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Math for Smart Kids is the grade school textbook which features online exercises in www.diwalearningtown.com to complement review of textbook lessons. The book addresses the learning needs in mathematics such understanding and skills in computing considerable speed and accuracy, estimating, communicating, thinking analytically and critically, and in solving problems using appropriate technology.

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- 1. Math for Smart Kids 4
- 2. Math for Smart KidsGrade 4TextbookPhilippine Copyright 2010 by DIWA LEARNING SYSTEMS INCAll rights reserved. Printed in the PhilippinesEditorial, design, and layout by University Press of First AsiaNo part of this publication may be reproduced or transmitted in any form or by any means electronic ormechanical, including photocopying, recording, or any information storage and retrieval systems, withoutpermission in writing from the copyright owner. Exclusively distributed by DIWA LEARNING SYSTEMS INC 4/F SEDCCO 1 Bldg. 120 Thailand corner Legazpi Streets Legaspi Village, 1229 Makati City, Philippines Tel. No.: (632) 893-8501 * Fax: (632) 817-8700 ISBN 978-971-46-0121-5The Editorial BoardAuthorDr. Estrella P. Mercado finished her PhD in Educational Management (with honor) and MA in Education at Manuel L. QuezonUniversity. She also holds an MEd in Special Education degree and a BS in Elementary Education degree from the PhilippineNormal University (PNU). She has been a classroom teacher, an Education supervisor, and an assistant chief of the ElementaryDivision of the Department of Education, Culture and Sports (DECS-NCR). She was awarded as Outstanding Female Educator in1998 by the Filipino Chinese Women Federation. She presently heads the Special Education Department at PNU. Consultant-AuthorLuzviminda M. Sibbaluca holds a master’s degree in Mathematics Education and a bachelor’s degree in Elementary MathematicsEducation (cum laude) both from the University of the Philippines-Diliman (UP-Diliman). She is one of the top ten successfulexaminees of the Licensure Examination for Teachers (LET) for Elementary in 2003. She is currently an assistant professor at theMathematics Department of the University of the Philippines Integrated School (UPIS).ReviewerMargaret M. Diaz-Atela has been teaching Mathematics since 1990. She has a bachelor’s degree in Secondary Education, majorin Mathematics, and a master’s degree in Teaching, major in Mathematics, both from UP-Diliman. She is presently an assistantprofessor at the Mathematics Department of UPIS.
- 3. Preface Math for Smart Kids is a series of textbooks in Mathematics forgrade school, which is designed to help pupils develop appreciation andlove for mathematics. This series also aims to help the learners acquire theskills they need to become computationally literate. The lessons in each textbook present mathematics concepts and principlesthat are anchored on the competencies prescribed by the Department ofEducation. Each lesson starts with Let’s Do Math, where mathematicsconcepts and principles are introduced through problems, stories, games,or puzzles. This section is followed by Let’s Look Back, which lists questionsthat will help the pupils to think critically on what has been introducedin the lesson and allow them to discover things on their own. For easyrecall of important points or concepts taken up in a lesson, the section Let’sRemember Our Learning has been included. Multilevel exercises are providedin Let’s Practice and Let’s Test Our Learning that will assess how much thepupils have learned from the lesson. The exercises will also determine if thepupils are ready to learn new mathematics skills. The development of themultiple intelligences of an individual is reflected in the different activitiesthat the pupils will perform—from concrete to semi-concrete, and fromsemi-abstract to abstract kind of learning. Situations and real-life problemsare provided in Let’s Look Forward to give the pupils opportunities to applywhat they have learned to their daily life experiences. This series of textbooks gives the learners the opportunity to exploreand enjoy Mathematics. Let’s have fun learning together! The Authors
- 4. Table of ContentsUnit 1 Addition and Subtraction of Whole NumbersChapter 1 Whole Numbers through BillionsLesson 1 Place Values through Billions ..............................................................2 2 Reading and Writing Numbers ............................................................6 3 Comparing and Ordering Whole Numbers ......................................... 10 4 Rounding off Numbers ...................................................................... 14Chapter 2 Addition of Whole NumbersLesson 1 Properties of Addition ....................................................................... 17 2 Adding Whole Numbers ................................................................... 22 3 Adding Three or More Addends ………………………………....................26 4 Estimating Sums ................................................................................ 29 5 Adding Three-digit Numbers Mentally ............................................... 32 6 Solving Word Problems Involving Addition ....................................... 35Chapter 3 Subtraction of Whole NumbersLesson 1 Subtracting Whole Numbers without Regrouping .............................. 40 2 Subtracting Whole Numbers with Regrouping ................................... 43 3 Estimating Differences ..................................................................... 46 4 Mental Subtraction ............................................................................ 49 5 Solving Word Problems Involving Subtraction ................................... 53 6 Combined Operations (Addition and Subtraction) .............................. 57Unit 2 Multiplication and Division of Whole Numbers, and Number TheoryChapter 4 Multiplication of Whole NumbersLesson 1 Properties of Multiplication .............................................................. 62 2 Multiplying Whole Numbers without Regrouping ............................. 67 3 Multiplying Whole Numbers with Regrouping .................................. 70 4 Multiplying Whole Numbers That Are Multiples of 10 ...................... 73 5 Estimating Products ........................................................................... 76 6 Mental Multiplication ........................................................................ 78
- 5. 7 Exponents ......................................................................................... 81 8 Solving Word Problems Involving Multiplication ............................... 85Chapter 5 Division of Whole NumbersLesson 1 Dividing Whole Numbers without Remainder ................................... 89 2 Dividing Whole Numbers with Remainder ....................................... 93 3 Dividing Whole Numbers That Are Multiples of 10 .......................... 97 4 Estimating Quotients ...................................................................... 101 5 Mental Division .............................................................................. 104 6 Solving Word Problems Involving Division ..................................... 107 7 Series of Operations ........................................................................ 111 8 Using a Calculator .......................................................................... 115Chapter 6 Number TheoryLesson 1 Divisibility Rules ............................................................................ 119 2 Prime and Composite Numbers ...................................................... 123 3 Greatest Common Factor ................................................................ 127 4 Multiples and Least Common Multiple ........................................... 130Unit 3 Fractions, Decimals, Ratio, and ProportionChapter 7 FractionsLesson 1 Kinds of Fractions .......................................................................... 134 2 Equivalent Fractions and Fractions in Lowest Terms ....................... 139 3 Comparing and Ordering Fractions ................................................. 144 4 Adding Similar Fractions ................................................................ 149 5 Subtracting Similar Fractions .......................................................... 153 6 Solving Word Problems Involving Addition and Subtraction of Similar Fractions ........................................................................ 157 7 Adding Dissimilar Fractions ............................................................ 163 8 Subtracting Dissimilar Fractions ..................................................... 167 9 Multiplying Fractions ..................................................................... 172 10 Solving Word Problems Involving Multiplication of Fractions ..................................................................................... 175Chapter 8 DecimalsLesson 1 Fractions and Decimals .................................................................. 179 2 Comparing and Ordering Decimals ................................................. 183
- 6. 3 Rounding off Decimals ................................................................... 187 4 Adding Decimals ............................................................................ 190 5 Subtracting Decimals ...................................................................... 194 6 Solving Word Problems Involving Addition and Subtraction of Decimals .................................................................................... 198 7 Solving Word Problems Involving More Than One Operation ......... 202 8 Multiplying Decimals ..................................................................... 206 9 Solving Word Problems Involving Multiplication of Decimals ......... 209Chapter 9 Ratio and ProportionLesson 1 Ratio .............................................................................................. 213 2 Proportion ...................................................................................... 218 3 Solving Word Problems Involving Ratio and Proportion .................. 222Unit 4 Geometry, Measurement, and GraphsChapter 10 GeometryLesson 1 Basic Geometric Concepts .............................................................. 226 2 Angles ............................................................................................ 232 3 Polygons ......................................................................................... 238 4 Circles ............................................................................................ 243 5 Space Figures ................................................................................. 247Chapter 11 MeasurementLesson 1 Metric Conversion .......................................................................... 250 2 Perimeter of Polygons ..................................................................... 254 3 Area of a Rectangle and a Triangle .................................................. 258 4 Volume of Rectangular Prisms ........................................................ 263Chapter 12 GraphsLesson 1 Bar Graphs ..................................................................................... 266 2 Constructing Bar Graphs ................................................................ 270 3 Line Graphs ................................................................................... 273 4 Constructing Line Graphs ............................................................... 278Bibliography ....................................................................................................... 282
- 7. Unit 1Addition and Subtractionof Whole Numbers
- 8. Chapter 1 Whole Numbers through Billions Lesson 1 Place Values through Billions The following table shows the estimated population of five member countries of the Asia-Pacific Economic Cooperation (APEC). Estimated Population Country (2008) Canada 33 212 696 China 1 330 044 544 Indonesia 237 512 352 Philippines 96 061 680 United States 303 824 640 Source: Time: Almanac 2009 Which of the countries have an estimated population that reached billions? From the table, you can see that China has an estimated population that has already reached billions. Study the place values of the digits in China’s population, that is, 1 330 044 544, in the place-value chart below. Billions Millions Thousands Units Period Period Period Period Ten Millions Ten Billions Thousands Thousands Thousands Hundreds Hundred Hundred Hundred Millions Millions Billions Billions Ones Tens Ten 1 3 3 0 0 4 4 5 4 4 Math for Smart Kids 4
- 9. The digit 1 is in the billions place and its value is 1 000 000 000. The digit 0 is in the millions and hundred thousands places. In bothplace values, 0 acts as a placeholder. The digits in a number are grouped by threes, starting from the right.Each group of three digits is called period.More examples: 1. The place values of the digit 2 in 237 512 352 are ones, thousands, and hundred millions. 2. The values of the digit 6 in 96 061 680 are 600, 60 000, and 6 000 000. 1. How are the place values arranged? How are they grouped? 2. Do all digits in a number have place values? Explain. 3. Do all digits in a number have values? Explain. Every digit in a given number has a place value and a value. The value that each digit represents depends on its place value. The digit 0 is used as a placeholder. It has a specific place value but its value remains 0. Digits are grouped into periods and each period is separated by a space or a comma. Addition and Subtraction of Whole Numbers
- 10. A. Write the place value and value of each underlined digit. Place Value Value 1. 65 896 235 000 _______________ _______________ 2. 7 329 136 495 _______________ _______________ 3. 429 326 527 _______________ _______________ 4. 3 829 425 612 _______________ _______________ 5. 345 391 426 _______________ _______________ B. Write the value of the given digit of the number 7 390 426 815. 1. 1 ____________ 6. 7 ____________ 2. 6 ____________ 7. 2 ____________ 3. 8 ____________ 8. 9 ____________ 4. 5 ____________ 9. 4 ____________ 5. 0 ____________ 10. 3 ____________ Study the following table. Answer the questions on the next page. Estimated Population Country (2008) Brunei 381 371 Cambodia 14 241 640 Indonesia 237 512 352 Laos 6 677 534 Malaysia 25 274 132 Myanmar 47 758 180 Math for Smart Kids 4
- 11. Philippines 96 061 680 Singapore 4 608 167 Thailand 65 493 296 Vietnam 86 116 560 Source: Time Almanac 2009 and CIA World Fact Book 1. Which ASEAN countries have a population with a digit that has a value of 100? 2. Which country has the largest population? What is the highest place value in this country’s population?A. Write the place value of each underlined digit. 1. 672 895 __________ 6. 3 000 425 __________ 2. 4 826 321 __________ 7. 6 725 398 000 __________ 3. 8 723 432 __________ 8. 72 829 426 125 __________ 4. 24 829 000 __________ 9. 43 826 725 __________ 5. 576 328 125 __________ 10. 49 000 126 345 __________B. Do what is asked. 1. Find the number that is 20 000 more than 395 034 300. 2. Write 2 nine-digit numbers that have digits whose values are 50 000 and 3 000 000. 3. Find the number that is 200 000 000 less than 382 930 400 239. 4. Find the numbers before and after 385 300 294 000. 5. Write the biggest number that can be formed using the digits 0 to 9, without repeating any digit. What are the numbers before and after this number? Addition and Subtraction of Whole Numbers
- 12. Lesson 2 Reading and Writing Numbers Asia is the largest continent in the world. Its land area measures 31 699 257 square kilometers (sq. km). It has an estimated total population of 4 052 000 000 as of mid- 2008.* How do you read the given numbers? The place-value chart is a helpful tool in reading and writing numbers through billions in different forms. Billions Millions Thousands Units Period Period Period Period Ten Millions Ten Billions Thousands Thousands Thousands Hundreds Hundred Hundred Hundred Millions Millions Billions Billions Ones Tens Ten 3 1 6 9 9 2 5 7 Standard form: 31 699 257 Word form: thirty-one million, six hundred ninety-nine thousand, two hundred fifty-seven Expanded form: 30 000 000 + 1 000 000 + 600 000 + 90 000 + 9 000 + 200 + 50 + 7 *Sources: 2008 World Population Data Sheet, www.prb.org, and Time: Almanac 2009 Math for Smart Kids 4
- 13. Billions Millions Thousands Units Period Period Period Period Ten Millions Ten Billions Thousands Thousands Thousands Hundreds Hundred Hundred Hundred Millions Millions Billions Billions Ones Tens Ten 4 0 5 2 0 0 0 0 0 0Standard form: 4 052 000 000Word form: four billion, fifty-two millionExpanded form: 4 000 000 000 + 50 000 000 + 2 000 000 From the two examples given, you can see that you multiply eachdigit of a number by its value to get the expanded form of a number. 1. How does a place-value chart help in writing numbers in word form? 2. How do you write numbers in expanded form? To read large numbers, read the number in each period, starting with the highest period, followed by the period name (without the –s). Do not mention the period name when reading the numbers in the units period. To get the expanded form of a number, multiply each digit of the number by its value. Addition and Subtraction of Whole Numbers
- 14. A. Write each number in word form. 1. 2 342 504 162 ____________________________________________________________ ____________________________________________________________ 2. 4 403 927 243 ____________________________________________________________ ____________________________________________________________ 3. 62 730 902 842 ____________________________________________________________ ____________________________________________________________ 4. 153 642 140 803 ____________________________________________________________ ____________________________________________________________ 5. 275 407 129 430 ____________________________________________________________ ____________________________________________________________ B. Write the following in standard form. 1. three billion, nine hundred twenty-two million, three hundred twelve thousand, one hundred forty-five _____________________________________ 2. forty-four billion, eight hundred fifty-three million, two hundred thousand, seven hundred sixty-five _____________________________________ 3. eight hundred billion, seven hundred fifteen million, six hundred twenty-seven thousand, four hundred two _____________________________________ 4. seventy billion, eight hundred forty-five million, nine hundred two thousand, five hundred fifty-one _____________________________________ Math for Smart Kids 4
- 15. 5. thirty-nine billion, seven hundred fifty million, one hundred five thousand, six hundred seventy-three _____________________________________ Write the orbit (in kilometers) of each planet in word and expandedforms. 1. Mercury – 57 050 000 ____________________________________________________________ ____________________________________________________________ 2. Venus – 108 110 000 ____________________________________________________________ ____________________________________________________________ Write the following numbers in expanded form. 1. 68 307 003 _______________________________________________________ __________________________________________________________________ 2. 593 695 330 693 _________________________________________________ __________________________________________________________________ 3. 492 403 206 202 ____________________________________________ __________________________________________________________________ 4. twenty billion, seven hundred million, ninety-nine thousand, eighteen _________________________________________________________ __________________________________________________________________ 5. five hundred seventy-three billion, eight million, five hundred thousand, five ___________________________________________________ __________________________________________________________________ Addition and Subtraction of Whole Numbers
- 16. Lesson 3 Comparing and Ordering Whole Numbers Land Areas of the Different Continents Continent Land Area (sq. km) Africa 30 246 121 Antarctica 14 200 000 Asia 31 699 257 Europe 23 039 279 North America 24 293 585 Oceania 8 515 144 South America 17 824 370 Source: Time: Almanac 2009 Which continents have a greater land area than Europe? To find out, compare the land area of each continent with that of Europe. Look at the underlined digits. These are the digits being compared. Europe and Africa Europe and North America 23 039 279 30 246 121 23 039 279 24 293 585 Europe and Antarctica Europe and Oceania 23 039 279 14 200 000 23 039 279 8 515 144 Europe and Asia Europe and South America 23 039 279 31 699 257 23 039 279 17 824 370 Hence, the continents that have a greater land area than Europe are Africa, Asia, and North America.10 Math for Smart Kids 4
- 17. To compare whole numbers with the same number of digits, comparethe digits starting from the highest place value. If the digits are the same,compare the digits in the next place value until you find different digits inthe same place value. When comparing numbers with different number of digits, thenumber with more digits is the greater number. The land areas given in the table can be arranged either in ascending(least to greatest) or descending (greatest to least) order. The following table shows the arrangement of the seven continents inascending order. Continent Land Area (sq. km) Oceania 8 515 144 Antarctica 14 200 000 South America 17 824 370 Europe 23 039 279 North America 24 293 585 Africa 30 246 121 Asia 31 699 257 To arrange numbers in ascending or descending order, compare thenumbers two at a time. Then, arrange them in the specified order. 1. How do you compare whole numbers? 2. How do you arrange numbers in ascending order? in descending order? Addition and Subtraction of Whole Numbers 11
- 18. To compare whole numbers with the same number of digits, compare the digits in the same place value, starting from the highest place value. If the digits are the same, compare the digits in the next place value until you find different digits in the same place value. When comparing numbers with different number of digits, the number with more digits is the greater number. To arrange numbers either in ascending or descending order, compare the numbers two at a time. Then, arrange them in the specified order. A. Compare each pair of numbers. Write , , or = in the box. 1. 483 399 386 483 399 836 2. 789 302 388 002 789 320 388 002 3. 40 309 204 40 000 000 + 3 000 000 + 9 000 + 200 + 4 4. 700 000 000 + 5 000 000 + 100 + 30 57 000 130 5. three billion, twenty million, five hundred two 3 020 000 502 B. Arrange the numbers from greatest to least. 1. 1 430 239, 1 421 695, 1 422 426 2. 2 561 326, 2 560 291, 2 563 427 C. Arrange the numbers from least to greatest. 1. 5 634 807, 5 189 346, 5 635 887 2. 79 847 000, 79 826 000, 79 835 0001 Math for Smart Kids 4
- 19. Arrange the given estimated population of some countries fromgreatest to least. Country Population Venezuela 28 439 218 Malaysia 27 468 000 Saudi Arabia 25 721 000 Uzbekistan 27 488 000 Afghanistan 28 150 000 (Based on July 2009 estimate by the UN Department of Economic and Social Affairs)A. Compare each pair of numbers. Write , , or = in the box. 1. 8 275 302 8 285 427 2. 782 321 000 783 324 000 3. 93 467 000 000 90 000 000 000 + 3 000 000 + 400 000 + 60 000 + 7 4. 84 672 923 000 eighty-four billion, six hundred seventy-two million, nine hundred twenty-three thousandB. Arrange the given numbers in the box. Use the given numbers at the start and end of each set as your guide. 1. 5 483 490 _______ _______ ________ 5 549 035 5 488 394 5 510 359 5 499 294 2. 14 593 299 ______ ________ _______ 14 101 304 14 405 395 14 123 493 14 443 395 Addition and Subtraction of Whole Numbers 1
- 20. Lesson 4 Rounding off Numbers The following table shows the number of livestock raised in 2006. About how many goats were raised? Livestock Number of Live Animals pigs 13 046 680 goats 3 735 816 buffalo 3 357 956 Source: Time: Almanac 2009 To answer the question, round off the given number of goats to the nearest millions. Identify the digit in the place value you are rounding off to (3). Look at the digit to its right (7). If it is 5 or more, round up. Add 1 to the digit in the place value you are rounding off to. Then, replace all the digits to the right with zeros. If it is less than 5, retain the digit in the place value you are rounding off to and replace all the digits to the right with zeros. Since 7 5, round up. Therefore, 3 735 816 rounded off to the nearest millions is 4 000 000. Example: Round off P3 296 000 000 to the nearest billions. The digit in the billions place is 3. The digit to its right is 2. Since 2 5, round down or retain the digit in the place value you are rounding off to. Thus, P3 296 000 000 rounded off to the nearest billions is P3 000 000 000.1 Math for Smart Kids 4
- 21. How do you round off a number to a specified place value? To round off a number to a specified place value, look at the digit to the right of the place you are rounding off to. If the digit is 5 or more, add 1 to the digit in the place value you are rounding off to and replace all the digits to its right with zeros. If the digit is less than 5, retain the digit in the place value you are rounding off to and replace all the digits to its right with zeros. Round off each number to the highest place value. 1. 7 405 385 724 ______________________ 2. 38 486 406 493 ______________________ 3. 90 394 593 294 ______________________ 4. 6 394 395 305 ______________________ 5. 8 538 395 302 ______________________ 6. 503 495 694 364 ______________________ 7. 824 386 399 912 ______________________ 8. 80 143 586 392 ______________________ 9. 65 388 200 372 ______________________ 10. 823 495 385 385 ______________________ Addition and Subtraction of Whole Numbers 1
- 22. Answer the following: 1. What is the least number that can be rounded off to 5 000 000? 2. What is the greatest number that can be rounded off to 64 280 000? 3. Give two numbers that can be rounded off to 390 000 000. A. Round off each number to the indicated place value. 1. 8 905 346 millions _________________ 2. 58 394 724 146 hundred thousands _________________ 3. 49 385 284 124 millions _________________ 4. 723 781 545 365 hundred billions _________________ 5. 185 234 524 567 ten millions _________________ 6. 5 584 816 127 thousands _________________ 7. 6 389 878 392 billions _________________ 8. 562 493 827 921 ten billions _________________ 9. 43 678 453 ten millions _________________ 10. 267 289 054 125 hundred billions _________________B. Answer the following word problems. 1. There were 573 405 people who joined an online group. About how many hundred thousands of people joined the group? 2. Last year, 1 995 394 passengers preferred to take economy flights. This year, the number of passengers decreased by 500 000. About how many million people took economy flights this year?1 Math for Smart Kids 4

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