NCERT Class 5 Mathematics Maths Mela Chapter 06 The Dairy Farm PDF Download

Chapter 6: The Dairy Farm

Let Us Think

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.

   a) \( \times \) =

   b) \( \times \) =

   c) \( \times \) =

   d) \( \times \) =

   e) \( \times \) =

   f) \( \times \) \( \times \) =

2. Place the digits 2, 5, and 3 appropriately to get a product close to 100. Share your reasoning in class.
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.

   \[ 30 \times 2 = 60 \]

   \[ \_ \times \_ = 60 \]

   \[ \_ \times \_ = 60 \]

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.

Teacher's Note

When you see \( 30 \times 2 = 60 \), remember that this is the same as grouping: 30 groups of 2 items each, or 2 groups of 30 items each. Different arrangements can give the same total. Try drawing out the pouches in rows and columns to see how the same product can come from different multiplication facts.

Which number am I?

1. 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.

Did you use all the clues to find the number? Which clues did not help you in finding the number?

2. 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	\( \times \)
   10	2	36	\( + \)
   12	4	3	\( \div \)
   			\( - \)

   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?

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.

\[ 2 \times 3 = \]

\[ 3 \times 2 = \]

\[ 8 \times 5 = \]

\[ 5 \times 8 = \]

\[ 12 \times 9 = \]

\[ 9 \times 12 = \]

\[ 10 \times 5 = \]

\[ 5 \times 10 = \]

\[ 8 \times 20 = \]

\[ 20 \times 8 = \]

Number of groups: 6
Group size: 13

\[ 6 \times 13 = \]

\[ 13 \times 6 = \]

The number of groups and the group size are interchanged in each case above, but the total number of butter packets remain the same.

What is \( 9 \times 0 \)? \( 0 \times 9 \)?

Is this true for the product of any two numbers? Discuss in class.

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) \( 4 \times 10 = \) _____

   b) \( 20 \times 10 = \) _____

   c) \( 10 \times 40 = \) _____

   d) \( 10 \times 10 = 100 \)

   e) \( 20 \times 50 = \) ______

   f) \( 80 \times 10 = \) ______

   g) \( 3 \times 100 = 100 \times 3 = 300 \)

   h) \( 8 \times 100 = \) _____ = ______

   i) \( 10 \times 100 = \) _____ = ______

Teacher's Note

When multiplying by 10, each digit shifts one place to the left, so a zero is added at the right. For \( 4 \times 10 = 40 \), the 4 moves from the ones place to the tens place. Check your work by thinking about what happens to the place values: tens become hundreds, ones become tens. The number gets 10 times larger.

What will happen if we multiply numbers by 1,000?

\[ 2 \times 1,000 = 2 \text{ thousand} = 2,000 \]

\[ 5 \times 1,000 = 5 \text{ thousand} = 5,000 \]

\[ 10 \times 1,000 = 10 \text{ thousand} = 10,000 \]

\[ 20 \times 1,000 = 20 \text{ thousand} = 20,000 \]

\[ 30 \times 10 = 300 \]

\[ \times 2 \quad \times 2 \]

\[ 30 \times 20 = 600 \]

Notice the underlined numbers.

\[ 30 \times 20 = \]

\[ 3 \times 10 \times 2 \times 10 = 6 \times 100 \]

Notice the underlined numbers. Remember, we can multiply numbers in any order.

1. Find answers to the following questions. Fill in the table below and describe the pattern. Discuss in class.

   \[ 100 \times 90 = \_ \text{,}000 \]

   \[ 30 \times 20 = 600 \]

   \[ 400 \times 10 = \_ \_ \_ \]

   \[ 700 \times 4 = \_ \text{,} \_ 00 \]

   \[ 60 \times 50 = \_ \_ \_ \_ \]

   \[ 10 \times 45 = \_ \_ \_ \_ \]

How should we write 450 in the table below?

Many Ways to Multiply

What is \( 18 \times 5 \)?

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. \( 8 \times 5 \) is 40. \( 10 \times 5 \) is 50. Then I added 40 and 50 together to get 90.

I did \( 20 \times 5 \), which is 100. Then I took away \( 2 \times 5 \), which is 10. So, \( 100 - 10 = 90 \).

Half of 18 is 9. \( 9 \times 5 \) is 45 and \( 9 \times 5 \) is 45. I added 45 and 45 together to get 90.

\( 18 \times 5 = 9 \times 10 \). So, 90.

Do you think they are all correct? Why do you think so?

Let us fill in the table and observe the patterns.

Key Points

• The order of numbers in multiplication does not change the product. For example, \( 3 \times 5 = 5 \times 3 = 15 \). This property is called the commutative property of multiplication.
• When you multiply a number by 10, each digit moves one place value to the left, adding a zero at the right. When you multiply by 100, each digit moves two place values to the left, adding two zeros.
• Multiplication can be done in many ways. You can break numbers into parts (like splitting 18 into 10 and 8), use doubling and halving, or break numbers into tens and ones to make the calculation easier.
• Place value tables help you write the products of multiplication in thousands, hundreds, tens, and ones, making it clear how the digits shift when multiplying by 10, 100, or 1,000.
• When multiplying two numbers that include factors of 10, you can multiply the non-zero digits first, then multiply by the tens. For example, \( 30 \times 20 = 3 \times 10 \times 2 \times 10 = 6 \times 100 = 600 \).

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