Diwa Textbooks - Math for Smart Kids Grade 3 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.

1. Math for Smart Kids 3

2. Math for Smart Kids
Grade 3
Textbook
Philippine Copyright 2010 by DIWA LEARNING SYSTEMS INC
All rights reserved. Printed in the Philippines
Editorial, design, and layout by University Press of First Asia
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from the copyright owner.
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DIWA LEARNING SYSTEMS INC
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ISBN 978-971-46-0119-2
The Editorial Board
Author
Dr. Estrella P. Mercado finished her PhD in Educational Management (with honor) and MA in Education at Manuel L. Quezon
University. She also holds an MEd in Special Education degree and a BS in Elementary Education degree from the Philippine
Normal University (PNU). She has been a classroom teacher, an Education supervisor, and an assistant chief of the Elementary
Division of the Department of Education, Culture and Sports (DECS-NCR). She was awarded as Outstanding Female Educator in
1998 by the Filipino Chinese Women Federation. She presently heads the Special Education Department at PNU.
Consultant-Author
Luzviminda M. Sibbaluca holds a master’s degree in Mathematics Education and a bachelor’s degree in Elementary Mathematics
Education (cum laude) both from the University of the Philippines-Diliman (UP-Diliman). She is one of the top ten successful
examinees of the Licensure Examination for Teachers (LET) for Elementary in 2003. She is currently an assistant professor at the
Mathematics Department of the University of the Philippines Integrated School (UPIS).
Reviewer
Margaret M. Diaz-Atela has been teaching Mathematics since 1990. She has a bachelor’s degree in Secondary Education, major
in Mathematics, and a master’s degree in Teaching, major in Mathematics, both from UP-Diliman. She is presently an assistant
professor at the Mathematics Department of UPIS.

3. Preface
Math for Smart Kids is a series of textbooks in Mathematics for
grade school, which is designed to help pupils develop appreciation and
love for mathematics. This series also aims to help the learners acquire the
skills they need to become computationally literate.
The lessons in each textbook present mathematics concepts and
principles that are anchored on the competencies prescribed by the
Department of Education. Each lesson starts with Let’s Do Math, where
mathematics concepts and principles are introduced through problems,
stories, games, or puzzles. This section is followed by Let’s Look Back, which
lists questions that will help the pupils to think critically on what has been
introduced in the lesson and will allow them to discover things on their
own. For easy recall of important points or concepts taken up in a lesson,
the section Let’s Remember Our Learning has been included. Multilevel
exercises are provided in Let’s Practice and Let’s Test Our Learning that will
assess how much the pupils have learned from the lesson. The exercises
will also determine if the pupils are ready to learn new mathematics skills.
The development of the multiple intelligences of an individual is reflected
in the different activities that the pupils will perform—from concrete
to semi-concrete, and from semi-abstract to abstract kind of learning.
Situations and real-life problems are provided in Let’s Look Forward to give
the pupils opportunities to apply what they have learned to their daily life
experiences.
This series of textbooks gives the learners the opportunity to explore
and enjoy Mathematics. Let’s have fun learning together!
The Authors

4. Table of Contents
Unit 1 Addition and Subtraction of Whole Numbers
Chapter 1 Numbers through Hundred Thousands
Lesson 1 Place Values of Numbers through Hundred .....................
Thousands…..………………….. ......................................... 2
Lesson 2 Reading and Writing Numbers ....................................... 6
Lesson 3 Comparing Numbers.................................................... 11
Lesson 4 Ordering Numbers ...................................................... 15
Lesson 5 Rounding off Numbers ................................................ 18
Lesson 6 Odd and Even Numbers .............................................. 23
Lesson 7 Roman Numerals ......................................................... 27
Chapter 2 Addition of Whole Numbers
Lesson 1 Properties of Addition .................................................. 32
Lesson 2 Adding Whole Numbers without Regrouping ............... 36
Lesson 3 Adding Whole Numbers with Regrouping .................... 40
Lesson 4 Estimating Sums .......................................................... 44
Lesson 5 Mental Addition........................................................... 48
Lesson 6 Solving Word Problems Involving Addition
of Whole Numbers ...................................................... 51
Chapter 3 Subtraction of Whole Numbers
Lesson 1 Subtracting Whole Numbers without Regrouping ........ 57
Lesson 2 Subtracting Whole Numbers with Regrouping ............. 61
Lesson 3 Estimating Differences................................................. 65
Lesson 4 Mental Subtraction ...................................................... 69
Lesson 5 Solving Word Problems Involving Subtraction
of Whole Numbers ...................................................... 73
Lesson 6 Combined Operations: Addition and Subtraction ......... 78
Lesson 7 Solving Two-step Word Problems................................. 82

5. Unit 2 Multiplication and Division of Whole
Numbers
Chapter 4 Multiplication of Whole Numbers
Lesson 1 Properties of Multiplication ......................................... 88
Lesson 2 Multiplying Whole Numbers without Regrouping ........ 94
Lesson 3 Multiplying Whole Numbers with Regrouping ............. 99
Lesson 4 Multiplying by Multiples of 10 ....................................104
Lesson 5 Estimating Products ....................................................107
Lesson 6 Mental Multiplication .................................................110
Lesson 7 Solving Word Problems Involving Multiplication
of Whole Numbers .....................................................113
Lesson 8 Series of Operations ....................................................117
Chapter 5 Division of Whole Numbers
Lesson 1 Dividing Whole Numbers without Remainder .............121
Lesson 2 Dividing Whole Numbers with Remainder ..................126
Lesson 3 Dividing by Multiples of 10.........................................130
Lesson 4 Estimating Quotients ..................................................133
Lesson 5 Mental Division ..........................................................136
Lesson 6 Solving Word Problems Involving Division
of Whole Numbers .....................................................139
Lesson 7 Series of Operations ....................................................143
Lesson 8 Using a Calculator ......................................................148
Unit 3 Number Theory, Fractions, and Decimals
Chapter 6 Number Theory
Lesson 1 Prime and Composite Numbers ..................................152
Lesson 2 Factors and Multiples..................................................156
Lesson 3 Greatest Common Factor ............................................159
Lesson 4 Least Common Multiple..............................................162
Chapter 7 Fractions
Lesson 1 Kinds of Fractions .......................................................164
Lesson 2 Similar and Dissimilar Fractions .................................170
Lesson 3 Expressing Fractions in Lowest Terms.........................173
Lesson 4 Comparing and Ordering Fractions .............................177

6. Lesson 5 Adding Fractions ........................................................181
Lesson 6 Subtracting Fractions ..................................................184
Lesson 7 Fractional Part of a Set ................................................187
Chapter 8 Decimals and Money
Lesson 1 Place Values of Decimals.............................................191
Lesson 2 Comparing and Ordering Decimals .............................197
Lesson 3 Adding Decimals ........................................................202
Lesson 4 Subtracting Decimals ..................................................206
Lesson 5 Reading and Writing Money Values.............................210
Lesson 6 Solving Word Problems Involving Decimals ................216
Unit 4 Geometry, Measurement, and Graphs
Chapter 9 Geometry
Lesson 1 Lines and Line Segments.............................................222
Lesson 2 Polygons and Circles ...................................................226
Lesson 3 Space Figures ..............................................................230
Lesson 4 Symmetry and Tessellation .........................................233
Chapter 10 Measurement
Lesson 1 Linear Measurement ...................................................239
Lesson 2 Perimeter of Polygons .................................................243
Lesson 3 Area of a Square and a Rectangle ................................246
Lesson 4 Measuring Mass..........................................................250
Lesson 5 Measuring Capacity ....................................................253
Lesson 6 Measuring Time..........................................................256
Lesson 7 Calendar and Exact Time between Dates ....................262
Chapter 11 Graphs
Lesson 1 Pictograph and Bar Graph ...........................................267
Lesson 2 Constructing a Pictograph ...........................................271
Lesson 3 Constructing a Bar Graph ...........................................277
Bibliography ......................................................................................282

7. Unit
Addition and Subtraction
of 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 TV
shows 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 grouped
into two periods—the units period and the thousands period. Periods are
groups 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: hundreds
2. 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 organize
the 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. 730 496
B. 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 last
five 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-four
6 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 a
large number, read the digits in the highest period followed by the period
name. Do not read the period name for the units.
Thus, 407 525 is read as “four hundred seven thousand, five hundred
twenty-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 computer
company the amount of three hundred sixty-five thousand, four hundred
fifty 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 the
cost of each package to the family’s budget of P168 500.
Start comparing the numbers by comparing the digits in the same
place value starting from the highest place value. If the numbers have
the same number of digits, compare the digits in the next place value
until you find different digits in the same place value. If the numbers
have different number of digits, the number with more digits is the larger
number.
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 > 168 500
Package 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. 237 098 237 089
B. 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 thousand
C. 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 the
technician identify the owner of the two computers.
219 943
219 49
3 files
files
Use <, >, 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 fifty
14 Math for Smart Kids 3

21. Lesson 4 Ordering Numbers
Poptropica Funbrain educational
games Web site was viewed 14 583
times in June, 14 540 times in July,
and 15 102 times in August. In which
month was this Web site viewed the
most number of times? In which
month was it viewed the least number
of times?
First, compare the numbers two at a time to identify the greatest
number.
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 times
in 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 identify
which candy is the bestseller and which one he should order less.
Candy Sales in Pesos Candy Sales in Pesos
Buttertoffee 25 350 Nutty Knots 30 500
Chocopop 28 395 Peach Twist 21 235
Strawberry Swirl 30 100 Cream Roll 21 430
A. 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. Where
should 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 to
fix 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 the
Cordillera range. Round off to the nearest thousands the heights of
Mt. 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 the
right of the place value to which you want to round off a number. If the
digit on the right is 4 or less, round down. If the digit on the right is 5 or
more, 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. 15 425
20 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 the
underlined digit. Then, arrange the cities from least to greatest based on
their 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 indicated
place 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. 676 493
22 Math for Smart Kids 3

29. Lesson 6 Odd and Even Numbers
Miss Soriano wants to group her pupils into two groups with equal
number of members. The class 3-Ilog has 34 pupils while the class
3-Dagat has 35 pupils. Which section can be grouped equally into two
groups?
3-Ilog 3-Dagat
Dividing each class by 2, the class 3-Ilog will have 17 members in
each group. However, the class 3-Dagat will have 1 extra pupil.
Numbers that can be divided equally by 2 are even numbers. The
number 34 is an even number.
Numbers that have a remainder 1 when divided by 2 are odd
numbers. 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, 35
2. 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? Share
the games that you know with the class. Explain why it is important to
have 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 the
extra 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. Which
of 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
5
Portrait 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 in
Portrait 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 = 30
28 Math for Smart Kids 3

35. More examples:
1. Change to Hindu-Arabic numerals.
a. MMCCCLXXII = 2 372
b. MMMCDXLIII = 3 443
2. 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. MMCDXXIX
B. 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 the
order of the addends does not change the sum.
18 + 17 = 17 + 18
35 = 35
The associative property of addition states that changing the
grouping of the addends does not change the sum.
(21 + 4) + 6 = 21 + (4 + 6)
25 + 6 = 21 + 10
31 = 31
32 Math for Smart Kids 3