. d. Solve for the answer.
house
market
100 50 25
50 25
25¢ 25¢
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Group 4: Finding the exact weight of the vegetables Vegetable Weight Okra 1.25 kg Eggplant 1.8 kg Squash 1.20 kg String beans 1.50 kg Sayote 1.75 kg Kangkong 1.25 kg
a. Write the number of kilograms of every vegetable. b. Determine the operation to be used. c. Solve for the total weight of the vegetables.
3. Practice Exercises
a. The following pupils are joining the picnic together with their contributions.
Anna – 75.50 Maria – 162.75 Jenny – 84.00 Remy – 95.25 Jenny – 87.50
b. If you add Anna’s, Maria’s and Jenny’s contributions, how much would that be? c. What is the total amount of their contribution?
4. Generali zation
How will you add mixed decimals?
a. Write the numbers in column. b. Align the decimal points. c. Add, regroup if necessary.
C. App lication
Dyad: “Counting money” 1. Every pair will be given a box which consists of coins and bills. 2. The pair should determine the amount of money in the box.
IV. Evaluation
Solve: 1) 2.37 + 22.7 = 2) 26.50 + 41.21 + 2.27 = 3) Canteen sales slip: (Teacher should prepare a sales slip.)
a. If you have 20.00, what items can you buy from it? b. Write the items and the price then solve.
4) Grocery sales slip: If you have 50.00, what items can you buy from it? Why?
V. Assignment
Add: 1) 2.72, 43.43 2) 26.28, 143.48
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3) 738.75, 443.20, 10.00 4) Jose is 155 cm tall last year. This year, he grew by 2.2 cm. How tall is he now? 5. A butcher weighed two hogs. The first hog weighed 43.5 kg and the second 39.3 kg, what is the
total weight of the two hogs? Valuing: � If you have 50.00, are you going to spend it all? Why?
Subtracting Mixed Decimals I. Learning Objectives
Cognitive: Subtract mixed decimals through hundredths with or without regrouping Psyc homotor: Write the mixed decimals in column Affective: Practice ways of conserving water
II. Learning Content
Skill : Subtracting mixed decimals through hundredths with or without regrouping References: BECPELC II.B.2.2 Materials: flash cards, written exercises on a cartolina, picture, a glass of water Value: Water conservation
III. Learning Experiences
A. Preparatory Activities 1. Drill
Subtract the following numbers (using flash cards) 42 63 87 78 91 49
 21  40  11  25  50  23
32 96 88 54 65 73  24  77  39  15  38  59
2. Review
Subtraction of decimals with regrouping
0.51 0.72 0.84 0.60 0.90  0.38  0.56  0.45  0.27  0.63
3. Motivation
Show a glass of water. Talk about the importance of water. Ask pupils to give ways of
conserving and preserving our water resources. Show the picture of the water level gauge at La Mesa Dam. Tell them what this is all about.
171
B. Developmental Activities 1. Presentation
a. Read and analyze this problem. At the start of summer, the water level at La Mesa Dam stood at 1.3 metres. By the
end of summer, it dipped by 0.4 m. What was the water level at the end of summer? b. Answer the following:
1) What are the given facts? 2) What is asked? 3) How will you find the answer?
c. Let us use the number line to find the answer.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
d. Show how it is done by presenting a place value chart. Regrouping 1 ones to make 13 tenths
Ones . Tenths 1 . 13
 0 . 4 0 . 9
e. Show how the answer may be checked by adding.
To check: 0.4
+ 0.9 1.3
f. Present the skills by using the shortcut method,
Using the shortcut method: 1.3
 0.4 0.9
g. Give 3 more examples for them to work on using the shortcut method.
Find the difference: 1.86 3.27 1.19
 0.65  1.48  0.42
2. Guided Practice a. Find the difference.
1) 4.4 2) 8.7 3) 8.6 4) 5.8 5) 98.25  2.3  6.4  4.2  4.5  6.9_
b. Subtract: 1) 45.45 2) 83.78 3) 98.05 4) 70.78 5) 89.30
 13.12  27.39  76.27  14.27  42.87
0.9 0.4
1.3
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c. Study the following items. Draw a check mark on the blank if the difference is correct. If it is not, write the correct answer on the blank provided for. 1) 35.25 2) 82.40 3) 49.38 4) 426.00 5) 830.01
 16.30  46.53  18.26  317.62  242.37 19.15 35.87 32.12 11.62 587.74
3. Generali zation
How do we subtract mixed decimals?
Subtracting mixed decimals is just like subtracting whole numbers. Be sure the decimal points are in column before subtracting. Regroup as needed.
C. App lication
Read the problem then solve on your paper. The winner in a 100metre dash took 10.7 seconds to reach the finish line, while the runner
up took 11.4 seconds. What was the difference in speed between the runners?
IV. Evaluation A. Subtract the following:
1) 7.2 2) 34.8 3) 92.7 4) 25.9 5) 98.25  3.0  12.4  14.8  15.4  22.05
B. Write these numbers in column and find the difference.
1) 2) 49.70 3) 75.09
8.72  3.80  25.45  38.09
4) 75.09 5) 95.80
 50.30  44.08
C. Read and solve the following problems: 1) Marco’s big brother is 1.10 metres tall. The difference between Marco’s height and that of his
brother is 0.35 metre. How tall is Marco? 2) The high jump record for the day was 2.15 metres. Joseph’s high jump was 2.08 metres.
How much higher was the record jump for the day than Joseph’s high jump? 3) Bert weighs 50.45 kilograms and his brother Ernie weighs 48.85 kilograms. How much more
does Bert weigh than his brother? 4) A set of coloring pencils costs 65.53 and a box of crayons cost 48.95. How much
more was the cost of the set of coloring pencils than the crayon? 5) Davao City got 19.2 cm of rain last year and 16.83 cm of rain this year. How many cm was
the decrease? V. Assignment
A. Write the decimal numbers in column. Then find the difference. 1) 42.04 – 8.93 = 3) 5.71 – 1.69 = 5) 14.61 – 0.53 =
2) 10.2 – 8.4 = 4) 72.04 – 12.63 =
B. Write the following in column then subtract.
1) 58.01 – 12.78 = 3) 96.5 – 40.75 = 5) 100.08 – 27.27 =
2) 358.1 – 101.11 = 4) 701.2 – 556.09 =
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Analyzing 1Step Word Prob lems involving either Add ition or Subtraction of Decimals I. Learning Objectives
Cognitive: Analyze 1step word problems involving either addition or subtraction of decimals including money through: a. telling what is asked, the given facts and correct operation to be used b. transforming the word problem into a number sentence c. stating the complete answer
Psyc homotor: Write the information correctly Affective: Practice wise use of money
II. Learning Content
Skill : Analyzing 1step word problems involving either addition or subtraction of decimals including money
References: BECPELC II.B.3.1.1 – 1.4 textbooks in Math 4
Materials: activity cards, strips of cartolina with steps in analyzing word problems Value: Spending money wisely
III. Learning Experiences
A. Preparatory Activities
1. Drill Number pocket chart The first group to complete the chart is the winner.
Place the operation to be used. (The operation may be changed as the need arises.) Write any number Space provided for the answers
+ A (6) B C D E F G 9 15
10 11 12 13 14
2. Review
Aling Rosa sold 350 green mangoes and yellow mangoes. If she sold 175 green
mangoes, how many yellow mangoes did she sell? Tell about the following: a. number of yellow mangoes b. 350 and 175 mangoes c. subtraction
3. Motivation
Luz bought a cartolina worth 10.00 and colored papers worth 24.25. How
much did she pay for these items?
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Answer the following questions: a. Who bought the cartolina and colored papers? b. Where do you think she will use these things? c. If you buy something from the store, what do you think you should do? d. What do you notice about 10.00 and 24.25? e. If you were Luz and you still have extra money would you still buy other things
besides cartolina and colored papers? Why?
B. Developmental Activities
1. Presentation If you want to know how much did Luz pay, what will you do?
We will work together in answering the problem by doing group work/activities. You may go to your own groups now.
2. Group Activities
Strategy 1: Acting out Materials: cartolina, colored papers, money (real/play) How much will Luz pay for the cartolina and colored papers? a. Members of the group will act out the problem (roleplaying) b. Pupils will show how to solve the problem by themselves through their own
understanding.
Strategy 2: Following d irections Materials: activity sheet, miniboards Note: Teacher will prepare questions to be answered by the pupils. Guide Questions: Know:  What is asked?
 What are given? Decide:  What operation will be used?  What is the mathematical sentence? Solve: Answer: Look back:  Is your answer correct? Why?
Strategy 3: Writing important words Materials: miniboards, activity sheets Things to do: Complete the statement below as you analyze the problem. a. The question is _____. b. The given facts are _____. c. The operation to be used is _____. d. The mathematical sentence is _____. e. The solution is _____. f. The answer is _____.
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Strategy 4: Illustrating/Drawing Materials: chalk, markers, miniboards, manila paper Do the following: Illustrate/draw the important facts that will help you solve the problem. Explain your answer.
3. Analysis/Abstraction
Note: In the analysis, the teacher must use the data presented by the pupils. a. Did you read the problem? b. Did you understand?
Start getting information from: Acting out – strategy 1 Illustrating/Drawing – strategy 4
Writing important words – strategy 3 Following directions – strategy 2
Correlation of ideas is important by asking questions that follow the steps in analyzing the problem.
4. Practice Exercises
a. John swam a distance of 0.4km. Daniel swam a distance of 0.62 km. How much farther
did Daniel swim than John? b. Hans weighs 62.2 kg, while his friend Carlo weighs 70.5 kg. What is the total weight of
the two boys? For Problem A • What is asked? • What are the given data? • What operation will you use? For Problem B • Write the number sentence • Solve the problem • Check the answer by using illustrations • State the complete answer
5. Generali zation
In analyzing 1step word problems involving either addition or subtraction of decimals,
follow the following steps: a. know what is asked b. know the given facts c. determine the process to be used d. write the mathematical sentence e. solve for the answer
C. App lication
1. Atty. Sison paid 450.00 for a pair of shoes and 375.00 for a shirt. What is the total cost
of the items? 2. Danica ran a 100metre dash in 15.3 seconds for the first trial, then for the second trial, it took
her 11.50 seconds. How many seconds less was her time during the second trial than on her first trial? Answer the following questions for each problem: a. What is asked in the problem?
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b. What are given? c. What is the process to be used? d. What is the mathematical sentence? e. What is the answer?
IV. Evaluation
Analyze the problems below. 1. Mother had 6.8 kg of chicken in the refrigerator. If she cooked 3.9 kg, how many kilos of chicken
were left?
a. What is asked? b. What are given?
2. Greg has a basket of ripe mangoes weighing 152.72 kilos while his brother has 163.50 kilos. How
many kilos do they have in all?
a. What is the operation to be used? b. Write the number sentence c. What is the answer?
V. Assignment
Read and analyze the problems below. Follow the steps in analyzing word problems. 1. Paro spends 260.45 for snacks and 150.50 for fare to school every week. How much does
she spend weekly for her snacks and fare? 2. Gracia needs 15.5 metres of cloth for her sala set cover and 35.62 metres for window curtains.
How many more metres are for the window curtains than for the sala set cover?
Solving Word Prob lems I. Learning Objectives
Cognitive: Solve word problems involving either addition and subtraction of decimals
including money Psyc homotor: Tell the steps in problem solving Affective: Shows accuracy and cooperation in solving word problems
II. Learning Content
Skill : 1. Solving word problems involving either addition or subtraction of decimals
2. Showing accuracy in solving word problems References: BECPELC II.B.3.1
textbooks in Math Materials: flash cards, list of prices of school supplies, money, dice/cubes with numbers
written on it Values: Accuracy and cooperation
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III. Learning Experiences
A. Preparatory Activities 1. Drill
Copy and complete each table by adding and subtracting the decimals down and across.
2.5 0.05 0.25 3.2
65.7 23.36 7.95 4.00
2. Review
Use strips of cartolina with the steps in analyzing problems written on it. The steps
involved in problem solving should be reviewed to be able to cope with the lesson. A notebook is on sale for 13.00. An eraser is on sale for 3.75. How much will both
cost? a. What is asked in the problem? b. What are the given facts? c. What is the word clue?
d. What operation will you use? e. What is the mathematical sentence?
3. Motivation
Can you buy 2 pencils with 5.00? (one pencil costs 1.75) If you are the saleslady in a store, what should you do to show accuracy in giving change?
B. Developmental Activities
1. Presentation
Let us go back to the problem in our review, what is the missing step? Can you solve the
problem now? Group Activity Group 1 – Work on the problem individually Group 2 – Work with a partner Group 3 – Work in three’s Group 4 – Work with a group (Note: The teacher will find out if all groups have the same answers.)
2. Analysis/Abstraction
How did you get the answer? Let us find out if your answers are correct. Notebook  13.00 Eraser  3.75 16.75 amount spent
What did you add to 13.00? Why did you do that?
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3. Practice Exercises Read and solve. a. Efren bought 125.50 worth of fruits while Dina bought 215.85 worth of fruits. How
much less did Efren buy? b. Mike recieved 150 for his birthday. He wanted to buy a pair of shoes worth 237.25.
How much more money does he need?
4. Generali zation How do you solve word problems involving addition of decimals?
C. App lication
Work with a “learning barkada.” (Pupils will solve the problem by learning barkadas – by 5s.) 1. Gracia needs 15.5 metres of cloth for her sala set and 35.62 metres for window curtains.
How many metres does she need in all? 2. Maila spend 260.45 for snacks and 150.50 for fare to school every week. How much
does she spend weekly for her snacks and fare? 3. On her birthday, Nelia received 150.00 from her grandmother. How much more does she
need if she wants to buy a pair of shoes worth 250.00? IV. Evaluation
Solve these problems. 1. Allan is 176.02 cm tall Harold is 155.40 cm. tall. How many cm taller is Allan than Harold? 2. Hans has a basket of mangoes weighing 145.55 kilos while his brother has 162.75 kilos. How
many kilos do they have in all? 3. Ellen had 5.5 rolls of white cloth. She used 3.8 rolls for uniform. How many rolls of cloth did she
have left? 4. Karl bought a tshirt at 129.50, a pair of rubber shoes at 275.00, and a pair of socks at
27.75. How much did he pay in all? V. Assignment
1. Father bought 6 shirts from one store and 3 more in another store. If each costs 99.00, how
much did she spend for them? 2. Daisy ran a 100metre dash in 14.6 seconds. The second time she ran, it took her 13.95
seconds. How many seconds less did she ran the second time? Analyzing 1 to 2Step Word Problems involving Add ition and Subtraction of Decimals including Money I. Learning Objectives
Cognitive: Analyze 1 to 2step word problem involving addition and subtraction of decimals
including money Psyc homotor: Write the answers to questions correctly Affective: Spend money wisely
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II. Learning Content
Skill : Analyzing 1 to 2step word problem involving addition and subtraction of decimals including money
References: BECPELC II.B.3.2.1 – 2.4 Materials: charts, cartolina strips, activity sheets Value: Thrift
III. Learning Experiences
A. Preparatory Activities
1. Drill
Use the letters of the alphabet with their corresponding values to answer the exercises that follow.
0.05 0.10 0.25 0.50 1.00 2.00 A B C D E F
G H I J K L
M N O P Q R
S T U V W X
Y Z
Example: Find the value of your name.
ALELI – 0.05 + 2.00 + 1.00 + 2.00 + 0.25 = 5.30 a. Find the value of your full name. b. Find the value of your best friend’s name. c. Find the cost of a smile and a frown. Which is more expensive? d. Find a word that is worth 0.50. e. What is the most expensive word you can find with less than 10 letters?
2. Review
What are the steps in solving 1step word problems involving either addition or subtraction? Solve the problems following the given steps. a. Paolo grows fast. In January, he grew by 1.75 cm. In July, he grew by 2.75 cm. In
December, he grew by 1.80 cm. By how many centimetres did he grow in a year’s time? b. Mylene bought a notebook for 22.50. If she gave the seller 50.00, how much
change did she receive?
3. Motivation How much money does your mother give you everyday for your allowance? Do you
spend all your money or do you save some amount? Why do you save some amount from your allowance? What do you do with the money that you save? Do you spend it wisely?
B. Developmental Activities
1. Presentation
Joanne saved 15.00 from her allowance last week and 9.50 this week. If
she used 7.50 for buying a ballpen, how much money does she have left? How are you going to answer the problem?
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2. Group Activity Activity 1
Materials: strips of paper/miniboard, markers, chalk Supply the missing data.
Activity 2
Match column A with column B. A B
1. The problem is asking for… a. ( 15.00 + 9.50) – 7.50 = n 2. The given facts are… b. 17.50 3. The hidden question is … c. Amount of money left 4. The processes to be used are… d. How much did she earn? 5. The mathematical sentence is … e. 15.00, 9.50, 7.50 6. The answer to the problem is … f. addition and subtraction
3. Analysis/Abstraction
What did we do with the problem? How did we analyze the problem? Did you follow the steps? How do you compare the steps in analyzing 1step from a 2step word problem?
What is asked?
What are the given facts?
What is the hidden
question?
What are the processes to
be used?
What is the mathematical
sentence?
What is the answer?
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4. Guided Exercises Choose the letter of the correct answer.
Remy bought a glass of juice for 6.50 and a sandwich for 8.50. How much
change did she get from 20.00?
1) What is asked in the problem? a. Remy’s change from her 20.00 b. Total cost of a glass of juice and a sandwich c. Amount she had d. Amount of money given to her.
2) What are the processes to be used to solve the problem?
a. addition and division b. addition and multiplication c. addition and subtraction d. addition and addition
3) What is the mathematical sentence?
a. 20.00 ÷ ( 6.50 + 8.50) = n b. 20.00 x ( 6.50 + 8.50) = n c. 20.00  ( 6.50 + 8.50) = n d. 20.00 + ( 6.50 + 8.50) = n
4) What is the hidden question?
a. How much money did she pay in all? b. How much change did she receive? c. How much money does she have in her wallet? d. How much money did she spend?
5) What is the answer to the problem?
a. 4.00 b. 5.00 c. 6.50 d. 8.50
5. Generali zation
How do you analyze a 2step word problem?
In analyzing word problems, we have to follow the following guide questions. a. What is asked in the problem? b. What are the given facts? c. What is the hidden question? d. What operations will be used? e. What is the mathematical sentence? f. What is the correct answer?
182
C. App lication Analyze this problem. Answer the questions that follow.
Mrs. Ventura bought an umbrella for 110.95 and a pair of slippers for 26.95. How much change did she receive from her 500peso bill? 1) What is asked in the problem? 2) What are the given facts? 3) What is the hidden question? 4) What processes will be used to solve the problem? 5) What is the mathematical sentence? 6) What is the answer to the problem?
IV. Evaluation Read and understand the problems. Answer the questions below. 1. For his project, Mark spent 38.50 for battery and 16.25 for a small bulb. How much did he
spend for his project? How much change will he receive from his 100peso bill? a. What is asked in the problem? b. What are the given facts? c. What is the hidden question? d. What are the operations to be used? e. What is the mathematical sentence suited to the problem? f. What is the correct answer?
2. Ethel used 28.5 cm and 32.5 cm of wire to hang pictures in her classroom. She cut these pieces from a 90 cm long piece. How much of the 90 cm piece of wire was left?
3. Ofelia has 12.5 m of lace. She will use 8.5 m for her dress and 5.3 m for her uniform. How many more metres of lace does she need? (The pupils will answer the same set of questions for problems 2 and 3)
V. Assignment Analyze each problem given below. Answer the following questions. 1. What is asked in the problem? 2. What are the given facts? 3. What is the hidden question? 4. What processes will be used to solve the problem? 5. What is the mathematical sentence?
a. Araceli wanted to buy a notebook for 12.25 and a ballpen for 3.75. She had only 13.25. How much more does she still need to buy the two school supplies?
b. Mrs. Montoya bought 3 chickens weighing 1.25 kg, 1.5 kg and 1.4 kg. After cooking some for
lunch, she had 1.70 kg left. How many kilograms of chicken did she cook? Solving 1 to 2Step Word Prob lems I. Learning Objectives
Cognitive: 1. Solve 1 to 2step word problems involving addition and subtraction of decimals including money 2. Determine the hidden question in the word problem
Psyc homotor: Illustrate word problems Affective: Develop industry early in life
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II. Learning Content
Skill s: 1. Solving 1 to 2step word problems involving addition and subtraction of decimals including money 2. Determining hidden question in the word problem
References: BECPELC II.B.3.2 Materials: chart on problem solving, play money Values: Industry and thoughtfulness
III. Learning Experiences
A. Preparatory Activities 1. Drill
Traveling Game The teacher will use flashcards with basic addition and subtraction facts. Divide the class into 4 groups (columns). Flash a basic fact and the first pupil to answer has to advance one pace. The game continues until all the basic facts have been flashed. The group/column that has advanced the most number of paces wins.
2. Review
Let’s analyze and solve this problem.
Felisa bought a half kilo of lanzones for 55.00. If she gave a 100.00 bill, how much change did she receive?
• What is asked? • What are given? • What is the operation to be used? • What is the number sentence? • What is the answer?
3. Motivation
Present a situation.
Edgar has a problem. It will be his mother’s birthday next week. He wanted to buy a
birthday gift for her but he doesn’t have money? How can he solve his problem? Discuss the pupils’ answers. What kind of a boy is Edgar?
B. Developmental Activities
1. Presentation
a. Solve Edgar’s problem in the motivation by reading this problem.
Edgar a balut vendor, earned 199.50 in one night and 223.25 the second night. He bought a birthday gift for his mother worth 175. How much money was left?
184
Think: What is asked? (There is a question in the problem that needs to be answered first before the given question can be answered. This is called the hidden question.) What is the hidden question? (How much did he earn in two nights?) What are given? (These are the facts needed to solve the problem.) Plan: How can you solve the problem? Get the sum of 199.50 and 223.25 then subtract 175.00 from the result. (This is the number sentence.) ( 199.50 + 223.25) – 175 =N
Solve: Step 1 Step 2 199.50 422.75 + 223.25  175.00 422.75 247.75
Look Back: Is your answer correct? Check your answer.
175.00 + 247.75 = 422.75 Answer: Edgar had 247. 75 left
b. Acting out strategy
Call a group of children to act out the problem. The setting will be a small carinderia
with menu for lunch. Today’s menu is displayed so children can order. They will use play money.
Today’s Menu
Fish Sinigang……………… 18.50 Adobo…………………………. 20.00 Kare kare……………………… 25.00 Pinakbet……………………….. 16.50 Rice…………………………….. 4.50 Banana………………………….. 2.50
Rosa: I would like to order fish sinigang, pinakbet and rice.
(She will give 50.00) Mely: Here is your change. Jojo: I have only 25.50. What can I have for lunch? I like fish sinigang, adobo and rice. How much more do I need? Mely: I’ll call Nick to help us. Questions: a. How much do you think was Rosa’s change? What is the hidden question? (Solution
will be shown to the class) b. Can Jojo have the food he wants? Why? How much more does he need? What is the
hidden question? (Show the solution on the board) c. Look back and check the answers.
2. Fixing Skill s
a. Solve the following.
1) Mr. De Leon bought 12.2 litres of gasoline on Monday, 15.4 litres on Wednesday and 13.5 litres on Saturday. How many litres of gasoline did he buy in all?
185
2) Sonia had 39.40. She spent 4.50 for a pencil and 15.00 for a sandwich and saved the rest. How much did she save?
b. Solve the following.
1) Josie used 28.5 cm and 32.5 cm of wires to hang pictures in Aling Nena’s carinderia. He cut these pieces from a 90 cm long piece. How much of the 90 cm piece of wire was left?
2) Mother has 3 kg of chicken legs in the freezer. She fried 1.75 kg. How many kg of chicken legs were left in the freezer?
c. Illustrate and solve the problem.
1) The Boy Scouts have to walk a distance of 8 km. After walking 2.5 km, they stopped to rest. Then after resting, they walked again a distance of 3.2 km then stop to rest again, How many km do they need to walk?
3. Generali zation
a. What must you do in order to understand a word problem? b. What do you do in analyzing a word problem?
C. App lication
You asked 100.00 bill from your mother because you need to buy a new pair of socks worth 45.95 and a handkerchief worth 35.95. How much change will you get? Follow the steps in problem solving.
IV. Evaluation
Study the following menu below then answer the questions that follow. Read, analyze and solve the problems following the steps in problem solving. 1. What is asked in the problem? 2. What is/are the given facts? 3. What is the word clue/s? 4. What are the processes to be used? 5. What is the mathematical sentence? 6. Solve the problem and express the answer.
Menu
Spaghetti – 23.75 Mango juice – 7.50 Palabok – 21.50 Gulaman – 6.00 Lugaw – 8.50 Nilaga (pork) – 22.50 Rice – 5.00 Pinakbet – 15.00 Fish – 12.00
1 – Mila ordered palabok and gulaman. How much did she pay? 2 – Arnel paid 50.00 for nilaga and rice. How much was the change? 3 – It was Luis’ birthday. He ordered spaghetti, palabok, mango juice and gulaman. If he paid a
hundred pesobill and gave a tip of 5.00, how much is his change? V. Assignment
Solve for the answer. 1. Vicky bought a kilo of rice for 21.50 and a bar of soap for 19.00. How much did she spend
in all? 2. Caesar bought an old bicycle for 650.00. he spent 325.00 for repair and 50.75 for
painting. Later he sold it at 1,750.50. How much was his gain?
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3. Donna bought a kg of sugar for 21.20, a can of oil for 35.75, and a toothpaste for 26.50. If she gave the cashier 100.00, how much change did she receive?
Identifying Proper Fractions/Improper Fractions/Mixed Form I. Learning Objectives
Cognitive: Identify proper fractions/improper fractions/mixed form from a given
set of fractions including those with denominators of 10 and 100 Psyc homotor: Illustrate proper fraction/improper fraction/mixed form Affective: Show carefulness in handling sharp materials
II. Learning Content
Skill s: 1. Identifying proper fractions/improper fractions/mixed form 2. Illustrating proper fractions/improper fractions/mixed form References: BECPELC II.C.1.1 Materials: fraction strips, blocks, set of small objects Value: Carefulness
III. Learning Experiences
A. Preparatory Activities 1. Drill
Have the pupils give the fraction for the shaded part in each picture.
1) 2) 3)
2. Review Fractional numbers.
Give the fraction for each. Write the fraction opposite each picture. Which is the
numerator? Which is the denominator? Is the numerator less or greater than the denominator.
3. Motivation
Look at these fractions
1 5 4 4 6 8
Ask: “Is the numerator greater than the denominator?” Let’s find out what kind of fractions are these?
187
B. Developmental Activities 1. Presentation
a. Study the number line. 0 1 2 3 4
2
0 2
1 2
2 2
3 2
4 2
5 2
6 2
7 2
8
What is half the distance between 0 and 1? (2
1 )
What is another half added to 1? (1 or 2
3 )
What is another half added to 3? (32
1 or 2
7 )
Numbers like 12
1 , 22
1 , 32
1 are mixed forms, that is a whole number
mixed with a fractional number Looking at the number line, can you give fraction which are more than one? What do we call these fractions? What are the fractions in the number line less than 1? What do we call these fractions?
b. Show fraction pies.
Ask a pupil to get and show 42
, another one to show 45
. Compare the two. Have
another pair of pupils do the same with thirds (32
, 36
) Compare them. Lead them to see
that 42
and 32
are less than a whole while 45
and 36
are more than a whole. Which are
the proper fractions? Which are the improper fractions?
c. Make comparison During the carpentry class, the boys cut pieces of wood for making shelves where
they could display their projects. The picture below shows how they cut the pieces of wood. Compare them.
3 1 1 whole 4 4
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Valuing: � What do we use in cutting wood? What should you remember when using sharp
materials like the saw?
Analysis of data 1) Is 1 more than a whole? 4 2) Does a proper fraction has the value of less than one? 3) Does it have a value of more than one? • Presenting a set of fractions (3, 1, 2, 5)
5 3 5 2 • Compare the given fractions with respect to their numerators and denominators
Ask: Which of the following fractions is not a proper fraction? 5 2 Why do you think it is not a proper fraction?
• Showing that 5 is greater than 1 2
1 whole 1 whole 1 half
Ask: How many halves do we have? 5 2 How many wholes do we have? (2) How many half more? (1)
 Letting the pupils know that 5 is an improper fraction. 2
 Asking what value does an improper fraction have?  Compare the numerator and denominator of an improper fraction  Point out that 5 is equal to 2 1. 2 2  Introduce the term improper fractions and mixed forms by saying:  5 , 5 , 3 are called improper fractions. 2 4 2  What value does each improper fraction have? (greater than 1)  Continue by saying that 2 1 , 2 1 , 1 1 are called mixed forms. 2 4 3  What are mixed forms?
2. Fixing Skill s
a. Circle the proper fractions, box the improper fractions and cross the mixed forms.
1) 54
, 197
, 38
, 52
, 117
2) 14
, 156
, 10025
, 621
3) 32
, 25
, 81
, 103
, 131
4) 1811
, 21
, 343
, 38
, 1013
5) 100200
, 5
10, 6
21
, 31
1 2
1 2
1 2
1 2
1 2
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b. Make a proper fraction and an improper fraction using the pair of numbers. Numbers Proper Fractions Improper Fractions 1) 7, 9 ____________ ____________ 2) 18, 4 ____________ ____________ 3) 25, 26 ____________ ____________ 4) 3, 2 ____________ ____________ 5) 5, 11 ____________ ____________
c. Answer the following. 1) Rosa cut a piece of cloth into 6 pieces. She used 2 of these pieces to make a
handkerchief. What part of the cloth did Rosa use? 2) Mr. Ramos is taking care of 100 fowls. If 28 of them are ducks, what part of all the
fowls are ducks? What kind of fraction is it?
d. Draw and shade objects to show these fractions.
1) 86
2) 45
3) 141
4) 231
3. Generali zation
How do proper, improper and mixed numbers differ from each other? a. Proper fractions are fractions whose numerators are less than their denominators. b. Improper fractions are fractions whose numerators are greater than or equal to their
denominators c. Mixed numbers have a whole number and a proper fraction written together.
C. App lication
Do this on your paper.
Yaya Lucing bought 43
kg of brown sugar and 16 kg of flour. She also bought 121
kg of
bananas. Copy the weight of each item she bought and write opposite it what kind of fraction it is. IV. Evaluation
1. Copy the improper fractions in each set.
a. 53
, 411
, 100
9 b.
911
, 7
20,
82
c. 4
15,
31
, 79
2. Which is the mixed number. Encircle it.
a. 76
, 52
, 1731
b. 5
12,
2016
, 41
c. 241
, 376
, 583
3. Using the following set of numbers make a proper, improper and mixed number.
Proper Improper Mixed a. 6, 8, 2 _____ _____ _____ b. 1, 2, 3 _____ _____ _____ c. 24, 25, 4 _____ _____ _____ d. 4, 11, 7 _____ _____ _____ e. 2, 4, 5 _____ _____ _____
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4. Draw, shade and illustrate objects showing these fractions. Then identify if they are proper, improper or mixed.
a. 25
b. 59
c. 7
10 d. 5
43
e. 53
V. Assignment
Write whether each of the fractions below is a proper, improper or mixed number.
1) 32
2) 7
15 3) 6
73
4) 1116
5) 198
6) 410081
7) 2750
8) 185
9) 5
28 10)
310
Fractions involving Regions, Sets and Number Line I. Learning Objectives
Cognitive: 1. Identify fractions involving regions, sets and number lines 2. Use fractions to represent division Psyc homotor: Illustrate fractions correctly Affective: Show enjoyment in one’s work
II. Learning Content
Skill s: 1. Visualizing fractions including those with denominators of 10 and 100 2. Illustrating given fractions
References: BECPELC II.C.1.1.1 – 1.1.2 textbooks in Math 4 Materials: cutouts, drawings, number line, scissors, paper, crayons, ruler, pencil Value: Enjoyment in one’s work
III. Learning Experiences
A. Preparatory Activities
1. Review
Can you identify the following shapes?
2. Motivation
Draw some lines on the shapes. Do this by groups.
What did we do to the shapes? ( Draw some lines) What happened to the shapes? (The shapes were divided into parts.) How do you feel while doing your work? Did you enjoy it?
191
B. Developmental Activities
1. Presentation
a. Into how many parts are the shapes divided? 1) 6 parts 2) 4 parts 3) 7 parts
4) 2 parts 5) 6 parts b. Let the pupils do the following by groups.
(Each group is provided with the materials.)
Group 1 – shade 3 parts of the circle
Group 2 – shade 2 parts of the square
Group 3 – shade 5 parts of the rectangle
Group 4 – shade 1 part of the triangle
Group 5 – shade 4 parts of the hexagon
What portion of the whole do the shaded areas represent?
1) 63 2)
42 3)
75 4)
21
5) 64
What does fraction mean in these examples? (Fraction is a part of a whole.)
c. Present another example. Look at this set of flowers.
What part of the set of flowers do the flowers with leaves represent? What does fraction mean in these examples?
(Fraction is a part of a set or a group)
192
d. Show them this number line. A B C
100
1010
What part of the line is point A? point B? point C?
(Point A is 103
of the line. B is 105
and C is 108
)
What does fraction mean in these examples? (Fraction is a part of a line)
e. Let the pupils study carefully the three figures drawn below.
A B C
1 101
100
1
 Are the figures of the same size?  Which square represents 1 whole?  Into how many equal strips is the second square divided?
 What is the fraction name for 1 strip? 101
For 2 strips? 102
3 strips? 103
 Into how many equivalent part is the third square divided?
 What is the fraction name for 1 of the equivalent parts? 100
1
2 of the equivalent parts? 100
2 3 of the equivalent parts?
1003
 How are the fractions used in these examples? (Fractions can be used to name every part of a whole)
f. Let us look back at how the fractions in figure B and C are written.
What symbol is used to separate the numerator from the denominator?
Let us find out if fractions can really represent division. Show the process:
1.00.110
Is the answer correct? 1 0 Look at the illustration in figure B.
X What part of the whole is shaded? 0.1
193
2. Guided Practice/Fixing Skill s Answer on your paper.
What fraction of all the balls are the following? a) big b) medium c) small d) small and black e) medium and white
What fractions of all the balls are the following? (Please use the same illustration) a. big and white b. outside the box c. inside the box d. big and outside the box e. small and inside the box Prepare the following materials: scissors, paper, crayon, ruler and pencil. Do the following activities
a. Cut a circle. Fold it equally into 4 equal parts. Cut out 41
of it.
b. Cut a square. Draw 6 trees inside it. Color 21
of it.
c. Cut a rectangle. Divide it into 10 equal parts by drawing lines horizontally. Color 106
of it.
3. Generali zation
What is a fraction? How will you represent a fraction?
A fraction is a part of a whole. It represents a part of a set, a part of a line and can be used to name every part of a whole. It can also mean division.
C. App lication
Answer the following: 1. There were 12 kinds of fruits inside Karen’s basket. Five are mangoes. What fraction of the
fruits were not mangoes? (answer: 127
)
2. Aling Rosa bought ten pieces of pan de sal. Her children ate seven pieces. What fraction of
the ten pan de sals was eaten? (answer: 10
7)
194
IV. Evaluation
A. Shade the illustration given to show the fractional part. 1) 2)
3) 4)
5) 1 9 9 9
B. Draw the following fractions.
1) 43
2) 86
3) 109
4) 1510
5) 10015
C. Solve each problem. Write your answers in fraction form. Make necessary illustrations to show
your answers. 1. A kindergarten teacher has 12 balls in a box. Four of the balls are red. There are 3 blue and
the rest are green. What fraction of the balls are a. Red? b. Blue? c. Green?
2. Mother baked a big cake for Lita’s birthday. She divided the cake into 16 equal parts. She served 10 pieces to Lita’s guests. What fraction of the cake did mother serve to the guests? What fraction of the cake was not served?
V. Assignment
Draw a picture of the following fractions.
1) 103
2) 10025
3) 125
4) 2010
5) 155
Similar and Diss imilar Fractions in a given Set of Fractions I. Learning Objectives
Cognitive: Identify similar and dissimilar fractions from a given set of fractions Psyc homotor: Illustrate similar and dissimilar fractions through diagrams Affective: Work cooperatively in group activities
3 12
4 8
20 100 12
7 10 12
6 9 12
195
II. Learning Content
Skill s: 1. Identifying similar and dissimilar fractions 2. Visualizing similar and dissimilar fractions References: BECPELC II.C.1.2 textbooks in Math 4 Materials: diagrams Value: Cooperation
III. Learning Experiences
A. Preparatory Activities 1. Drill
Conduct a drill on reading and writing fractions and mixed numbers.
a. Have them read the following: 52
, 61
, 84
, 421
, 273
b. Write the following : onethird, eightfifths, fivehalves
2. Review Identify and write whether each of the following is a proper fraction, improper fraction or a mixed number.
53
55
48
241
74
3. Motivation
Daisy was asked to draw these different shapes on the black board.
How many shapes did Daisy draw? What are the shapes that Daisy drew?
B. Developmental Activities 1. Presentation
(Note: Give the importance of cooperation while doing the group activity) a. Method 1
1) Ask the pupils the number of circles, triangles and squares which Daisy drew.
196
2) Let them write a fraction to tell what part of the whole set are circles, triangles and
squares. (93
circles, 92
triangles, 94
squares)
3) Ask the pupils what they have observed with the denominators. What do these fractions have in common? (They have the same denominators.) What kind of fractions are these? (similar fractions)
b. Method 2
1) Let them focus on the shaded shapes which Daisy drew.
What part of the circles are shaded? 32
What part of the triangles are shaded? 21
What part of the squares are shaded? 43
2) Ask the pupils what they have observed with the denominators. What do you notice about the denominators? (they have different denominators) What do we call these fractions? (dissimilar fractions)
3) Discuss the difference between similar and dissimilar fractions and give examples.
2. Guided Practice
a. Tell which sets of fractions contain similar fractions and dissimilar fractions. Write S for similar and D for dissimilar fractions on the blanks before each number.
_____ 1) 107
, 102
, 108
_____ 2) 136
, 131
, 138
_____ 3) 84
, 109
, 75
_____ 4) 75
, 93
, 1411
_____ 5) 32
, 43
, 1510
b. Encircle the similar fractions and box the dissimilar fractions in each set.
1) 87
, 89
, 85
, 83
3) 164
, 1615
, 163
, 116
5) 118
, 71
, 203
, 115
2) 218
, 2015
, 2110
, 135
4) 51
, 53
, 51
, 58
, 54
c. Look for patterns. Fill in the blanks. Then write S if the set is a set of similar fractions and
D if the set is a set of dissimilar fractions.
_____1) 1011
, 1112
, 1213
, ___, ___ _____2) 1510
, ___, ___, 154
, 152
197
_____3) 1718
, ___, 1720
, 1721
, ___
_____5) 81
, 83
, ___, 87
, ___
_____4) 22
, 24
, 28
, ___, ___
3. Generali zation
What are similar fractions? What are dissimilar fractions?
Similar fractions are fractions with the same denominators. Dissimilar fractions are fractions with different denominators.
C. App lication
Read and answer on your paper.
Alice spent 32
of an hour cleaning the yard and burning the dried
leaves of trees. Write 2 other fractions that are similar to 32
.
IV. Evaluation
A. Put a check mark on the blank if the set of fractions are similar fractions. Put a cross if the set of
fractions are dissimilar fractions.
_____1) 114
, 126
, 82
, 65
, 203
_____3) 73
, 78
, 7
13,
725
, 76
_____5) 65
, 92
, 89
, 103
, 1513
_____2) 2011
, 2016
, 205
, 201
, 207
_____4) 97
, 86
, 64
, 113
, 185
B. Box the similar fractions and draw a triangle to enclose the dissimilar fractions in each set of
fractions.
1) 2515
, 54
, 308
3) 2014
, 206
, 2010
5) 108
, 73
, 115
2) 127
, 126
, 125
4) 115
, 162
, 105
C. Illustrate the following through diagrams. Then identify whether they are similar fractions or
dissimilar fractions.
1) 104
, 106
, 103
, 105
2) 73
, 52
, 65
, 43
198
3) 41
, 21
, 61
, 71
5) 64
, 62
, 63
, 65
4) 82
, 74
, 98
, 63
V. Assignment
A. Select from the following groups of fractions the sets of similar fractions. Encircle the letter of the
correct answer.
1. a.61
,98
,156
b.41
,105
,73
c.87
,83
,82
2. a. 54
,82
,113
b. 152
,151
,159
c. 51
,43
,42
3. a. 98
,86
,75
b. 31
,97
,92
c. 57
,34
,46
A. Choose from the groups of fractions below the sets of dissimilar fractions.
1. a. 81
,87
,82
b.2520
,2019
,196
c. 95
,93
,97
2. a. 109
,1512
,1217
b. 121
,127
,128
c. 74
,71
,75
3. a. 1110
,117
,116
b. 54
,52
,53
c. 52
,83
,73
Renaming Decimals and Whole Numbers to Fraction I. Learning Objectives
Cognitive: Rename decimals and whole numbers to fractions from a given set of
decimals/whole numbers Psyc homotor: Write fractions as decimals Affective: Use leisure time wisely
II. Learning Content
Skill : Renaming decimals and whole numbers to fractions from a given set of fractions References: BECPELC II.C.1.3 Materials: pictures, illustrations Values: Wise use of leisure time, speed and accuracy
199
III. Learning Experiences
A. Preparatory Activities
1. Drill
a. Write the fraction for the shaded part on each drawing.
1. 4. 2. 5. 3.
b. Game
Pupils are grouped into fives. Teacher prepares decimal numbers written on flash cards and words written on strips of cartolina. Place them on the table to be posted on the board by the group one at a time.
Match the decimal with its word. The group who finishes matching correctly in the shortest time will win.
0.56 sixtyseven hundredths 0.67 two and four hundredths 4.08 Fiftysix hundredths 2.04 Sixtyseven and fortythree hundredths 67.43 Four and eight hundredths
2. Review
Review in giving the place value of each digit in a decimal number. Answer the following questions.
a. In 0.97, what is the value of 9? b. In 0.6, what is the value of 6? c. In 2.84, what does 2 represent? d. In 4.027, what is the value of 2? e. In 6.245, what does 4 represent?
3. Motivation What is your favorite hobby? What do you do with your free time? Is your hobby
interesting? Do you spend some of your allowance for your hobby?
200
B. Developmental Activities
1. Presentation Let us read on how a girl works on her hobby.
2. Group Activity
Activity 1 – Collecting Stamps Lea arranged some stamps in her album. Each column can hold 10 stamps. One
column had 7 stamps only. What part of the column was filled up? Study the illustration and then answer the questions or give the needed information.
a. How many stamps are there in the first column? Second column? b. What fractional name can you give to the first column? Second column? c. What is the denominator of the fractions? What does it mean? d. Express the fractional part of the stamps in second column in decimal form. e. What shows that seven tenths is a decimal number? f. How many digits are there after the decimal point? g. How many decimal places are there if the decimal number is in tenths?
Activity 2
Look at the figures and answer the questions.
a. How do we read 1.3? What does the word “and” tell us in reading decimal numbers? How
many digits are there after the decimal point? If you’re going to write 1.3 in fraction, what will be the denominator? What does it mean? Note: Ask the same set of questions for letters b and c.
b.
Fraction _____ Decimal _____
201
c. Fraction _____ Decimal _____
Activity 3 Write the following as decimals. 1) 3 = _____ 10 3) 2 4 = _____ 10 5) 644 = _____ 1 000
2) sixtytwo hundredths = _____ 4) twentyfour and six thousandths = _____
3. Generali zation
How do we rename fractions as decimals and vice versa?
a. One place to the right of the decimal point has a value of tenths. It represents a fraction whose denominator is 10.
b. Two places to the right of the decimal point has a value of hundredths. It represents a fraction whose denominator is 100.
c. Three places to the right of the decimal point has a value of thousandths. It represents a fraction whose denominator is 1 000.
d. The decimal point is read “and.”
C. App lication 1. Let us have more practice. In this activity, you are going to work in groups. Each group will
consist of 10 players. This is a relay game, the first one will answer item one then the second in line will answer item two and so on. The group with the most number of correct answers wins the game.
202
U U     � �
U U     � �
U U     � �
U U     � �
U U     � �
U U    
U U U � � � Z Z Z Z
U U U � � � Z Z Z Z
U U U � � � � � Z Z
U U U � � � � � Z Z
2. Write in fraction form, the decimal numbers in the problem.
Irene spends her time properly. She goes to school for 6.25 hours, makes her
assignments for 2.625 hours, plays for 1.5 hours, does her household chores for 1.75 hours, sleeps for 10.2 hours and the rest she spends for other activties.
3. Write the decimal for each expanded form.
a. 27 + 101
+ 100
2 = _____
b. 9 + 103
+ 100
6 = _____
c. 615 + 107
+ 100
4 = _____
d. 83 + 107
+ 100
3 = _____
e. 104 + 101
+ 105
= _____
IV. Evaluation
1. Write a fraction and a decimal for the shaded part.
a. b. c. d.
Instruction: Write a decimal and fraction for every shape/illustration in the 10 x 10 grid.
203
2. Write the following in decimals.
a. Fortytwo and five tenths c. Two and three tenths e. Eightyfive thousandths
b. One hundred five and seven hundredths d. Three hundred five thousandths
V. Assignment
Complete the table below.
Fraction Decimal Fraction Decimal
a. 106
_____ f. _____ 0.525
b. 2 103
_____
g. 105
_____
c. _____ 0.16 h.
100078
_____
d. 12100
5
_____ i. _____ 0.4
e. 10032
_____
j. 5102
_____
Ordering Similar Fractions I. Learning Objectives
Cognitive: Order similar fractions written in different forms from least to greatest and vice
versa Psyc homotor: Write fractions in correct sequence Affective: Share things with others
II. Learning Content
Skill s: 1. Ordering similar fractions from least to greatest and vice versa 2. Comparing fractions References: BEC – PELC II.C.2.a textbooks in Math 4 Materials: flash cards, fraction bars, charts, activity sheets Value: Sharing
III. Learning Experiences
A. Preparatory Activities 1. Drill
Write > or < to compare the numbers below.
29 _____ 31 37 ______ 35 43 ______ 40 48 _____ 52 36 ______ 28 56 ______ 48
204
2. Review Tell whether the fraction is similar, dissimilar, mixed or improper fractions.
a. 41
and 42
b. 46
c. 53
and 32
d. 132
3. Motivation
Which would you rather have 52
of a cake or 53
of a cake? Why? (53
is larger than 52
)
Suppose you were given a bigger part and your younger sister still wants more? What would you do? Are you willing to share some of the things you have with other people? Why?
B. Developmental Activities
1. Presentation
a. Read the problem.
In an art class, leaders were asked to share their cartolinas with their members.
Francis used 83
of the cartolina, John used 81
and Luis used 84
.
Who used the least materials? Who used the most materials? Ask: Can you order the fraction from least to greatest? Method 1 – Representing fractions through regions 1) Study the fraction bars
83
81
84
2) Compare the shaded parts of the regions. 3) What will be the order of fraction from least to greatest?
(81
, 83
, 84
)
Method 2 – Presenting fractions through a number line Study the number line.
0 1 2 3 4 5 6 7 8 8 8 8 8 8 8 8 8
Method 3 – Using symbols > and <
81
< 83
< 86
205
b. Study this other example: 2 42
, 3 42
, 1 43
Arrange the fractions in order from greatest to least. Compare the whole numbers 2,3,1 Which number is the greatest? The least? What will be the order of fraction from greatest to least?
(The order is 3 42
, 2 42
and 1 42
)
2. Guided Practice
a. Identify the fractions of the shaded parts, then order them from least to greatest, then
from greatest to least. 1)
____ ____ ____
2)
____ ____ ____
3)
____ ____ ____
Least to greatest Greatest to least A B C
b. Arrange each set of fractions from least to greatest then from greatest to least.
1) 54
, 51
, 53
2) 94
, 98
, 92
3) 126
, 1122
, 2125
c. Order these fractions from greatest to least.
1) 63
, 61
, 64
2) 156
, 155
, 153
3) 442
, 541
, 243
d. Arrange the fractions in each set from least to greatest then from greatest to least.
1) 10055
, 10088
, 10075
, 10010
2) 126
, 124
, 123
, 122
3) 251
, 153
, 352
4) 231
, 133
, 332
5) 83
, 88
, 82
206
3. Generali zation How do we order similar fractions?
In ordering similar fractions, compare the numerators, the greater the numerators, the greater the value of the fractions.
C. App lication Read the problem then answer the questions that follow.
Chris sold 158
kilogram of calamansi, Roy sold 154
kilogram, Robert 156
kilogram and Vin
1511
kilogram.
1. Who sold the least number of calamansi? 2. Who sold the most number of calamansi? 3. Order the fractions from greatest to least.
IV. Evaluation
1. Order the fractions from least to greatest. Write them inside the appropriate illustrations.
a. 3 , 1 , 2 , 5 a. 6 6 6 6
b. 4 , 5, 1, 7 b. 8 8 8 8
c. 3 , 2 , 5, 1 c. 7 7 7 7
2. Order the fractions from greatest to least. Write them inside the appropriate illustrations.
a. 1211
,129
,123
,126
a.
b. 109
,104
,105
,107
b.
3. Order each set of fractions from the greatest to least. a. 3 , 1 , 2 , 5 b. 4 , 2 , 6 , 11 c. 4 , 1 , 2 , 10
8 8 8 8 10 10 10 10 15 15 15 15
207
4. Arrange the fractions from least to greatest.
a. 96
,99
,91
,97
b. 42
,41
,44
,43
5. Arrange the given set of fractions according to the headings written in the box. Write your
answers under the correct column.
Set of Fractions Least to Greatest Greatest to Least
1) 82
, 83
, 81
, 86
2) 128
, 122
, 1211
, 127
3) 156
, 153
, 159
, 1512
4) 92
4,94
8,93
7,91
2
5) 32
2,33
5,31
1,32
4
V. Assignment
A. Arrange from least to greatest.
a. 148
,143
,147
b. 119
,112
,118
c. 51
,53
,52
B. Order from greatest to least.
a. 93
,98
,96
b. 107
,109
,103
Changing Improper Fractions to Mixed Forms and Vice Versa I. Learning Objectives
Cognitive: Change improper fractions to mixed forms and vice versa Psyc homotor: Illustrate how to change improper fractions to mixed forms and vice versa Affective: Show cooperation in group activities
II. Learning Content
Skill s: 1. Changing improper fractions to mixed forms and vice versa 2. Making illustrations on changing improper fractions to mixed forms and vice versa References: BECPELC II.C.2.1 Materials: colored chalk, fraction strips Value: Cooperation
208
III. Learning Experiences
A. Preparatory Activities
1. Drill Drill on division of numbers with remainder (flash cards).
9 ÷ 5 = 12 ÷ 5 = 14 ÷ 4 = 10 ÷ 3 = 2. Review
Identifying improper and proper fractions and mixed forms.
3 21
, 49
, 45
, 2 21
, 43
, 6
10,
23
, 1 41
What fraction names the shaded parts?
3. Motivation Have you experienced wearing a gown? In what occasion did you wear it?
Aling Mimi sew the gown which her daughter wore during the Flores de Mayo. Aling Mimi
used 25
metres of cloth. How many metres of cloth did she use?
B. Developmental Activities
1. Presentation
Let the pupils have a group activity. What should you do so that your group will finish the work on time or even ahead of the others? Why? a. Show the illustration.
21
21
21
21
21
21
21
+ 21
+ 21
+ 21
+ 21
= 25
1 whole + 1 whole + 21
= 221
209
. Discuss the steps to solve the problem using the given illustration. 1) How many 2 are there in 5?
2 2 2) How many wholes are there in 5?
2 3) How many more halves are left? 4) What processes are you going to use? 5) Without using the illustration, how can we change improper fraction to mixed
number? a) Divide the numerator by the denominator
252
14−
b) The quotient will be the whole number. c) The remainder will be the numerator and denominator will still be the same
c. Using the story problem.
1) How many metres of cloth did Aling Mimi use? 2) What kind of fraction is 5?
2 3) How will you change 5 to a mixed number?
2 4) If you change 5 to a mixed number what will it be?
2 5) What can you say about Aling Mimi? What kind of mother is she?
d. Give additional examples.
Changing 14
3 to an improper fraction through illustrations.
44
43
1) What is the fraction name for 1? 2) How many fourths do we have in all?
3) What is the improper fraction for 1 4
3 ?
4) What processes are you going to use? 5) How can we changed mixed number to improper fraction without the illustration?
a) Multiply the denominator by the whole number b) Add the product to the numerator c) Copy the denominator Example.
43
1 = 4
3)14( +x =
47
denominator whole
numerator
21
2
210
2. Fixing Skill s a. Change the following to mixed form.
1) 7
10 2)
911
3) 1112
4) 37
5) 1215
b. Give the improper fraction and mixed form for each exercise.
1)
1 and 123
2)
1212
and 123
c. Change to mixed form. 1) 13 2) 24 3) 31 4) 20 5) 44 6 7 6 6 8
d. Change to improper fractions.
1) 44
3 2) 29
1 3) 78
4 4) 54
3 5) 68
2
e. Solve each problem.
1) Lily has 25
3 buko pies. How many fifths of buko pies does she have?
2) Nena sliced each watermelon into 12 equal pieces to sell. She has 60 pieces. a) What fraction represents all the pieces? b) How many watermelons did Nena slice? c) She was able to sell 32 pieces in the morning. What mixed number represents
the pieces she sold in the moring? d) She sold the rest of the pieces in the afternoon. What mixed number represents
them? 3. Generali zation
How do we change improper fractions to mixed forms? How do we change mixed forms to improper fractions?
1. To change an improper fraction to a mixed number, divide the numerator by the denominator, the quotient becomes the whole number. The remainder becomes the numerator and the divisor becomes the denominator of the fraction.
2. To change a mixed fraction to an improper fraction, multiply the whole number by the denominator, add the product to the numerator then write the sum over the given denominator.
C. App lication
Read and solve the problem. 1. Rex has 8 litres of gasoline. What is the mixed form of 8?
3 3
2. Regina bought 24
3 metres of linen for a tablecloth. Change 24
3 into an improper fraction.
211
IV. Evaluation A. Write the improper and the mixed number that names the figure.
B. Change each mixed number to improper fractions.
1) 13 21
2) 765
3) 453
C. 1. Change 5
26 and
730
to mixed number.
2. Change 13 92
and 7 54
to improper fraction
D. Solve.
1. Myra has 5 5
1 buko pie. How many fifths of buko pie does she have?
2. How many halves are there in 3 21
?
3. Name each point as a mixed number and an improper fraction. 2 3 A B C D E F G H I J K 1) A 2) C 3) E 4) G
4. How many eights can you make out of 2 84
metres of ribbon?
5. A roll of cloth is 36 metres long. If this would be distributed equally to 15 people, how many metres would each person have?
V. Assignment
A. Find the missing number for each ____.
1) 23
1 = 3
2) 137
2 = 7
3) 52
1 = 2
B. Copy and complete the table. Find the pattern.
1. In 1 2
2 2
? ?
2. Out 1 2
1 1 1 2
2
Changing One (1) to Fraction Form and Vice Versa I. Learning Objectives
Cognitive: Change one(1) to fraction form and vice versa Psyc homotor: Manipulate fraction blocks showing how to change 1 to fraction form and vice
versa Affective: Show love and kindness to others
212
II. Learning Content
Skill : Changing one (1) to fraction form and vice versa References: BECPELC II.C.2.2 Materials: fraction strips Values: Love and kindness
III. Learning Experiences
A. Preparatory Activities
1. Drill
Basic division facts.
2 ÷ 2 = n 4 ÷ 4 = n 10 ÷ 10 =n 3 ÷ 3 = n 6 ÷ 6 = n
2. Review
Choose the equivalent fraction inside the parenthesis.
a. 21
= (52
,42
,22
) 41
= (105
,92
,82
)
b. 31
= (85
,102
,93
) 51
= (93
,124
,153
)
3. Motivation
Distribute fraction blocks for the pupils to manipulate and form into wholes. Have them
show their fraction blocks like this:
How many fourths are there in a whole? Are 4 fourths equal to 1? (yes) How many halves are there in a whole? Are 2 halves equal to 1? (yes)
B. Developmental Activities
1. Presentation
Mrs. Soriano bought a large bibingka and divided it into 8 equal parts. She gave 1 part to each of her 7 children and reserved the remaining part but her youngest daughter asked for another piece so she gave the remaining one, How many parts of bibingka were eaten?
1 4
1 4
1 4
1 4 1
2 1 2
213
2. Analysis
a. What kind of mother is Mrs. Soriano? b. If you were Mrs. Soriano would you do the same? Why? c. How many parts of bibingka were eaten?
Show this illustration.
1 =
88 1 =
44 1 =
33
Look at the illustrations.
a. How can 1 be expressed as a fraction? Is 88 equal to 1? Is
44 = 1. How about
33 ?
b. What have you noticed in the numerator and denominator? c. How can we rename 1 as a fraction?
1 = 33
44 = 1
d. Guide the pupils that 1 can be changed to a fraction and a fraction equal to 1 can be changed to a whole number. The fraction names for 1 have similar numerators and denominators.
3. Fixing Skill s
a. Give the fractions for each whole.
1) 2) 3) b. Write the missing number.
1) 1 = __?__ 2) 1 = 12 3) 1 = 18 5 ? ? 4) 1 = __?__ 5) 8 = 1
30 ?
c. Choose the fraction that is equal to one for each set. Write the letter only.
1) a. 1 b. 2 c. 3 d. 4 4 4 4 4 2) a. 5 b. 4 c. 3 d. 2 5 5 5 5
214
3) a. 4 b. 5 c. 6 d. 7 7 7 7 7 4) a. 4 b. 6 c. 8 d. 9 8 8 8 8 5) a. 1 b. 2 c. 2 d. 2 2 2 3 4
d. Rename or change 1 to 10 equivalent fractions.
4. Generali zation
How do we rename 1(one) as a fraction?
We rename one (1) as a fraction with the same numerator and denominator. And any fraction with the same numerator and denominator is equal to 1.
C. App lication
Answer the following problem: 1. Mother divided a cake among her 3 children. Write a fraction that is equal to one whole cake.
(answer 33
)
2. Merlyn gave 31
of melon to her sister and 32
to her brothers. How many melon did she
share? (1)
IV. Evaluation
A. Write the missing number on the blank.
1) 20 = ___ 2) 14 = ___ 3) 1 = ___ 4) 1 = 16 5) 10 = ___ 20 14 13 ___ 10
B. Fill in the box to express 1 as a fraction.
1) 1 = ___ 2) 1 = 5 3) 1 = 100 4) 9 = ___ 10) 25 = ___ 10 ___ ___ 9 25
C. Read and answer.
1. Mrs. Fields sliced a bibingka into 8 equal parts. How many eighths did she make? 2. How many eighths can you make with a cake?
C. Rename or change 1 to 5 equivalent fractions.
V. Assignment
Choose the fraction that is equal to one for each set. Write only the letter of your answer.
1. a. 1 b. 3 c. 4 d. 9 4 4 4 4
4. a. 1 b. 2 c. 2 d. 2 2 2 3 4
215
2. a. 1 b. 2 c. 2 d. 3 2 2 3 4 3. a. 9 b. 4 c. 7 d. 8 7 7 7 7
5. a. 9 b. 5 c. 8 d. 11 9 6 7 5
Add ing Similar Fractions I. Learning Objectives
Cognitive: 1. Visualize addition of similar fractions
2. Add similar fractions Psyc homotor: Compute for the sum correctly Affective: Help in household chores
II. Learning Content
Skill : Adding similar fractions References: BECPELC II.D.1.1 – 1.2 Materials: activity sheets, paper plates, charts, fraction bars, real objects Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Identify similar fractions from each set of fractions below.
a. 2, 3, 1, 2 b. 5, 2, 1, 5 3 2 3 5 6 3 6 8 c. 3, 3, 2, 2 d. 8, 1, 2, 1 4 8 3 4 9 8 9 4
2. Review Express each fraction in lowest terms.
a. 6 = b. 10 = c. 6 = d. 9 = e. 3 = 8 12 9 15 6
3. Motivation
Place two pencils on one of your hand and one pencil on the other hand. Ask: “If I put together 2 pencils and 1 pencil, what do I get?” (3 pencils) Do the same with 2 stones and 2 pencils. Say: “If I put together 2 stones and 2 pencils, do I get 4 pencils? (no) 4 stones? (no) Why not?” (objects are not alike) “Today, our lesson is something similar to this.”
216
B. Developmental Activities
1. Presentation
a. Use a paper plate cut into fourths to represent a “puto”. Have one pupil take 41
of the
puto. Have another pupil remove 42
of it. Ask: What part of
the puto was taken? Show addition of fractions. 1 2 3 4 4 4 Ask: Do you add the numerators? (yes) Do you add the denominators? (no)
b. Display fraction bars like : 1 2
6 6
What kind of fractions are they? (similar)
What is the sum? (63
)
Is 63
in lowest terms? (no)
How can you express it in lowest terms? (Divide the numerator and denominator by their greatest common factor.)
so, 6
3 ÷ 3
3 = 2
1
c. Have the pupils read the word problem.
Flordeliza always helps her mother at home. She cooks lunch in 105
of an hour.
Then she cleans the kitchen in 103
of an hour. What part of an hour does she spend
working in the kitchen? Valuing: � What kind of a daughter is Flordeliza? � How do you help your mother at home?
217
Fold a piece of paper into tenths and say, suppose this part represent the time
Ella spent cooking (mark 105
with a red crayon) and this part for the time she spent
cleaning the kitchen (mark 103
with a blue crayon)
How much time did she spend working in the kitchen that day? 108
Show the solution on the board. 5 + 3 = 8 10 10 10 Is 8 the final answer? (no) 10 What shall we do with the answer? (Express in lowest terms)
Show how this is done. 10
8 ÷ 2
2 = 5
4
2. Guided Practice
a. Complete the mathematical sentence. Express the answers in lowest terms, if needed. 1) 2) 3) 1 + 2 = 4 + 1 = 1 + 2 = 5 5 6 6 4 4 4) 5) 2 + 4 = 3 + 1 = 9 9 8 8
b. Write the missing fractions to complete each equation.
1) 5 + _____ = 8 4) 13 + 1 = _____ 12 12 18 18
2) _____ + 4 = 5 5) _____ + 3 = 6 6 6 8 8 3) 2 + _____ = 6 7 7
c. Copy and complete each magic square. Find the sum. The sum in each column and each row is the same.
8
11 9
11 5
11 1
11 6
11
218
d. Answer: 114
, 113
, 112
, 117
Magic Sum: 1115
or 114
1
8
10 1
10
3 10
4 10
Answer: 106 ,
105 ,
107 ,
109 ,
102
Magic Sum: 1015
or 121
3. Generali zation
How do you add similar fractions?
To add similar fractions, add the numerators and write the sum over the common denominator. Express the answer in lowest terms if needed.
C. App lication
Read and solve on your paper.
Katrina spent 42
of an hour sweeping the yard and 41
of an hour watering the plants. How
long did she work? IV. Evaluation
A. Add and express each sum to lowest terms if possible.
1. 1 + 2 = 4. 2 + 1 = 6 6 8 8 2. 2 + 5 = 5. 4 + 3 = 12 12 21 21 3. 1 + 3 =
5 5
B. Find the sum. Express it in lowest terms if possible. 1. 1 + 2 + 4 = 4. 1 + 2 + 4 = 9 9 9 10 10 10 2. 2 + 5 = 5. 4 + 3 = 12 12 21 21
3. 3 + 2 + 5 =
15 15 15
219
C. Solve each problem. Express your answer in lowest term, if possible. 1. What is the sum of 6 , 2 and 4 ? 20 20 20 2. Lanie sliced a watermelon into eight equal parts. She ate 1 of it. Her sister Rica ate
8 3 of the watermelon. How much watermelon did both of them eat? 8
3. Mrs. Montoya cooked pork and chicken adobo. She mixed 3 kilo of 8
pork and 2 kilo of chicken. How many kilos of pork and chicken did she cook? 8
4. A painter bought 2 litres of green paint for the walls and 2 litres of blue 5 5
paint for the windows. How many litres of paint did he buy in all? V. Assignment
A. Write in the third column the sum of the fractions on the first two columns.
Sum
A 1 4
2 4
B 3 8
2 8
C 4 10
3 10
D 6 12
2 12
E 3 15
4 15
B. Look at the figure below. Each fraction in the circles are given codes.
IA 3 20
IB 4 20
2C 5 20
2B 9 20
2A 2 20
3A 1 20
3B 8 20
3C 7 20
3D 6 20
4A 10 20
4B 11 20
220
C. Substitute the fraction for each code then find the sum:
1. IA + IB = 3. 2A + 2B +2C = 5. 3A + 3B + 3C + 3D = 7. IA + 2A + 3A = 9. IB + 2B + 3B =
2. 2C + 3C = 4. IB + 2C +3D = 6. IA + 2B + 3C = 8. 2A + 3B = 10. 4A + 4B =
Adding a Fraction and a Whole Number I. Learning Objectives
Cognitive: Add a fraction and a whole number Psyc homotor: Illustrate the fractions that are being added artistically Affective: Show gratitude to others
II. Learning Content
Skill : Adding fractions and a whole number References: BECPELC II.D.1.3 Materials: flash cards, chart, activity sheet, real objects, circleagogogame board and
chips Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill Add the following similar fractions.
1) 1 + 2 = 2) 1 + 2 = 3) 3 + 1 = 4) 1 + 2 = 4 4 8 8 5 5 8 8 5) What is 4 more than 7 ?
12 12
2. Review
How do we add similar fractions?
3. Motivation Have you received a gift from someone? What did you feel?
B. Developmental activities
1. Presentation
a. Read this situation: During Estelita’s birthday party, she received 2 metres of red cloth from her mother
and another 21
metre of blue cloth from her father. She was very thankful for these gifts
so she hugged her parents tightly. How many metres of cloth did she receive in all?
221
b. Analysis ��:KDW�GLG�(VWHOLWD�FHOHEUDWH" ��:KDW�GLG�VKH�UHFHLYH" ��+RZ�GLG�VKH�VKRZ�KHU�JUDWLWXGH�WR�KHU�SDUHQWV" ��,I�\RX�ZHUH�(VWHOLWD��ZRXOG�\RX�GR�WKH�VDPH"�:K\"
c. Show the illustration.
1st gift Æ Red Cloth – 1 metre Red Cloth – 1 metre 2nd gift Æ Blue Cloth 2 +
21 = 2
21
21 metre
d. Discuss the steps to solve the problem using the given illustration.
� Describe the illustration � Determine the sum of the 3 figures. � Write the solution.
2 + 21 = 2
21 or 2
+ 21
21
2
Using the story problem. � What are the given facts? � What is asked in the problem? � What kind of numbers are added? � What is done to the whole number/fraction? � How did you get the answer?
2. Guided Practice
a. Supply the missing numbers using the illustrations given.
1)
_____ + _____ = _____ 2) _____ + _____ = _____
222
3)
_____ + _____ = _____
b. Find the sum then present an illustration.
1) 6 + 1 3 2) 5 + 2 4 3) 3 + 5 4
c. Circleagogo
5 + 6 2
4 + 1 3
6 + 2 3
1 + 4 3
7 + 1 2
14 + 7 8
3 + 4 10
3 + 4 2
5 + 9 7
8 + 2 6
4 + 5 3
9 + 7 10
15 + 7 18
6 + 2 3
22 + 8 15
25 + 4 8
223
Directions:
1. Two players share the same “circleagogo” game board. 2. Each player has 4 markers or chips. 3. Each player takes turn solving a problem or calling out its answer. The player then places
one of his or her markers on that circle. 4. This procedure continues until each player has all four markers on the game board. 5. The players take turns sliding one of their markers along a line to an adjoining circle as they
call out the answer to the problem in that circle. 6. If a player solves a problem incorrectly, he or she may not move a marker. 7. A player can move only to a circle that has no marker. No jumping allowed. 8. Sliding continues until one player is able to position his or her four markers in a diagonal,
horizontal or vertical line, or a small square made of adjacent circles. That player wins. Examples of winning positions.
3. Generali zation How do we add a fraction to a whole number?
To add a fraction to a whole number or viceversa, write the whole number first and annex the fraction.
C. App lication Read and solve the problem.
Mang Bino planted 2 of his plot with cabbage. Since there were still few seedlings
left, he used 31
of another plot. How many plots did he use in all in planting cabbage?
IV. Evaluation
A. Find the sum. 1) 18 + 1 = 2) 3 + 6 = 3) 6 + 12 = 9 4 8 4) 5 + 7 = 5) 1 + 14 =
8 7 B. Supply the missing number by filling in the box.
1) 5 + 16 = ___ 2) 6 + ___ = 6 7 3) ___ + 12 = 12 3 8 8 4 4) 20 + ___ = 20 1 5) 2 + 9 = ___
3 5
224
C. Solve these problems.
1. On his trip to Naga, Albert rode 6 hours on a train and 4
3 hour on a bus. How many hours
did he travel in all?
2. Marissa used 5
4 metre of white cloth and 2 metres of blue cloth to sew a dress. How
many metres of cloth did she use in all?
3. Mr. Pasco put 5 metres of wire, 8 metres of rope and 2
1 metre of string in his garden
fence. How many metres of materials did he use in all? 4. In a contest, Romeo was able to leap 3 metres from one point to another. His teammate
Jose was able to leap 32
metre. What is the total distance that they covered?
V. Assignment
Find the sum. Express your answer in simplest form if necessary.
1) 2 + 5 = 2) 9 + 18 = 3) 12 + 3 = 12 10 4 4) 6 + 18 = 5) 9 + 10 + 5 = 20 8
Adding Similar Fractions Mentally I. Learning Objectives
Cognitive: Add similar fractions mentally Psyc homotor: Compute for the sum with ease and accuracy Affective: Show attentiveness in adding similar fractions mentally
II. Learning Content
Skill : Adding similar fractions mentally References: BECPELC II.D.1.4 Materials: pictures, chart, activity sheet, real objects, fraction cards Value: Attentiveness
III. Learning Experiences
A. Preparatory Activities
1. Drill Basic addition facts
9 7 8 +4 +3 +3
225
2. Review Find the sum.
a. 3 + 2 b. 4 + 5 c. 6 + 1 3 6 4
3. Motivation a. Show a picture of a birthday party. Talk about how pupils celebrate their birthday.
1) What do you see in the picture? 2) How many of you celebrate your birthday? 3) How do you celebrate your birthday? 4) What food does your mother prepare on your birthday?
b. If somebody is talking or giving an answer, what do you think you should do? Why? B. Developmental Activities
1. Presentation
a. Read this story problem.
On Rosa’s birthday, her classmates came. They were seated in many tables. On one table a child ate oneeighth of a cake. Another child ate twoeighths of a cake. What part of the cake did the two children eat altogether?
b. Show this illustration. (Using the problem.) 1 + 2 = 3 8 8 8 c. Discuss the steps to solve the problem using the given illustration. d. Describe the shaded portion of the two circles. e. Determine the sum of the two shaded portion. f. Write the resulting addition equation.
1 + 2 = n 8 8
g. Present another story problem.
Crissie finished 1 of her project on Friday. She finished 4 of her
8 8 project on Saturday night. What part of the project was finished by Saturday night?
Find the answer. 1 + 4 = n
8 8
226
2. Guided Practice
A. Complete each. Give the answer orally. 1) 2) 2 + 1 = ___ 2 + 5 = ___ 5 5 8 8
3) 4) 5) 2 + 3 = ___ 4 + 3 = ___ 3 + 1 = ___ 6 6 10 10 6 6 B. Add the following fractions mentally.
1) 72
+ 71
= 2) 107
+ 105
= 3) 133
+ 135
= 4) 93
+ 95
= 5) 1510
+ 152
=
C. Solve these problems as fast as you can.
1) In a P.E. class, Pilar ran 2 metre. Lina ran 3 metre and Susan 7 7
ran 1 metre. What part of a metre did the 3 girls run? 7
2) Randy picked 3 basketfuls of mangoes while Robert picked 4 8 8
basketful of chicos. How many basketfuls of fruits did the two boys pick in all? 3) The Grade IV pupils will decorate 1 of the stage with flowers and
8 6 with curtains. What part of the stage will be decorated?
8
3. Generalization
How do you add similar fractions mentally? To add similar fractions mentally, add the numerators in your mind, then use it over the
the denominator.
C. App lication
Read and use mental math to solve.
Bobby played basketball for 63
hour in the morning and 62
hour in the afternoon.
How long did he play basketball on that day?
IV. Evaluation
A. Add mentally. Write the answer on your paper.
1) 94
+ 93
= 2) 205
+ 203
= 3) 112
+ 112
= 4) 255
+ 252
= 5) 183
+ 185
=
227
B. Supply the missing numbers.
1) 165
+ ___ = 167
2) ___ + 154
= 158
3) 103
+ 105
=
4) 128
+ ___ = 1210
5) ___ + 2010
= 2015
C. Add mentally. Write only the answer on your paper.
1) 103
+ 104
+ 101
= 2) 82
+ 81
+ 83
= 3) 124
+ 123
+ 122
=
4) 95
+ 91
+ 92
= 5) 206
+ 204
+ 203
=
V. Assignment
Fill in the missing fractions. Legend: + + =
A 3 6
5 6
B 2 8
3 8
1 8
C 3 10
2 10
7 10
D 2 9
1 9
8 9
E 4 15
2 15
10 15
Subtracting Similar Fractions I. Learning Objectives
Cognitive: Subtract similar fractions Psyc homotor: Make an illustration to show subtraction of similar fractions Affective: Participate actively in class activities
II. Learning Content
Skill s: 1. Subtracting similar fractions 2. Making illustrations to show subtraction of similar fractions Reference: BECPELC II.D.2.1
228
Materials: textbook, number lines showing similar fractions, flash cards for similar fraction, chart showing shaded regions of similar fractions, learning activity sheet, pupil’s show me cards
Values: Thoughtfulness, active participation III. Learning Experience
A. Preparatory Activities
1. Drill Reading of similar and dissimilar fractions using flash cards
43
42
108
64
2518
3033
3540
1520
2. Review
Adding similar fractions using show me cards of pupils
Examples: 104
+ 103
= _____ 209
+ 206
= _____
126
+ 124
= _____ 158
+ 155
= _____
3. Motivation
Read this problem: Ester and her mother bought a rice cake near Quiapo church. They divided the cake into
12 equal parts. They ate 123
of it and brought home the rest. What part of the rice cake did
they bring home? Did Ester and her mother show thoughtfulness to the members of their family? How? If you were Ester, would you do the same?
B. Developmental Activities 1. Presentation
a. Show the illustration below. b. Discuss the steps to solve the problem.
Steps: 1) Subtract the numerator. 2) Write the difference over the common denominator. 3) Express the answer in lowest terms, if possible.
43
129
123
1212
or=−
229
c. Present another way of subtracting similar fractions. • Write a number sentence on the board based on the number line below.
0 1 2 3
3 3 3
31
31
32 =−
• Ask a pupil to draw an arrow on the number line to show 32
. Ask : “If we subtract 31
where does the arrow go?” Have one pupil put the arrow going backward. “What is the difference?”
2. Guided Practice Activity Sheet Read the problem carefully then do what is asked for.
Irene put 41
cup of sugar in the gelatin and 42
cup of sugar in the leche flan. Which
dessert used more sugar? By how much more? Do this in Dyads: Present an artistic illustration to show how you solved the problem Supply the missing fraction.
a) 163
___1615 =− b)
43
___128 =−
c) 211
___217 =− d)
83
84
___ =−
e) 51
53
___ =−
Copy and complete each magic square. Solve for the difference horizontally and
vertically. Find the magic difference. a)
308
309
307
302
30
6
230
Answer Key: 3018
3010
309
303
b)
2520
2510
2512
258
Answer Key: 256
253
257
251
251
3. Generali zation
How do we subtract similar fractions?
We subtract the numerator only then write the difference over the common
denominator. C. App lication
Solve the following problem on your paper.
A vendor had 87
bottle of soy sauce. A customer bought 85
of it. What part of the soy sauce was
left?
IV. Evaluation
1. Find the difference. Shade the needed part to show your answer. a.
87
81
_________
231
b.
108
101
_________ c.
43
41
_________ d.
64
62
________ e.
65
62
__________
B. Find the difference. Express your answer in lowest terms, if possible.
a. =−42
48
b. =−144
148
c. =−157
1510
d. =−84
87
e. =−103
106
C. Write the figures and then find the difference.
a. fivesevenths – foursevenths b. ninetenths – sixtenths c. twelvefifteenths – eightfifteenths d. threesixths – onesixth e. eightninths – fourninths
232
V. Assignment
Subtract and reduce the answer to lowest terms, if possible.
a. =−91
94
b. =−102
108
c. =−127
129
d. =−142
146
e. =−183
187
Subtracting Fractions from Whole Numbers I. Learning Objectives
Cognitive: Subtract fractions from whole numbers Psyc homotor: Illustrate fractions that are being subtracted Affective: Work accurately
II. Learning Content
Skill s: 1. Subtracting fractions from whole numbers 2. Illustrating fractions to be subtracted References: BECPELC II.D.2.2 textbooks in Math 4 Materials: chart showing illustrative examples or stepbystep procedure, fraction bars,
cards, learning activity sheets, flash cards Values: Taking care of books, accuracy
III. Learning Experiences
A. Preparatory Activities 1. Drill
Reading similar fractions using flash cards 2 3 5 4 4 8
4 6 6 4 10 10 2. Review
Renaming one as a fraction. Have them give fraction names for one such as:
2 3 4 5 6 2 3 4 5 6
3. Motivation
Talk about how they take care of their things then proceed to reading this problem.
Before the opening of classes, Rosario bought 1 metre of plastic to cover her notebooks.
Only 41
of the material was left unused. What part of the plastic did she use?
233
B. Developmental Activities 1. Presentation
a. Show this illustration.
1 1 1 1 4 4 4 4
b. Discuss the steps to solve the problem using the given illustration.
1) Into how many parts is the metre of plastic divided? 2) How many metre of plastic was left unused? 3) What part of the plastic did she use? 4) What will you do to solve the answer?
c. Present another problem by computation.
1) Rename 3 as 244
3 244
2) Copy 41
below 44
–41
–41
3) Subtract the fractions, then 2 44
copy the whole number
2. Guided Practice a. Supply the missing numbers using the illustrations given.
1.
________  _________ = _________ 2. ________  _________ = _________ 3. ________  _________ = _________
234
b. Find the difference. 1) 2 2) 5 3) 6
32
41
73
c. Illustrate the fractions that are being subtracted.
1) 1  104
2) 2  83
3) 3  65
3. Generali zation
How do we subtract fractions from a whole number?
We rename the whole number as a mixed number with a fraction equal to one whose denominator is similar to the denominator of the given fraction, then subtract the fractions
C. App lication
Read and solve this problem.
Romeo bought 1 whole illustration board. He shared 43
of it with his friends. What part of the
illustration board was left with him?
IV. Evaluation 1. Subtract.
a. 6___ b. 9___ c. 4___
32
− 53
− 43
−
d. 3___ e. 8___
52
− 73
−
2. Find the difference.
a. 6  83
= b. 9  42
= c. 8  53
= d. 14  87
= e. 12  107
=
3. Solve these problems.
a. Mrs. Montoya bought 2 metres of lace. She used 43
metre for the collar of her dress. How
many metres of lace were not used?
b. From 8 metres of cord, 43
metre was cut. How many metres of cord were left?
c. If 93
is subtracted from 5, what is the difference?
d. What is the difference between 12 and 126
?
e. Mother divided a cake into 8 equal parts. Her children ate 85
of the cake. How many was left?
235
V. Assignment Subtract the fraction from the whole number.
a. 6  62
= c. 9  84
= e. 3  65
=
b. 7  54
= d. 2  85
=
Subtracting Mentally Similar Fractions I. Learning Objectives
Cognitive: Subtract mentally similar fractions Psyc homotor: Compute for the difference with ease and accuracy Affective: Work accurately and cooperatively
II. Learning Content
Skill : Subtracting mentally similar fractions Reference: BECPELC II.D.2.3 Materials: textbook, fraction cards and bars, flash cards, chart showing illustrative
examples, learning activity sheets Values: Cooperation, helpfulness, accuracy
III. Learning Experience
A. Preparatory Activities
1. Drill Conduct a race on basic subtraction facts using flash cards. Example:
8 6 9 8 7 6 4  4  3  4  3  2  4  2
2. Review
How do we subtract fraction from a whole number? Find the difference.
a) 2 – 32
= b) 3 – 54
= c) 5 – 63
d) 6 – 43
e) 8 – 86
3. Motivation
Talk about how they help their mother at home. Have them read this story problem.
236
Mother went to the market with Norman to help her carry the things she will buy. Mother
bought 43
kilogram of meat. She cooked 42
kilogram. How many kilogram was left?
Do you also help your mother at home? Why? What character trait do you show? B. Developmental Activities
1. Presentation
a. Show this illustration.
41
43
– 42
= 41
b. Discuss the steps to solve the problem using the given illustration.
 Describe the shaded parts of the two bars.  Determine the difference of the two shaded bars.  Write the resulting subtraction equation.
(43
– 42
= 41
)
c. Present another way of subtracting mentally similar fractions.
Have them spread their fraction cards face down, select any two cards of the
same color and match them to the corresponding fraction bars. Then have them compute the difference between the two fractions and record their answers.
2. Guided Practice
Activity Sheet Subtract the following fractions orally.
a. 32
– 31
= b. 86
– 82
= c. 127
– 122
=
d. 64
– 62
= e. 109
– 104
=
4 5
3 5
237
Super TicTacToe
98
– 93
= 126
– 122
= 169
– 163
= 105
– 102
= 158
– 153
=
217
– 211
= 1615
– 163
= 109
– 107
= 83
– 81
= 147
– 144
=
2018
– 208
= 64
– 61
= 75
– 72
= 53
– 51
= 1510
– 153
=
Directions:
1) Two players share the same game board. Each player has 13 chips as markers with
color different from his or her opponents. 2) Each player takes his or her turn solving a problem mentally before he or she places
a marker on that square on the game board. 3) The players try to make as many tictactoes as possible by aligning their markers
horizontally, vertically or diagonally. The players also try to block each other from making a tictactoe.
4) A marker may belong to more than one tictactoe. 5) The game continues until all the squares are covered. 6) Each player counts his or her tictactoes and totals the points. Points are awarded
as follows. Three in a row counts as 1 point. Four in a row counts as 3 points and five in a row counts as 5 point.
7) If a player solves a problem incorrectly, he or she loses a turn. 8) The player with the most points wins.
Do this in dyads or by 4s using fraction cards.
Player’s Choice
Spread the cards face down. Each player chooses two cards of the same color
and subtracts the two fractions. Chance option: If a player wants to try to increase his/her difference, one more
card may be chosen. However, before choosing the third card, the player must discard one of the other two cards. The player with the greatest difference wins all the cards used in the round, including any discarded cards. If players have the same difference, all cards from the round are placed aside. The winner from the next round gets these cards. When all the cards are played, the player with the most cards wins.
3. Generali zation
How do you subtract mentally similar fractions?
Subtract the numerator then write the answer over the denominator.
9 10
1 10
238
C. App lication Read and solve mentally. Express the answer in lowest terms. Write the answer on your paper.
One Saturday, Andy and Ernie walked around the park. Andy walked a distance of
105
kilometre while Ernie walked 103
kilometre. Who walked longer? How much?
IV. Evaluation
1. Subtract mentally the following fractions.
a. 97
– 93
= b. 105
– 104
= c. 86
– 85
=
d. 109
– 104
= e. 1210
– 124
=
2. Find the missing number.
a. 108
 _____ = 106
b. _____  206
= 204
c. 126
– 124
= _____
d. 2015
 _____ = 205
e. _____  158
= 154
3. Solve the problem as fast as you can.
a. Romeo had 108
metre of wire. He used 107
metre for his project. How many metres of wire
was left?
b. Kenneth helped his father weed the garden for 85
hour on Saturday and 82
hour on Sunday.
How much longer did he work on Saturday than on Sunday?
c. Janice bought 109
metre of lace. She used 105
metre for her handkerchief. How many
metres of lace was left?
d. A babysitter filled the feeding bottle with 43
milk. If the baby drank only 42
, how much milk
was left in the bottle?
e. For the Clean and Green program, the Boy Scouts bought 54
sack of garden soil. Only 53
sack was used. How many sacks of garden soil was left?
239
V. Assignment Subtract mentally.
a. 108
– 104
– 102
= b. 1816
– 1810
=
c. 2011
– 202
= d. 1510
– 155
– 153
=
e. 2512
– 257
=
Solving Word Prob lems involving Add ition of Similar Fractions wi thout Regrouping I. Learning Objectives
Cognitive: Solve word problems involving addition of similar fractions without regrouping Psyc homotor: Make illustrations in solving word problems Affective: Show cooperation in solving word problems
II. Learning Content
Skill s: 1. Solving word problems involving addition of similar fractions without regrouping.
2. Making illustrations in solving word problems References: BECPELC II.D.3.1
textbooks in Math 4 Materials: flash cards, word problems written on manila paper or pieces of paper, learning
activity sheet Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill Oral drill on adding basic addition facts using flash cards 8 5 4 6 7 + 1 + 3 + 5 + 2 + 2
2. Review
Addition of similar fractions using flash cards
52
+ 51
= 83
+ 82
= 104
+ 102
= 95
+ 93
=
3. Motivation
Is it important to join in your school activities? Why? How do you feel when joining school activities like field trips?
240
B. Developmental Activities 1. Presentation
a. Read and understand well this problem.
The Grade 4 class will hold their party for winning the cleanliness contest. They will
hold their party in the school hall. Twofourths of the class will clean the hall and 41
will
decorate it. What part of the class will clean and decorate the hall? Help them in the analysis of data by answering some questions like: 1) What are given in the problem? 2) What is asked in the problem? 3) What operation will you use? Why?
4) What is the number sentence? 42
+ 41
= N
5) Have them make the necessary computation.
42
+ 41
= 43
of the class will clean and decorate the hall.
b. Read and solve this problem.
Mrs. Bustamante bought a rectangular cake. She divided it into 8 equal parts. Her
son ate 83
and her daughter ate 82
of it. How many parts of the cake were eaten?
1) What will you do to solve the problem? 2) Finish the illustration given by shading the needed part then find the answer.
_________ + _________ = __________
2. Guided Practice (At this point, remind the pupils the importance of participating actively in all activities that will be given them.) Write these word problems on pieces of paper. Fold them and put them in a box.
Divide the class into three to four groups. Have each group draw one problem from the box. Give each group 15 seconds to discuss the problem. Ask a group member to solve the problem on the board. Check it afterwards.
1) Dindo had a painting session in his art class. He painted 52
of the oslo paper blue and 51
green. What part of the paper is painted blue and green?
2) The grade 4 pupils will decorate 81
of the stage with flowers and 86
with curtains. What
part of the stage will be decorated?
241
3) Nilo harvested 115
kilogram of pechay and 114
kilogram of string beans. How many
kilograms of vegetables did he harvest in all? 3. Generalization
How do we solve word problems?
To solve word problems, identify the given facts, what is asked and determine the operation to be used, then find the correct answer by doing the necessary computations.
C. App lication Read and solve on your paper.
Tootsie spent 42
of an hour sweeping the yard and 41
of an hour watering the plants.
How long did she work? IV. Evaluation
A. Read and solve the problems carefully. Remember the steps in problem solving.
1. Charisse spent 32
of an hour for scrubbing and sweeping the floor and 31
hour wiping the
furniture. How long did she work in the living room?
2. Bernard bought 93
kg of peanuts in the morning and 92
kg of cashew nuts in the afternoon.
How many kg of nuts does he have?
3. Mother brought home a ripe papaya. She gave Randy 61
and Arianne 62
. What part of the
whole papaya did she give to the children? B. Read and solve these problems correctly.
1. Bobby likes to walk. This morning, he walked 72
kilometre from his house to Tommy’s house.
Then he walked 73
kilometre from Tommy’s house to the market. What is the total distance
that Bobby walked?
2. Twofifths piece of wood was used by Mang Jose to make the roof of the doghouse while 53
piece of wood was used to make the walls. How much wood was used for the doghouse?
3. Philip picked 83
basketful of mangoes. Robert picked 82
basketful of chico while Richard
picked 81
basketful of papaya. How may basketful of fruits did the boys pick in all?
242
C. Solve these problems. Make some necessary illustrations.
1. Marco is working on his science project. He spent 123
of an hour in the morning, 122
of an
hour in the afternoon and 124
of an hour in the evening. How much time did Marco spend on
his project?
2. Mrs. Santos used 81
cup of celery, 81
cup of carrots, 82
cup of mushroom and 83
cup of
cabbage in her vegetable salad. How much vegetables did she use?
3. Robin was asked to make the props for the school play. He used 93
roll of green ribbon, 91
roll of yellow ribbon and 92
roll of red ribbon. How many roll of ribbon did he use?
V. Assignment
Read and solve following the steps in problem solving.
1. Mother bought a whole pizza and sliced it into 6 equal parts. She ate 61
of the pizza and her son
ate 62
of it. What part of the whole pizza was eaten?
2. Lara sold 3 pieces of ribbon. One piece was 102
metre long, another piece was 103
metre long,
and the third piece was 101
metre long. What was the total length of the ribbon sold?
Construct problems about addition of similar fractions. Make use of the given illustrations. Analyze them carefully.
1)
+ 4 + 2 =
8 8
2) + 2 + 1 = 6 6
243
Solving Word Prob lems involving Subtraction of Similar Fractions wi thout Regrouping I. Learning Objectives
Cognitive: Solve word problems involving subtraction of similar fractions without regrouping Psyc homotor: Follow directions in solving a word problem Affective: Show cooperation in solving word problems
II. Learning Content
Skill s: 1. Solving word problems involving subtraction of similar fractions without regrouping
2. Following given directions in solving word problems Reference: BECPELC II.D.3.2
textbooks in Math 4 Materials: flash cards, word problems written on pieces of paper, learning activity sheets,
crayons, strips of paper for pupils Value: Cooperation
III. Learning Experiences
A. Preparatory Activities 1. Drill
Oral drill on subtracting basic subtraction facts using flash cards.
8 9 10 9 7  5  4  6  5  2
2. Review
Conduct a contest on finding the magic difference using the magic squares. Subtract
across and down. a.
2011
204
205
202
b.
2520
258
259
254
244
3. Motivation
Is it important to follow directions correctly? Why? Let us see if you can follow some directions in order to solve a problem. 1) Get a strip of paper. 2) Fold it into 4 equal parts.
3) Color 42
red and 41
of it green.
4) What part of the strip is left uncolored? Write your answer at the back of the colored paper.
B. Developmental Activities
1. Presentation
a. Read and understand well this problem.
Father cut 32
of a piece of wood. He used 31
for covering a hole on the floor and the
remaining part for repairing a window. What part did he use for the window? Help them in the analysis of data by answering some questions.
1) What are given in the problem? 2) What is asked in the problem? 3) What operation will you use? 4) Write your computation with label.
b. Read the problem carefully. Answer the questions about it.
Harold and Cito sold 100
8 kg of old newspapers on Saturday and
10072
kg on Sunday.
What is the difference in the weight of the newspapers sold on Saturday and Sunday? Answer the questions below.
1) What is asked in the problem? 2) What are the given facts? 3) What process will be used? 4) Write the mathematical sentence for the problem. 5) What is the correct answer?
2. Guided Practice
(At this point, remind the pupils the importance of working together in all activities that will be given to them.)
Write these word problems on pieces of paper cut in rectangular form. Post them on a piece of manila paper cut into a house shape, hiding the written problems. Ask each group to pick up one problem and cooperatively work on it following the steps in problem solving. Have one member explain their answers.
Problem #1
A gardener sold 41
sack out of 43 sack of
potatoes, what fractional part of the potatoes was left?
Problem #2
Lita mixed 106 litre of
fruit juice with 108 litre of
water. How much more water was used than fruit juice?
245
Hidden problems written at the back.
3. Generali zation
How do we solve word problems?
To solve word problems, identify the given facts, what is asked and determine the operation to be used, make the number sentence, then find the correct answer by doing the necessary computations.
C. App lication
Read the problem and solve on your paper.
The girls used 43
kilogram of cabbage and 42
kilogram of lettuce in their cooking
class. How many more kilogram of cabbage than lettuce was used?
IV. Evaluation
Read and solve the problems. Follow the steps in problem solving.
1. Aling Mila bought 43
kilogram of grapes. She gave 42
kilogram to her mother. How many
kilogram of grapes was left to her?
2. Lando cut a bamboo stick which was 43
metre long. He used 41
metre for a garden peg. How
many metre of bamboo stick was left?
3. Mother bought 106
metre of ribbon. She used 103
metre for her gift to father. What part of the
ribbon was left?
Problem #3
Janice bought 82 metre
of green ribbon and 85
metre of blue ribbon for a key holder. How much more blue ribbon did she buy than green ribbon?
Problem #4
Cris biked 53 km on
Saturday and 51 km on
Sunday. What is the difference of the distance Cris covered?
1 2
3 4
246
4. Marco has 86
metre of illustration board. He used 84
of it for his drawing. What part of his
illustration board was left?
5. Father bought 127
litre of gasoline. He used 125
litre in going to a nearby town. How many litre of
gasoline was left unused?
6. Aunt Mary cooked 108
kilogram of spaghetti. She gave 104
kilogram to her neighbors. How much
spaghetti was left for her children?
7. Mrs. Santos bought 8 2010
metres of cloth. She used 6 207
metres for bed sheet and pillowcases.
How many metres of cloth were left?
8. In a buko pie eating contest held during a school fair, Dale ate 126
of a pie while Amy ate 123
of
the pie. How much more did Dale eat than Amy? 9. The scouts were assigned to plant a garden plot divided into 6 equal parts. They finished planting
64
of the area. What part of the plot was not planted?
V. Assignment
Read and solve following the steps in problem solving.
1. Aling Charing had 87
litre of coconut vinegar. She used 81
litre for adobo and the rest for paksiw.
How many litre of coconut vinegar was left for her paksiw?
2. Roel and Mario removed weeds from their lawn. Roel finished weeding 41
of the lawn while Mario
finished 42
. What part of the lawn was left unweeded?
Write a story problem that involves subtraction of similar fractions. Be ready to dramatize the problem
Visualizing Multiplication of Fractions I. Learning Objectives
Cognitive: Visualize multiplication of fractions Psyc homotor: Illustrate multiplication of fractions correctly Affective: Show generosity to others
II. Learning Content Skill s: 1. Visualizing multiplication of fractions 2. Identifying a given fraction References: BECPELC II.E.1.1
textbooks in Math Materials: strips of cartolina with different shapes, cutouts of fractions, learning activity
sheet, crayon Value: Generosity
247
III. Learning Experience
A. Preparatory Activities
1. Drill
Answer the basic multiplication facts using flash cards.
3 5 4 2 3 5 x 2 x 3 x 3 x 3 x 6 x 6
2. Review
Identifying fractions using cutouts of fraction. Name the fraction for the shaded part.
3. Motivation
Acting out a problem.
Ask a group of eight pupils to stand in two rows in front of the class. Ask 43 of the group
to sit down then ask 31 of the group who sat down to kneel. What part of the whole group
would still be kneeling?
What did you do to find the answer? How do we get 21 of
43 ?
31 of
43
43 of the group
B. Developmental Activities
1. Presentation
a. Present the word problem.
Mayumi bought 31 metre of linen cloth. She used
21 of it to make a
handkerchief for her Mother. What part the cloth was used for the handkerchief?
What kind of a daughter is Mayumi? Is it good to be generous? Why?
248
Guide the pupils in analyzing the problem. Let them give the number sentence
for 21 of
31 . Help them visualize and interpret the multiplication sentence. Make
necessary illustrations. Give emphasis to the double shaded part.
61
31
21 of
31
Present the multiplication sentence by computation.
21 of
31 =
21 x
31 =
21 x
31 =
61 metre was used
b. Give another presentation.
Draw a rectangle on the board and mark it into fourths. Then draw a line dividing the
whole rectangle into two. Shade 21 of
41 .
What part of the whole rectangle is shaded twice? (81 )
What is 21 of
41 then? (
81 )
Show this on the board: 21 of
41 =
81
41
21 of
41
2. Guided Practice
(Remind the pupils to work neatly and share coloring materials.) Activity Sheets Match the picture in column A with the multiplication sentence in column B. Write only the letter of the correct answer. A B
1) a. 42 of
21
249
2) b. 21 of
21
3) c. 31 of
43
Complete the multiplication sentence appropriate for the given figures. 1) 2) 3) ___ of ___ ___ of ___ ___ of ___ Draw or visualize each multiplication of fractions
1) 52 of
21 2)
53 of
31 3)
63 of
41
3. Generali zation
How do you visualize multiplication of fractions?
Divide the whole by the first denominator having equal parts then shade parts according to its numerator. Divide again the whole by the second denominator with intersected lines and then shade using the second numerator. The double shaded part is the product of the two fractions.
C. App lication
Read and solve on your paper. Write the multiplication sentence then express your answer in lowest terms if possible.
Rorie has 43 metre of red ribbon. She used
21 of it in decorating a gift package for
her mother. What part of a metre of ribbon was used in decorating the gift package for her mother?
What kind of daughter is Rorie? Are you like Rorie? In what way?
IV. Evaluation
1. Draw the following fractions.
a. 53 of
31 c.
53 of
41 e.
42 of
21
b. 32 of
51 d.
52 of
21
250
2. Illustrate the following fractions.
a. 83 of
42 b.
52 of
42 c.
63 of
41
d. 73 of
21 e.
85 of
32
3. Visualize each multiplication of fractions.
a. 53 of
62 b.
85 of
32 c.
74 of
81
d. 94 of
43 e.
43 of
64
V. Assignment
Complete the table.
Fraction Illustration Product
a. 32 of
21 _____ _____
b. _____ _____
c. 31 of
21 _____ _____
Finding the Fractional Part of a Number I. Learning Objectives
Cognitive: Find a fractional part of a number Psyc homotor: Form sets of objects using counters Affective: Work cooperatively in group activities
II. Learning Content
Skill : Finding fractional part of a number References: BECPELC I.E.1.2 Materials: flash cards, cutouts of fractions, learning activity sheets, counters like buttons,
seeds, etc., number cards from 0 to 9 Value: Cooperation
251
III. Learning Experiences
A. Preparatory Activities
1. Drill Oral drill on basic multiplication facts using flash cards
3 8 7 6 4 5 x 4 x 3 x 5 x 4 x 9 x 5
2. Review
Give the multiplication sentence suited for the given illustrations.
a. b. c.
3. Motivation
a. Divide the class into groups of four. Give each group 20 counters (e.g. buttons, seeds,
etc.) and number cards from 0 to 9. b. Ask the groups to use their counters to show the following.
Example: 21 of 12 = 6
1) 31 of 15 2)
31 of 18 3)
51 of 20
Whose group finished first? Why do you think you were able to
finish first? B. Developmental Activities
1. Presentation
Ramil has 20 marbles in a jar. Onefifth of it are red marbles. How many red
marbles are in the jar?
a) Help them analyze the data in the problem. 1) What part of the marbles are red? 2) How many marbles are there inside the jar?
3) Write the mathematical sentence. (51 of 20)
4) Get 51 of 20. What is your answer?
5) How did we get the fractional part of the number?
252
b) Let them work on more complex exercises using their counters.
Example: 52 of 10 = 4
Have them divide 10 into 5 equal parts (2 counters each), then get 2 parts (2 x 2).
c) Present it by computation.
Example: 83 of 16 = n
Whole number 16 ÷ 8 = 2 x 3 = 6 denominator numerator of fraction of fraction
Example: 54 of 25 = n
54 of 25 =
54 x 25 = 4 x (25 ÷ 5) = 4 x 5 = 20
d) Give another example.
How will you find 43 of 32?
Ask a volunteer to solve it on the board.
43 of 32 = n 32 ÷ 4 = 8 x 3 = 24
2. Group Activity
Activity Sheet
Complete the equation.
a) 21 of 20 = _____ b)
31 of 12 = _____ c)
41 of 16 = _____
Write the answer.
a) 81 of 48 = _____ b)
71 of 21 = _____ c)
32 of 9 = _____
253
Solve these problems. If there are 60 minutes in an hour, how many minutes are there in
a. 21 of an hour? b.
31 of an hour? c.
41 of an hour?
3. Generali zation
How do you get the fractional part of a number?
To get the fractional part of a number, multiply the number by the numerator of the fraction then divide the product by the denominator.
C. App lication
Read and solve on your paper.
Joshua had 12 colored pencils. If 41 of them are broken, how many pencils are
broken?
IV. Evaluation
1. Find the answer.
a. 101 of 200 = n b.
121 of 36 = n c.
52 of 20 = n d.
43 of 16 = n e.
72 of 14 = n
2. Write the answer.
a. 53 of 30 = n b.
53 of 60 = n c.
54 of 50 = n d.
72 of 28 = n e.
43 of 24 = n
3. Draw sets of objects to show the equations and solve for the answer.
Equation Illustration Solution and Answer
a. 1 of 15 3
b. 2 of 30 5
c. 5 of 16 8
d. 4 of 25 5
e. 4 of 28 7
V. Assignment A. Find the answer.
1) 42 of 16 2)
83 of 40 3)
54 of 50 4)
92 of 81 5)
32 of 18
254
B. Solve for the answer.
1. Ruela had 30 stamps. She gave away 65 of them. How many stamps were left?
2. Mang Jose picked 100 pieces of mangoes. He sold 54 of the mangoes. How many mangoes
were left?
3. Johnny has 12 crayons. What if 41 of them are broken? How many crayons are broken?
4. Mang Jack has 10 jars of paint. Onefifth of them are yellow. How many are yellow?
5. Anna had 9 colored pencils. He lost 31 of them. How many colored pencils were lost?
Translating Express ions I. Learning Objectives
Cognitive: Translate expressions such as 21
of 32
, 32
of 61
to mathematical sentences
Psyc homotor: Illustrate expressions using shaded regions Affective: Show resourcefulness in doing one’s project
II. Learning Content
Skill s: 1. Translating expressions such as 21
of 32
, 32
of 61
2. Multiplying a fraction by another fraction References: BEC – PELC II E 1.2.1 & E 2
Materials: flash cards, cutouts of fractions, learning activity sheet, chart showing illustrations Value: Resourcefulness
III. Learning Experiences
A. Preparatory Activities
1. Drill Contest on basic multiplication facts using flash cards.
3 7 5 2 6 3 x 2 x 2 x 2 x 3 x 3 x 5
2. Review Naming fractions Give the fraction for the shaded part.
3. Motivation
Get 21
sheet of Grade 4 paper. Fold 21
of your paper. What is 21
of a half? What word in
this sentence has an equivalent symbol in mathematics? What symbol can be replaced by the word “of”?
255
B. Developmental Activities
1. Presentation
Nancy found a piece of white cloth in an old chest of her grandmother. She cut
32
of it, then she used 21
of this for her apron’s pockets. What part of the whole
piece of cloth did Nancy use for her apron’s pockets?
a. Help the pupils in the analysis of data.
1. What kind of a girl is Nancy? 2. If you were Nancy, would you do the same? Why? 3. What part of the cloth did Nancy cut? 4. What part of the cloth did Nancy use for the apron’s pockets? 5. Write the mathematical sentence.
b. Help them visualize and interpret the multiplication sentence.
21
of 32
1. Show them this illustration.
2. Ask them to shade 32
of this illustration then doubly shade 21
of it.
Answer:
c. Present the multiplication sentence from the expression. Expression to Mathematical Sentence
21
of 32
means 21
x 32
= n, where n is for the answer
21
x 32
= 62
or 31
d. Present another example
What is 32
of 61
?
32
of 61
means 32
x 61
= n
32
x 61
= 182
or 91
2. Group Activity
a. Write the mathematical sentence for the following expressions.
1) 61
of 32
= 2) 21
of 43
= 3) 31
of 63
=
256
b. Translate the following expressions to mathematical sentences then find the product.
1) 21
of 53
= 2) 31
of 74
= 3) 51
of 83
=
c. Illustrate the following expressions using shaded regions and translate into mathematical
sentences then find the product using cancellation method.
1) 21
of 61
= 2) 51
of 21
= 3) 31
of 52
=
3. Generali zation
How do you translate expressions such as 21
of 32
into mathematical sentence?
To translate expressions like 21
of 32
into mathematical sentence, we change
“of” to “x” symbol which means ‘times’ to form the multiplication sentence.
C. App lication
Read and solve on your paper.
During a toothbrushing demonstration for dental week, several Grade 4 pupils used
21
of the 43
full tube of toothpaste. What part of the whole tube of toothpaste was used?
IV. Evaluation
1. Translate the following expressions to multiplication sentences.
a. 42
of 21
= b. 32
of 51
= c. 53
of 31
= d. 63
of 41
= e. 52
of 31
=
2. Complete the data in the chart.
Expressions Multipli cation Sentence
a. 31
of 52
b. 21
of 43
c. 51
of 21
d. 41
of 32
e. 53
of 21
257
3. Name the doubleshaded region by writing two fractions using the word “of” then translate them into a multiplication sentence.
a. c. e. _____ of _____ _____ of _____ _____ of _____
_____ x _____ _____ x _____ _____ x _____ b. d.
_____ of _____ _____ of _____ _____ x _____ _____ x _____ V. Assignment
Translate the following expressions to multiplication sentence.
a. 72
of 43
= b. 21
of 54
= c. 31
of 74
= d. 42
of 83
= e. 51
of 21
=
Multiplying a Fraction by another Fraction I. Learning Objectives
Cognitive: Multiplying a fraction by another fraction Psyc homotor: Illustrate multiplication of fractions Affective: Show generosity to others through sharing
II. Learning Content
Skill : Multiplying a fraction by another fraction References: BECPELC II.E.2 Materials: chart, multiplication table, picture, rectangular regions, showmeboards, learning
activity sheets Value: Generosity
III. Learning Experiences
A. Preparatory Activities
1. Drill
Conduct a drill on the basic multiplication facts. Present a table similar to the one below. As the teacher points to a number, the pupils will write their answers on their magic slates or showmeboards. X 4 8 6 3 7 2 9 0 1 6
258
2. Review
Review expressing fractions in lowest terms Write each fraction in its lowest terms
a. 102
= ___ b. 156
= ___ c. 328
= ___ d. 155
= ___ e. 128
= ___
3. Motivation
Show a picture of a cake and say, “Suppose you have a whole cake. You cut it into
halves and give 21
of a half to your neighbor. What part of the whole cake did you give
away?” Valuing: � Is it good to share food with neighbors? Why?
B. Developmental Activities
1. Presentation
a. Present the lesson by asking four groups of pupils to follow the directions written in activity sheets.
1) Ask representatives from each group to post their work on the board as he/she reports about it.
2) Teacher checks which groups have the correct illustration.
3) Ask: What is 21
of 41
then?
Show this on the board : 21
of 41
= 81
Tell someone to change it into a multiplication sentence. What do we do with the numerators to get the numerator of the product?
How about the denominator of the product?
When we have the expression 21
of 41
, what process do we use?
b. Present another method involving cancellation to simplify multiplication of fractions. Show that in cancellation, one divides a numerator and a denominator by a common factor. When all common factors have been used, multiply to find the product. The product should be in its lowest terms.
ACTIVITY SHEET 1) Draw a rectangle on a white paper. 2) Divide it into fourths. Shade one fourth. 3) Draw a line dividing the whole rectangle into two.
4) Shade 21
of 41
5) Answer this: What part of the whole rectangle is shaded twice?
259
Example: 1 2
5 x 14 = 2 71 153 3 c. Introduce cancellation using 3 fractions.
Example: 1 3 1 3 x 6 x 7 = 3 42 71 124 8
2. Guided Practice a. Use the picture to find the product. Express the answer in its lowest terms if possible.
1) 2) 3)
21
x 31
21
x 21
21
x 51
b. Find the product using cancellation. Write the product in its lowest terms if possible.
1) 83
x 54
= ____ 2) 75
x 103
= _____ 3) 158
x 125
= ____
c. Multiply using cancellation. Write the product in its lowest terms if possible.
1) 127
x 149
= ____ 2) 32
x 109
x 83
= _____ 3) 54
x 1615
x 21
= ____
3. Generali zation
How do we multiply a fraction by another fraction?
To multiply fractions, multiply the numerator by the numerator and the denominator by the denominator. Express the product in its lowest terms if possible.
C. App lication
Read and solve on your paper. Express the answer in its lowest terms if possible.
1. A butter cake recipe needs 43
cup milk. How many cup of milk is needed to make 21
?
2. A sewer made pockets for shirts. First, she cut 32
metre of the material. Then, she used 43
of
the material she had cut for pockets. How much material did the sewer use for pockets? IV. Evaluation
A. Multiply. Write the answer in its lowest terms if possible.
a. 31
x 81
= b. 21
x 32
= c. 54
x 21
= d. 81
x 54
= e. 41
x 52
=
B. Find the product. Express it in simplest form if possible.
a. 32
x 106
= b. 42
x 32
= c. 43
x 73
= d. 41
x 85
= e. 51
x 155
=
C.
1. Find the product. Shade the correct part of each region to show your answer.
260
a. 31
x 21
= b. 32
x 21
=
D. Multiply using cancellation. Write the product in its lowest terms if necessary.
c. 32
x 1615
= d. 126
x 423
= e. 32
x 86
x 1412
=
V. Assignment
Find the value of n. Reduce to lowest terms if possible.
a. 31
x 21
= n c. 32
x 52
= n e. 52
x 101
= n
b. 54
x 31
= n d. 31
x 43
= n
Analyzing Prob lems I. Learning Objectives
Cognitive: Analyze word problems involving multiplication of fractions Psyc homotor: Write the answers to the questions correctly Affective: Show active participation and cooperation in class discussions
II. Learning Content
Skill : Analyzing word problems involving multiplication of fractions References: BECPELC II.E.3.1.1 – 3.1.4
textbooks in Math 4 Materials: activity sheets, miniboards, textbooks, strips of cartolina Values: Active participation and cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill
Have some exercises on multiplication facts in the form of a game.
Partners 5 x 5 6 x 3 3 x 3 7 x 3 5 x 6 9 x 5 9 x 8 8 x 7 6 x 4 4 x 8 8 x 8 7 x 4 6 x 8 9 x 7 4 x 9 6 x 7 8 x 5 5 x 4 25 21 56 24 63 45 9 72 32 64 42 28
18 30 48 36 40 20
a. Two players share the same gameboard.
Factors
Products
261
b. One player cuts out 30 cards and places them at random face down on the table/desk. Player A turns over 2 cards. If these cards match, he/she takes the cards. For example, if player A turns over two cards 8 x 7 and 56, he/she takes these cards, they match.
c. If the cards do not match, the player leaves them faceup. player B now turns over 2 more cards and matches any cards that are face up on the table.
d. Each player alternates until all the cards are turned faceup. e. The player who accumulates the most cards wins. f. The player can reshuffle the cards and play more games. g. The teacher may change the given numbers.
2. Review
a. Have a game on rearranging steps in analyzing word problems. b. The group that finishes first is the winner.
3. Motivation
Present this word problem.
Marissa bought 31
of a metre of cotton cloth. She used 21
of it to make a
tablecloth. What part of a metre was used for the tablecloth?
a. Who is talked about in the problem? b. What did she do?
B. Developmental Activities
1. Presentation
How will you find the answer to the problem? How are you going to work with the other members of your group? Why do you have to cooperate with the other members of the group?
2. Group Activities
Strategy 1 – Acting ou t the problem a. Members of the group are to act out the problem. b. The group should follow the steps in analyzing the problem.
1) What is asked? _____ 2) What are the given facts? _____ 3) What is the operation to be used? _____ 4) What is the mathematical sentence? _____ 5) What is the answer? _____
Strategy 2 – Following d irections
Place the given word/s in their proper order or step.
Given data:
1 and 1 metres of cloth 3 2
What part of a metre was used for the tablecloth?
1 metre 6
1 x 1 = n 3 2
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First – Second – Third – Fourth – Fifth 
Strategy 3 – Supplying the missing data 1) The problem is asking for _____. 2) _____ and _____ are the given data. 3) The process to be used is _____. 4) The mathematical sentence is _____. 5) _____ is the final answer.
Strategy 4
Number the given data from first to fifth using the following steps:
1) The problem asks for the _____. 2) The given facts are the _____. 3) The process to be used is _____. 4) The mathematical sentence for the problem is _____. 5) The answer is _____.
Given data: 31
x 21
= n 61
metre of cloth 31
of 21
metre of cloth used multiplication
4. Analysis/Abstraction What did we do to the problem? How did we analyze the problem? Did you follow the steps?
Multiplication
Analyzing word problems involving multiplication of fractions
First Second Third Fourth Fifth
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3. Guided Exercises
Choose the letter of the correct answer.
Esmer bought 53
kilo of sugar for the icing of a cake. Only 21
of it was used.
How much sugar was used?
1) What is asked in the problem? a. amount of sugar used c. amount of sugar in a plastic bag
b. amount of sugar bought d. amount of sugar in a cup 2) What is the process to be used?
a. addition c. multiplication b. subtraction d. division
3) What is the mathematical sentence for the problem?
a. 21
+ 43
= n b. 21
x 43
= n
c. 21
 43
= n d. 21
÷ 43
= n
Mary had 53
metre of lace. She used 32
of it for her project.
What part of the lace was used for her project?
Match column A with column B.
A B 1) What is asked in the problem? a. part of lace used 2) What are the given data?
b. 32
x 53
3) What is the process to be used? c. multiplication 4) What is the mathematical sentence for the problem? d.
156
or 32
5) What is the answer? e.
32
, 53
4. Generali zation
How do we analyze problems involving multiplication of fractions?
In analyzing word problems involving multiplication of fractions, we should follow the following steps: a. Find what is asked b. Find the given data c. Know the process to be used d. Give the mathematical sentence for the problem e. Solve for the answer
264
C. App lication Supply the missing words.
Roy used 31
of the 87
metre of bamboo stick for his lantern. How much of
the stick was used?
1. The problem is asking for _____. 2. The answer to the problem is _____. 3. The mathematical sentence is _____. 4. The process to be used is _____. 5. The _____ and _____ are the given data.
IV. Evaluation
Connie had 43
of a cake. She gave 21
of it to her friend. What part of the cake
did Connie give away?
Choose the letter of the correct answer. 1. What is asked in the problem?
a. Pieces of the whole cake b. Part of the cake that is given away c. Parts of the cake that were eaten d. Pieces of the cake that were broken away
2. What are the given facts?
a. 21
part of the cake
b. 43
part of the cake
c. 21
and 43
of a cake
d. 83
part of a cake
3. What is the mathematical sentence?
a. 21
x 43
= n
b. 21
+ 43
= n
c. 43
– 21
= n
d. 43
÷ 21
= n
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4. What is the process to be used? a. addition b. subtraction c. multiplication d. division
5. What is the answer?
a. 63
c. 93
b. 83
d. 123
V. Assignment
Write the word/s that show the steps in analyzing word problems. Get the data from the problems given.
A. What is asked in the problem? B. What are the given facts? C. What is the process to be used? D. What is the mathematical sentence? E. What is the answer?
1. David had 43
can of horse manure. He needs 21
of it to fertilize his garden plots. What part of
the can of horse manure did he use?
2. Rennie bought 21
litre of paint. He used 43
of it for their class in Industrial Arts. How much
paint was used?
3. A chocolate recipe needs 43
cup of milk. How many cups of milk are needed to make 21
?
4. Nene gave 21
of 1 kilo of peanuts to her sister. What part of a kilo did her sister receive?
5. Maria ate 31
of 61
of a pie. What part of the pie did Maria eat?
Solving Word Prob lems I. Learning Objectives
Cognitive: Solve word problems involving multiplication of fractions Psyc homotor: Follow specific directions in solving word problems Affective: Show cooperation and sportsmanship in performing group work
266
II. Learning Content
Skill : Solving word problems involving multiplication of fractions Reference: BECPELC II.E.3.1 Materials: textbook, flash cards, charts where problems are written, learning activity sheet Values: Cooperation and sportsmanship
III. Learning Experience
A. Preparatory Activities
1. Drill
Oral drill on basic multiplication facts using flash cards Ex.
5 x 4
6 x 3
7 x 6
8 x 9
9 x 2
2. Review
What are the steps in solving word problems?
3. Motivation
Are you ready for a contest on multiplication of fractions? Using flash cards, conduct a
contest on multiplying fractions. Do this by groups. Emphasize to work cooperatively and accept their losses if some groups win. Did the members of the group cooperate with one another? How? What did the loser group do? Is it important to be a good sport? Why?
B. Developmental Activities
1. Presentation
a. Present a word problem.
Precious bought home 54
of a round cake. She gave her brother 31
of it. What part of
the whole cake did she give to her brother?
1) Help them analyze the word problem. a) What is asked in the problem? b) What are the given facts? c) What operation will you use? d) Write the number sentence. e) What is the answer?
2) Show the multiplication sentence by computation.
54
of 31
= 54
x 31
= 154
part of the cake
b. Read the problem. Answer the questions on your paper.
Virgie had 108
kilogram of carrots to sell. She sold 43
of it. What part of a kilogram of
carrots was left?
267
1) What is asked in the problem? 2) What are the given facts? 3) What is the word clue? 4) Determine the operation to be used. 5) Give the mathematical sentence for the problem. 6) What is the correct answer? 7) Draw a picture for the problem.
c. Present a set of problems and let them solve these by groups. Ask a representative to
explain their work. Solve for the following problems.
1) Joe jogs daily for 21
hour. How long does he jog in a week?
2) Charisse found 43
of a cake on the table. She ate 21
of it. What part of the cake did
she eat?
3) Peter bought 2 kilos of lanzones. He gave 31
of it to me. What part of a kilo of
lanzones did he give to me?
2. Generali zation How do we solve word problems involving multiplication of fractions?
In solving word problems involving multiplication of fractions, we must determine what is asked, what are given, and what is/are the word clue/s. Decide what operation to be used and what is the number sentence then solve the problem.
C. App lication
Read and solve on your paper.
Aling Myrna divided the bibingka into five equal parts. Nardo got one slice and gave half of the slice to Gerard. What part of the whole bibingka did Gerard get?
IV. Evaluation
For each of the problem, write what is asked and the mathematical sentence then solve for the answer. Do these on your paper.
1. Elvira had 43
of a cake. She gave 21
of it to her younger sister. What part of the whole cake did
Elvira give away?
2. Dante had 43
can of horse manure. He used 21
of it to fertilize his garden plots. What part of the
can of horse manure did he use?
Read and solve the problems. Follow the steps in problem solving.
1. Catherine had 53
metre of lace. She used 32
of it for her project. What part of the lace was used
for her project?
268
2. John had 54
of the plot vacant. He planted 41
of it with pechay. What part of the plot was planted
with pechay?
3. Mrs. Garcia had 108
kg of flour. She used 21
kg of it for baking a pudding. How much flour did she
used?
Solve for the following problems.
1. In the hospital, 107
cavan of rice is cooked in a day. How many cavans of rice is cooked in 31
of
a day?
2. Fourfifths of Benjie’s garden is planted with vegetables. Of the vegetables planted, 87
is
cabbage. What part of the garden is planted with cabbage?
3. Jojo has 32
metre of string. He used 21
of it for tying a small box. What part of the metre was
used for tying the small box? V. Assignment
Solve for the following problems.
1. Danny and Lily packed 43
of the canned goods. Twothirds of these were sardines. What part of
the canned goods packed were sardines?
2. Mother cooked fried chicken for her son’s birthday party. She prepared 43
litre of cooking oil.
However, she used only 21
of it. What part of the cooking oil was used?
3. Elisa had 63
of a cake. She gave 21
of it to her friend. What part of the whole cake did Elisa give
away?
Kinds of Plane Figures I. Learning Objectives
Cognitive: Identify the different kinds of plane figures Psyc homotor: Draw plane figures correctly Affective: Appreciate the shapes around us
Show awareness to the things around us II. Learning Content
Skill : Identifying the different kinds of plane figures References: BECPELC III.A.1.1 textbook Materials: cutouts of different shapes, real objects, illustrations/drawings, coins Values: Appreciation and awareness of the things around us.
269
III. Learning Experiences
A. Preparatory Activities
1. Drill
Game of numbers “Connecto”
7 x 8 6 x 9 4 x 7 3 x 9 5 x 9
2 x 8 9 x 9 7 x 8 3 x 6 3 x 4 5 x 3
3 x 4 6 x 8 5 x 6 7 x 7 8 x 4
7 x 9 0 x 9 4 x 7 9 x 6 5 x 6 7 x 6
2 x 8 7 x 9 7 x 5 3 x 7 4 x 6
270
a. Two players share the same “connecto” game board. One player uses a red crayon to connect the circle, and the other player uses a blue crayon to connect the triangles.
b. The player who first completes an unbroken path from one side of the game board to the other side is the winner.
Where are the numbers written? What kind of plane figures are these?
2. Review
Lucia and Claudine went to visit their Lola Clara in the city. They rode on a bus which rolled out into the highway. They saw signs like these as they were traveling.
Can you tell the shapes of the sign boards? Can you identify them? What do signs tell us? What are the importance of the signs to us? Why should we follow these signs?
7 x 5 8 x 3 6 x 9 4 x 5 6 x 8 8 x 8
9 x 9 8 x 3 0 x 4 6 x 6 9 x 4
3 x 7 6 x 6 3 x 9 4 x 4 7 x 7 4 x 9
5 x 3 8 x 6 7 x 6 5 x 8 8 x 9
3 x 6 4 x 5 9 x 6 4 x 4 7 x 8
4 x 7 9 x 4 5 x 8 8 x 7 8 x 4 8 x 9
SLOW
STOP
DETOUR SPEED LIMIT
30 KPH
271
3. Motivation Do you know the song, “Bahay Kubo”? What does it tell? If you were to describe the
vegetables, how does each vegetable look like? Who can give the tune of the song?
B. Developmental Activities
1. Presentation
Introduce the lesson with a song to the tune of “Bahay Kubo”
What is Mang Kiko made of? (2x)
and
, and
That is what Mang Kiko made of. What are the figures mentioned in the song? Can you identify each figure?
2. Group Activities
Group 1: Tracing the dots
a. Trace the dots and identify the figure.
1) 2) 3)
b. Describe each figure.
Group 2: Writing
Write A inside the figure with 3 sides, B inside the figure with no sides and C inside the figure with 4 sides.
272
Group 3: Act ou t
a. Let 10 pupils form a figure with 4 sides, 3 sides and enclosed figure with no sides. b. Describe each figure
Group 4: Cut it out
a. blue – figures with 4 sides b. red – figures with 3 sides c. yellow – enclosed figures with no sides
Group 5: Naming figures
Name some things inside the room with the following: a. enclosed figure with no sides b. 4 sides c. 3 sides
3. Analysis/Abstraction
Note: Teacher will get the data based on the report of the pupils. a. Are the figures the same? Why are the figures similar? b. and the same? Why?
4. Practice Exercises
Bring Me Game a. Let the pupils form five lines with five members b. Members in the group will work as one in bringing things according to what the teacher
wants them to bring. (things in the bag)
5. Generali zation
What do we call a closed figure? How about a figure with 3 sides? What about with 4 sides?
Plane figures are closed figures. Plane figures with 3 sides are called triangles. Those with 4 sides are called quadrilaterals.And those without sides are called circles.
C. App lication
1. Name game (body or sign language) a. circle b. triangle c. quadrilateral
2. Naming/Describing game
a. toys b. appliances at home c. things inside the room
273
IV. Evaluation
Count the number of plane figures in the illustration. (Work in pairs) How many quadrilaterals are there? Triangles? Circles?
V. Assignment
Identify the different body parts of the doll and describe each figure.
274
Triangles
I. Learning Objectives
Cognitive: Identify the parts of a triangle Identify the different triangles according to sides and angles
Psyc homotor: Draw the different a triangles according to sides and angles Affective: Show orderliness in doing the activity
II. Learning Content
Skill : Identifying the parts of a triangle Reference: BECPELC III.A.1.2.a Materials: textbooks, cutouts of triangles, protractor, art paper Value: Orderliness in doing an activity
III. Learning Experiences
A. Preparatory Activities
1. Drill
Show pictures showing polygons with different sides and let the pupils identify them.
2. Review Show cutouts of different plane figures and let the pupils identify them. (circle, square,
triangle, rectangle, rhombus, parallelogram, trapezoid)
3. Motivation Present a figure made up of triangles.
Example:
Let the pupils observe the figure. What is this figure? What is it made of? Valuing: � Later, you will be working with your group, how are you going to work so that the
outcome will be good? Is it good to observe proper order in working with other people? Why?
275
B. Developmental Activities
1. Presentation
a. Present a big cutout of a triangle. Look at the triangle. What can you say about this triangle? What does a triangle have? How many sides does a triangle have? Show us the sides. How many vertices does it have? Show us the vertices. How many angles does a triangle have? Show us the angles. (Tell the pupils that a triangle can be named by its vertices.) A B C
This is a triangle ABC or ABC. Show the base of the triangle.
b. Present the trace drawings of triangles on the board (according to sides). X L
Q Y Z M N R S
Let the pupils measure the lengths of each side of the triangle using their ruler. What do you notice about the 3 triangles? Can you name the 3 triangles by their vertices?  What kind of triangle is XYZ?  What can you say about the measurements of the sides? Ask the same questions for LMN and QRS. Introduce equilateral, scalene and isosceles triangles.
2. Group Activity
Distribute cutouts of triangles to the 3 groups In the cutouts, an arrow is pointed to the angle that is to be measured using the protractor.
After measuring, introduce the three kinds of triangle according to the measurement of angles. (right triangle, obtuse triangle, acute triangle)
276
Provide the pupils cutouts of the different kinds of triangles. Ask them to tear off each of
the three angles in it and then put the three vertices together so that the three angles fit. This will show them that the three angles form a straight line. What do you think is the measurement of the three angles of a triangle?
3. Generali zation
a. What are the parts of a triangle?
(The parts of a triangle are the sides, the vertices/angles and the base) b. What are the kinds of triangles according to sides?
• An equilateral triangle has three equal sides • An isosceles triangle has two equal sides • A scalene triangle has 3 acute angles
c. What are the kinds of triangles according to angles? • An acute triangle has 3 acute angles • A right triangle has one right angle • An obtuse triangle has one obtuse angle
IV. Evaluation
1. What kind of triangles are the following? A B C D E F
2. Name the part of the triangle that is indicated below. A B C AC, AB – BC –
A, B, C –
277
C. App lication
1. Draw different kinds of triangles according to sides. 2. Provide each pupil with a cutout of a triangle. Have them use a ruler to measure each side of their
triangles. Call on the pupils one by one to tell their classmates the measurements they got. Their classmates will identify the kinds of triangles according to the lengths of the sides.
3. Have the pupils get three pieces of art paper. Challenge them to apply what they know about triangles to form a right triangle, an isosceles triangle and a scalene triangle by folding and cutting their art papers. Present them to the class afterwards.
V. Assignment
A. Draw the following:
1. right triangle 2. scalene triangle 3. obtuse triangle 4. equilateral triangle
B. Name the triangles in each figure. Identify each one of them.
B A C
E
C. How many triangles do you see in the figure? Name them. F J I K G H
Parts of a Quadrilateral I. Learning Objectives
Cognitive: Identify the parts of a quadrilateral Psyc homotor: Construct quadrilaterals Affective: Sportsmanship during games
D
278
II. Learning Content
Skill : Identifying the parts of a quadrilateral References: BECPELC III.A.1.2.b textbooks in Math 4 Materials: cutouts of quadrilaterals Value: Sportsmanship
III. Learning Experiences
A. Preparatory Activities
1. Drill
Square Deal (Stress sportsmanship when playing games) a. Two players share the game board. b. Starting at any black square on the game board, player A connects it to a neighboring
black square with a horizontal or vertical line. Player B then connects any 2 neighboring black squares. Diagonal lines are not allowed.
c. The players may connect two neighboring black squares anywhere on the game board. d. If the player is unable to answer the problem correctly, the other player has a chance to
give the correct answer and place his or her initials in the square and receive the point. e. Play ends when all 25 squares are completed. The player who has scored the most
points wins.
8 x 9 54  6 18 + 7 23  8 96 ÷ 2
19 + 8 33  6 72 ÷ 2 7 x 5 72 ÷ 8
6 x 8 45 ÷ 9 37 + 6 43  9 36 ÷ 3
7 x 9 56 ÷ 7 28  5 51  2 51 ÷ 3
21  9 96 ÷ 3 3 x 8 36 ÷ 4 19 12
279
2. Review
Match the name of a quadrilateral in column A with its figure in column B.
A B
1) parallelogram A. 2) rhombus 3) rectangle B. 4) square 5) trapezoid C. D. E.
3. Motivation Look at the objects inside our room. What different shapes do you see? I have here a
story problem. I want you to listen carefully then use your imagination to answer the questions.
B. Developmental Activities
1. Presentation
The Valdez family lives at St. Jude Village, City of San Fernando. Beautiful landscapes
surrounding the houses are a sight to see. The different structures and trees planted along the streets make life worth living for. Can you imagine the different shapes in the place?
2. Analysis/Discussion
Let the pupils answer the questions in dyads. Tell them to describe each figure that they
have made. a. What shapes can you imagine?
(Pupils will draw different shapes on the board. Lead them to illustrate a square ground.) • Ask them about the shapes and the number of the sides and vertices of the figures.
(a square, has 4 equal sides) b. What is the common shape of the houses in the village?
• Ask them about the number of sides and vertices it has. (Introduce the term rectangle and its number of sides)
c. What is the shape of the floor tiles? (Lead them towards identifying the shape rhombus.)
• Ask them about the shape and its number of sides and vertices. d. Have you seen this figure?
(Ask them about the number of sides and vertices and other characteristics. Lead them towards identifying it as a trapezoid.)
280
e. How many of you have seen this shape? Ask them about the number of sides and vertices and its other characteristics. Lead
them in identifying it as a parallelogram. f. What is common among all the figures?
(They all have 4 sides and 4 vertices.) g. Introduce the term quadrilateral.
3. Guided Exercises
a. Match the quadrilateral in column A with its description in column B. Write the letter of the
correct answer. A B 1) a. It has 4 equal sides, but have no right
angles.
2) b. It has one pair of parallel sides.
3) c. It has 2 pairs of equal sides and 4 right angles.
4) d. It has 2 pairs of parallel sides.
5) e. It has 4 equal sides and 4 right angles.
b. Identify the quadrilaterals drawn below.
1) 2) 3) 4) 5)
_______ ________ ________ _______ ________
c. Name the sides and vertices of each quadrilateral.
1) B E 2) K M
C X L N
d. Draw the following quadrilaterals. 1) Square 2) Rectangle 3) Trapezoid 4) Rhombus 5) Parallelogram
281
e. Name the sides and vertices of each quadrilateral.
4. Generali zation What are the parts of a quadrilateral?
The parts of a quadrilateral are the sides and vertices. Quadrilaterals are plane figures having 4 sides.
IV. Evaluation
1. Color the square blue, the rhombus green, the rectangle red, the parallelogram pink and the
trapezoid violet.
2. Identify the sides and vertices of the following quadrilaterals. L M A E
K N B F
3. Name the quadrilateral described. a. Has 4 equal sides and 4 right angles b. Has 2 pairs of parallel sides c. Has 1 pair of parallel side d. Has 4 equal sides but has no right angles e. Has 2 pairs of equal sides and 4 right angles
4. Identify the sides and angles of the following quadrilaterals.
Y Z O P
X W S M
5. Use the figure to identify the following: a. square b. rectangle c. rhombus d. parallelogram e. trapezoid
A B C D E F G H L N O P I M S J K R T
282
V. Assignment A. Name the sides and vertices of the following quadrilaterals.
S T Y Z O P X M N B U V
B. Put a cross inside each quadrilateral.
C. Draw different quadrilaterals. Label their sides and vertices. D. Bring objects representing the 5 quadrilaterals learned in class.
Parts of a Circle I. Learning Objectives
Cognitive: Identify the parts of a circle Psyc homotor: Draw a circle and show its parts Affective: Show cooperation in group activities
II. Learning Content
Skill s: 1. Identifying the parts of a circle 2. Drawing a circle and showing its parts References: BECPELC III.A.1.2
textbooks in Math 4 Materials: cutouts of circles, drawing of circles, colored chalk Value: Cooperation
283
III. Learning Experiences
A. Preparatory Activities
1. Drill Crazy Quil t (number games)
a. Two players use one game board. The players share four crayons (any 4 colors). b. The first player picks a problem in the wheel and solves it. If the player solves the
problem correctly, he or she colors in that block on the wheel. If the player calls out a wrong answer, he or she loses a turn to color and so on.
c. The player who has the most colored parts wins.
2. Review
Below is a picture of a house. Identify the square, the rectangle, the trapezoid and the parallelogram by naming the parts of the house.
5 x 7
9 x 4
9 x 9 9 x 10
8 x 9
6 x 6
6 x 7
7 x 9
8 x 4 6 x 5
8 x 9
7 x 6
8 x 7 3 x 8
8 x 8
9 x 5
6 x 4
9 x 3
9 x 4 8 x 12
9 x 6
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3. Motivation
a. Present drawings of circles of different sizes. b. Ask pupils to describe the circles they see. Have them give the characteristics of a circle.
B. Developmental Activities
1. Presentation
a. Present the lesson through a group activity.
 What should you do if you are in a group?  Why do you think you should cooperate with one another?
Group 1: Activity 1) Give the pupils cut outs of circles 2) Ask the pupils to fold the circle into 2 equal parts. 3) Ask the pupils to mark the center of the circle with an X. 4) Then mark the fold A and B at both ends. 5) Introduce the term diameter for this line segment. Guide them in giving the definition
of a diameter. 6) This time, fold the circle into 4 equal parts. Mark the fold A, B, C and D. 7) Then introduce the term radius. Let them define the radius. 8) Ask the pupils to compare line segments XA, XB, XC and XD 9) What do you call the line that surrounds the circle? 10) Introduce the term circumference. Have them give the definition of a circumference.
C radius A X B A X B diameter D
Group 2: Act ou t 1) Let one half of the class stand and hold hands together. What plane figure did you
form? 2) Tell one of your pupils to stand at the center. 3) Another set of pupils will form a line that passes through the center.
What did the line do to the circle? What do you call this in HEKASI? (horizontal line at the center)
4) Form a line from the center point to one point of the circle. How do you describe this line?
5) How do you compare the first line to that of the second line? Which is longer? Which is shorter?
6) Let the pupils name these lines in connection to the parts of a circle.
285
Group 3 1) Cut the following pieces of string/rope:
a. 1 metre
b. 21
of a metre
c. 41
of a metre
2) Get a metre of string/rope, put it around a pot or pail until the ends meet. What plane figure did you form?
3) Put a stone at the center.
4) Using the second piece of string (21
of a metre), place it at the center. What did this
line do to the circle? If you put this line horizontally and vertically, what does it make to the circle?
5) Get the last piece of rope/string, put it anywhere on the circle, what can you say about it? Which one is longer? Shorter?
2. Guided Practice
(At this point, remind the pupils the importance of cooperation in group work) a. Group the pupils. b. Ask each group to draw a circle with O as the center point. c. Name the diameter RS. d. Name the radii: radius OR, radius OS, radius OP and radius OY. e. Post the circle on the board.
3. Fixing Skill s
a. Study this circle. Write the parts of this circle. b.
X W T Y Z
b. Use the same circle. Answer the following questions:
• What is the diameter of the circle? • What are its radii?
c. Draw a circle. Show its diameter, radii and circumference.
5. Generali zation What is a diameter? A diameter divides the circle into 2 equal parts. What is a radius? A radius is a line segment from the center of the circle to any part of the circumference. What is a circumference? Circumference is a line that surrounds the circle.
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C. App lication Using the circle below, name: 1. The center 2. 5 radii
K P O R M N
IV. Evaluation
A. Using the same circle, tell what is named in each number below. Write the diameter or radius. 1. ON = _____ 2. OR = _____ 3. PR = _____ 4. OK = _____ 5. OP = _____
B. Draw a circle showing the following.
1. S as the center 2. ST as a diameter 3. SY as a radius 4. SX as a radius 5. SO as a radius
V. Assignment
1. If the radius of a circle is 10 cm, how long is its diameter? 2. How long are the radii? 3. Show that circle by means of a drawing.
Describing and Constructing Plane Figures I. Learning Objectives
Cognitive: Describe plane figures according to sides, corners, shapes and their functional use
Psyc homotor: Construct plane figures using a ruler or a compass Affective: Manifest selfconfidence and cooperation in working with others
II. Learning Content
Skill s: 1. Describing plane figures 2. Constructing plane figures using ruler/compass Reference: BECPELC III.A.1.3.1 & 1.4
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Materials: cutouts of plane figures like square, rectangle, parallelogram, triangle, circle, and pentagon, ruler, compass
Values: Cooperation and selfconfidence III. Learning Experiences
A. Preparatory Activities
1. Drill
Mathematics Word Drill: Describe the following plane figures. A B C Parallelogram Circle Rectangle Plane Figure Polygon Pentagon Triangle Rhombus Trapezoid
(Group the pupils into three. Have them work cooperatively on the words given to them. Whoever finished first in describing the plane figures assigned to them will be declared the winner)
2. Review
What are points? What are lines? Line segments? Differentiate a line from a line segment.
3. Motivation
Call 3 pupils in front. Give each of them a thin piece of wire. Tell them to make a plane
figure. At the signal “go” they will start making their figure. Afterwards, let them describe what they have made.
B. Developmental Activities
1. Presentation
Prepare cutouts of plane figures using materials such as cardboard or used folders. Put
the cutouts in a box or paper bag. Blind fold a pupil and ask him/her to pick a figure from the box. Let him/her guess what the figure is. Have him/her describe the figure according to sides, corners and shapes. (e.g. it has four equal sides and four corners)
Activities
Show the pupils the cutouts prepared for the day’s lesson. Let them describe their shapes/sides.
Example: square – 4 sides
rectangle – 2 pairs of parallel sides with square corners triangle – 3 sides circle – round, no flat sides pentagon – 5 sides hexagon – 6 sides
Ask the pupils to draw the shapes on the board and encourage them to give some more examples.
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2. Analysis and Discussion Ask a pupil to come to the board and draw the plane figure as described by a classmate.
Let the classmate describe the figure without saying the figure’s name. Emphasize that the pupils should describe the figures clearly so that their classmate can draw them accurately. Ask pupils where do these shapes can be usually seen. How are they used?
3. Fixing Skill s
a. Activity 1
Connect the dots to complete the figures. Match column A with column B. Write the letter of the correct answer on the blank before the number. A B _____1) Rectangle a. b. _____2) Rhombus _____3) Circle c. _____4) Square d. e. _____5) Parallelogram
b. Activity 2
Give the pupils colored papers. Let them construct different plane figures. Each one
of them should construct at least 5 figures.
c. Activity 3 Draw the following plane figures. 1) circle 4) trapezoid 2) square 5) parallelogram 3) rectangle
(During the activities, emphasize to the pupils that they should cooperate with each other and must have selfconfidence)
4. Generalization
What are plane figures? How will you describe each figure according to their shapes,
sides and corners? – square, triangle, rectangle, rhombus, etc. How are these shapes used in our daily lives?
C. App lication
Draw and identify the plane figure represented by the following objects:
1. 2. 3.
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4. 5. IV. Evaluation
A. Draw the following objects. Under the pictures drawn, identify and describe the plane figure/s represented by each. 1. alphabet block 4. door 2. tent 5. kite 3. orange
B. Identify the plane figure described in each statement.
______ 1. It has 3 sides and vertices. ______ 2. It has 2 pairs of parallel sides. ______ 3. It is made up of points that are equidistant from the center. ______ 4. It has five corners. ______ 5. All the sides and corners are equal.
V. Assignment
A. Draw a big square. Inside it, draw a small triangle. At the three sides of the triangle, draw three
small circles. At the center of the triangle draw an oblong. What kind of figures have you drawn? B. Draw 10 plane figures. Describe the plane figures you have drawn.
Parts of an Angle I. Learning Objectives
Cognitive: Identify parts of an angle Psyc homotor: Draw an angle showing its parts Affective: Participate actively ingroup work
II. Learning Content
Skill s: 1. Identifying the parts of an angle 2. Drawing angles References: BECPELC III.A.2, 2.1 textbooks in Math 4 Materials: drawing and cut outs of angles Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill
Identify the following lines: a. b. c.
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2. Review
What is a ray? Name the rays in the illustration.
B C E F A D
3. Motivation
What do you think will be formed when the endpoint of the two rays meet?
B. Developmental Activities
1. Presentation
a. Ask a pupil to draw a point on the board and name this point O. b. Ask another pupil to draw a ray with O as the end point and name this ray OR. c. Ask another pupil to draw another ray using O as the common end point and name this
ray OZ. Their drawing may look like this: Z R O
e. Introduce the term vertex. The common endpoint of ray OR and OZ is called vertex.
The rays are called the sides. What figure have you formed? (angle) What angle have you formed? ZOR or ROZ
The vertex is always named by the middle letter. What are the parts of an angle?
2. Group Work
(Remind the pupils the importance of participating actively in all the activities) Give the vertex and the 2 sides of the angles below.
a. B b. P G A C H 3. Fixing Skill s
a. Identify the parts of each angle.
1) B 2) D 3) L Y O O Y G A
b. Draw an angle, label its parts.
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4. Generali zation
What are the parts of an angle? The parts of an angle are the vertex and the sides. What is the vertex? The common endpoint of two rays is called the vertex.
C. App lication Name the angles that can be found in the illustration. How many angles can be formed? Identify the sides of each angle.
D C E B F A G H IV. Evaluation
A. Give the endpoint and the two sides of each angle below.
1. B 2. G 3. G 4. Z 5. A L A J U Y E P S Y C
B. Can you find the angles in the figure below? Name the angles formed and the parts of each angle.
A D O B C
C. Draw 5 angles. Name the angles and label its parts.
V. Assignment
Name as many angles as you can in the figure below. What is the vertex of all the angles? Name 5 sides of any angle.
J I K H S L O M N
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Different Kinds of Angles I. Learning Objectives
Cognitive: 1. Visualize the different kinds of angles as acute, right, obtuse 2. Name different kinds of angles such as right angle, acute angle and obtuse
angle Psyc homotor: Construct the different kinds of angles Affective: Show sportsmanship in a contest
II. Learning Content
Skill s: 1. Naming different kinds of angles 2. Constructing different kinds of angles References: BECPELC III.A.2.2, 2.2.1
textbooks in Math 4 Materials: flash cards, pieces of cartolina, two strips of cardboard joined by a fastener Value: Sportsmanship
III. Learning Experiences
A. Preparatory Activities
1. Drill
Identify the parts of each angle below. 1) T 2) S 3) T 4) O 5) R P D A D G E L G
2. Review Name the angles you can find in the drawing below.
C B D A X E H F G
3. Motivation Show the pupils different cutouts of angles. Ask: What can you say about the angles? Are they the same?
B. Developmental Activities
1. Presentation
a. Showing cutouts of cartolina. 1) Show a piece of cartolina to the class.
C B A
E O
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2) Describe the angle formed at B. It looks like a square corner. Introduce the word righ t angle. It measures 90 degrees.
3) Give the pupils two strips of cardboard joined together by a fastener. 4) Make other angles using the strips of cardboard with the right angle as the guide. 5) Open the strips wider to show angle ABF.
F C B A
6) Which is bigger the right angle or the new angle formed? 7) Introduce the word obtuse. It means more than 90 degrees but less than 1800. 8) Ask the pupils to put the cartolina closer.
H C
B A 9) Compare the new angle formed with the acute and the right angles. 10) Introduce the word acute. It measures less than 90 degrees.
b. Display intersecting lines and see if the pupils can identify the angles formed. Call their
attention to the lines that are perpendicular to each other. Let them point to the squares that are formed at the vertex.
Present a protractor and show them how to measure the angles. Introduce the term degrees (o) as a measure of angles.
Let them measure all other angles on the board or on display. Have them group the angles that measure 900, more than 900 and less than 900. Name the kinds of angles.
c. Act Out – Contest
Divide the class into 5 groups. Call a member from each group as the contestant.
Using two arms, let the pupils form an angle with their arms. The pupil who will form the angle nearest to the correct measurement earns a point. The group that has the most number of point wins. If your group did not win the contest, what would you do? Would you feel bad? Why?
L M
M
P
Q R
S
O
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2. Analysis/Abstraction
a. What kind of angles did you form? b. Are the angles the same? c. Do they have different measurements?
3. Fixing Skill s
Group Work – Remind the pupils the importance of cooperation in group activities. a. Study this drawing below. Name as many angles as you can find. Tell whether each
angle is obtuse, acute or right. The group with the most correct answers wins. R S T P X U W
b. Study this drawing. Name the angles and tell whether the angle is right, obtuse or acute.
1. 2. 3. 4. 5.
4. Generali zation
What are the different kinds of angles? (right, acute, obtuse) What is a right angle? A right angle measures 900 What is an acute angle? An acute angle measures less than 900 What is an obtuse angle? An obtuse angle measures more than 900 but less than 1800
C. App lication
Look around us. 1. Name at least 2 objects with right angles. 2. Name at least 2 objects with an acute angle. 3. Name at least 2 objects with an obtuse angle.
IV. Evaluation
A. What kind of angle is in each number below?
1. A C 2. F 3. S Y 4. B 5. A B U N O I M T G
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B. Study the drawing below. Name each kind of angle below. 1. BAC = _____ C D 2. CAD = _____ 3. DAE = _____ 4. DAF = _____ B A E 5. EAF = _____
F C. Construct the following angles using your protractor.
1. AEI – right angle 2. BIG – acute angle 3. TOP – obtuse angle 4. GET – acute angle 5. CAN – right angle
V. Assignment
Make the following using cardboard or cartolina. 1. Make 2 cutouts of acute angles 2. Make 2 cutouts of obtuse angle 3. Make 2 cutouts of right angle
Class ifying Angles I. Learning Objectives
Cognitive: Classify angles as right, acute and obtuse Psyc homotor: Construct right, acute and obtuse angles Affective: Participate actively in group work
II. Learning Content
Skill : Classifying angles as right, acute and obtuse References: BECPELC III.A.2.3 textbooks in Math 4 Materials: clock, charts, illustrations Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill
a. What is an angle? b. Name each angle below.
1) A 2) C 3) L P 4) S 5) C
N T U A A W O P W
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2. Review
Guessing Game: Guess who I am, then ask somebody to show such angle on the board. a. I am an angle. I’m smaller than a right angle. I measure less than 90 degrees. Who am I?
(acute angle) b. I am an angle which is bigger than a right angle, I measure more than 90 degrees. Who
am I? (obtuse angle) c. I am an angle which forms the corner of a book. I measure 90 degrees. Who am I? (right
angle)
3. Motivation
(Show 3 groups of angles to the class.) Ask: How are these angles grouped? Let’s find out.
B. Developmental Activities
1. Presentation (9:00)
Look at this clock. What time does the clock show? (9:00) What kind of angle is formed? (right angle) What other time do the hands of the clock form right angles? (3:00, 12:15) Draw the clocki on the board. When the clock strikes 10:00, what kind of angle is formed? (acute angle) What other time of the day do the hands of the clock form acute angles? (2:00, 1:00, 11:00) When the clock strikes 4:00, what kind of angle is formed? (obtuse angle) What other time of the day do the hands of the clock form obtuse angles? (5:00, 7:00, 8:00)
Observe the figure. Answer the following a. Name 2 right angles. b. Name 4 acute angles. c. Name 2 obtuse angles. d. Name an angle that looks the same in size as angle CBD. e. Name an angle that looks the same in size as angle DBF.
2. Fixing Skill s
Group Work (Remind pupils on the importance of cooperation) Group 1  make 5 cutouts of right angles. Construct or paste them on a piece of cartolina and
post them on the board. Group 2  make 5 cutouts of obtuse angles. Construct or paste them on a piece of cartolina
and post them on the board. Group 3  make 5 cutouts of acute angles. Construct or paste them on a piece of cartolina
and post them on the board.
Name the angles formed in the picture. Classify them according to their kind.
A C
B
E D
F
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Right Ang le Acute Ang le Obtuse Ang le
E H B G C A I W X L M Y Z
U V
T R S K J
3. Generali zation
What are the different kinds of angles?
The different kinds of angles are right angle, acute angle, and obtuse angle. A right angle measures exactly 90° . An acute angle measures less than 90° . An obtuse angle measures greater than 90° but less than 180° .
C. App lication
Bring me game Group 1 – Bring me 5 objects with acute angles. Group 2 – Bring me 5 objects with obtuse angles. Group 3 – Bring me 5 objects with right angles.
IV. Evaluation
A. What kind of angle is in each group? 1. BAD = 90O 2. LAY = 110 O 3. MAC = 70 O COW = 90O DOG = 120 O DIP = 60 O BAT = 90O POT = 130 O TOY = 20 O
B. Look at the angles below. Classify them as to right, obtuse and acute angle.
DOE = 115 O ARM = 75 O CAT = 85 O CAN = 95 O POW = 105 O ROW = 90 O
C. Construct 2 examples of acute angles, 2 obtuse angle and 1 right angle.
P Q
O N
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V. Assignment
1. On a piece of bond paper construct 5 acute angles, 5 obtuse angles and 5 right angles. 2. Create a picture of your own house and draw windows and a door. Find out what angles are
formed.
Congruent Angles I. Learning Objectives
Cognitive: Identify congruent angles Psyc homotor: Construct congruent angles Affective: Participate actively in group work
II. Learning Content
Skill : Identifying congruent angles References: BECPELC III.A.2.4 textbooks in Math 4 Materials: protractor, several examples of congruent figures, rectangular and square pieces
of paper, compass Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill
Ask the pupils to name the different kinds of angles formed by 2 rectangular strips fastened together.
2. Review
What is a right angle? An acute angle? An obtuse angle?
3. Motivation
Show 2 pieces of the same size of paper. Look at these pieces of paper. Which is
bigger? Which is smaller? Why? (they are both of the same size)
B. Developmental Activities
1. Presentation a. Present 2 right angles. Ask the pupils to place the square corner of a cardboard on each
angle.  Do they have the same measure? Do angles ABC and XOY match exactly? (yes)
Why? (they have the same size or measure) So we say angles ABC and XOY are congruent.
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A X B C O Y
b. Show another 2 angles of equal measure. Ask some pupils to measure the angles using a protractor.  Are the measures of two angles equal? (yes)
So angle LMN is congruent to angle RST. L N S M R T
c. Show a compass to the class. (the compass can be used to find out if the angles are congruent) To use the compass, open it, fit its points on the two given points on the rays of the first angle. Then without moving the points of the compass, place them on the two given points on the other angle.  Do they match exactly? Are they congruent? (yes) Why? (They have the same
measurement.)
2. Fixing Skill s Group Activity (Emphasize cooperation among group members in doing the activity) Give each group a sheet of paper wherein 6 angles are shown, 4 of which are congruent. a. By using a piece of cardboard, find out what angles are congruent. b. By using a protractor, find out which angles are congruent c. By using a compass, find out which angles are congruent
3. Generali zation
When are angles said to be congruent?
Angles are said to be congruent when they have the same angle measure and sides.
C. App lication
Draw or construct 2 pairs of congruent angles.
IV. Evaluation
A. Which angles are congruent?
B E H O E N Q R V F
C D G I L M O P S T U
B. 1. Use the piece of cardboard to find out which angles are congruent. 2. Use the protractor or compass to find out which angle are congruent. 3. Draw 2 pairs of congruent angles.
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V. Assignment
1. On a piece of bond paper, construct 3 pairs of congruent angles. 2. Choose the pairs of angles that are congruent. You may use a compass to find out if they have
the same measure.
A X L M N B C Y Z
I D Q H E J F S R Perimeter of a Triangle I. Learning Objectives
Cognitive: 1. Find the perimeter of a triangle
2. Derive a formula for finding the perimeter of a triangle Psyc homotor: Measure the perimeter of a triangle Affective: Tell the importance of tree conservation
II. Learning Content
Skill s: 1. Finding the perimeter of a triangle 2. Deriving a formula for finding the perimeter of a triangle Reference: BECPELC IV.A.1 Grade School Mathematics 4 Mastering Mathematics 4 TM pp.129130 Mastering Math 4 TX pp.192193 Materials: modules or illustrations of triangles, ruler Value: Conservation of trees
III. Learning Experience
A. Presentation
1. Drill Drill on adding numbers mentally Example: 10 21 45 170 180
+13 +25 +45 +130 +120
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2. Review Review on identifying the different kinds of triangle. Show models of triangle. (scalene, right, equilateral)  What kind of triangle is this? (right triangle)  Why? Because it has a right angle. (Do the same with the other kinds of triangle.)
3. Motivation
Let’s estimate the sum of the sides of each triangle in centimetres.
(Write the estimation of each group on the board.) Let’s see who got the correct estimation.
B. Developmental Activities
1. Presentation
a. Provide each group with the same size of triangles. b. Ask the pupils to do actual measurements of the triangles. c. Compare the results of their estimation and their actual measurements. d. Commend those whose estimates are close to the actual measurements e. Tell the class that what they have measured is the perimeter of a triangle. f. How did you measure the triangle? (By measuring all its sides) g. So, can you think of a formula for finding the perimeter of a triangle? (P = S1 + S2 + S3)
Don Mario has a triangular piece of land that is planted with coconut trees. He wants to
enclose it with a fence. How long will his fence be if the sides measure 24 metres, 18 metres and 20 metres? What is the perimeter of his land? Illustrate his piece of land.
2. Fixing Skill s
a. Find the perimeter of each triangle.
Triangle S1 S2 S3 Perimeter 1 5 cm 4 cm 3 cm ___ cm 2 12 m 21 m 15 m ___ m 3 10 dm 8 dm 12 dm ___ dm
b. Give the pupils a set of 3 triangles. Use a ruler to measure the sides. Find the perimeter
in centimeters. Use the formula in finding the perimeter of a triangle.
1) 2) 3)
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Valuing: � Do you know what a coconut tree is? � Is this tree important? Why? � Why is this tree referred to as a tree of life? � What do you think we should do to this tree? Why?
c. Find the perimeter of the following. Use the formula you have learned.
1) A triangle whose sides measure 12 cm, 15 cm and 10 cm 2) A triangle whose sides measure 20 cm, 18cm and 13 cm 3) A triangle whose sides measure 25 cm, 28 cm and 22 cm
3. Generali zation
What is a perimeter? (A perimeter is the sum of the length of the sides of a polygon. A
perimeter is the distance around a polygon) How do you find the perimeter of a triangle? (By adding all its sides) What is the formula for finding the perimeter of a triangle? (P = S1 + S2 + S3 )
C. App lication
1. a. Distribute cutouts of triangles of different sizes. b. Measure all the sides. c. Find the perimeter.
Triangle A = Side 1 _______ cm Side 2 _______ cm Side 3 _______ cm Perimeter _______ cm Triangle B = Side 1 _______ cm
Side 2 _______ cm Side 3 _______ cm
Perimeter _______ cm
Triangle C = Side 1 _______ cm Side 2 _______ cm Side 3 _______ cm
Perimeter _______ cm
2. Draw 2 triangles and find the perimeter. (Answers will depend on the given measurement of the triangles.)
IV. Evaluation
A. Fill in the blanks below. 1. Perimeter = 18 dm + 12 dm + 10 dm P = _____cm 2. Perimeter = 10 m + 10 m + 12 m P = _____cm 3. Perimeter = 15 cm + 15 cm + 15 cm P = _____cm 4. Perimeter = 8 m + 5 m + 18 m P = _____cm 5. Perimeter = 12 cm + 12 cm + 12 cm P = _____cm
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B. Complete the table below. Triangle S1 S2 S3 Perimeter
1 14 m 15 m 16 m 2 10 cm 12 cm 14 cm 3 18 cm 5 cm 15 cm 4 12 cm 10 cm 15 cm 5 15 mm 20 mm 20 mm
C. Find the perimeter of each triangle below. Show how you found the perimeter using the formula.
1. 2. 3. 4. 5.
V. Assignment
Bring to class 5 cutouts of triangles with the measurements of sides. Let their partners find the
perimeter of each triangle.
Perimeter of a Polygon I. Learning Objectives
Cognitive: 1. Derive a formula for finding the perimeter of a polygon 2. Find the perimeter of a polygon Psyc homotor: Measure the perimeter of a polygon Affective: Show accuracy in measuring
II. Learning Content
Skill s: 1. Deriving a formula for finding the perimeter of a polygon 2. Finding the perimeter of a polygon Reference: BECPELC IV.A.1.2 Materials: textbook, real objects, diagrams, illustration, cut outs of polygons, meter stick,
tape measure Value: Accuracy
III. Learning Experience
A. Preparatory Activities
1. Drill
Identifying polygons by means of a guessing game Example: I am a polygon with four equal sides. Who am I?
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2. Review Ask what unit of measure is appropriate for objects such as these: • distance between buildings • sides of a handkerchief • safety pin
3. Motivation
Show a plain handkerchief. Do you carry your handkerchiefs everyday? Why? What are the uses of a handkerchief?
B. Developmental Activities
1. Presentation
a. Show a piece of lace and a square handkerchief. If I’m going to sew lace around my handkerchief would this lace be enough? Get the
children’s opinion. What are we going to do to be sure on the length of the lace? Let the pupils measure the sides and compute for the distance around. Ask what they measured and why. Tell them to describe what they measured leading them to use the phrase distance around. Introduce the term perimeter for this distance. Have the pupils illustrate the object (handkerchief) on the board with the corresponding measures and ask one pupil to write the number sentence for this.
(25 + 25 + 25 + 25) or (4 x 25)
The formula in finding the perimeter of a square is S + S + S + S or P = 4 x S
b. Show a picture frame hanging in the classroom. What is the shape of the picture frame? (rectangle)
Measure the sides of the frame. What can you say about the lengths? Widths? To find the perimeter, just add the sides.
The formula in finding the perimeter of a rectangle is L1 + W1 + L2 + W2 or P = 2L + 2W or P = 2 (L + W)
c. Show some polygons to be measured and have them compute the perimeter.
Example:
P = 5 + 6 + 5 + 5 + 6 + 5 P = 3 + 15 + 3 + 5 + 7 + 5 + 7 + 5 = 32 cm = 50 cm
How do you measure the perimeter of the other polygons?
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2. Fixing Skill s a. Find the perimeter of each figure.
b. Group the pupils into 4 groups and have them find the perimeter of the following: 1) their classroom 2) a table top 3) a pupil’s desk top 4) chalk board
In each case, they will have to decide on the appropriate unit of measurement.
What do you mean by the word appropriate? What is the other term for appropriate? Why do we have to be accurate in measuring things?
3. Generali zation
What is perimeter? How do you find the perimeter of a polygon? Give the formula for finding the perimeter of a square, rectangle, and the other polygons.
C. App lication
1. Have the pupils draw a rectangle. Ask them to measure the perimeter and record it.
2. Let the pupils draw the diagonal of the rectangle. Instruct them to cut the rectangle along its
diagonal and arrange the parts to form a triangle.
3. Let them measure its perimeter and record. Discuss why the perimeter is now bigger. (Longer sides are on the outside.)
4. Let the pupils rearrange the two triangles to form a parallelogram. Have them measure its perimeter and compare this with the first two perimeters.
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IV. Evaluation
A. Give the perimeter of each figure. 1) 2) 3)
8.5 cm 10 cm
15 cm 7 cm 12.5 cm 4) 5)
B. Find the perimeter. Use the formula.
Formula Perimeter S = 5 cm
L = 20 cm
W = 10 cm
S = 4 cm 15 cm 12 cm V. Assignment
Make cutouts of polygons. Write the measurement of each side. Solve for the perimeter.
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Solving Prob lems on Perimeter I. Learning Objectives
Cognitive: Solve word problems involving perimeter measure Psyc homotor: Solve word problems with accuracy Affective: Participate actively in group work
II. Learning Content
Skill : Solving word problems involving perimeter measure References: BECPELC IV.A.1.3.1 Mastering Mathematics 4 TX p.192193; TM p. 129131 Materials: picture chart, pocket chart, flash cards Values: Cooperation and accuracy
III. Learning Experience
A. Preparatory Activities
1. Drill
What formula do we use to find the perimeter of a:  rectangle  triangle  pentagon  square  rhombus  octagon
Find your answers in the pocket chart.
2. Review
What must be remembered in solving word problems? What are these steps?
3. Motivation Who comes to school by just walking? How far do you walk from your home to the
school? Do you know how to find it?
B. Developmental Activities 1. Presentation
Vince walked from his house to the school then to the market and then back home. How
far did he walk? house market school
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a. What distances are given in the problem? b. What is asked in the problem? c. What is the word clue? d. What process is needed to solve the problem? e. What is the number sentence? f. What is the answer to the problem?
2. Fixing Skill s
We will have our groupings now. What will you do while working? Each group will solve a problem. Follow the steps in problem solving. Post the manila
paper on the board for checking.
a. First Group
Sonny walked around a small basketball court. The rectangular court is 8 metres long and 4 metres wide. What is the perimeter of the rectangular court?
b. Second Group
Jay enclosed his vegetable garden with a fence. The five sides of the garden
measure 10, 12, 12, 14 and 8 metres respectively. How long will be the fence?
c. Third Group
An equilateral triangle has a perimeter equal to the perimeter of a rectangle whose length is 12 m and whose width is 8.7 m. Find the measurements of the sides of the equilateral triangle.
2. Generali zation
How do we solve word problems? How do we get the perimeter of a polygon?
To solve word problems, we follow the steps suggested. To find the perimeter, we follow the formula applicable.
C. App lication Solve this word problem by yourself.
For your project in EPP, you make a square frame that measures 45 centimetres on one side. What is the perimeter of the frame?
IV. Evaluation
Solve the word problems. Follow the steps in problem solving. 1. Jocelyn’s flower garden has a length of 10 metres and a width of 6 metres. Find the perimeter of
the garden. 2. One side of a square playground of San Isidro Central School measures 120 metres. How many
metres of chicken wire are needed to enclose the playground? 3. There are 15 regular hexagonal poster frames in Willy’s gallery. Each side of the frame is 22 cm
long. How much wood had been used for the frames? 4. A tablecloth is 225 cm long and 95 cm wide. How long is the lace needed to put as an edging for
the tablecloth? 5. A softball diamond is 20 metres long on each side. How many metres does a player run if he
makes a homerun?
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V. Assignment
A. Solve the following: 1. Rex bought an octagonal mirror with each side measuring 25 cm. What is the perimeter of
the mirror? 2. Jelleni jogs around a triangular park which measures 425 metres, 350 metres and 435
metres. How far will she jog if she goes around the park twice? B. Make 2 word problems involving any of the polygons learned.
Unit of Measures used in Measuring the Area of a Triangle/Parallelogram I. Learning Objectives
Cognitive: Tell the unit of measures used for measuring the area of a triangle/parallelogram Psyc homotor: Measure the area of a triangle/rectangle Affective: Measure with accuracy
II. Learning Content
Skill : Giving the unit of measures used for measuring the area of a triangle/parallelogram
References: BECPELC IV.B.1.1 and 1.2 Mastering Mathematics 4 Materials: cut outs of parallelograms and triangles, geoboard, rubber band, cardboard,
ruler, objects with flat surfaces, eg. book, box, notebook, table Values: Sharing, cooperation, and accuracy
III. Learning Experience
A. Preparatory Activities
1. Drill Guessing Game: I am a quadrilateral with one pair of parallel sides (trapezoid) I am a quadrilateral with opposite sides parallel (parallelogram) I am a polygon with three sides (triangle) I am a special rectangle with all sides of the same length and four right angles (square)
2. Review
Review on using the appropriate unit of measure. Complete each sentence with centimetre, decimetre or metre. 1) Our classroom is 7 _____ long. 2) My comb is 1_____long. 3) The 25centavo coin is 2 ____ wide. 4) My book is 2 _____ long. 5) Pepe’s belt is 66 _____ long.
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3. Motivation Show a picture of a house.  What figures can you see in this picture? Give emphasis to the triangles and parallelograms which can be found in the drawing. How can we measure these figures? Why do we need to have an exact measurement in constructing our houses?
B. Developmental Activities
1. Presentation
a. Show a model of a parallelogram. “What is this?” A E B
D C If we cut EC and connect it to AD, what figure shall we form? (rectangle) Can we
measure the inside part of the rectangle? (yes) How? (By using square units) What are these square units? (square centimetres, square decimetres, square metres) What do we call the number of units inside a figure? (area) Can we say that the area of a rectangle is the same as the area of a parallelogram in the given illustration? (yes) What are the units used for measuring the area of a parallelogram? (square centimetres, square decimetres, square metres) (Show by actual demonstration)
b. Present the figure of the parallelogram again.
Draw a line from A to C.
A B D C
What two figures did we form? (2 triangles) Can we also measure the area of the triangles? (yes) What are the units of measure
used for measuring the area of a triangle? (sq. cm, sq. dm, sq. m) (Show by actual demonstration using a sq. cm)
c. Present a geoboard having nails 1 cm apart from each other. By means of a rubber band,
form a parallelogram and a triangle. Ask how many square cm are inside the parallelogram? Inside the triangle?
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2. Fixing Skill s a. What appropriate unit of measure will you use to find the area of the following:
1) notebook 2) folder (long) 3) teacher’s table 4) blackboard or chalkboard 5) classroom
b. Give cutouts of parallelograms and triangles and let the pupil measure each one using square centimetres or square decimetres.
c. Multiintelligence Using geoboards let the children form figures of parallelograms and triangles and
indicate the number of square centimetres for each.
3. Generali zation
What is area? (The number of square units that covers a surface) What units of measure do we use in measuring the area of triangles and parallelograms? (We use square units like square centimetres, square decimetres and square metres.)
C. App lication
Use any one of the square units (sq. cm or sq. dm) for measuring the area of the following. 1. An object inside or outside the classroom which is shaped like a triangle. 2. An object in and out of the classroom which resembles a parallelogram.
IV. Evaluation
A. What appropriate unit of measure will you use to find the area of: 1. a table 2. roof of a dog house 3. a garden 4. a blackboard 5. a notebook
B. Use a geoboard to indicate a parallelogram with an area of 8 sq. cm and a triangle with 6 sq. cm.
C. Use the following square units to measure each of the following:
1. square centimetres 2. square decimetres
a. b.
V. Assignment
Make two cutouts of triangles of different sizes and two cutouts of parallelograms also of different sizes. Indicate the unit of measure to be used for measuring the area.
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Formula for Finding the Area of a Parallelogram I. Learning Objectives
Cognitive: Derive a formula for finding the area of a parallelogram Psyc homotor: Show relationship among units of square measure Affective: Participate actively in class activities
II. Learning Content
Skill s: 1. Deriving a formula for finding the area of a parallelogram 2. Visualizing the area of a parallelogram References: BECPELC IV.B.1.3 – 1.4 textbooks in Math 4 Materials: cutouts of squares, coloring materials, learning activity sheets Values: Sharing one’s idea and active participation
III. Learning Experiences
A. Preparatory Activities
1. Drill
Magic Squares Multiply each number in the given square by 2. This forms a new magic square with a sum of 60.
Number game with the use of flash cards. 2. Review
Find the exact measurement (length and width) of the following using centimetres.
a. desk b. notebook c. Grade IV pad
3. Motivation Mavee bought a rectangular carpet measuring 5 metres long and 4 metres wide. What is
the area of the carpet? a. What did Mavee buy? b. What are carpets for?
Do you know the story about the magic carpet? Name the hero who owns the magic carpet. Do you believe that there is a magic carpet?
c. What is the shape of the carpet? Do all carpets have the same shape? Why?
16
6
2
10
12
14
8 18 4
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B. Developmental Activities
1. Presentation
Handson Activities (Dyad)
a. Activity Sheet: materials – graphing paper, crayons 1) Illustrate the rectangular carpet using the graphing paper. 2) Indicate the measurement horizontally and vertically. Look at each side. 3) Count the number of squares found in the figure. 4) Color/shade the squares found inside the figure. 5) Write the formula for the figure.
b. Activity Sheet: cutouts of squares (50 cm on each side) 1) Get some pieces of square cutouts. 2) Place 5 squares horizontally. Make 4 rows of this. 3) Count the number of squares used to complete the rectangle. 4) Give the formula for the figure.
2. Analysis/Abstraction
a. What is the shape of the cutouts that you used? b. What did we do with the cutouts? What shape did we form? c. What does the rectangular figure consist of?
 The square cutouts inside the figure represent the units in finding the area of the figure.
3. Practice Exercise
a. How many square units can you make in the following figures? Illustrate. Write the formula.
1) 2) 3) 2m 6m
4m 20m 4) 30m 50m
b. Acting – out
Pupils forming columns and rows 1) columns – 4 2) columns – 10 3) side – 5 rows – 3 rows – 5
Let a pupil count the total number of pupils in each activity.
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4. Generali zation
Area is the number of square units that covers a region. Area is expressed in square units. The formula in finding the area of a  square: A = S x S or S2  rectangle: A = L x W
C. App lication
Find the area of each region. Group 1 – Illustrate and shade with crayons to indicate the square units. Group 2 – Construct a figure using the shaded portion.
1. Region A 2. Region B 3. Region C L = 10m L = 25cm S = 8dm W = 9m W = 12cm
IV. Evaluation
Illustrate and shade the part that tells about the given data. 1. A living room which measures 9 metres long and 8 metres wide. 2. The chapel is rectangular in shape. It is 10 metres long and 7 metres wide. What is its floor area?
V. Assignment
Use graphing paper. Shade the indicated portion to show the following. a. S = 8cm b. L = 7m c. L =10m
W = 6m W = 12m
Area of a Parallelogram I. Learning Objectives
Cognitive: Find the area of a parallelogram in square metres or square centimetres Psyc homotor: Illustrate and draw to find the area of parallelograms Affective: Share one’s own ideas with others
II. Learning Content
Skill : Finding the area of a parallelogram Reference: BECPELC IV.B.1.b Materials: textbook, graphing or grid paper, learning activity sheet Value: Sharing one’s ideas
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III. Learning Experience
A. Preparatory Activities 1. Drill
This number game will be used to measure how far the pupils can utilize the multiplication facts.
“ Grab It” 9 1 3 7 5 6 8 4 2 3 8 7 1 5 4 2 6 9
a. Each child will give the two factors of a given product below. b. Pupils will give the product as fast as they can, who ever is the first to give the correct
answer is the winner. c. In a game like what we had a while ago, if you know the answer to the question, what do
you think you should do? Why do you have to share your ideas to others? 2. Review
Give the formula.
a. b. c.
3. Motivation
Situation:
Mr. Tan is covering the floor area of his sala with square tiles. How many square
tiles does he need?
If you are Mr. Tan, how are you going to do it? What are you going to do with the square tiles? Can you paste it on? What will you put on it so that it will not be removed?
18 32 64 35 27
72
25
16
48
36
45
81
28
40
54
12
14
24
21
20
15
56
30
42
63
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B. Developmental Activities 1. Presentation
Mr. Tan’s sala has 8 rows of square tiles. There are 10 tiles in each row.
2. Group Activity
Group 1 a. Illustrate the floor area of Mr. Tan’s sala. b. Indicate the measurements on each side. c. Multiply the length and width. What is the answer?
Group 2 a. Write the length and width of Mr. Tan’s sala. b. Solve by multiplying the two given numbers. c. Label your answer by expressing it in square units.
Group 3
___ metres
___ metres
a. What is the length? How about the width? b. How many squares are there? c. If you multiply the length and the width, what is the answer? Group 4
Mr. Tan’s sala measures 8 metres wide and 10 metres long. What is the area?
a. How long is the sala of Mr. Tan? How wide is it? b. Based on the illustration made, how many squares are inside the rectangular sala? What
will you do to find the answer? c. Suppose Mr. Tan’s sala measures 8 metres on each side, what is its area? d. What operation did you use? How did you do it?
3. Practice Exercise
Find the area. a. 10 cm 30 cm 10 cm
b. A = L = 10 mm A = S = 20 mm W = 6 mm
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c. Fred’s chicken farm has a length of 45 metres and a width of 35 metres. What is its area? Illustrate and solve to find the area of the chicken farm.
4. Generali zation
How do we find the area of a rectangle? How about a square?
To find the area of a rectangle, multiply the length by the width. To find the area of a square, multiply the side by itself. Area is expressed in square units.
C. App lication Find the area.
1) L = 10 mm 2.) L = 25 cm W = 9 mm W = 12 cm A = ___ A = ___
3) 3 cm 4) 5 cm 4 cm
5) Mang Pedro’s square vegetable garden measures 5 metres on one side. Find the area of the garden
IV. Evaluation
1. Find the area. 10 cm 15 m
12 cm
2. Find the missing number. L= 12 m S = 10 dm W = 6 m A = _____ A = _____
3. A glass top measures 130 cm by 46 cm. Will it fit a table that measures 127 cm by 62 cm? Why?
V. Assignment
1. Measure the length and width of your dining table then solve for its area. 2. Find the area of your classroom.
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Formula for Finding the Area of a Triangle I. Learning Objectives
Cognitive: Derive a formula for finding the area of a triangle Psyc homotor: Draw and illustrate the area of a given triangle Affective: Cooperate in all activities
II. Learning Content
Skill s: Deriving a formula of a triangle Visualizing the area of a triangle Reference: BECPELC IV.B.1.3 and 1.4 Materials: textbook, cutouts of rectangles and triangles, learning activity sheets, straws Value: Cooperation
III. Learning Experience
A. Preparatory Activities
1. Mental Exercises
a. How many different triangles can you find in each figure?
b. Create as many different triangles as you can from the straw pieces.
2. Review
Find the equation for the following: 1) 2) 3)
10 m
5 m
20 m
12 m
20 m
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4) 5)
3. Motivation
Manny bought a piece of cloth measuring 10 decimetres long and 6 decimetres wide.
She cut it diagonally to make 2 pieces of pennants for the barrio fiesta parade. What is the area of each piece? What do people do during fiesta? What do they usually prepare? Are the flaglets important during fiestas? Why?
B. Developmental Activities 1. Presentation
a. Activity Sheet
1) What is the area of the piece of cloth? How did you get it? 2) What did Manny do to the piece of cloth? What figures were formed? 3) Do you know the area of this figure? What formula can you form from this? 4) Illustrate how to get the formula of the triangle.
b. Discussion
At this point, show the pupils on how to get the formula of the triangle.
• Answer the questions on the activity sheet.
6 dm = height (h)
10 dm = base (b)
Area of a triangle = 21
x (b x h)
= 21
x (10 x 6)
2. Guided Exercises
Write the equation for each triangle using the formula.
a. b. c. 5 cm 4 cm 8 m 7 cm 6 cm 12 m
8 m
15 m
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d. Using the meter stick, measure the sides of the teacher’s table and write the equation if it is divided diagonally.
3. Generali zation
How will you derive the formula of the triangle? What do you call the vertical line? The horizontal line?
Vertical line is the height. Horizontal line is the base.
Formula: area of triangle = 2
hxb=
21
x (b x h)
4. Practice Exercise
Give the equation for each triangle.
a. b. 5 m 4 m
4 m 10 m c. A triangularshaped lot has a base of 15 m and a height of 20 m.
Give the equation using the formula. IV. Evaluation
1. Give the formula then write the mathematical sentence.
A B 8 m 5 m 4 m
2. Nena’s handkerchief measures 20 cm long in each side. What is the formula in finding the area
of the figure if you divide it diagonally? What is the area? V. Assignment
1. What is the area of the largest triangle that can be formed on a 10 by 10 geoboard? Give the
formula and the equation.
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2. Give the formula in finding the area of the triangle. Write the equation. a. b. b – 30 cm
h – 12 cm 10 cm 15 cm
Area of a Triangle I. Learning Objectives
Cognitive: Find the area of a triangle Psyc homotor: Solve problems in finding the area of a triangle Affective: Show cooperation by sharing one’s ideas
II. Learning Content
Skill : Finding the area of a triangle References: BECPELC IV.B.1.a
Mathematics 4 Materials: meter stick, ruler, tape, scissors, cutouts Values: Cooperation and sharing one’s ideas
III. Learning Experience
A. Preparatory Activities
1. Drill Let the pupils give the answers by multiplying two adjacent numbers until the time the triangle is completed.
Triangle Round Up
2. Review
Using cutouts of triangular flaglets with labels on each side, ask the pupils to give the formula in finding the area of a triangle. Let them give the equation for each triangular flaglet.
2
9 4
8 1 2
6 4 9 8
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3. Motivation
Amado made a triangular lantern with a base of 30 cm and a height of 25 cm. What is the
total area of the lantern? Ask: What are lanterns for?
What will you do to make the lanterns beautiful? What is the shape of the lantern?
B. Developmental Activities
1. Presentation
Using the given word problem, let each group do the assigned activity. Group A 1) Illustrate on how to find the area of the triangle. 2) Solve for the area of the triangle. Group B 1) Using a cartolina, show the exact measurement of the triangle. 2) Label each side and find the area of the triangle. Group C 1) Show a rectangular shape that measures 25 cm high and a base of 30 cm. 2) Cut the figure diagonally and solve the area. Group D 1) Solve for the area. 2) Explain your answers. 3) How did you work with other members of your group? Why?
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2. Analysis/Organization
a. What is the exact measurement of the triangular cloth? h – 25 cm b – 30 cm 25 cm 30 cm
b. How will you find the area of the triangle?
A = 21
x (25 x 30) = 2
750
= 2
)3025( x = 375 cm2
c. Look at the answer, what did you notice?
The answer must be expressed in square units.
3. Practice Exercise
Find the area of the triangle. a. b. h – 10 m b – 12 m 3 cm 4 cm
c. A triangularshaped lot has a base of 20 m and a height of 15 m. What is the area?
4. Generali zation How did you get the area of a triangle?
To get the area of a triangle, we multiply the base by its height then divide it by 2.
The formula is: A = 21
(b x h)
C. App lication
Manny is planning to have 2 triangular flaglets for the school activity. He has 1 whole piece of
cartolina with length of 80 cm and 75 cm wide. Find the area of each triangle. a. If you are Manny, what will you do? b. What will you do to find the area of the triangle? c. What is the area of the triangle?
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IV. Evaluation
1. Here is a diagram of the lot bought by Jose. He subdivided it diagonally. The resulting 2 lots are triangular. He gave one lot to his nephew. What is the area of the lot?
25 m 28 m
2. Act out: • 7 pupils will represent the height • 10 pupils will represent the base • What is the area? • How will you go about it?
V. Assignment
Find the area. 1.
4 cm 6 cm
2. The triangular lot has a base of 20 m and a height of 15 m. What is the area of the lot?
3. Measure a piece of a grade 4 paper, find the measurement of the length and the width. Fold it diagonally and solve the area of the triangle formed.
Measuring Volume using NonStandard Units of Measure I. Learning Objectives
Cognitive: 1. Measure volume using nonstandard units of measurement
2. Compare the nonstandard units of measuring volume in terms of consistency and accuracy
Psyc homotor: Approximate measurement of volume Affective: Show helpfulness towards other members of the group
II. Learning Content
Skill : Making and measuring volume using the nonstandard units Reference: BECPELC IV C.1 & 2 & 3 Materials: textbook, text manuals, cubes, marbles, coins, buttons, pebbles, seeds, boxes,
tin cans Values: Helping one another and sharing one’s ideas
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III. Learning Experience
A. Preparatory Activities
1. Drill
Dyad Activity Let the pupils answer the activity as a warmup exercise.
a. Draw 100 dots on a piece of paper to form ten rows with ten dots each, like this:
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b. The purpose of the game is to see how many squares you can make. Players take turns to draw lines that fill in the horizontal or vertical gaps between 2 dots. If there are three lines filled in and you can make a square by drawing a fourth, do so and write your initial inside the square, marking it off as your own. The player who forms the most squares wins.
2. Review
Read and solve orally. Explain your answer. Illustrate how to get the answer.
A basketball court in a barangay measures 9 metres by 5 metres. What is the area?
3. Motivation
To fit these cubes into a box, one layer from the top and one layer from the longer side have to be removed. How many cubes will be left?
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B. Developmental Activities
1. Presentation
If you’re going to answer the situation above, how are you going to do it? Do you know what are cubes? How do cubes look like? How many edges are in a cube?
2. Group Activity
Group 1 Materials needed: 2 match boxes, buttons, coins a. Put pieces of buttons in pile columns inside the match box. b. Count the number of buttons equivalent to the following:
1) length 2) width 3) height
Group 2 Materials: seeds, 2 tin cans (condensed milk cans), pebbles a. Place the seeds in a can. b. Ask the following questions:
1) How many seeds are there in the can? 2) How will you know the number of seeds inside the can? 3) Are there spaces which are not filled in by the seeds? 4) Do the seeds occupy all the space in the can?
Group 3 Materials: marbles, chalk box a. Place the marbles in the chalk box. b. Ask the following questions:
1) What did you observe when you put marbles in the chalk box? 2) Do the marbles occupy space? 3) Can you give the actual number of marbles without counting it? How?
Group 4 Materials: cubes, chalk box a. Put pieces of cubes in pile column inside the chalk box. b. Count the number of cubes in the following:
1) length 2) width 3) height Can you tell how many cubes are inside the chalk box?
How did you get it?
Valuing: � How did you work with your group? � Let each group report what they have done.
3. Analysis/Abstraction
a. How will you compare the marbles in a chalk box with that of the cubes in the chalk box? b. In what combination can you easily count the number of materials in a chalk box? c. How did you put the cubes in the chalk box? d. Do you know what we call the amount of space occupied by a solid figure?
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4. Practice Exercises
Do the following: a)
shoebox, small plastic balls
1) If you put small plastic balls in the shoebox, can it occupy space? Why do balls occupy space?
2) What do you call the amount of space occupied by a solid figure?
b) square box, cubes
1) Can these cubes occupy space in the square box? 2) What do we call when the cubes occupy space in the square box?
5. Generali zation
Volume is the amount of space occupied by a solid figure.
C. App lication
1. Aquarium
Can you determine the volume of these materials? How will you do it? a. sand b. water c. fish
2. Pork and Beans
a. What are inside this can? b. How will you know the number of beans inside this can? c. What does the number of beans tell about?
3. Rubber band/marbles in the box
a. What are inside the box? b. Can you tell the number of rubber bands/marbles in this box? c. How will you know the number of rubber bands/marbles?
IV. Evaluation
Choose the correct answer and explain your answer. Which has an accurate volume? a. milk in a can or stones in a can? b. water in a glass or squash seeds in a glass?
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c. How many cubes will fit in each box?
V. Assignment
Draw the number of squares. Determine the number of pieces in it. a. Match box b.Box of paper clips
4 cm
2 cm 3 cm Bar Graph
I. Learning Objectives
Read and interpret data presented in a bar graph using the following parts:
a. title b. legend c. labels
II. Learning Content
Skill s: Reading and interpreting bar graph References: BECPELC V.A.1.1 & 1.2 Teacher’s workbook textbooks in Math 4 Materials: pieces of colored cartolina, different shapes, cut outs of fruits and flowers Value: Helping one another with a cause
III. Learning Experience
A. Preparatory Activities
1. Drill Number Games: Matching of numbers with colors Example: pair of numbers with the sum of 10, 12, 15, 20, etc. (Note: the pairs of numbers are written in a piece of cartolina of different colors.)
a. Each pupil will be given a piece of cartolina with a number written on it. b. Tell the pupils to put the piece of cartolina in a color coding scheme after they have
given their answers. c. After putting the pieces of cartolina in groups, ask them what they have observed and
how the pieces of cartolina are put together.
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d. Tell the pupils that this data will be needed in the day’s lesson. If you are to put the pieces of cartolina, how will you go about it? Can you think of the
title for this? What is it?
2. Motivation Show this illustration to the class. What are the information given in this illustration?
45 40
35 30 25 20
15 10
5 0 8 9 10 P5 P10 P15 1 2 3 4 5 6
B. Developmental Activities
1. Presentation
Activity Sheet
Group 1 a. Gather all the pieces of cartolina and group them together. b. Count the number of pieces of cartolina in every group. c. Write the total number of pieces of cartolina d. Indicate/write it on the table given to you. Group 2 a. Grouping according to age. b. Count it out and write the number of pupils per age c. Write the data on the table given to you. Group 3 a. Group the pupils according to the amount of allowance they have for the day. b. Count it out and write the number of pupils with the same amount of allowance. c. Write the data on the table given to you. Group 4 a. Ask the pupils to group themselves according to the number of siblings they have. b. Count it out and write the data on the table given to you.
Nu
mbe
r of
pup
ils
Age Amount of baon
Number of siblings Color
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2. Discussion a. What did you do with the data given to you? b. How did we present it? c. Do you know this figure?
3. Analysis/Organization a. Introduce the lesson by telling the pupils about the graph, its parts and the
importance of each part. b. Get one data from the pupils’ work and try to ask the following questions.
a. What does the horizontal line tell? b. What does the vertical line tell?
c. Ask about the data in detail Example: Group 1: a) How many blue cartolina pieces are there? Yellow?
b) Which has the greater number of pieces? c) Which has less?
d) What is the title of the bar graph?
4. Practice Exercises
0 100 200 300 400 500 600 700 800 900 1000
K
I
II
III
IV
V
VI
1. Who borrowed the most number of books? 2. How many books were borrowed by Grade VI? 3. Who borrowed the least number of books? 4. How many more books did Grade IV borrowed than Grade VI? 5. Arrange from lowest to highest the books borrowed by the different grade levels.
5. Generali zation
What is a graph? A graph is a diagram which shows how two or more sets of information are related.
What is a bar graph? How do you read and interpret a bar graph? A bar graph uses bars of different heights or lengths to show and compare information.
There are two kinds of bar graph, horizontal bar graph and vertical bar graph. The information in a bar graph can be read and interpreted using the title, legend and labels.
Books borrowed this week
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C. App lication Grouping of pupils according to height. Grouping of pupils according to length of hair.
(Ask the questions: Most numbered group Least numbered group How many more How many less)
IV. Evaluation
1.
0102030405060708090
100
1 2 3 4 5 6 7
a. What is the title of the graph? b. Who gave the least number of kilograms? c. How many kilograms were given by section 7? d. How many kilograms were given by sections 1 and 3? e. Who gave the biggest kilograms?
2.
0
2
4
6
8
10
12
14
Grade 2 Grade 3 Grade 4 Grade 5 Grade 6
Old Newspaper Drive
Sections in Grade IV
Number of Dropo uts for Schoo l Year 1996 1997
Num
ber
of d
rop
outs
Kilo
gra
ms
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a. What is the title of the graph? b. Which grade has the highest number of drop outs? c. How many more drop outs does Grade 3 have than Grade 5? d. What is the rank of Grade 4 in the number of drop outs? e. In what school year was the number of drop outs taken?
V. Assignment
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29
30
31
32
33
34
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
1. What day has the highest temperature? 2. What day has the least temperature? 3. What are the days with the same number of degrees? 4. What is the difference between the highest and the lowest temperature? 5. Find the average temperature.
Constructing Bar Graph I. Learning Objectives
Cognitive: Construct a bar graph Psyc homotor: Organize data presented in a bar graph Affective: Participate actively in the class discussion
II. Learning Content
Skill : Organizing data presented in a bar graph Reference: BECPELC V.A.2.1 Materials: textbook, manipulative materials, average grades, ages, scores
in the test Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill Number Game: Pass the Basket a. Each child will get a number in the basket
Room Temperature for a Week
Tem
pera
ture
o C
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b. Tell the pupils that every number has a puzzle written at the back and the one holding it will give the answer. The game will continue as the need arises.
2. Review
0
10
20
30
40
50
IV1 IV2 IV3 IV4 IV5 IV6 IV7
Answer the following questions: a. What section has the least enrolment? b. What section has the greatest enrolment? c. What sections have the same enrolment? d. What is the average number of pupils?
3. Motivation
Joseph’s grade in the third grading period Math – 92 Science – 90 Makabayan – 89 English – 91 Filipino – 88 Alice Test Results Number of Quizzes Scores 1 85 2 95 3 90 4 80 5 90
Let your pupils study the grades of Joseph and ask them, “Why do you think Joseph
has this kind of grades? What do you think you should do so you can get the same grades as Joseph?
B. Developmental Activities
1. Presentation
How are we going to construct a graph? Based on the data used in the review, study the data and interpret it so you can construct a bar graph.
a. What are the parts of a bar graph? b. Where do you put the titles/names?
Num
ber
of P
upils
Sections in Grade IV
Number of Pupils in Grade IV
334
2. Activity
Groups 1 & 3 – Using the data of Joseph’s grade, construct a bar graph. Groups 2 & 4 – Construct a bar graph using the scores of Alice Test Results
3. Analysis/Abstraction
a. How did you construct the bar graph? a. What is the interval used in A? In B? b. Did you shade properly the bar that represent given data? c. What is the title of your graph? d. What is the label for the data written horizontally? Diagonally?
4. Practice Exercises
Construct a bar graph for the following data:
Kinds of Flowers Number of Flowers Rose 20 Daisy 25 Gumamela 35 Sunflower 40 Santan 30
5. Generali zation
What are the important ideas that you know in constructing a bar graph? A graph is a diagram which shows how two or more sets of information are related. The horizontal line is the xaxis and the yaxis is the vertical line.
C. App lication
1. Prepare a bar graph for the monthly sales of Ronnie’s sarisari store.
Month Sales April 5,000.00 May 3,500.00 June 6,000.00 July 5,500.00 August 8,000.00 September 9,250.00 October 7,750.00
2. Copy the information given below and make a bar graph. Grades of Mayen in English quizzes Quiz Number Grade 1 87 2 84 3 90 4 78 5 85 6 82
335
IV. Evaluation
Make a horizontal bar graph based on empty bottles. Grade Number of Bott les 1 200 2 400 3 300 4 200 5 500
V. Assignment
Using the data above, construct a vertical bar graph.