Building Number Sense: Whole Numbers

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STUDY GUIDE

GRADE 4 | UNIT 1

Building Number Sense: Whole Numbers

Table of Contents

Introduction ............................................................................................................................. 3

Test Your Prerequisite Skills ................................................................................................. 4

Objectives .............................................................................................................................. 5

Lesson 1: Place Values of Digits in Whole Numbers

- Warm Up! ...................................................................................................................... 5

- Learn about It! ............................................................................................................. 6

- Let’s Practice! ............................................................................................................... 9

- Check Your Understanding!..................................................................................... 14

Lesson 2: Reading and Writing Numbers up to 100 000

- Warm Up! .................................................................................................................... 16

- Learn about It! ........................................................................................................... 17

- Let’s Practice! ............................................................................................................. 21


Lesson 3: Rounding Off Numbers to the Nearest Thousand and Ten Thousand

- Warm Up! .................................................................................................................... 30

- Learn about It! ........................................................................................................... 31

- Let’s Practice! ............................................................................................................. 33


Lesson 4: Comparing and Ordering Numbers

- Warm Up! .................................................................................................................... 38

- Learn about It! ........................................................................................................... 39

- Let’s Practice! ............................................................................................................. 43


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STUDY GUIDE


Challenge Yourself! .............................................................................................................. 50

Performance Task ................................................................................................................ 50

Wrap-up ............................................................................................................................ 52

Key to Let’s Practice! ............................................................................................................. 54

References ............................................................................................................................ 56


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STUDY GUIDE

GRADE 4 | MATHEMATICS

UNIT 1

Building Number Sense: Whole Numbers In our younger years, we have learned how to count, and our knowledge of

the set of numbers kept expanding as we recognize more patterns. We

became familiar with whole numbers and have used them to represent the

amount or measurement of certain objects around us.

Just like the information that the astronomers gather

using spacecraft from the largest planet in our solar

system, Jupiter: According to NASA Science’s Solar

System Exploration, Jupiter’s diameter is 139 822 km.

That would be 11 times wider than our planet’s

diameter, which is 12 742 km. It is said that if Jupiter

would be the size of a basketball, the Earth will

comparatively take the size of a nickel.

Whole numbers may be considered as building blocks

of more complex concepts in mathematics. It is

important that we know how to read and write such

numbers as they may be tapped into by future

generations who want to explore more of our world.

This unit extends our knowledge of whole numbers to place values such as

hundred thousands, and how they are read, written, ordered, and compared.

Click Home icon to go back to

Table of Contents


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STUDY GUIDE

Before you get started, answer the following items to help you assess your

prior knowledge and practice some skills that you will need in studying the

lessons in this unit.

Fill in the blank with the correct symbol, number, word, or phrase.

1. The place value of 2 in 235 is ________________________.

2. The place value of 5 in 7 953 is ________________________.

3. The place value of 0 in 20 370 are ________________________ and

________________________.

4. Eight thousand and four hundred fifty written as a numeral is

________________________.

5. Two hundred twenty-three in numerals is ________________________.

6. 1 256 rounded off to the nearest hundred is ________________________.

7. 562 rounded off to the nearest ten is ________________________.

8. Write the correct relation symbol (>, <, or =) to make the statement

correct: 5 678 ____ 5 768.

• Giving the Place Value and Value of a Digit in Numbers up to

10 000

• Reading and Writing Numbers Up to Ten Thousand in

Symbols and in Words

• Rounding Numbers to the Nearest Ten and Hundred

• Comparing Numbers Up to 10 000 Using Relation Symbols

• Ordering Numbers Up to 10 000

Test Your Prerequisite Skills


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STUDY GUIDE

9. Between 235 and 2 345, ________________________ is the greater

number.

10. When 54, 45, 51, 65, and 34 are arranged from lowest to highest, the

result is ________________________.

At the end of this unit, you should be able to

• give the place value and value of a digit in numbers up to 100 000;

• read and write numbers up to a hundred thousand in symbols and in

words;

• round off numbers to the nearest thousand and ten thousand;

• compare numbers up to 100 000 using relation symbols; and

• order numbers up to 100 000 in increasing or decreasing order.

Arrange Yourselves

Materials Needed: 5” x 8” illustration

boards, markers

Instructions:

1. The class is to be divided into 5 groups.

Lesson 1: Place Values of Digits in Whole Numbers

Objectives

Warm Up!


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STUDY GUIDE

2. Each member of the group will be given an illustration board where

he or she will write a digit. It is preferred that the members of each

group have different digits.

3. The teacher shall tell the groups to arrange themselves according to

a certain order or form a certain number and at the teacher’s signal,

each group may start rearranging themselves. The following are the

suggested arrangements:

a. Arrange the digits from highest to lowest (or lowest to highest)

b. Create an odd or an even number. This should involve all

members.

c. Form the smallest or highest possible number that can be formed

with the digits in the group.

4. Once the group has finished arranging its members, all members

shall shout their group name.

5. The group that is fastest to arrange themselves correctly for the

most number of times is declared the winner.

There are several patterns of numbers that you can arrange which will result

in a different value. It is very important that you know the difference of each

value to fully understand whole numbers.

For instance, the number 146 947 has 6 digits.

What is the difference between a digit and a number? How do we form numbers?

Learn about It!


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STUDY GUIDE

We count numbers by making use of groupings by 10. We call this the base-

10 numeration system. We only need the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

to represent all numbers.

Start from the ones and notice how the place value is always 10 times bigger

than the place value on its right.

10 groups of

10 000

10 groups of

1 000

10 groups of

100

10 groups of

10

10 groups of

1 1s

100 000 10 000 1 000 100 10 1

Hundred

Thousands

Ten

Thousands Thousands Hundreds Tens Ones

always 10 times bigger than the place value on its right

Definition 1.2: Place value tells the position of each

digit in a given number.

Definition 1.1: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called

digits. They are single numbers combined

to form a numeral.


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STUDY GUIDE

Shown below are the place values of the digits in 146 947.

Hundred

Thousands

Ten


1 4 6 9 4 7

The place value of the digit 6 is thousands.

In any whole number, the digit with the smallest value is the rightmost digit

or the digit in the ones place.

Since the place value of the digit 6 is thousands, its value is 6000. The value

was taken by multiplying 6 by 1000.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 1 4 6 9 4 7

We can use the same chart to find the value of the other digits:

Definition 1.3: Value is the product of the digit

and its place value.

6 000


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STUDY GUIDE

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 1 4 6 9 4 7

Example 1: What is the place value and the value of the digit 8 in 850 243?

Solution: Put each digit in its corresponding place value in the place

value chart.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 8 5 0 2 4 3

The place value of 8 is hundred thousands and its value is 800 000.

Let’s Practice!

6 000 7

40 900 40 000 100 000

800 000


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STUDY GUIDE

Try It Yourself!

What is the place value and the value of the digit 1 in 154 000?

Example 2: How much bigger is 7 in the ten thousands place than 8 in the

thousands place?

Solution: The value of 7 in the ten thousands place is 70 000. The value

of 8 in the thousands place is 8 000.

Get their difference to find the answer.

7 in the ten thousands place is bigger

than 8 in the thousands place by 62 000

units.

Try It Yourself!

How much bigger is 6 in the hundred thousands place than 9 in the tens

place?

Example 3: Write down the largest possible number that can be formed

using the digits 1, 2, 4, 5, 7, and 9 together with the place value

and value of each digit.


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STUDY GUIDE

Solution:

Step 1: Arrange the numbers from highest to lowest: 9, 7, 5, 4, 2, and 1.

Step 2: Write each digit in the table below following its order from

highest to lowest.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 9 7 5 4 2 1

Step 3: The place value of 9 is hundred thousands. Its value is 900 000.

The place value of 7 is ten thousands and its value is 70 000.

The place value of 5 is thousands and its value is 5 000.

The place value of 4 is hundreds and its value is 400.

The place value of 2 is tens and its value is 20.

The place value of 1 is ones and its value is 1.

Try It Yourself!

Write the lowest possible number that can be formed using the digits 5,

7, 4, 1, 2, and 3 together with the place value and value of each digit.


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STUDY GUIDE

Real-World Problems

Example 4: Beatrice’s mother is having trouble in

remembering the password in her

ATM card. She wants to help her

mother recall the password by asking

some descriptions of the number.

These are the facts her mother

recalls:

1. The password has 6 digits.

2. The first four digits to the left is the birth month and day of

Beatrice. (Beatrice was born on 30 November 2008.)

3. The next two digits represent the day of her parent’s

wedding which is on 14 September 2005.

Solution: Beatrice can use a table to determine the digits of the

password based on the clues. It is important to know the

position of each digit in the number.

Clue 1: Since the password is a 6-digit number, this means the place

value of the first digit to the left is hundred thousands.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits


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STUDY GUIDE

Clue 2: The second clue tells the digits positioned from hundred

thousands to hundreds. Beatrice’s birth date is 30 November

2008. Her birth month in numerals is 11 and the day is 30. This

means that the digits in hundred thousands, ten thousands,

thousands, and hundreds place, respectively, are 1, 1, 3, and 0.

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

1 1 3 0

Clue 3: The last two digits which are located in the tens and ones place

values form the day of Beatrice’s parent wedding which is 14.

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

1 1 3 0 1 4

Thus, the password of Beatrice’s mother in her ATM card is 113014.


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STUDY GUIDE

Try It Yourself!

Michelle typed a five-digit number on her tablet.

She gave her friends four clues to determine

the number. What number is it based on these

clues?

a. The highest place value, the hundreds place

value, and the ones place value all have the

same digit.

b. The tens place value is one less than thousands place value.

c. The hundreds place value is 9 greater than the tens place.

d. The ones place value is 9.

1. Identify the place value and value of the digit 9 in each of the following

numerals.

a. 204 869 b. 947 245 c. 395 205

2. Use the table provided on the next page to identify the municipality in

the province of Rizal with the given population.

a. Its population has a 6 in the ten thousands place.

b. Its population has the digit 3 with a value of 30 000.

Check Your Understanding!

XX XX9


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STUDY GUIDE

c. Its population has the digit 4 in the ones place, and a digit 2 in the

thousands place.

Top 5 Municipalities Population1 in 2015

(Source: Philippine Statistics Authority)

Municipality Population

Rodriguez (Montalban) 369,222

Cainta 332,128

Taytay 319,104

Binangonan 282,474

Santa Maria 256,454

3. Jason wrote down a three-digit number and dared the class to guess

what it was. See if you can guess the number. He gave them a few

clues as follows:

a. The digit in the hundreds place is 8 greater than the digit in the

ones place.

b. The sum of all the digits in the three place values is 15.

c. The digit in the ones place is 1.

1 Source: Philippine Statistics Authority


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STUDY GUIDE

Fill It Up!

Materials Needed: 1 whole white cartolina, markers

Instructions:

1. The class shall be divided into groups of 4 or 5.

2. Each group shall copy the format shown in the following deposit slip

onto the cartolina. They are to fill up the entire space of the cartolina.

Lesson 2: Reading and Writing Numbers up to 100 000

Warm Up!


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STUDY GUIDE

3. Using the given details below, each group will fill out the improvised

deposit slip with the correct entries.

• Cash: One thousand pieces of 500-peso bills

Two hundred pieces of 100-peso bills

• Date: 01/08/2018

• Account Number: 110 222 3456

• Account Name: Juan dela Cruz

4. The groups shall then compare their outputs with the rest of the class.

Patrick purchased a house and needs to issue a check worth ₱154,678 as

down payment. How will he write the amount in words?

Learn about It!


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STUDY GUIDE

How do we write numbers in words?

In the previous lesson, you learned about place values. We can place the

number 154 678 in the place value chart as shown below.

Hundred

Thousands

Ten


1 5 4 6 7 8

Did you notice how numbers with more than three digits always have a

comma or a space in between the sets of three digits?

This grouping is called a period.

The first period is called the ones period. It is formed with the first three

digits of the number. The second period, called the thousands period is

formed with the next three digits of the number.

Period Thousands Ones

Place Value Hundreds Tens Ones Hundreds Tens Ones

Digits 1 5 4 6 7 8

Definition 2.1: Periods are the sets of three digits

into which numerals are grouped.


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STUDY GUIDE

Reading and Writing Numbers in Words

Step 1: Group the number into three digits starting from the right and put

a space in between. This is to separate the numbers by class or

period.

Step 2: From the left, read the number per group just like reading a three-

digit number, then include the period name.

"154" is "read as one hundred fifty-four thousand."

"678" is read as "six hundred seventy-eight”.

Take note that in the last group, we do not include the period name ones.

Therefore, 154 678 is written in words as one hundred fifty-four thousand,

six hundred seventy-eight.


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STUDY GUIDE

Writing numbers in words is useful when filling out checks, deposit slips,

receipts, and many more.

The table below shows the correct spelling of numbers in words. These are

the number words you need to be familiar with. Other number words are

just a combination of these words.

Note that you need to use a hyphen (-) between words for numbers like forty-

eight, eighty-two, twenty-five, and the like.

Writing Numbers in Standard and Expanded Forms

So far, you have learned how to read and write numbers in words.

154 678 is in standard form, while one hundred fifty-four thousand, six

hundred seventy-eight is in word form.


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STUDY GUIDE

Notice how we can expand 154 678 into

100 000 + 50 000 + 4 000 + 60 + 70 + 8.

What do you notice about how they are expanded? Aside from its standard

and word forms, we can represent numbers using its expanded form.

Example 1: Write 146 947 in expanded form.

Solution: To write a number in expanded form, we simply find the sum

of all the values of its digits.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 1 4 6 9 4 7

Therefore, 146 947 in expanded form is

100 000 + 40 000 + 6 000 + 900 + 40 + 7.

Definition 2.2: The expanded form of a number is written

as the sum of all the values of its digits.

Let’s Practice!

6 000 7

40 900 40 000 100 000 value


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STUDY GUIDE

Try It Yourself!

Write 542 343 in expanded form.

Example 2: Express 685 002 in word form.

Solution:

Step 1: Group the number into three digits starting from the right.

Step 2: Write in words the number per group just like writing a three-digit

number, then include the period name except for the last group.

Thus, 685 002 in words is six hundred eighty-five thousand two.

Note: Hyphenate all compound numbers from twenty-one to

ninety-nine.


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STUDY GUIDE

Try It Yourself!

Write 567 230 in word form.

Example 3: Express nine hundred forty-nine thousand three hundred sixty-

seven in (a) standard form and (b) expanded form.

Solution:

a. Standard form

Step 1: We first identify the digits for the thousands period.

“nine hundred forty-nine thousand” means that 949 are the

digits in the hundred thousands, ten thousands, and thousands

place values.

949 __ __ __

Step 2: We identify the digits for the ones period.

“three hundred sixty-seven” means that 367 are the digits in

the hundreds, tens, and ones place values.

949 367

Thus, nine hundred forty-nine thousand three hundred sixty-seven

in standard form is 949 367.


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STUDY GUIDE

b. Expanded form

Step 1: We find the value of each digit of the number.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 9 4 9 3 6 7

Thus, nine hundred forty-nine thousand three hundred sixty-seven

in expanded form is 900 000 + 40 000 + 9 000 + 300 + 60 + 7.

Try It Yourself!

Express one hundred twenty-six thousand and four hundred thirty-five in

standard and expanded forms.

Real-World Problems

Example 4: Kenny will put his earnings from his business in the bank. He

needs to fill out the required information in the deposit slip

that looks like the following:

9 000 7

60 300 40 000 900 000 value


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STUDY GUIDE

To make sure that he brought an accurate amount of cash, he

wants to write the details before he go to the bank. He will use

the table below for his notes.

Word form Standard form Expanded form

If Kenny has one hundred 1000-peso bills and five 500 bills,

what he will write in the table? What will he write on the right

portion of the deposit slip?

Solution:

One hundred 1000 bills and five 500 bills are equivalent to

100 × 1000 = 100 000 and 5 × 500 = 2 500

100 000 + 2 500 = 102 500


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STUDY GUIDE

To write 102 500 in words, we group the digits according to

period and read each period as we would read any three-digit

number, mentioning the period name, except for the last:

102 500

one hundred two thousand

102 500

five hundred

102 500 in words is one hundred two thousand five

hundred.

To find its expanded form, we write it as a sum of the values of

its digits.

Place

Value

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Digits 1 0 2 5 0 0

Thus, the expanded form is 100 000 + 2 000 + 500.

2 000 0

0 500 0 100 000 value


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STUDY GUIDE

Here are what Kevin should put in his notes:

Word form Standard form Expanded form

one hundred two

thousand five

hundred

102 500 100 000 + 2 000 + 500

The following shows how he is to fill out the right side of the

deposit slip:

Note: In the first column, he is to write the denomination or the value

of the bill; in the second column, he is to write the number of

pieces; and in the third column, the amount is obtained by

multiplying the value of the bill to the number of pieces.


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STUDY GUIDE

Try It Yourself!

Kenny will buy a second-hand pickup truck for his business. He already

met the seller and is about to close the deal with an amount of ₱255

500. He will deposit the amount in the bank and will pay using a

manager’s check.

What should she write in the highlighted boxes of the manager’s check

below?


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STUDY GUIDE

1. Complete the table below.

Standard Form Expanded Form Word Form

10 235

21 988

one hundred eighty-

nine thousand fifty

900 000 +40 000 + 700 +2

2. Container vans being transformed into restaurants have grown some

popularity in Mr. Dionisio’s vicinity. He decided to purchase one to

house a new branch for his snow ice cream business. The container van

costs ₱199,999 and Mr. Dionisio issued a check for the purchase. How

should he write the amount in words?



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STUDY GUIDE

Roll – Round – Solve!

Materials Needed: die, paper, pen

Instructions:

1. Each student has to find a partner, and both

will serve as the two players.

2. The two shall agree who shall roll the die

first.

3. The first player shall roll the die 4 times to form a 4-digit number.

4. Both players shall record the number in their own tables and round

it to the nearest ten, nearest hundred, and nearest thousand.

5. The second player shall also roll the die 4 times to form a four-digit

number.

6. Both players shall again record the number in their own tables and

round it to the nearest ten, hundred, and thousand.

7. Both players are then going to find the sum of the two numbers and

also round it to the nearest ten, hundred, and thousand.

8. Lastly, the two players shall compare if they got the same answers

for all cells in the table.

Lesson 3: Rounding Off Numbers to the Nearest

Thousand and Ten Thousand

Warm Up!


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STUDY GUIDE

This is the table that each of the players may use:

Player Actual

Number

Nearest

Ten

Nearest

Hundred

Nearest

Thousand

1

2

Sum

The distance from Manila to London is 10 728

kilometers or about 11 000 kilometers.

11 000 is a rounded number. Rounded numbers

tell us about how many.

How do we round off numbers?

Look at the number 10 728 below.

10 784 is between 10 000 and 11 000 but is closer to 11 000 than to 10 000.

We can say that 10 784 rounded off to the nearest thousand is 11 000. It is

approximately equal to 11 000.

Learn about It!


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STUDY GUIDE

There is another way to round off numbers aside from using the number

line.

Steps in Rounding Off Numbers

Step 1: Determine which digit is to be rounded off. Then, look at the digit to

its right.

In 10 728, the thousands digit is 0 and the digit to the right of 0 is 7.

Step 2: Round off the number using the following rules:

• If the digit to the right of the digit to be rounded off is below 5

(0, 1, 2, 3, or 4), then the digit to be rounded off remains the

same.

• If the digit on the right of the digit to be rounded off is 5 or above

(5, 6, 7, 8, or 9), then the digit to be rounded off is increased by

one.

Since 7 is more than 5, we increase 0 by one.


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STUDY GUIDE

Step 3: Change the digits to its right to zero.

Thus, 10 728 rounded to the nearest thousands is 11 000.

Example 1: Round off 197 243 to the nearest thousands.

Solution:

Step 1: Determine which digit is to be rounded off. Then, look at the

digit to its right.

In 197 243, the thousands digit is 7 and the digit to its right is 2.

Step 2: Round off the number using the rules mentioned in the

discussion:

Since 2 is less than 5, 7 will remain the same.

Let’s Practice!


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STUDY GUIDE

Step 3: Change the digits to its right to zero.

1 9 7 0 0 0

Thus, 197 243 rounded to the nearest thousands is 197 000.

Try It Yourself!

Round off 256 543 to the nearest thousands.

Example 2: Identify the place value to which 234 789 is to be rounded off

to become 200 000.

Solution: Working backwards, we check the digit directly to the left of all

the zeros. It is the digit 2 in the hundred thousands place. Most

likely, it is in this place value that the number was rounded off.

We can check by rounding off 234 789 to the nearest hundred

thousand. The digit directly to the right of the digit on the

hundred thousands place is 3. Since 3 is less than 5, the digit 2

stays the same, and all digits to the right are changed to zero.

This gives the answer of 200 000.

Thus, the place value to which it is to be rounded off is indeed

the hundred thousands place value.


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STUDY GUIDE

Try It Yourself!

Determine the place value to which 756 465 is to be rounded off to

become 760 000.

Example 3: Write the least and the greatest whole number that becomes

420 000 when rounded off to the nearest ten thousand.

Solution: Since the round-off place is the ten thousands place, we can

think of the possible digits to its right such that the digit 2

remains unchanged or the digit 2 is the result of adding 1.

1. The greatest possible digit to the right of 2 such that the

digit 2 remains unchanged is 4.

2. The least possible digit to the right of the digit 2 such that

the digit 2 becomes the result of adding 1 is 5.

Therefore, the greatest possible number that rounds off to 420

000 is 424 999 and the least possible number is 415 000.

Try It Yourself!

Write the least and the greatest whole number that becomes 600 000

when rounded off to the nearest hundred thousand.


36

STUDY GUIDE

Real-World Problems

Example 4: Nina wanted to buy a laptop for her

new work as a writer in a publishing

company. She considered the

COMTECH brand for her laptop. The

price shown in COMTECH’s website

was ₱15,399. But Nina wants to see

the laptop in person to check and see the actual specifications.

She decided to buy the laptop from its physical store in the

mall. It was mentioned that the price in the website might not

be updated and may differ from the price in the physical store.

Customers are advised to consider the whole range of possible

prices that round off to the same value when rounded to the

highest place value.

If Nina will base on the price indicated in the website, what is

the range of the possible prices of the laptop that Nina needs

to consider?

Solution:

By rounding off to the highest place value (the ten thousands

place), 15 399 becomes 20 000. This means 15 399 is only one

of the possible values from the range Nina needs to consider.

If 20 000 is the rounded off value, 2 could have resulted from

an addition of 1 in the ten thousands place if the digit to the

₱15,399


37

STUDY GUIDE

right is 5 or more, or it could have been retained if the digit to

the right is 4 or less.

Thus, the range of prices Nina needs to consider is ₱15 000 up

to ₱24 999.

Try It Yourself!

Aling Lucita is creating a budget list for her

family expenses in a month. She has recalled

spending ₱15 268 for their expenses last

month and almost the same in the previous

months. What could be the possible range of

amounts that Aling Lucita must allot for their

next monthly expenses so she does not allot

too much nor become short on her budget? Assume that the money

should not exceed to ₱20 000.

1. Round off 28 495 to the nearest

a. ten thousand

b. thousand

c. ten



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STUDY GUIDE

2. Determine the place value to round off to if

a. 10 361 becomes 10 000

b. 211 432 becomes 211 000

c. 562 112 becomes 600 000

3. What are the lowest and highest values that becomes 270 000 when

rounded to the nearest ten thousand?

4. Audrey goes home to the province via airplane to see her nephew.

The plane’s pilot announces during the flight that they have reached

a height of around 39 000 feet. If the altitude was rounded off to the

nearest thousand, what is the range of possible heights of the plane?

Search for the Firstborn

Materials Needed: board, chalk or marker

Instructions:

1. The whole class is to participate in this activity.

2. Each student shall write his or her name. Beside the name, the

student shall write his or her birthday (with month, day, and year).

Lesson 4: Comparing and Ordering Numbers

Warm Up!


39

STUDY GUIDE

3. The whole class are to work together to arrange the members of the

class in order of birthday. They can start arranging them by year, then

by month, then by day.

4. The aim of the whole class is to identify the person who was born first

among all.

In 2016, the Philippine Statistics Authority reported the total land area of the

following regions.

Which region is bigger, Northern Mindanao or Central Mindanao? Which of

the given regions has the smallest land area? Which region has the largest

land area?

How do we compare the measures of the areas?

Learn about It!


40

STUDY GUIDE

Relation Symbols

For example, 782 > 728 is read as “seven hundred eighty-two is greater than

seven hundred twenty-eight.”

For example, 101 < 110 is read as “one hundred one is less than one hundred

ten.”

Comparing Numbers

1. Compare the number of digits. The number with the higher number of

digits has a higher value.

Definition 4.3: The symbol for equal to is =. It is used

when both numbers have the same value.

Definition 4.2: The “less than” symbol < is used when

the number on the left has a lower value

than the number on the right.

Definition 4.1: The “greater than” symbol > is used when

the number on the left has a higher value

than the number on the right.


41

STUDY GUIDE

Since 23 957 is a whole number and has more digits than 2630,

23 957 is greater than 2630.

2. Compare the digits with the same place value from left to right. If the

digits are the same, move to the next place value.

Comparing the digits in the tens place, we can see that 8 has a lower

value than 9. So, 9385 < 9394.

Ordering Numbers

Ascending order is the same as increasing order.

To arrange the numbers 56 468, 25 362, 28 362, 45 565, and 45 537 in

ascending order, simply compare the numbers and list them from least to

greatest.

1. Compare the number of digits. All numbers are whole numbers and have

the same number of digits.

Definition 4.4: Ascending order means arranging

numbers from least to greatest.


42

STUDY GUIDE

2. Compare the digits of the same place value from left to right. You may list

the numbers down vertically.

56 468

25 362

28 362

45 565

45 537

Since 25 362 and 28 362 have the same digits in the ten thousands

place, we look at the digits in the thousands place.

56 468

25 362

28 362

46 565

45 537

Therefore, the first two numbers are 25 362, 28 362. Repeat the steps for

the rest of the numbers and we come up with the following order:

25 362, 28 362, 45 537, 45 565, and 56 468

Descending order is the same as decreasing order.

Definition 4.4: Descending order means arranging

the numbers from greatest to least.


43

STUDY GUIDE

To arrange the numbers 36 521, 3636, 42 424, 98 999, and 99 000 in

descending order, simply compare the numbers two at a time and list them

from greatest to least.

99 000, 98 999, 42 424, 36 521, 3636

Example 1: What is the correct relation symbol to put between the given

numbers?

204 560 ____ 200 967

Solution: Since the first two digits from left to right are the same, we will

compare the value of the third digit

204 560 ____ 200 967

4 is greater than 0. Thus, 204 560 > 200 967.

Try It Yourself!

What is the correct relation symbol in 802 370 ____ 812 370.

Let’s Practice!


44

STUDY GUIDE

Example 2: Arrange the following numbers in ascending order:

102 365, 120 250, 102 065, 99 065, 120 520

Solution:

Step 1: Compare the number of digits. Those with a smaller number of

digits are smaller in value.

99 065

102 365

120 250

102 065

120 520

Step 2: Compare the digits of the same place value from left to right.

99 065

102 365

102 065

120 250

120 520

Therefore, the numbers arranged in ascending order are as

follows:

99 065, 102 065, 102 365, 120 250, 120 520


45

STUDY GUIDE

Try It Yourself!

Arrange the following numbers in descending order:

415 015, 120 567, 405 670, 210 690, 112 067

Example 3: Write the possible digits in the blank that make the statement

true.

13 ___ 65 < 13 132

Solution: Since the first two digits are the same, we compare the third

digit from the left of both numbers. The third digit of 13 132 is

1.

Therefore, the possible digits that we can use to make the

statement true are digits less than 1. Therefore, the only

possible digit is 0.

Try It Yourself!

Write the possible digit in the blank that make the statement true:

1_4 520 < 194 520


46

STUDY GUIDE

Real-World Problems

Example 4: The table below shows the total land area of four regions in the

Philippines.

a. Which region is larger, Northern Mindanao or Central

Mindanao?

b. Arrange the given numbers in descending order.

Solution:

a. Since both areas have the same first and second digits from

the left, we compare the third digit.

Since 3 > 0, Central Mindanao has a larger land area than

Northern Mindanao.


47

STUDY GUIDE

b. Descending order means ordering the numbers from greatest

to least. Central Luzon, Northern and Central Mindanao have

the same number of digits, while the National Capital Region

has the least number of digits. Therefore, we put 63 600 at the

bottom.

Starting from the left, Central Luzon’s area starts with the digit

2 while the rest start with the digit 1. We can put 2 147 036 at

the top of the list. Therefore,


48

STUDY GUIDE

Try It Yourself!

The following are the diameters of the

planets in our solar system2. Arrange them

in descending order.

2 Source: NASA Science Solar System Exploration

Planet Diameter (km)

Earth 12 742

Jupiter 139 822

Mars 6 779

Mercury 4 879

Neptune 49 244

Saturn 116 464

Uranus 50 724

Venus 12 104


49

STUDY GUIDE

1. Fill in the blank with the correct relation symbol.

100 834 ______ 100 843

2. Arrange the following numbers in ascending order:

720 525

702 524

703 525

730 524

3. Arrange the following numbers in descending order:

350 641

305 468

306 641

360 468

4. Write in the blank all the possible digits that make the statement true.

73 566 > ___1 999

5. Chris browses an online catalog of different models of professional

camera. He was also considering a budget; thus, he needs to arrange

his options according to the prices of the camera as follows:

₱24 800

₱20 900

₱20 150

₱26 712

₱20 600

Arrange the prices in increasing order.



50

STUDY GUIDE

1. Roll a die three times to obtain three digits. Then list all the numbers

you can form using the digits. Arrange the numbers in ascending and

descending order.

2. Which is quicker, counting up to 50 in ones or counting up to 500 in

tens? Why?

3. Is it possible that when you round off a number, the result has more

digits than the original number? If your answer is yes, cite an example.

You are a financial analyst and your first clients are your parents. Interview

your parents about the monthly expenses of your family. Trace back your

expenses in the previous 12 months, if possible. Record these using the table

below.

Name of the Client:

Number of members in the family:

Month Monthly Expenses Description

Example:

January

P15, 265

Utility bills (Electricity,

water, etc.),

Food and other

supplies

Performance Task

Challenge Yourself!


51

STUDY GUIDE

1. Arrange the values of the monthly expenses in ascending order.

2. After writing the required information, answer the following questions:

a. On what month did your family incur the lowest expenses? What

could have been the reason?

b. On what month did your family incur the highest expenses? What

could have been the reason?

c. Estimate the amount of your monthly expenses.

i. Around how much was the least possible monthly expense that

your family incurred?

ii. Around how much were the highest monthly expenses that your

family incurred?

d. What can each family member contribute to lessen the family’s

expenses?

Ask someone from your family to record you while you read the answers to

these questions in front of your family and send the video via USB or email to

your teacher.

Performance Task Rubric

Criteria

Below

Expectation

(0–49%)

Needs

Improvement

(50–74%)

Successful

Performance

(75–99%)

Exemplary

Performance

(99+%)

Completeness

and Reliability

of Information

A significant

amount of

information is

missing.

The information

provided in the

report is

complete but

unreliable.

The

information

provided in the

report is

complete and

reliable.

The information

provided is

complete and

reliable, and has

a clear basis.


52

STUDY GUIDE

Accuracy of

Computation

and Analysis of

Data

There are a

significant

number of

errors in

computations

that lead to

wrong analysis

of data.

There are a few

errors in the

computation but

there is no clear

basis in the

analysis of data.

All

computations

are correct and

the data are

analyzed

properly.

All computations

are correct with

complete

solution. The

data are

analyzed with

clear basis.

Organization

and delivery

Majority of the

content of the

video is not

aligned to the

given questions.

Delivery was

unclear for a

huge portion of

the report.

Some content of

the video is not

aligned to the

given questions.

Delivery was

unclear for a few

portions of the

report.

The content of

the video is

aligned with the

given

questions.

Delivery of the

report was

clear.

The content of

the video is

aligned with the

given questions

and with added

information.

Delivery of the

report was clear.

Place Value of Numbers Up to 100 000

Hundred

Thousands

Ten


100 000 10 000 1 000 100 10 1

Wrap-up


53

STUDY GUIDE

Ways to Write Numbers

in words in standard form in expanded form

Relation Symbols

> (is greater than) = (is equal to) < (is less than)

Key Terms & Formulas

Terms Description

Place value and

value

Place value tells the position of each digit in a

given number. The value of a digit is the product

of the digit and its place value.

Rounding off Whole

Numbers

To round off numbers,

1. Identify the digit to be rounded off. Then,

look at the digit to its right.

2. Follow the rule:

If it is below 5, retain the digit in the round

off place. If it is 5 or above, add 1 to the

digit in the round off place.

3. Then change all the digits to the right of the

round off place to zeros.


54

STUDY GUIDE

Ascending and

Descending Order

Ascending order is another term for increasing

order. Descending order means arranging the

numbers from greatest to least.

Comparing and

Ordering Numbers

If the number of digits is the same, compare the

digits in each place value starting from the left.

Lesson 1

1. The place value is hundred thousand and the value is 100 000.

2. by 599 910 units

3. 123, 457

The place value of 1 is hundred thousands and its value is 100 000.

The place value of 2 is ten thousands and its value is 20 000.

The place value of 3 is thousands and its value is 3 000.

The place value of 4 is hundreds and its value is 400.

The place value of 5 is tens and its value is 50.

The place value of 7 is ones and its value is 7.

4. 91 909

Lesson 2

1. 542 343 = 500 000 + 40 000 + 2 000 + 300 + 40 + 3

2. 567 230 = five hundred sixty-seven thousand two hundred thirty

3. one hundred twenty-six thousand four hundred thirty-five = 126 435

= 100 000 + 20 000 + 6 000 + 400 + 30 + 5

Key to Let’s Practice!


55

STUDY GUIDE

4. In the box beside ₱ on the upper right corner: 255 500

In the box beside “PESOS”: two hundred fifty-five thousand five hundred

only

Lesson 3

1. 257 000

2. Ten thousand

3. The greatest possible number is 649 999 and the least is 550 000.

4. ₱15 000 to ₱20 000

Lesson 4

1. <

2. 415 015, 405 670, 210 690, 120 567, 112 067

3. 0 to 8

4.

Planet Diameter (km)

Jupiter 139 822

Saturn 116 464

Uranus 50 724

Neptune 49 244

Earth 12 742

Venus 12 104

Mars 6 779

Mercury 4 879


56

STUDY GUIDE

Dela Cruz, Eduardo, Jr., et al. Soaring 21st Century Mathematics: Grade 4 K to

12. Philippines: Phoenix Publishing House, Inc., 2015

Solar System Exploration NASA Science. ”Planets.” Accessed January 7, 2018.

https://solarsystem.nasa.gov/planets/

Tabilang, Alma, et al. Mathematics – Grade 4 Learner’s Material. 1st ed.

Philippines: Lexicon Press, Inc., 2015

References

Documents

Building Number Sense: Whole Numbers