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Page 1
6 6
Chapter Chapter
The Dairy Farm
1. The given shapes stand for numbers between 1 and 24. The same shape
denotes the same number across all problems. Find the numbers hiding
in all the shapes.
3. A dairy has packed butter milk pouches in the following manner. Find
the number of pouches kept in each arrangement. One is done for you.
2. Place the digits 2, 5, and 3 appropriately to get
a product close to 100. Share your reasoning
in class.
×
By now, we know several multiplication facts. We have also learnt how
to multiply two numbers. We will continue to explore different ways of
multiplying in this chapter.
Let Us Think
___ × ___ = 60 30 × 2 = 60
a)
× =
b)
× =
c)
× =
d)
× =
e)
× =
f)
× × =
Chapter 6.indd 70 Chapter 6.indd 70 05-07-2025 15:04:23 05-07-2025 15:04:23
Page 2
6 6
Chapter Chapter
The Dairy Farm
1. The given shapes stand for numbers between 1 and 24. The same shape
denotes the same number across all problems. Find the numbers hiding
in all the shapes.
3. A dairy has packed butter milk pouches in the following manner. Find
the number of pouches kept in each arrangement. One is done for you.
2. Place the digits 2, 5, and 3 appropriately to get
a product close to 100. Share your reasoning
in class.
×
By now, we know several multiplication facts. We have also learnt how
to multiply two numbers. We will continue to explore different ways of
multiplying in this chapter.
Let Us Think
___ × ___ = 60 30 × 2 = 60
a)
× =
b)
× =
c)
× =
d)
× =
e)
× =
f)
× × =
Chapter 6.indd 70 Chapter 6.indd 70 05-07-2025 15:04:23 05-07-2025 15:04:23
4. Which number am I?
I am a two-digit number. Find me with the help of the following clues.
(a) I am greater than 8.
(b) I am not a multiple of 4.
(c) I am a multiple of 9.
(d) I am an odd number.
(e) I am not a multiple of 11.
(f) I am less than 50.
(g) My ones digit is even
(h) My tens digit is odd.
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
5. Make your own numbers.
Choose any two numbers and one operation from
the grid. Try to make all the numbers between
0 and 20. For example, 2 can be formed as 4 – 2.
Could you make all the numbers?
100 25 5
10 2 36
12 4 3
×
+
÷
–
Which numbers could you not make? Is it possible to make these
numbers using three numbers? You can use two operations, if needed.
Which numbers between 0–20 can you get in more than one way?
___ × ___ = 60
___ × ___ = 60
What other groups can you make? What other groups can you make?
Did you use all the clues to
find the number? Which clues
did not help you in finding
the number?
71
Chapter-6 The Dairy Farm.indd 71 Chapter-6 The Dairy Farm.indd 71 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
Page 3
6 6
Chapter Chapter
The Dairy Farm
1. The given shapes stand for numbers between 1 and 24. The same shape
denotes the same number across all problems. Find the numbers hiding
in all the shapes.
3. A dairy has packed butter milk pouches in the following manner. Find
the number of pouches kept in each arrangement. One is done for you.
2. Place the digits 2, 5, and 3 appropriately to get
a product close to 100. Share your reasoning
in class.
×
By now, we know several multiplication facts. We have also learnt how
to multiply two numbers. We will continue to explore different ways of
multiplying in this chapter.
Let Us Think
___ × ___ = 60 30 × 2 = 60
a)
× =
b)
× =
c)
× =
d)
× =
e)
× =
f)
× × =
Chapter 6.indd 70 Chapter 6.indd 70 05-07-2025 15:04:23 05-07-2025 15:04:23
4. Which number am I?
I am a two-digit number. Find me with the help of the following clues.
(a) I am greater than 8.
(b) I am not a multiple of 4.
(c) I am a multiple of 9.
(d) I am an odd number.
(e) I am not a multiple of 11.
(f) I am less than 50.
(g) My ones digit is even
(h) My tens digit is odd.
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
5. Make your own numbers.
Choose any two numbers and one operation from
the grid. Try to make all the numbers between
0 and 20. For example, 2 can be formed as 4 – 2.
Could you make all the numbers?
100 25 5
10 2 36
12 4 3
×
+
÷
–
Which numbers could you not make? Is it possible to make these
numbers using three numbers? You can use two operations, if needed.
Which numbers between 0–20 can you get in more than one way?
___ × ___ = 60
___ × ___ = 60
What other groups can you make? What other groups can you make?
Did you use all the clues to
find the number? Which clues
did not help you in finding
the number?
71
Chapter-6 The Dairy Farm.indd 71 Chapter-6 The Dairy Farm.indd 71 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
The number of groups and the group size are interchanged in each case
above, but the total number of butter packets remain the same.
Patterns in Multiplication by 10s and 100s
Note for Teachers: Encourage the learners to understand that when we multiply a
number by 10, it becomes 10 times, and each digit moves one place value to the left.
Multiplying by 100 makes the number 100 times larger, shifting each digit two place
value to the left. Let them notice the pattern of zeros in the place value table.
1. Let us revise multiplication by 10s and 100s.
a) 4 × 10 = _____ d) 10 × 10 = 100 g) 3 × 100 = 100 × 3 = 300
b) 20 × 10 = _____ e) 20 × 50 = ______ h) 8 × 100 = _____ = ______
c) 10 × 40 = _____ f) 80 × 10 = ______ i) 10 × 100 = _____ = ______
Number of
groups: 6
Group size: 13
What is 9 × 0? 0 × 9? What is 9 × 0? 0 × 9?
Is this true for the product of any two numbers? Discuss in class. Is this true for the product of any two numbers? Discuss in class.
6 × 13 =
13 × 6 =
12 × 9 =
9 × 12 =
10 × 5 =
5 × 10 =
8 × 20 =
20 × 8 =
e)
f)
g)
Order of Numbers in Multiplication
Daljeet Kaur runs a milk processing unit. She has arranged the butter packets
in the following ways. Find the number of butter packets in each case. What
pattern do you notice (or observe)? Discuss in class.
2 × 3 =
3 × 2 =
a)
8 × 5 =
5 × 8 =
b)
72
Chapter-6 The Dairy Farm.indd 72 Chapter-6 The Dairy Farm.indd 72 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
Page 4
6 6
Chapter Chapter
The Dairy Farm
1. The given shapes stand for numbers between 1 and 24. The same shape
denotes the same number across all problems. Find the numbers hiding
in all the shapes.
3. A dairy has packed butter milk pouches in the following manner. Find
the number of pouches kept in each arrangement. One is done for you.
2. Place the digits 2, 5, and 3 appropriately to get
a product close to 100. Share your reasoning
in class.
×
By now, we know several multiplication facts. We have also learnt how
to multiply two numbers. We will continue to explore different ways of
multiplying in this chapter.
Let Us Think
___ × ___ = 60 30 × 2 = 60
a)
× =
b)
× =
c)
× =
d)
× =
e)
× =
f)
× × =
Chapter 6.indd 70 Chapter 6.indd 70 05-07-2025 15:04:23 05-07-2025 15:04:23
4. Which number am I?
I am a two-digit number. Find me with the help of the following clues.
(a) I am greater than 8.
(b) I am not a multiple of 4.
(c) I am a multiple of 9.
(d) I am an odd number.
(e) I am not a multiple of 11.
(f) I am less than 50.
(g) My ones digit is even
(h) My tens digit is odd.
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
5. Make your own numbers.
Choose any two numbers and one operation from
the grid. Try to make all the numbers between
0 and 20. For example, 2 can be formed as 4 – 2.
Could you make all the numbers?
100 25 5
10 2 36
12 4 3
×
+
÷
–
Which numbers could you not make? Is it possible to make these
numbers using three numbers? You can use two operations, if needed.
Which numbers between 0–20 can you get in more than one way?
___ × ___ = 60
___ × ___ = 60
What other groups can you make? What other groups can you make?
Did you use all the clues to
find the number? Which clues
did not help you in finding
the number?
71
Chapter-6 The Dairy Farm.indd 71 Chapter-6 The Dairy Farm.indd 71 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
The number of groups and the group size are interchanged in each case
above, but the total number of butter packets remain the same.
Patterns in Multiplication by 10s and 100s
Note for Teachers: Encourage the learners to understand that when we multiply a
number by 10, it becomes 10 times, and each digit moves one place value to the left.
Multiplying by 100 makes the number 100 times larger, shifting each digit two place
value to the left. Let them notice the pattern of zeros in the place value table.
1. Let us revise multiplication by 10s and 100s.
a) 4 × 10 = _____ d) 10 × 10 = 100 g) 3 × 100 = 100 × 3 = 300
b) 20 × 10 = _____ e) 20 × 50 = ______ h) 8 × 100 = _____ = ______
c) 10 × 40 = _____ f) 80 × 10 = ______ i) 10 × 100 = _____ = ______
Number of
groups: 6
Group size: 13
What is 9 × 0? 0 × 9? What is 9 × 0? 0 × 9?
Is this true for the product of any two numbers? Discuss in class. Is this true for the product of any two numbers? Discuss in class.
6 × 13 =
13 × 6 =
12 × 9 =
9 × 12 =
10 × 5 =
5 × 10 =
8 × 20 =
20 × 8 =
e)
f)
g)
Order of Numbers in Multiplication
Daljeet Kaur runs a milk processing unit. She has arranged the butter packets
in the following ways. Find the number of butter packets in each case. What
pattern do you notice (or observe)? Discuss in class.
2 × 3 =
3 × 2 =
a)
8 × 5 =
5 × 8 =
b)
72
Chapter-6 The Dairy Farm.indd 72 Chapter-6 The Dairy Farm.indd 72 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
What will happen if we multiply numbers by 1,000?
2 × 1,000 = 2 thousand = 2,000
5 × 1,000 = 5 thousand = 5,000
10 × 1,000 = 10 thousand= 10,000 20 × 1,000 = 20 thousand = 20,000
1,000 1,000
1,000 1,000 1,000 1,000 1,000
30 × 10 = 300 30 × 10 = 300
×2 ×2 ×2 ×2
3 30 × 0 × 2 20 = 0 = 6 600 00
Notice the underlined numbers Notice the underlined numbers
30 × 20 = 30 × 20 =
3 3 × 10 × × 10 × 2 2 × 10 = × 10 = 6 6 × 100 × 100
Notice the underlined numbers. Notice the underlined numbers.
Remember, we can multiply numbers Remember, we can multiply numbers
in any order. in any order.
100 × 90 = __,000
30 × 20 = 600
400 × 10 = ___
700 × 4 = _ , _ 00
60 × 50 = ____
10 × 45 = ____
Problem Th H T O
10 × 45 =
30 × 20 = 6 0 0
400 × 10 =
700 × 8 =
100 × 90 = 9 0 0 0
How should we write 450 in the table below? How should we write 450 in the table below?
2. Find answers to the following questions. Fill in the table below and
describe the pattern. Discuss in class.
Problem Th H T O
60 × 50 =
220 × 20 =
11 × 300 =
Problem Th H T O
80 × 90 =
10 × 63 =
40 × 12 =
73
Chapter-6 The Dairy Farm.indd 73 Chapter-6 The Dairy Farm.indd 73 04-07-2025 11:57:15 04-07-2025 11:57:15
Page 5
6 6
Chapter Chapter
The Dairy Farm
1. The given shapes stand for numbers between 1 and 24. The same shape
denotes the same number across all problems. Find the numbers hiding
in all the shapes.
3. A dairy has packed butter milk pouches in the following manner. Find
the number of pouches kept in each arrangement. One is done for you.
2. Place the digits 2, 5, and 3 appropriately to get
a product close to 100. Share your reasoning
in class.
×
By now, we know several multiplication facts. We have also learnt how
to multiply two numbers. We will continue to explore different ways of
multiplying in this chapter.
Let Us Think
___ × ___ = 60 30 × 2 = 60
a)
× =
b)
× =
c)
× =
d)
× =
e)
× =
f)
× × =
Chapter 6.indd 70 Chapter 6.indd 70 05-07-2025 15:04:23 05-07-2025 15:04:23
4. Which number am I?
I am a two-digit number. Find me with the help of the following clues.
(a) I am greater than 8.
(b) I am not a multiple of 4.
(c) I am a multiple of 9.
(d) I am an odd number.
(e) I am not a multiple of 11.
(f) I am less than 50.
(g) My ones digit is even
(h) My tens digit is odd.
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
5. Make your own numbers.
Choose any two numbers and one operation from
the grid. Try to make all the numbers between
0 and 20. For example, 2 can be formed as 4 – 2.
Could you make all the numbers?
100 25 5
10 2 36
12 4 3
×
+
÷
–
Which numbers could you not make? Is it possible to make these
numbers using three numbers? You can use two operations, if needed.
Which numbers between 0–20 can you get in more than one way?
___ × ___ = 60
___ × ___ = 60
What other groups can you make? What other groups can you make?
Did you use all the clues to
find the number? Which clues
did not help you in finding
the number?
71
Chapter-6 The Dairy Farm.indd 71 Chapter-6 The Dairy Farm.indd 71 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
The number of groups and the group size are interchanged in each case
above, but the total number of butter packets remain the same.
Patterns in Multiplication by 10s and 100s
Note for Teachers: Encourage the learners to understand that when we multiply a
number by 10, it becomes 10 times, and each digit moves one place value to the left.
Multiplying by 100 makes the number 100 times larger, shifting each digit two place
value to the left. Let them notice the pattern of zeros in the place value table.
1. Let us revise multiplication by 10s and 100s.
a) 4 × 10 = _____ d) 10 × 10 = 100 g) 3 × 100 = 100 × 3 = 300
b) 20 × 10 = _____ e) 20 × 50 = ______ h) 8 × 100 = _____ = ______
c) 10 × 40 = _____ f) 80 × 10 = ______ i) 10 × 100 = _____ = ______
Number of
groups: 6
Group size: 13
What is 9 × 0? 0 × 9? What is 9 × 0? 0 × 9?
Is this true for the product of any two numbers? Discuss in class. Is this true for the product of any two numbers? Discuss in class.
6 × 13 =
13 × 6 =
12 × 9 =
9 × 12 =
10 × 5 =
5 × 10 =
8 × 20 =
20 × 8 =
e)
f)
g)
Order of Numbers in Multiplication
Daljeet Kaur runs a milk processing unit. She has arranged the butter packets
in the following ways. Find the number of butter packets in each case. What
pattern do you notice (or observe)? Discuss in class.
2 × 3 =
3 × 2 =
a)
8 × 5 =
5 × 8 =
b)
72
Chapter-6 The Dairy Farm.indd 72 Chapter-6 The Dairy Farm.indd 72 7/2/2025 3:34:40 PM 7/2/2025 3:34:40 PM
What will happen if we multiply numbers by 1,000?
2 × 1,000 = 2 thousand = 2,000
5 × 1,000 = 5 thousand = 5,000
10 × 1,000 = 10 thousand= 10,000 20 × 1,000 = 20 thousand = 20,000
1,000 1,000
1,000 1,000 1,000 1,000 1,000
30 × 10 = 300 30 × 10 = 300
×2 ×2 ×2 ×2
3 30 × 0 × 2 20 = 0 = 6 600 00
Notice the underlined numbers Notice the underlined numbers
30 × 20 = 30 × 20 =
3 3 × 10 × × 10 × 2 2 × 10 = × 10 = 6 6 × 100 × 100
Notice the underlined numbers. Notice the underlined numbers.
Remember, we can multiply numbers Remember, we can multiply numbers
in any order. in any order.
100 × 90 = __,000
30 × 20 = 600
400 × 10 = ___
700 × 4 = _ , _ 00
60 × 50 = ____
10 × 45 = ____
Problem Th H T O
10 × 45 =
30 × 20 = 6 0 0
400 × 10 =
700 × 8 =
100 × 90 = 9 0 0 0
How should we write 450 in the table below? How should we write 450 in the table below?
2. Find answers to the following questions. Fill in the table below and
describe the pattern. Discuss in class.
Problem Th H T O
60 × 50 =
220 × 20 =
11 × 300 =
Problem Th H T O
80 × 90 =
10 × 63 =
40 × 12 =
73
Chapter-6 The Dairy Farm.indd 73 Chapter-6 The Dairy Farm.indd 73 04-07-2025 11:57:15 04-07-2025 11:57:15
Many Ways to Multiply
Problem TTh Th H T O
2 × 1,000 = 2 0 0 0
5 × 1,000 = 5 0 0 0
10 × 1,000 = 1 0 0 0 0
20 × 1,000 = 2 0 0 0 0
3 × 5,000 =
8 × 3,000 =
5 × 7,000 =
Problem TTh Th H T O
20 × 100 =
40 × 500 =
60 × 300 =
600 × 30 =
80 × 900 =
70 × 600 =
5 × 7,000 =
What is × 18 5
First, I doubled 18 to get 36. Then I doubled 36 to get 72
and then I added 18 to 72 to get 90.
I separated 18 into 8 and 10. 8×5 is 40. 10×5 is 50.
then I added 40 and 50 together to get 90.
I did 20×5, which is 100. Then I took away 2×5,
which is 10. So, 100 –10 = 90.
Half of 18 is 9. 9×5 is 45 and 9×5 is 45.
I added 45 and 45 together to get 90.
18×5 = 9×10. So, 90.
Do you think they are Do you think they are
all correct? Why do all correct? Why do
you think so? you think so?
Let us fill in the table and observe the patterns.
74
Chapter-6 The Dairy Farm.indd 74 Chapter-6 The Dairy Farm.indd 74 04-07-2025 11:57:26 04-07-2025 11:57:26
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FAQs on NCERT Textbook: The Dairy Farm - Mathematics (Maths Mela) Class 5 - New NCERT
| 1. What are the main activities involved in a dairy farm? |  |
Ans. A dairy farm primarily involves the milking of cows, feeding and caring for the animals, maintaining their health, and managing the production of dairy products like milk, cheese, and butter. Farmers must ensure that cows are well-fed and healthy to produce quality milk.
| 2. How do dairy farms contribute to the economy? | |
Ans. Dairy farms play a significant role in the economy by providing employment opportunities, supporting local businesses, and contributing to the agricultural sector. They produce essential food items that are consumed widely, thus helping in trade and commerce.
| 3. What are some common breeds of dairy cows found on dairy farms? | |
Ans. Common breeds of dairy cows include Holstein, Jersey, Guernsey, and Ayrshire. Each breed has unique characteristics, such as milk production capacity and quality, which farmers consider when choosing which breeds to raise.
| 4. Why is it important to ensure the health of dairy cows? | |
Ans. Ensuring the health of dairy cows is crucial for maintaining high milk production and quality. Healthy cows are less susceptible to diseases, which can reduce costs for farmers and ensure a steady supply of milk and dairy products for consumers.
| 5. What are the environmental considerations of running a dairy farm? | |
Ans. Running a dairy farm involves several environmental considerations, such as managing waste, conserving water, and reducing greenhouse gas emissions. Sustainable practices, like proper manure management and crop rotation, can help minimize the farm's environmental impact while maintaining productivity.
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