NCERT Class 5 Mathematics Maths Mela Chapter 13 Animal Jumps PDF Download

Chapter 13: Animal Jumps

Find the Hidden Numbers

Numbers put in this box get multiplied by a number and come out.

1. Can you guess the multiplier if you see the 4 numbers coming out of the box?
2. Is there more than one possible multiplier?
3. What numbers might have been put inside the box?

Share your thoughts in the class. You can also play this game with your friends.

The multipliers 1, 2, and 4 that you found above are the factors of the numbers that have come out of the box, that is, 28, 36, 48, and 72. In fact, these are the common factors of all the numbers. The numbers 28, 36, 48, and 72 are multiples of 1, 2 and 4.

The product of two or more factors gives a multiple.

A number, when arranged in an array, shows the factors of that number. Are there other numbers that are factors of 15? Try to make other arrays for the number 15.

[Figure: Arrays showing 3 × 5 = 15 with factors and multiple labeled, See in your textbook]

Let us make arrays for the number 12.

[Figure: Arrays showing 3 × 4 = 12, 2 × 6 = 12, and 1 × 12 = 12, See in your textbook]

Let Us Do

Make different arrays for the following numbers. Identify the factors in each case.

1. 10
2. 14
3. 13
4. 20
5. 25
6. 32
7. 37
8. 46
9. 54

Numbers like 13 and 37 are called prime numbers. Why?

Teacher's Note

A prime number has exactly two factors: 1 and itself. When you try to make arrays for 13 or 37, only one arrangement works: \( 1 \times 13 \) and \( 1 \times 37 \). This is the key difference from numbers like 12, which can be arranged in multiple ways. Recognizing prime numbers will help you in factorization problems later.

Animal Jumps

A rabbit takes a jump of 4 each time. A frog takes a jump of 3 each time. Use the number line to figure out the numbers they will both touch. If the rabbit and the frog start from 0, the numbers both of them will touch are called the common multiples of 3 and 4.

[Figure: Number line from 0 to 12 showing rabbit jumps by 4 and frog jumps by 3, See in your textbook]

12 is the first common multiple of 3 and 4. What are some other common multiples of 3 and 4? You can continue the number line or take help from the times tables of 3 and 4.

What do you notice about the common multiples of 3 and 4? Discuss in class.

1, 2, 3, 4, 6, and 12 are all factors of 12. Each of the numbers can divide 12 completely. 12 is a multiple of these numbers.

Do you see why 12 is a multiple of 1, 2, 3, 4, 6, and 12?

\( 2 \times \underline{\phantom{00}} = 12 \) \( 3 \times \underline{\phantom{00}} = 12 \)

\( 12 \times \underline{\phantom{00}} = 12 \) \( 1 \times \underline{\phantom{00}} = 12 \)

The number itself is always a multiple of itself.

A spider takes a jump of 3 every time. A grasshopper takes a jump of 6 each time. Use the number line to find the common multiples of 3 and 6.

[Figure: Number line from 0 to 12 showing spider jumps by 3 and grasshopper jumps by 6, See in your textbook]

6 and 12 are two common multiples of 3 and 6. You can continue the pattern to find more common multiples. What do you notice about the common multiples of 3 and 6? Discuss.

Let us write the multiples of two numbers - 4 and 6.

Multiples of 4-4, 8, 12, 16, ...

Multiple of 6-6, 12, 18, ...

12 and 24 are two of the common multiples of 4 and 6. List a few more.

Let Us Do

1. Find 5 common multiples of the following pairs of numbers.
   1. 2 and 3
   2. 5 and 8
   3. 2 and 4
   4. 3 and 9
   5. 5 and 10
   6. 9 and 12
   7. 8 and 12
   8. 6 and 8
   9. 6 and 9

What do you notice about the common multiples of different pairs of numbers? Discuss in class.

2. Food is available at the end of a cobbled road. Robby, the rabbit, takes a jump of 4 each time. Deeku, the deer, takes a jump of 6 each time. They both start at 0. Will both Robby and Deeku reach the food? Who will reach first? How do you know? Explain your answer.

[Figure: Cobbled road with hexagonal stepping stones numbered with animal characters, See in your textbook]

3. Mowgli's friends live along the trail on the marked places below. Which of his friends will he be able to visit, if he jumps by 2 steps starting from 0?

[Figure: Trail map showing Mowgli and friends at various numbered positions, with positions including animals at 4, 12, 14, 50 and others, See in your textbook]

Teacher's Note

When you jump by 2 steps starting from 0, you touch only the even numbers: 0, 2, 4, 6, 8, and so on. These are all multiples of 2. If a friend's position is an odd number, like 3, 5, or 9, you cannot visit them. This helps you understand that common factors determine which numbers you can reach with equal jumps.

4. Let us find some common factors of the numbers 24 and 36. Note that all jumps in the following questions start from 0.
   1. Can we jump by 2 steps at a time to reach both 24 and 36? Yes/No. 2 is/is not a common factor of 24 and 36.
   2. Can we jump by 3 steps at a time to reach both 24 and 36? Yes/No. 3 is/is not a common factor of 24 and 36.
   3. Can we jump by 4 steps at a time to reach both 24 and 36? Yes/No. 4 is/is not a common factor of 24 and 36.
   4. What other jumps can we take to reach both 24 and 36?
   5. How many common factors can you find for 24 and 36? List them.
   6. What about jumping by 1 step each time to reach both 24 and 36?
5. What are the common factors of 12 and 13?

The number itself and 1 are always factors of any number.

Did Mowgli meet the ant, frog, bird and the rabbit? Notice their positions - 4, 12, 14, and 50. 2 is a common factor of these numbers.

Which of his friends will he be able to meet if he jumps by 3 steps?

3 is a common factor of the numbers 9, 21, 39, and 57.

Which numbers will he touch if he jumps by 5 steps?

5 is a common factor of the numbers \phantom{00000000000000000000}.

Which numbers will he touch if he jumps by 10 steps?

10 is a common factor of the numbers \phantom{00000000000000000000}.

A common factor of two or more numbers exactly divides each the numbers.

Key Points

• A factor of a number divides it completely with no remainder. When you arrange objects in an array, the dimensions show you the factors.
• A multiple is made by multiplying a number by another whole number. If you jump by equal steps on a number line starting from 0, you touch only the multiples of that step size.
• A common factor of two numbers divides both of them completely. A common multiple of two numbers is a number that both are factors of.
• The number 1 is a factor of every number, and every number is a multiple of itself. Prime numbers have exactly two factors: 1 and the number itself.

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