building number sense: whole numbers
TRANSCRIPT
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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
- Check Your Understanding!..................................................................................... 29
Lesson 3: Rounding Off Numbers to the Nearest Thousand and Ten Thousand
- Warm Up! .................................................................................................................... 30
- Learn about It! ........................................................................................................... 31
- Let’s Practice! ............................................................................................................. 33
- Check Your Understanding!..................................................................................... 37
Lesson 4: Comparing and Ordering Numbers
- Warm Up! .................................................................................................................... 38
- Learn about It! ........................................................................................................... 39
- Let’s Practice! ............................................................................................................. 43
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- Check Your Understanding!..................................................................................... 49
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.
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Table of Contents
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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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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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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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Shown below are the place values of the digits in 146 947.
Hundred
Thousands
Ten
Thousands Thousands Hundreds Tens Ones
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
Thousands Thousands Hundreds Tens Ones
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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Place
Value
Hundred
Thousands
Ten
Thousands Thousands Hundreds Tens Ones
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
Thousands Thousands Hundreds Tens Ones
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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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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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
Thousands Thousands Hundreds Tens Ones
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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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
Thousands Thousands Hundreds Tens Ones
100 000 10 000 1 000 100 10 1
Digits
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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
Thousands Thousands Hundreds Tens Ones
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
Thousands Thousands Hundreds Tens Ones
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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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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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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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
Thousands Thousands Hundreds Tens Ones
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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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
Thousands Thousands Hundreds Tens Ones
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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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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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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b. Expanded form
Step 1: We find the value of each digit of the number.
Place
Value
Hundred
Thousands
Ten
Thousands Thousands Hundreds Tens Ones
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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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
Thousands Thousands Hundreds Tens Ones
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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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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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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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?
Check Your Understanding!
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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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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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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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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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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.
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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
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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
Check Your Understanding!
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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!
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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!
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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.
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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.
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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.
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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!
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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
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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
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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.
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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,
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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
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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.
Check Your Understanding!
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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!
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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.
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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
Thousands Thousands Hundreds Tens Ones
100 000 10 000 1 000 100 10 1
Wrap-up
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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.
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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!
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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
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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