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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 3
- 2. Math for Smart KidsGrade 3TextbookPhilippine 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 or mechanical,including photocopying, recording, or any information storage and retrieval systems, without permission in writingfrom 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 978-971-46-0119-2The 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 andprinciples that are anchored on the competencies prescribed by theDepartment of Education. Each lesson starts with Let’s Do Math, wheremathematics concepts and principles are introduced through problems,stories, games, or puzzles. This section is followed by Let’s Look Back, whichlists questions that will help the pupils to think critically on what has beenintroduced in the lesson and will allow them to discover things on theirown. For easy recall of important points or concepts taken up in a lesson,the section Let’s Remember Our Learning has been included. Multilevelexercises are provided in Let’s Practice and Let’s Test Our Learning that willassess how much the pupils have learned from the lesson. The exerciseswill also determine if the pupils are ready to learn new mathematics skills.The development of the multiple intelligences of an individual is reflectedin the different activities that the pupils will perform—from concreteto semi-concrete, and from semi-abstract to abstract kind of learning.Situations and real-life problems are provided in Let’s Look Forward to givethe pupils opportunities to apply what they have learned to their daily lifeexperiences. 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 Numbers through Hundred ThousandsLesson 1 Place Values of Numbers through Hundred ..................... Thousands…..………………….. ......................................... 2Lesson 2 Reading and Writing Numbers ....................................... 6Lesson 3 Comparing Numbers.................................................... 11Lesson 4 Ordering Numbers ...................................................... 15Lesson 5 Rounding off Numbers ................................................ 18Lesson 6 Odd and Even Numbers .............................................. 23Lesson 7 Roman Numerals ......................................................... 27Chapter 2 Addition of Whole NumbersLesson 1 Properties of Addition .................................................. 32Lesson 2 Adding Whole Numbers without Regrouping ............... 36Lesson 3 Adding Whole Numbers with Regrouping .................... 40Lesson 4 Estimating Sums .......................................................... 44Lesson 5 Mental Addition........................................................... 48Lesson 6 Solving Word Problems Involving Addition of Whole Numbers ...................................................... 51Chapter 3 Subtraction of Whole NumbersLesson 1 Subtracting Whole Numbers without Regrouping ........ 57Lesson 2 Subtracting Whole Numbers with Regrouping ............. 61Lesson 3 Estimating Differences................................................. 65Lesson 4 Mental Subtraction ...................................................... 69Lesson 5 Solving Word Problems Involving Subtraction of Whole Numbers ...................................................... 73Lesson 6 Combined Operations: Addition and Subtraction ......... 78Lesson 7 Solving Two-step Word Problems................................. 82
- 5. Unit 2 Multiplication and Division of Whole NumbersChapter 4 Multiplication of Whole NumbersLesson 1 Properties of Multiplication ......................................... 88Lesson 2 Multiplying Whole Numbers without Regrouping ........ 94Lesson 3 Multiplying Whole Numbers with Regrouping ............. 99Lesson 4 Multiplying by Multiples of 10 ....................................104Lesson 5 Estimating Products ....................................................107Lesson 6 Mental Multiplication .................................................110Lesson 7 Solving Word Problems Involving Multiplication of Whole Numbers .....................................................113Lesson 8 Series of Operations ....................................................117Chapter 5 Division of Whole NumbersLesson 1 Dividing Whole Numbers without Remainder .............121Lesson 2 Dividing Whole Numbers with Remainder ..................126Lesson 3 Dividing by Multiples of 10.........................................130Lesson 4 Estimating Quotients ..................................................133Lesson 5 Mental Division ..........................................................136Lesson 6 Solving Word Problems Involving Division of Whole Numbers .....................................................139Lesson 7 Series of Operations ....................................................143Lesson 8 Using a Calculator ......................................................148Unit 3 Number Theory, Fractions, and DecimalsChapter 6 Number TheoryLesson 1 Prime and Composite Numbers ..................................152Lesson 2 Factors and Multiples..................................................156Lesson 3 Greatest Common Factor ............................................159Lesson 4 Least Common Multiple..............................................162Chapter 7 FractionsLesson 1 Kinds of Fractions .......................................................164Lesson 2 Similar and Dissimilar Fractions .................................170Lesson 3 Expressing Fractions in Lowest Terms.........................173Lesson 4 Comparing and Ordering Fractions .............................177
- 6. Lesson 5 Adding Fractions ........................................................181Lesson 6 Subtracting Fractions ..................................................184Lesson 7 Fractional Part of a Set ................................................187Chapter 8 Decimals and MoneyLesson 1 Place Values of Decimals.............................................191Lesson 2 Comparing and Ordering Decimals .............................197Lesson 3 Adding Decimals ........................................................202Lesson 4 Subtracting Decimals ..................................................206Lesson 5 Reading and Writing Money Values.............................210Lesson 6 Solving Word Problems Involving Decimals ................216Unit 4 Geometry, Measurement, and GraphsChapter 9 GeometryLesson 1 Lines and Line Segments.............................................222Lesson 2 Polygons and Circles ...................................................226Lesson 3 Space Figures ..............................................................230Lesson 4 Symmetry and Tessellation .........................................233Chapter 10 MeasurementLesson 1 Linear Measurement ...................................................239Lesson 2 Perimeter of Polygons .................................................243Lesson 3 Area of a Square and a Rectangle ................................246Lesson 4 Measuring Mass..........................................................250Lesson 5 Measuring Capacity ....................................................253Lesson 6 Measuring Time..........................................................256Lesson 7 Calendar and Exact Time between Dates ....................262Chapter 11 GraphsLesson 1 Pictograph and Bar Graph ...........................................267Lesson 2 Constructing a Pictograph ...........................................271Lesson 3 Constructing a Bar Graph ...........................................277Bibliography ......................................................................................282
- 7. UnitAddition and Subtractionof Whole Numbers 1
- 8. Chapter 1 Numbers through Hundred Thousands Lesson 1 Place Values of Numbers through Hundred Thousands According to a survey, about 125 308 families watch various TVshows around 8:00 PM to 9:00 PM every day.Study the place-value chart below. Thousands Units Hundreds Tens Ones Hundreds Tens Ones 1 2 5 3 0 8 The digit 1 is in the hundred thousands place. Its value is 100 000. The digit 2 is in the ten thousands place. Its value is 20 000. The digit 5 is in the thousands place. Its value is 5 000.2 Math for Smart Kids 3
- 9. The digit 3 is in the hundreds place. Its value is 300. The digit 0 is in the tens place. Its value is 0. The digit 8 is in the ones place. Its value is 8. The digits of a number up to hundred thousands can be groupedinto two periods—the units period and the thousands period. Periods aregroups of three digits in a number. Periods are separated by a space. 1. In writing numbers up to hundred thousands, what separates the digits in the thousands and units periods? 2. Why is zero important as a placeholder? Explain your answer.More examples:1. What is the place value of the underlined digit in each number? a. 378 205 Answer: ten thousands b. 487 329 Answer: hundreds2. What is the value of the digit 4 in each number? a. 395 304 Answer: 4 b. 406 396 Answer: 400 000 Each digit in a number has a unique place value. The value of a digit is determined by its place value. The digits of a number up to hundred thousands can be grouped into thousands period and units period. Each period has three digits and is separated by a space. Addition and Subtraction of Whole Numbers 3
- 10. A. Write the place value of the underlined digit. 1. 607 395 ______________ 2. 700 403 ______________ 3. 396 063 ______________ 4. 285 221 ______________ 5. 603 200 ______________B. Write the value of the underlined digit. 1. 730 306 ______________ 2. 362 305 ______________ 3. 900 274 ______________ 4. 523 464 ______________ 5. 363 204 ______________C. Identify the mystery numbers. 1. I am a six-digit number. Two of my digits have the values 300 and 4 000. All the digits in my thousands period are the same. The remaining digits are also the same and their sum is 10. 2. I am a six-digit number. If you add 1 to me, I will become a seven-digit number.4 Math for Smart Kids 3
- 11. Miss Gonzalez is a cashier in a department store. Help her organizethe earnings of the store by answering the following questions:1. How many P100 bills are needed to have P1 000?2. If each bundle of bills is P10 000, how many bundles are needed to have P100 000?A. Complete the table by writing the place value and value of each underlined digit. Place Value Value 1. 573 294 2. 306 355 3. 572 346 4. 694 693 5. 730 496B. Answer each question. 1. What number is 50 000 less than 284 395? 2. What are the numbers before and after 300 300? 3. What number is four greater than the thousands digit of 395 341? 4. What digit is in the hundreds place of the number before 299 500? 5. What is the least six-digit number? Addition and Subtraction of Whole Numbers 5
- 12. Lesson 2 Reading and Writing Numbers Helping Hands Foundation had a total of 5 364 volunteers in the lastfive years.Study the place-value chart. Thousands Units Hundreds Tens Ones Hundreds Tens Ones 5 3 6 4 There are three ways of writing a number. Standard form: 5 364 Expanded form: 5 000 + 300 + 60 + 4 Word form: five thousand, three hundred sixty-four6 Math for Smart Kids 3
- 13. Another example: Thousands Units Hundreds Tens Ones Hundreds Tens Ones 4 0 7 5 2 5 Standard form: 407 525 Expanded form: 400 000 + 0 + 7 000 + 500 + 20 + 5 A place-value chart can help in reading a large number. To read alarge number, read the digits in the highest period followed by the periodname. Do not read the period name for the units. Thus, 407 525 is read as “four hundred seven thousand, five hundredtwenty-five.” 1. How do you write a number in expanded form? 2. How can the place-value chart help you in reading numbers? To write a number in expanded form, write the value of each digit separated by a plus sign. Use a space to separate the thousands and units periods in writing numbers in standard form. To read a large number, read the digits in the highest period followed by the period name. Do not read the period name for the units. Addition and Subtraction of Whole Numbers 7
- 14. A. Write the following numbers in word form. 1. 93 265 _________________________________________________ _________________________________________________ 2. 12 842 _________________________________________________ _________________________________________________ 3. 124 683 _________________________________________________ _________________________________________________ 4. 855 469 _________________________________________________ _________________________________________________ 5. 499 456 _________________________________________________ _________________________________________________B. Write the following in standard form. 1. three hundred thirty-one thousand, four hundred twenty-one ____________ 2. forty-three thousand, thirty-five ____________ 3. sixty thousand, five hundred fifty-one ____________ 4. seven hundred thousand, eight hundred sixty-two ____________ 5. eighty-nine thousand, nine hundred forty-nine ____________C. Write the following numbers in expanded form. 1. 485 305 _____________________________________________ 2. 583 009 _____________________________________________ 3. 794 395 _____________________________________________ 4. 249 532 _____________________________________________ 5. 578 320 _____________________________________________8 Math for Smart Kids 3
- 15. Mr. Lopez is a school principal. He needs to pay a computercompany the amount of three hundred sixty-five thousand, four hundredfifty pesos for the machines and services for one year. Write on the check the amount Mr. Lopez must pay.A. Write the following numbers in words. 1. 822 345 ________________________________________________ ________________________________________________ 2. 704 286 ________________________________________________ ________________________________________________ 3. 695 137 ________________________________________________ ________________________________________________ 4. 540 273 ________________________________________________ ________________________________________________ 5. 492 488 ________________________________________________ ________________________________________________ Addition and Subtraction of Whole Numbers 9
- 16. B. Identify the number, then write it in standard and expanded forms. Standard Form Expanded Form 1. What is the least five- digit number? 2. What is the greatest six-digit number? 3. What is the greatest six-digit number you can form using the digits 5, 3, 5, 3, 0, and 4?10 Math for Smart Kids 3
- 17. Lesson 3 Comparing Numbers Package A Package B Package C P169 500 P168 999 P168 150 The Gonzales family wants to go on an Asian tour. Compare thecost of each package to the family’s budget of P168 500. Start comparing the numbers by comparing the digits in the sameplace value starting from the highest place value. If the numbers havethe same number of digits, compare the digits in the next place valueuntil you find different digits in the same place value. If the numbershave different number of digits, the number with more digits is the largernumber.Package A: Is P169 500 greater than P168 500? The digits of 169 500 and 168 500 differ in the thousands place. 9 > 8 ⇒169 500 > 168 500Package B: Is P168 999 greater than P168 500? The digits of 168 999 and 168 500 differ in the hundreds place. 9 > 5 ⇒ 168 999 > 168 500 Addition and Subtraction of Whole Numbers 11
- 18. Package C: Is P168 150 greater than P168 500? The digits of 168 150 and 168 500 differ in the hundreds place. 1 < 5 ⇒ 168 150 < 168 500 The Gonzales family’s budget is enough for the third package only.The family should choose package C. 1. How do you know if a number is greater or less than another number? 2. How will you compare numbers with different number of digits? In comparing numbers with the same number of digits, start comparing the digits in the highest place value. If the digits in the highest place value are the same, compare the digits in the next place value until you find different digits in the same place value. In comparing numbers with different number of digits, the number with more digits is the larger number. Use the symbols > (greater than), < (less than), or = (equal to) to compare numbers.12 Math for Smart Kids 3
- 19. A. Compare the numbers using >, <, or =. 1. 49 875 49 875 4. 386 302 386 203 2. 28 579 38 469 5. 486 089 476 098 3. 237 098 237 089B. Compare each pair of numbers using <, >, or =. 1. 359 306 thirty-five thousand, three hundred sixty 2. 783 406 700 000 + 80 000 + 3 000 + 400 + 60 3. 485 332 5 000 + 400 000 + 80 000 + 300 + 2 + 30 4. two hundred thousand, ninety-five 200 000 + 900 + 5 5. 100 000 + 1 000 + 1 one hundred one thousandC. Choose two numbers in the box to complete each comparison below. Answers should not be repeated. 1. 743 353 = __________ > __________ 783 430 775 832 2. __________ < 783 406 < __________ 743 353 780 823 734 383 3. __________ > __________ > 705 382 783 046 Addition and Subtraction of Whole Numbers 13
- 20. Anna’s computer has more files than Dina’s computer. Help thetechnician identify the owner of the two computers. 219 943 219 49 3 files filesUse <, >, or = to compare each pair of numbers. five hundred ninety-six 1. 569 394 thousand, three hundred four 2. ninety-three thousand, forty 93 400 four hundred three thousand, 3. 400 000 + 3 000 + 50 + 2 fifty-two 4. 900 + 3 + 8 000 + 501 983 500 000 + 10 5. seven hundred thousand, two 702 050 hundred fifty14 Math for Smart Kids 3
- 21. Lesson 4 Ordering Numbers Poptropica Funbrain educationalgames Web site was viewed 14 583times in June, 14 540 times in July,and 15 102 times in August. In whichmonth was this Web site viewed themost number of times? In whichmonth was it viewed the least numberof times? First, compare the numbers two at a time to identify the greatestnumber. 14 583 > 14 540 15 102 > 14 583 Arranging the numbers from greatest to least (descending order): 15 102 14 583 14 540 August June July Arranging the numbers from least to greatest (ascending order): 14 540 14 583 15 102 July June August Poptropica Funbrain Web site was viewed the most number of timesin August and the least number of times in July. How do you arrange numbers in ascending order? in descending order? Addition and Subtraction of Whole Numbers 15
- 22. There are two ways to order whole numbers—in ascending or descending order. To order numbers, first compare the numbers two at a time. Then, arrange the numbers from least to greatest (ascending) or greatest to least (descending).A. Arrange the numbers in each set in ascending order. 1. 67 304, 67 043, 67 430 __________________________________________________________ 2. 532 189, 523 981, 523 191 __________________________________________________________ 3. 812 472, 812 247, 821 274, 812 274 __________________________________________________________B. Arrange the numbers in each set in descending order. 1. 94 395, 93 593, 94 593 __________________________________________________________ 2. 405 324, 450 304, 450 403, 450 043 __________________________________________________________ 3. 823 496, 821 495, 821 954, 823 649 __________________________________________________________16 Math for Smart Kids 3
- 23. Mr. Sweet recorded his annual sales of candies. Help him identifywhich candy is the bestseller and which one he should order less. Candy Sales in Pesos Candy Sales in PesosButtertoffee 25 350 Nutty Knots 30 500Chocopop 28 395 Peach Twist 21 235Strawberry Swirl 30 100 Cream Roll 21 430A. Arrange the numbers in each set based on the given order. 1. 15 395, 15 325, 15 532 least to greatest _______________________________________________________ 2. 53 294, 55 305, 53 942 greatest to least _______________________________________________________B. Answer the following problems. 1. A restaurant had the following sales for four months. In which month did the restaurant have the greatest sales? In which month did it have the least sales? January: P153 200 February: P173 390 March: P153 900 April: P168 400 2. Use the digits 3, 5, 4, 1, 0, and 7 to write 3 six-digit numbers. Arrange the numbers you have formed from least to greatest. Addition and Subtraction of Whole Numbers 17
- 24. Lesson 5 Rounding off Numbers Roni’s car broke down when he reached the 27th kilometer (km)post. Emergency bays are located on the 20th and 30th km posts. Whereshould Roni go to fix his car? Study the number line below. Round up to 30 20 21 22 23 24 25 26 27 28 29 30 Round down to 20 The number 27 when rounded off to the nearest tens is 30. Since 27 is closer to 30, Roni should proceed to the 30th km post tofix his car.18 Math for Smart Kids 3
- 25. Here is another example. The following are some of the highest peaks in feet (ft) in theCordillera range. Round off to the nearest thousands the heights ofMt. Amuyao and Mt. Bangbanglang. Mt. Sapocoy 8 056 ft Mt. Bangbanglang 8 082 ft Mt. Amuyao 8 863 ft Mt. Pawoi 8 056 ft Round up to 9 000 8 000 8 100 8 200 8 300 8 400 8 500 8 600 8 700 8 800 8 900 9 000 Round down to 8 000 The number 8 863 can be rounded off to 9 000. The number 8 082 can be rounded off to 8 000. Mt. Amuyao is about 9 000 ft while Mt. Bangbanglang is about 8 000 ft. Another way of rounding off numbers is to look at the digit to theright of the place value to which you want to round off a number. If thedigit on the right is 4 or less, round down. If the digit on the right is 5 ormore, round up. Study these examples. Rounded off to the Rounded off to the Rounded off to the Number Nearest Tens Nearest Hundreds Nearest Thousands 4 392 4 390 4 400 4 000 13 425 13 430 13 400 13 000 636 591 636 590 636 600 637 000 Addition and Subtraction of Whole Numbers 19
- 26. 1. How will you know whether to round up a number or round it down? 2. How do you round off numbers without using a number line? To round off numbers, look at the digit to the right of the place value you are rounding off. If the digit is 5 or more, round up by adding 1 to the digit in the place value you are rounding off. Then, replace the remaining digits to the right of that digit with zero. If the digit to the right of the place value you are rounding off is less than 5, round down. Retain the digit in the place value you are rounding off. Then, replace the remaining digits to the right of that digit with zero.A. Identify the digit to the right of the digit with the highest place value. Then, round off the number to the highest place value. Digit to the right of the Rounded off number to Number digit with the highest the highest place value place value 1. 94 2. 104 3. 135 4. 4 567 5. 15 42520 Math for Smart Kids 3
- 27. B. Round off each number to the indicated place values. Nearest Nearest Number Nearest Tens Hundreds Thousands 1. 6 395 2. 48 243 3. 72 999 4. 395 302 5. 987 177 6. 7 305 7. 89 960 8. 90 463 9. 98 200 10. 394 806 Round off the population of each city to the place value of theunderlined digit. Then, arrange the cities from least to greatest based ontheir population. Population in Selected Cities in the Philippines City Population Cebu 798 809 Digos 145 514 Vigan 47 246 Iloilo 418 710 Lipa 260 568 Malabon 363 681 Source: National Statistical Coordination Board http://www.nscb.gov.ph/activestats/psgc/ (accessed 15 April 2009) Addition and Subtraction of Whole Numbers 21
- 28. Complete the table by rounding off the given numbers to the indicatedplace values. Ten Hundred Number Tens Hundreds Thousands Thousands Thousands 1. 534 678 2. 856 100 3. 480 431 4. 341 879 5. 767 001 6. 192 453 7. 328 741 8. 330 145 9. 495 262 10. 676 49322 Math for Smart Kids 3
- 29. Lesson 6 Odd and Even Numbers Miss Soriano wants to group her pupils into two groups with equalnumber of members. The class 3-Ilog has 34 pupils while the class3-Dagat has 35 pupils. Which section can be grouped equally into twogroups? 3-Ilog 3-Dagat Dividing each class by 2, the class 3-Ilog will have 17 members ineach group. However, the class 3-Dagat will have 1 extra pupil. Numbers that can be divided equally by 2 are even numbers. Thenumber 34 is an even number. Numbers that have a remainder 1 when divided by 2 are oddnumbers. The number 35 is an odd number. Addition and Subtraction of Whole Numbers 23
- 30. More examples:1. List all the odd numbers between 25 and 36. Answer: 27, 29, 31, 33, 352. How many even numbers are there from 30 to 50? Answer: 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50 There are 11 even numbers from 30 to 50. Numbers whose ones digit is 0, 2, 4, 6, or 8 are even numbers.Numbers whose ones digit is 1, 3, 5, 7, or 9 are odd numbers. How can you tell if a number is odd or even without using division? Whole numbers can be classified as even or odd. Whole numbers whose ones digit is 2, 4, 6, 8, or 0 are even numbers. Whole numbers whose ones digit is 1, 3, 5, 7, or 9 are odd numbers.24 Math for Smart Kids 3
- 31. A. Circle all the even numbers. Cross out () all the odd numbers. Find a pattern that will make this task easier. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 How many numbers in the table are odd? How many are even?B. Answer the following. 1. List and count all the odd numbers between 100 and 125. ______________________________________________ 2. List and count all the even numbers from 200 to 250. ______________________________________________ 3. List and count all the even numbers between 1 080 and 1 120. ______________________________________________ 4. List and count all the odd numbers from 5 603 to 5 629. ______________________________________________ Addition and Subtraction of Whole Numbers 25
- 32. What games have you played which require two equal groups? Sharethe games that you know with the class. Explain why it is important tohave two groups with equal number of members to play those games. What happens if there is an extra player? What can be the role of theextra player?A. Determine whether the given number is even or odd. Write E for even and O for odd numbers. 1. 506 _________ 6. 6 407 _________ 2. 301 _________ 7. 9 611 _________ 3. 640 _________ 8. 4 003 _________ 4. 508 _________ 9. 5 048 _________ 5. 461 _________ 10. 1 245 _________B. Identify the numbers described below. 1. What is the least five-digit odd number that you can form using the digits 0, 2, 4, 5, and 7?_________________________________ 2. What is the greatest six-digit even number that you can form using the digits 0, 1, 3, 5, 7, and 8? _________________________26 Math for Smart Kids 3
- 33. Lesson 7 Roman Numerals Belle saw two portraits of beautiful churches in the museum. Whichof the two portraits shows an older church? XCIV MCM V CCLX MDC This table shows the value of the letters used in Roman numerals. Roman Numerals I V X L C D M Hindu-Arabic 1 5 10 50 100 500 1 000 Numerals Addition and Subtraction of Whole Numbers 27
- 34. Portrait 1 MDCCCLXV = 1 000 + 500 + 300 + 50 + 10 + 5 = 1 865 1000 500 300 50 10 5Portrait 2 M C M XC I V = 1 000 + 900 + 90 + 4 = 1 994 1 000 900 90 4 The church in Portrait 1 was built in 1865 while the church inPortrait 2 was built in 1994. The church in Portrait 1 is older than the church in Portrait 2. Study the following combinations of Roman numerals: IV = 5 – 1 = 4 XC = 100 – 10 = 90 CD = 500 – 100 = 400 CM = 1 000 – 100 = 900 VI = 5 + 1 = 6 CX = 100 + 10 = 110 DC = 500 + 100 = 600 MC = 1 000 + 100 = 1 100 XXX = 10 + 10 +10 = 3028 Math for Smart Kids 3
- 35. More examples:1. Change to Hindu-Arabic numerals. a. MMCCCLXXII = 2 372 b. MMMCDXLIII = 3 4432. Change to Roman numerals. a. 2 762 = 2 000 + 700 + 60 + 2 Write a symbol for the value of each digit. MM + DCC + LX + II = MMDCCLXII b. 3 944 = 3 000 + 900 + 40 + 4 MMM + CM + XL + IV = MMMCMXLIV 1. When do you subtract the values of the letters in the Roman numeration system? 2. When do you add the value of letters? 3. What letters can be repeated? How many times can these letters be repeated? I, V, X, L, C, D, and M are Roman numerals. I, X, C, and M can be repeated up to three times only. When a letter with smaller value is written before a letter with bigger value, subtract their values. When a letter with smaller value is written after a letter with bigger value, add their values. Addition and Subtraction of Whole Numbers 29
- 36. A. Write the following in Hindu-Arabic numerals, then in words. Hindu-Arabic Roman Numeral Word Form Numeral 1. CCCXL 2. DCCVIII 3. MMXCII 4. MCCCXCVI 5. MMCDXXIXB. Write the following in Roman numerals. 1. 95 ________________________ 2. 784 ________________________ 3. 1 455 ________________________ 4. 2 882 ________________________ 5. 3 989 ________________________ In what year was each of the following churches built?1. Basilica de Sto. Niño de Cebu was built in MDLXV. ________________2. Binondo Church was built in MDXCVI. ________________30 Math for Smart Kids 3
- 37. A. Write the following in Roman numerals. 1. 2 527 ________________________ 2. 3 680 ________________________ 3. 1 979 ________________________ 4. 2 986 ________________________ 5. 3 454 ________________________B. Compare the numbers using <, >, or =. 1. 839 DCCCXXXIV 2. one thousand, seven MDCCLX hundred fifty-five 3. MMCDLXXIII 2 473 4. MMMXCVIII 3 000 + 400 + 8 5. two thousand, four hundred MMCMLXXIV seventy-four Addition and Subtraction of Whole Numbers 31
- 38. Chapter 2 Addition of Whole Numbers Lesson 1 Properties of Addition Study the number sentences Greta, Fred, and Diane are holding. Commutative Property Associative Property (21+4)+6=21+(4+6) Identity Property 18+17=17+18 17 + 0 = 17 The commutative property of addition states that changing theorder of the addends does not change the sum. 18 + 17 = 17 + 18 35 = 35 The associative property of addition states that changing thegrouping of the addends does not change the sum. (21 + 4) + 6 = 21 + (4 + 6) 25 + 6 = 21 + 10 31 = 3132 Math for Smart Kids 3

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