New Mathematics Connection P.1-P.6 sample chapter (update)

(b) 302

Hundreds Tens Ones
3 0 2

Number in words: Three hundred and two
Expanded form: 300 + 0 + 2

(c) 960

Hundreds Tens Ones
9 6 0

Number in words: Nine hundred and sixty
Expanded form: 900 + 6 + 0

Try It

1. Write the following numbers in the expanded form.

(a) 291 = (f) 798 =

(b) 847 = (g) 623 =

(c) 913 = (h) 462 =

(d) 389 = (i) 928 =

(e) 522 = (j) 784 =

Go to Exercise 4

New Mathematics Connection 19

E Number Patterns

Increasing Patterns
Pattern of 5

+5

0 5 10 15 20 25 30 35 40 45 50

From left to right, the next number is obtained by adding 5.
Note that in this pattern, the difference between any two consecutive
numbers is 5.
Pattern of 10

+10

0 10 20 30 40 50 60 70 80 90 100

From left to right, the next number is obtained by adding 10.
Note that in this pattern, the difference between any two consecutive
numbers is 10.

20 Chapter 1 Numbers up to 1,000

Pattern of 100

+100

0 100 200 300 400 500 600 700 800 900 1000

From left to right, the next number is obtained by adding 100.
Note that in this pattern, the difference between any two consecutive
numbers is 100.

Example 7

Recognise the pattern and find the next number.

+5

36 41 46 51 56 61 66

From left to right, the next number is obtained by adding 5.
So, the next number in this pattern is 66 + 5 = 71.
Answer: The next number is 71.

New Mathematics Connection 21

Decreasing Patterns
Pattern of 2

–2

0 2 4 6 8 10 12 14 16 18 20

From right to left, the next number is obtained by subtracting 2 from the
previous number.
Note that in this pattern, the difference between any two consecutive
numbers is 2.
Pattern of 10

–10

0 10 20 30 40 50 60 70 80 90 100

From right to left, the next number is obtained by subtracting 10 from the
previous number.
Note that in this pattern, the difference between any two consecutive
numbers is 10.

22 Chapter 1 Numbers up to 1,000

Pattern of 100

–100

0 100 200 300 400 500 600 700 800 900 1000

From right to left, the next number is obtained by subtracting 100 from the
previous number.
Note that in this pattern, the difference between any two consecutive
numbers is 100.

Example 8

Recognise the pattern and find the next number.

–2

127 129 131 133

From right to left, the next number is obtained by subtracting 2 from the
previous number.
So, the next number in this pattern is 127 – 2 = 125.
Answer: The next number is 125.

New Mathematics Connection 23

Try It

1. Complete the number pattern.

(a) 905, 910, 915, , ,

(b) 333, 433, 533, , ,

(c) 101, 111, 121, , ,

(d) 760, 750, 740, , ,

2. Fill in the blanks.
(a) +10 +10 +10 +10 +10

20

(b) +5 +5 +5 +5 +5

400

(c) -2 -2 -2 -2 -2

825

(d) -100 -100 -100 -100 -100

855

(e) +50 +50 +50 +50 +50

600 Go to Exercise 5

24 Chapter 1 Numbers up to 1,000

F Odd and Even Numbers

Numbers are grouped into odd numbers and even numbers.

Odd Numbers

Let us put the balls into groups of twos.

1 ball cannot be grouped into twos.

3 balls can be grouped into 1 group of twos with 1 ball left.

5 balls can be grouped into 2 groups of twos with 1 ball left.

7 balls can be grouped into 3 groups of twos with 1 ball left.

9 balls can be grouped into 4 groups of twos with 1 ball left. 25
Therefore, the amount of balls that can be grouped into groups of twos
with 1 ball left are 1,3,5,7,9.These numbers are called ‘odd numbers’.
The numbers whose ones place is 1, 3, 5, 7 or 9 are called odd numbers.

Example 9

Odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...

New Mathematics Connection

Even Numbers

Let us put the flowers into groups of twos.

2 flowers can be grouped into 1 group of twos with no flowers left.

4 flowers can be grouped into 2 groups of twos with no flowers left.

6 flowers can be grouped into 3 groups of twos with no flowers left.

8 flowers can be grouped into 4 groups of twos with no flowers left.

10 flowers can be grouped into 5 group of twos with no flowers left.
Therefore, the amount of flowers that can be put into groups of twos with
no flowers left are 2,4,6,8,10.These numbers are called ‘even numbers’.
The numbers whose ones place is 0, 2, 4, 6, or 8 are called even numbers.

Example 10

Even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22...

26 Chapter 1 Numbers up to 1,000

Try It

1. Write whether the following numbers are odd or even.

(a) 192 (b) 487

(c) 319 (d) 720

(e) 252 (f) 555

(g) 798 (h) 630

(i) 437 (j) 901

2. Fill in the blanks with odd or even.

(a)

There are 7 ice creams cones.

7 is an number.

(b)

There are 16 eggs.

16 is an number.

New Mathematics Connection 27

(c)

There are 6 cars.

6 is an number.

(d)

There are 5 boats.

5 is an number.

(e)

There are 4 teddy bears.

4 is an number.

(f)

There are 11 hats.

11 is an number. Go to Exercise 6

28 Chapter 1 Numbers up to 1,000

G Comparing Numbers

The sign > represents greater than.
The sign < represents smaller than.
The sign = represents is equal to.
The sign ≠ represents not equal to.

Example 11

Compare the following numbers.
(a) 232 and 456

Step 1: Both numbers are 3-digit numbers.
Step 2: Comparing the digits in the hundreds place, 4 is

greater than 2.

Therefore, 456 is greater than 232 or 232 is smaller than 456.
Answer: 456 > 232 or 232 < 456

(b) 497 and 449

Step 1: Both numbers are 3-digit numbers.
Step 2: Comparing the digits in the hundreds place, both

digits are the same.
Step 3: Comparing the digits in the tens place, 9 is greater

than 4.

Therefore, 497 is greater than 449 or 449 is smaller than 497.
Answer: 457 > 449 or 449 < 457

New Mathematics Connection 29

(c) 861 and 867

Step 1: Both numbers are 3-digit numbers.

Step 2: Comparing the digits in the hundreds place, both
digits are the same.

Step 3: Comparing the digits in the tens place, both digits
are the same.

Step 4: Comparing the digits in the ones place, 7 is greater
than 1.

Therefore, 867 is greater than 861 or 861 is smaller than 867.
Answer: 867 > 861 or 861 < 867

Try It

1. Fill in the boxes with > or < signs.

(a) 256 178 (b) 317 221 (c) 921 931

(d) 711 710 (e) 118 181 (f) 465 466

2. Fill in the boxes with = or ≠ signs.

(a) 634 634 (b) 781 718 (c) 491 941
835 (f) 365 356
(d) 832 832 (e) 825

Go to Exercise 7

30 Chapter 1 Numbers up to 1,000

H Ordering Numbers

If the numbers are arranged from the greatest to the smallest, it is in
decreasing order. If the numbers are arranged from the smallest to the
greatest, it is in increasing order.

Example 12

Arrange these numbers in decreasing and increasing order.
541, 587, 692, 543

Hundreds Tens Ones

5 4 1
5 8 7
6 9 2
5 4 3

Step 1: All the 4 numbers are 3-digit numbers.

Step 2: Comparing the digits in the hundreds place, the
number 692 is the greatest.

Step 3: Comparing the digits in the tens place, the number
587 is the greatest among the remaining 3 numbers.

Step 4: Comparing the digits in the ones place, the number
543 is the greatest between the 2 remaining numbers.

Arranging the numbers in decreasing order:
692 > 587 > 543 > 541

Arranging the numbers in increasing order:
541 < 543 < 587 < 692

New Mathematics Connection 31

Try It

1. Order the following numbers in increasing order.
(a) 417, 513, 912, 217

(b) , , ,

(c) 657, 321, 897, 654

(d) ,, ,

2. Order the following numbers in decreasing order.
(a) , , ,

(b) 727, 852, 963, 429

(c) , , ,

(d) 847, 942, 367, 453 Go to Exercise 8

32 Chapter 1 Numbers up to 1,000



Contents

1 Numbers: Up to 100,000 1
7
CHAPTER A Place Values
B Reading and Writing Arabic and 13
15
Thai Numerals up to 100,000 19
C Number Patterns 20
D Repeated Patterns
E Comparing and Ordering Numbers 22
24
2 Addition and Subtraction within 100,000 26

CHAPTER A Adding Two Numbers up to 100,000 28
B Subtracting Two Numbers up to 100,000 30
C Adding and Subtracting Two Numbers 31

up to 100,000 Mentally 34
D Mixed Equation 35
E Solving Word Problems
F Word Problems Involving Addition and

Subtraction
G Creating Word Problems

3 Multiplication 37

CHAPTER A Multiplying 3-Digit or 4-Digit Numbers By

1-Digit Number without Renaming 39

B Multiplying 3-Digit or 4-Digit Numbers By

1-Digit Number with Renaming 42

C Multiplying 2-Digit Numbers by 2-Digit Numbers 44

D Solve Word Problems Involving Multiplication

by 1-Digit Number 45

E Solve Word Problems Involving Multiplication

by 2-Digit Numbers 47

F Check that Answers are Reasonable 49

G Create Word Problems by Using Your Own Words 50

4 Division 52

CHAPTER A Showing Relationship between 53
Multiplication and Division 54

B Long Division 56
C Dividing 3-Digit or 4-Digit Numbers by
57
1-Digit Number without Remainder 59
D Dividing 3-Digit or 4-Digit Numbers By 60

1-Digit Number with Remainder
E Solve Word Problems Involving Division
F Check that Answers are Reasonable

5 Mixed Operations and Word Problems 62

CHAPTER A Solving Word Problems Involving Addition, 63
Subtraction, Multiplication and Division
64
B Writing Mixed Sentence and Finding 65
Short Answer from the Given Questions
67
C Check that Answers are Reasonable
69
6 Fractions 70
71
CHAPTER A Fractions that the Numerator is less than or
equal to the Denominator 72

B Compare and Arrange Sequence of Fractions 73
C Addition and Subtraction of Fractions 74
D Solving Word Problems on Addition and 75
77
Substation of Fraction 79
81
7 Money

CHAPTER A Expressing Money in Baht and Satang
B Addition and Subtraction of Money
C Solving Word Problems
D Read Income and Expense Memos
E Write Income and Expense Memos

8 Time 83

CHAPTER A Reading and Telling Time Using Period 89
in 24-Hour System
90
B Conversion of Time from Minutes to
Hours and Vice Versa 92

C Conversion of Time from Hours to Days 93
and Vice Versa
94
D Conversion of Time from Days to Weeks
and Vice Versa 96

E Conversion of Time from Days to Months 99
and Vice Versa 101
103
F Conversion of Time from Months to Years 105
and Vice Versa 107

G Conversion of Time from Days to Years 109
and Vice Versa 111
113
H Read Activity or Event Memos 114
I Write Activity or Event Memos 115
J Reading a Calendar 117
K Solving Word Problems on Time 119

9 Length

CHAPTER A Measuring Length
B Choosing Appropriate Units
C Comparing Lengths
D Eye-Estimation
E Converting Units of Length
F Solving Word Problems on Length

10 Weight 121

CHAPTER A Measuring Weight Using Standard Tools 122
B Measuring Weight 123
C Comparing Weights 124
D Eye-Estimation 125
E Converting Units of Weight 127
F Solving Word Problems on Weight 127

11 Volume and Capacity 129
130
CHAPTER A Measuring Volume and Capacity 131
B Choosing Appropriate Tools 133
C Comparing Volume and Capacity 135
D Eye-Estimation
E Solving Word Problems on Volume 137

and Capacity

12 Shapes and Symmetry 139

CHAPTER A Identify and Sort Two-Dimensional 141
Geometric Shapes 142

B Drawing Two-Dimensional Geometric Shapes 143
C Identifying Line of Symmetry for 145

Two-Dimensional Geometric Shapes
D Identifying Patterns

13 Foundation of Geometry 147

CHAPTER A Point 149
B Line 151
C Ray 158
D Line Segment 159
E Intersection 160
F Angle 167
G Application for Basic Geometrical Concepts 169

14 Picture Graphs and Data Analysis 171

CHAPTER A Collecting and Classifying Data 173
B Reading Pictographs 174
C Reading Bar Graphs 179

1 Numbers up to 100,000

Objectives

◆ To identify the place values;
◆ To read and write Arabic and Thai numerals up to 100,000;
◆ To count forward and backward;
◆ To write numbers in expanded form;
◆ To compare and order numbers;
◆ To apply knowledge to daily life.

Getting Started Counting by ten thousands, we have
10,000, 20,000, 30,000, 40,000,
If there are 10,000 50,000, 60,000, 70,000, 80,000,
strawberries in each box, 90,000, 100,000 strawberries.
how many strawberries are
there in 10 such boxes?

Mathematics Connection 1

Review Arabic Thai In Words
13
Numbers up to 1,000 245 Thirteen
Picture
401 Two hundred
Numbers up to 10,000 and forty-five
Picture
Four hundred
2 Chapter 1 Numbers up to 100,000 and one

1,000 , One thousand

Arabic Thai In Words

1,000 , One
thousand
2,000 ,
Two
3,000 , thousand

4,000 , Three
thousand
5,000 ,
Four
thousand

Five
thousand

6,000 , Six
thousand

7,000 , Seven
thousand

8,000 , Eight
thousand

9,000 , Nine
thousand

10,000 , Ten
thousand

Mathematics Connection 3

Counting by Ones

=

10 Flowers 1 Bunch
of flowers

10 Flowers make 1 bunch of flowers.

Counting by Tens

This makes 30 flowers.

3 Bunches of flowers

This makes 50 flowers.

5 Bunches of flowers

Numerals in Words

526 – Five hundred and twenty-six.
888 – Eight hundred and eighty-eight.
180 – One hundred and eighty.
442 – Four hundred and forty-two.

4 Chapter 1 Numbers up to 100,000

Odd and Even Numbers

The numbers whose ones place is 0,2,4,6 or 8 are called even numbers.
The numbers whose ones place is 1,3,5,7 or 9 are called odd numbers.

Count and Write in Arabic and Thai Numbers

(a)

Arabic 13 Thai
(b)

Arabic 110 Thai

Numbers in Expanded Form

We write the expanded form of numbers by splitting them into hundreds,
tens and ones.

Hundreds Tens Ones
42 2

Number in words: Four hundred and twenty-two
Expanded form : 400 + 20 + 2

Mathematics Connection 5

Symbols Used to Compare Numbers

The symbol > represents greater than.
The symbol < represents lesser than.
The symbol = represents equal to.
The symbol ≠ represents not equal to.

1. Draw the beads in the bead counter according to the place value.

(a) 225 (b) 567

Hundreds Tens Ones Hundreds Tens Ones

2. Write the number shown on the bead counter.
(a) (b)

Hundreds Tens Ones Hundreds Tens Ones

6 Chapter 1 Numbers up to 100,000

3. Write 439 in Thai numerals and in words.
In Thai numerals:

In words:

4. Write in Arabic numerals and in words.

In Arabic numerals:

In words:

5. Recognise the pattern and find the next number: 312, 412, 512, 612, ...

6. Write 727 in expanded form.

7. Arrange the numbers in decreasing order: 342, 432, 243, 234 and 423

A Place Values

In our previous class, we learnt about the place values up to thousands.
Now, we shall learn about place values up to hundred thousands.

Mathematics Connection 7

Example 1

Find the place value of the digits in 24,835.

Ten Thousands Hundreds Tens Ones
Thousands

Solution:
2 is in the ten thousands place and has the value of 20,000.
4 is in the thousands place and has the value of 4,000.
8 is in the hundreds place and has the value of 800.
3 is in the tens place and has the value of 30.
5 is in the ones place and has the value of 5.

So, the beads represent 20,000 + 4,000 + 800 + 30 + 5

The total is read as 24,835.

Think Aloud
Does increasing and decreasing number patterns help us to count
faster?

8 Chapter 1 Numbers up to 100,000

Example 2

Find the place value of all the digits in 23,076.

Ten Thousands Hundreds Tens Ones
Thousands

Solution:

2 is in the ten thousands place and has the value of 20,000.
3 is in the thousands place and has the value of 3,000.
0 is in the hundreds place and has the value of 0.
7 is in the tens place and has the value of 70.
6 is in the ones place and has the value of 6.
So, the beads represent 20,000 + 3,000 + 0 + 70 + 6
The total is read as 23,076.

Example 3

Find the place value and the value of the underlined digits.
(a) 87,253
Solution:

The digit 7 is in the thousands place and has a value of 7,000.
The digit 5 is in the tens place and has a value of 50.

Mathematics Connection 9

(b) 35,328
Solution:

The digit 3 is in the ten thousands place and has a value of 30,000.
The digit 8 is in the ones place and has a value of 8.

Place Value of Zero

Zero is used as a place holder. If zero is in the thousands, hundreds, tens or
ones place, then that place value is left empty on the bead counter.

Example 4

Find the place value of the digits in 10,900.

Ten Thousands Hundreds Tens Ones
Thousands

Solution:

1 is in the ten thousands place and has the value of 10,000.
0 is in the thousands place and has the value of 0.
9 is in the hundreds place and has the value of 900.
0 is in the tens place and has the value of 0.
0 is in the ones place and has the value of 0.
So, the beads represent 10,000 + 0 + 900 + 0 + 0
The total is read as 10,900.

10 Chapter 1 Numbers up to 100,000

Expanded Form

Expanded form is a method of writing a number and expressing it as a sum
of the values of each digit.
Look at the examples:

(a) 58,375 = 50,000 + 8,000 + 300 + 70 + 5
(b) 28,894 = 20,000 + 8,000 + 800 + 90 + 4

Try It

1. Draw the beads in the bead counter for each number.

(a) 26,543 (b) 47,320

Ten Thousands Hundreds Tens Ones Ten Thousands Hundreds Tens Ones
Thousands Thousands

(c) 20,471 (d) 67,045

Ten Thousands Hundreds Tens Ones Ten Thousands Hundreds Tens Ones
Thousands Thousands

Mathematics Connection 11

2. Write the number shown on the bead counter.
(a) (b)

Ten Thousands Hundreds Tens Ones Ten Thousands Hundreds Tens Ones
Thousands Thousands

(c) (d)

Ten Thousands Hundreds Tens Ones Ten Thousands Hundreds Tens Ones
Thousands Thousands

3. Write the place value of the underlined digits.

(a) 52,326 = (b) 65,125 =

(c) 9,764 = (d) 12,157 =

4. Fill in the blanks. ten.
(a) 10 ones =

(b) 1 hundred thousand = ten thousands.

(c) 10 hundreds = thousand.

(d) 10 tens = hundred.

12 Chapter 1 Numbers up to 100,000

5. Write the numbers in expanded form.
(a) 93,805 =
(b) 24,680 =
(c) 51,397 =
(d) 10,012 =
(e) 39,808 =

Go to Exercise 1

B Reading and Writing Arabic and Thai Numerals

up to 100,000

We have already learnt to write Arabic and Thai numerals from 0 to 1,000
in our earlier classes. Let us learn how to write Arabic and Thai numbers up
to 100,000.
Look at the bead counter below.

Ten Thousands Hundreds Tens Ones
Thousands

The bead counter represents 3 ten thousands, 6 thousands, 4 hundreds,
6 tens and 2 ones.

In Arabic numerals: 36,462

In Thai numerals : ,

In words:Thirty-six thousand, four hundred and sixty-two.

Mathematics Connection 13

Example 5

(a) Write the following Arabic numerals in Thai numerals.

ARABIC THAI
22,423 ,
81,706 ,

(b) Write the following Thai numerals in Arabic numerals.

THAI ARABIC
, 33,070
, 45,911

Try It

1. Write the following Arabic 2. Write the following Thai numerals
numerals in Thai numerals. in Arabic numerals.

ARABIC THAI THAI ARABIC

46,372 ,
57,918 ,
94,956 ,
17,170 ,
23,497 ,

Go to Exercise 2

14 Chapter 1 Numbers up to 100,000

C Number Patterns

Pattern of 3

+3

0 3 6 9 12 15 18 21 24 27 30

–3

From left to right, the next number is obtained by adding 3.
From right to left, the next number is obtained by subtracting 3.
Note that in this pattern, the difference between any two consecutive
numbers is 3.

Pattern of 4

+4

0 4 8 12 16 20 24 28 32 36 40

–4

From left to right, the next number is obtained by adding 4.
From right to left, the next number is obtained by subtracting 4.
Note that in this pattern, the difference between any two consecutive
numbers is 4.

Mathematics Connection 15

Pattern of 5

+5

0 5 10 15 20 25 30 35 40 45 50

–5

From left to right, the next number is obtained by adding 5.
From right to left, the next number is obtained by subtracting 5.
Note that in this pattern, the difference between any two consecutive
numbers is 5.

Pattern of 25

+25

0 25 50 75 100 125 150 175 200 225 250

–25

From left to right, the next number is obtained by adding 25.
From right to left, the next number is obtained by subtracting 25.
Note that in this pattern, the difference between any two consecutive
numbers is 25.

16 Chapter 1 Numbers up to 100,000

Pattern of 50

+50

0 50 100 150 200 250 300 350 400 450 500

–50

From left to right, the next number is obtained by adding 50.
From right to left, the next number is obtained by subtracting 50.
Note that in this pattern, the difference between any two consecutive
numbers is 50.

Example 6

Complete the number patterns.
(a) 66,750, 66,775, 66,800, 66,825

+25

66,750 66,775 66,800 66,825 66,850

It is an increasing pattern.The next number is obtained by adding 25.
So, the missing number in this pattern is 66,825 + 25 = 66,850

Mathematics Connection 17

(b) 40,000, 39,995, 39,990, 39,985

39,985 39,990 39,995 40,000

–5

It is a decreasing pattern.The next number is obtained by subtracting 5.
So, the missing number in this pattern is 39,985 – 5 = 39,980

Try It

1. Complete the number patterns.
(a) 90,105, 90,155, 90,205, 90,255,
(b) 10,390, 10,393, 10,396, 10,399,
(c) 14,444, 14,448, 14,452, 14,456,
(d) 45,450, 45,425, 45,400, 45,375,
(e) 99,855, 99,850, 99,845, 99,840,
(f) 65,627, 65,624, 65,621, 65,618,
(g) 24,025, 24,050, 24,075, 24,100,
(h) 78,344, 78,340, 78,336, 78,332,
(i) 81,550, 81,545, 81,540, 81,535,

Go to Exercise 3

18 Chapter 1 Numbers up to 100,000

D Repeated Patterns

Repeated patterns is a pattern in which the numbers are repeated in a
certain combination or the differences between consecutive numbers are
repeated in a certain combination.

Example 7

(a) 5, 10, 15, 5, 10, 15,

represents 5. represents 10.

represents 15.

So, the pattern is as follows: 5, 10, 15, 5, 10, 15, 5

(b) 2, 4, 6, 2, 4, 6,

The pattern followed for the first three numbers is as follows:
0+2=2
2+2=4
4+2=6
The next three numbers of the pattern follows the same pattern as the first
three numbers.
So, the pattern is as follows: 2, 4, 6, 2, 4, 6, 2

Fun Facts
In South Asia, a lakh refers to one hundred thousand.

Mathematics Connection 19

Try It

1. Recognise the pattern and find the number pattern.

(a) 1, 3, 5, 1, 3, 5, (b) 10, 20, 30, 10, 20, 30,

(c) 4, 8, 12, 4, 8, 12, (d) 11, 22, 33, 11, 22, 33,

Go to Exercise 4

E Comparing and Ordering Numbers

Comparing Numbers

Step 1: Check the number of digits in the two numbers.The number
with the most number of digits is the greater number.

Step 2: If the number of digits in the two numbers is equal, start
comparing the digits on the left most.The number with the
bigger digit is the greater number.

Step 3: If the digits on the left most are the same, we compare the next
digits and keep repeating until the digits are different.

Let us see some examples.

Example 8

Compare the numbers 19,871 and 21,462.

Solution:

Hundred Ten Thousands Hundreds Tens Ones

Thousands Thousands

1 9 8 71
2 1 4 62

20 Chapter 1 Numbers up to 100,000

Step 1: Both the numbers are 5-digit numbers.
Step 2: Now, compare the left most digits (ten thousands place) in the

given numbers. 1 is smaller than 2.

So, 19,871 is less than 21,462.
We write it as 19,871 < 21,462.

Example 9

Compare the numbers 50,005 and 50,050.

Solution:

Hundred Ten Thousands Hundreds Tens Ones

Thousands Thousands

5 0 0 05

5 0 0 50

Step 1: Both the numbers are 5-digit numbers.

Step 2: The digits in the ten thousands place, thousands place and
hundreds place are the same. So, we compare the digits in the
tens place. 0 is smaller than 5.

So, 50,005 is smaller than 50,050.
We write it as 50,005 < 50,050.

Ordering Numbers

Look at the example below.

Example 10

Arrange the following numbers in increasing and decreasing order.
37,508, 26,508, 26,608, 26,502

Mathematics Connection 21

Solution:

Hundred Ten Thousands Hundreds Tens Ones

Thousands Thousands

3 7 5 08

2 6 5 08

2 6 6 08

2 6 5 02

Step 1: Look at the digits in the ten thousands place. 3 is the biggest
Step 2: digit.

So, 37,508 is the biggest number.

Look at the next three numbers.

Hundred Ten Thousands Hundreds Tens Ones

Thousands Thousands

2 6 5 08

2 6 6 08

2 6 5 02

The digits in the ten thousands place and thousands place are
the same.

So, we compare the digits in the hundreds place. 6 is greater
than 5.

Hence, 26,608 is the second biggest number.

Step3: Now, look at the last two numbers.

Hundred Ten Thousands Hundreds Tens Ones

Thousands Thousands

2 6 5 08
2 6 5 02

22 Chapter 1 Numbers up to 100,000

The digits in the ten thousands, thousands, hundreds and tens place are
the same.
So, we compare the digits in the ones place. 8 is greater than 2.
Hence, 26,508 is the third biggest number.
Let us arrange the numbers in decreasing order.
37,508, 26,608, 26,508, 26,502
We write it as 37,508 > 26,608 > 26,508 > 26,502.
Now, let us arrange the numbers in increasing order.
26,502, 26,508, 26,608, 37,508
We write it as 26,502 < 26,508 < 26,608 < 37,508.

Try It

1. Fill in the boxes with < or > signs.

(a) 25,986 25,791 (b) 94,000 90,400
52,655
(c) 32,497 23,497 (d) 25,365 11,660

(e) 54,786 25,897 (f) 60,611 25,869
51,525
2. Fill in the boxes with = or ≠ signs. 66,333

(a) 63,163 63,000 (b) 25,689

(c) 45,125 45,125 (d) 51,525

(e) 12,345 34,123 (f) 36,633

Mathematics Connection 23

3. Arrange the numbers in increasing and decreasing order.
(a) 46,291, 32,656, 52,000, 23,471
Increasing order:
Decreasing order:
(b) 36,451, 32,961, 33,831, 31,911
Increasing order:
Decreasing order:
(c) 57,596, 57,496, 57,796, 57,976
Increasing order:
Decreasing order:
(d) 61,286, 61,210, 61,295, 61,221
Increasing order:
Decreasing order:
(e) 45,893, 45,899, 45,888, 45,998
Increasing order:
Decreasing order:

Go to Exercise 5

24 Chapter 1 Numbers up to 100,000



Contents

1 Numbers: More than 100,000 1

CHAPTER A Place Value 3
B Expanded Form 10
C Comparing and Ordering 11
D Counting Forward and Counting Backward 15

2 Addition and Subtraction more than 100,000 16

CHAPTER A Addition 17
B Subtraction 19
C Word Problems on Addition and Subtraction 21

3 Multiplication more than 100,000 23
24
CHAPTER A Multiplying 1-Digit Numbers
B Multiplying by Numbers with Two or 27
29
More Digits
C Word Problems Involving Multiplication

4 Division more than 100,000 31

CHAPTER A Short Division 32
B Dividing By 2-Digit Numbers 33
C Dividing By 3-Digit Numbers 35
D Solving Word Problems 37

5 Mixed Operations Addition, Subtraction, 39
Multiplication and Division:
CHAPTER 40
A Solving Word Problems Involving Addition,
Subtraction, Multiplication and Division 42

B Creating Word Problems Involving Addition, 44
Subtraction, Multiplication and Division 47
49
6 Time 51
53
CHAPTER A Reading and Telling Time 59
B Converting Units of Time
C Reading Time Schedule 61
D Reading and Writing Activity or Event Memos 64
E Solving Word Problems Related to Time 67
69
7 Fraction
71
CHAPTER A Knowing Fractions 77
B Proper Fraction, Improper Fraction 79
C Mixed Numbers
D The Relationship between Mixed and 83

Improper Fraction
E Comparing and Ordering Fractions
F Addition and Subtraction of Fractions
G Solving Word Problems on Addition and

Subtraction of Fraction

8 Decimals 85
89
CHAPTER A Knowing Decimals 92
B Comparing and Ordering Decimals 95
C Reading and Writing up to 3 Decimal 102
D Problem Solving of Adding and 106

Subtraction of Decimals 107
109
9 Lines and Angles 110

CHAPTER A Parallel and Perpendicular Lines 111
B Classify Angles
C Measuring the Size of the Angles 115

Using the Protractor 117
D Creating Angles when Determining 119

the Angle Size 121
123
10 Area 124
127
CHAPTER A Measuring Areas
B Finding Areas of Squares and

Rectangles by Counting
C Finding Area of Irregular Shapes
D Finding Area using Formula
E Word Problems

11 Geometry 129
131
CHAPTER A Circles 132
B Rectangles and Squares 133
C Symmetric Figures
134
12 Patterns 137
138
CHAPTER A Identifying Shape Patterns
B Creating New Figures and Patterns 140
141
13 Data Analysis 143
146
CHAPTER A Tables 148
B Pictographs 149
C Bar Graphs
D Knowing Average
E Word Problems