math for smart kids gr.3

Math for Smart Kids3

Math for Smart Kids Grade 3Textbook

Philippine Copyright 2010 by DIWA LEARNING SYSTEMS INCAll rights reserved. Printed in the Philippines

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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.

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

Table of Contents

Unit 1 Addition and Subtraction of Whole Numbers

Chapter 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 ......................................................... 27

Chapter 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 ...................................................... 51

Chapter 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

Unit 2 Multiplication and Division of Whole Numbers

Chapter 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 ....................................................117

Chapter 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 ......................................................148

Unit 3 Number Theory, Fractions, and Decimals

Chapter 6 Number TheoryLesson 1 Prime and Composite Numbers ..................................152Lesson 2 Factors and Multiples ..................................................156Lesson 3 Greatest Common Factor ............................................159Lesson 4 Least Common Multiple ..............................................162

Chapter 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

Lesson 5 Adding Fractions ........................................................181Lesson 6 Subtracting Fractions ..................................................184Lesson 7 Fractional Part of a Set ................................................187

Chapter 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 ................216

Unit 4 Geometry, Measurement, and Graphs

Chapter 9 GeometryLesson 1 Lines and Line Segments .............................................222Lesson 2 Polygons and Circles ...................................................226Lesson 3 Space Figures ..............................................................230Lesson 4 Symmetry and Tessellation .........................................233

Chapter 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 ....................262

Chapter 11 GraphsLesson 1 Pictograph and Bar Graph ...........................................267Lesson 2 Constructing a Pictograph ...........................................271Lesson 3 Constructing a Bar Graph ...........................................277

Bibliography ......................................................................................282

Addition and Subtraction of Whole Numbers 1

Unit

2 Math for Smart Kids 3

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.

Chapter 1


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 thousandsb. 487 329 Answer: hundreds

2. What is the value of the digit 4 in each number?a. 395 304 Answer: 4b. 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.


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.


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?


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


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


Another example:

Thousands Units


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.


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 _____________________________________________


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 ________________________________________________

________________________________________________


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?


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

Lesson 3 Comparing Numbers

Package AP169 500

Package BP168 999

Package CP168 150


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.


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 = __________ > __________

2. __________ < 783 406 < __________

3. __________ > __________ > 705 382

783 430775 832743 353780 823734 383783 046


Anna’s computer has more files than Dina’s computer. Help the technician identify the owner of the two computers.

Use <, >, or = to compare each pair of numbers.

1. 569 394 five hundred ninety-six thousand, three hundred four

2. ninety-three thousand, forty 93 400

3. 400 000 + 3 000 + 50 + 2 four hundred three thousand, fifty-two

4. 900 + 3 + 8 000 + 500 000 + 10 501 983

5. seven hundred thousand, two hundred fifty 702 050

219 493

files

219 943files


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?


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

__________________________________________________________


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.


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.

Lesson 5 Rounding off Numbers


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. SapocoyMt. BangbanglangMt. AmuyaoMt. Pawoi

8 056 ft8 082 ft8 863 ft8 056 ft

Round up to 9 000

8000 8100 8200 8300 8400 8500 8600 8700 8800 8900 9000

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.

Number Rounded off to the Nearest Tens

Rounded off to the Nearest Hundreds

Rounded off to the 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


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.

NumberDigit to the right of the digit with the highest

place value

Rounded off number to the highest place value

1. 942. 1043. 1354. 4 5675. 15 425


B. Round off each number to the indicated place values.

Number Nearest Tens Nearest Hundreds

Nearest Thousands

1. 6 3952. 48 2433. 72 9994. 395 3025. 987 1776. 7 3057. 89 9608. 90 4639. 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 PopulationCebuDigosViganIloiloLipaMalabon

798 809145 51447 246418 710260 568363 681

Source: National Statistical Coordination Board http://www.nscb.gov.ph/activestats/psgc/ (accessed 15 April 2009)


Complete the table by rounding off the given numbers to the indicated place values.

Number Tens Hundreds Thousands TenThousands

HundredThousands

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


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.

Lesson 6 Odd and Even Numbers


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.


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 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 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.

______________________________________________


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? _________________________


Belle saw two portraits of beautiful churches in the museum. Which of the two portraits shows an older church?

This table shows the value of the letters used in Roman numerals.

Roman Numerals I V X L C D M

Hindu-Arabic Numerals 1 5 10 50 100 500 1 000

Lesson 7 Roman Numerals

MDCCCLXV

MCMXCIV


Portrait 1

MDCCCLXV = 1 000 + 500 + 300 + 50 + 10 + 5 = 1 865

1000 500 300 50 10 5

Portrait 2

MCMXCIV = 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


More examples:

1. Change to Hindu-Arabic numerals.a. MMCCCLXXII = 2 372b. 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 = MMDCCLXIIb. 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.


A. Write the following in Hindu-Arabic numerals, then in words.

Roman Numeral Hindu-Arabic Numeral Word Form

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. ________________


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 of Whole Numbers

Lesson 1 Properties of Addition

Chapter 2

Study the number sentences Greta, Fred, and Diane are holding.

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

Commutative Property18+17=17+18

Associative Property(21+4)+6=21+(4+6) Identity Property

17 + 0 = 17

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