Representation on Number Line | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

Below are the steps to represent whole numbers on the number line:

• Draw a straight horizontal line.
• Mark a point at the extreme left as 0.

Mark points to the right of 0. Label them as 1, 2, 3, .... The distance between consecutive marks must be uniform; each such distance is called a unit and the points are said to be at a unit distance from one another.

Addition on the number line

To add two whole numbers using the number line, start at the first number and make jumps to the right equal to the second number. Each jump is of one unit.

Example: Find 4 + 7 using the number line.

Start at 4 on the number line.

Make 7 jumps of 1 unit each to the right from 4.

After the first jump you reach 5.

After the second jump you reach 6.

After the third jump you reach 7.

After the fourth jump you reach 8.

After the fifth jump you reach 9.

After the sixth jump you reach 10.

After the seventh jump you reach 11.

Therefore, 4 + 7 = 11.

Subtraction on the number line

To subtract a whole number from another using the number line, start at the minuend and make jumps to the left equal to the subtrahend. Each jump is one unit.

Example: Find 6 − 4 using the number line.

Start at 6 on the number line.

Make 4 jumps of 1 unit each to the left from 6.

After the first jump you reach 5.

After the second jump you reach 4.

After the third jump you reach 3.

After the fourth jump you reach 2.

Therefore, 6 − 4 = 2.

Multiplication on the number line

Multiplication can be seen as repeated addition on the number line. To compute a × b, start at 0 and make a jumps of size b, or b jumps of size a - both give the same result.

Example: Find 4 × 3 using the number line.

Start at 0 on the number line.

Make 4 jumps of 3 units each to the right from 0.

After the first jump you reach 3.

After the second jump you reach 6.

After the third jump you reach 9.

After the fourth jump you reach 12.

Therefore, 4 × 3 = 12.

Division on the number line

Division can be represented as repeated subtraction or as counting equal jumps. To divide a number by d, start at the dividend and make jumps of size d to the left until you reach 0. The number of jumps is the quotient.

Example: Find 10 ÷ 2 using the number line.

Start at 10 on the number line.

Make jumps of 2 units each to the left from 10 until you reach 0.

After the first jump you reach 8.

After the second jump you reach 6.

After the third jump you reach 4.

After the fourth jump you reach 2.

After the fifth jump you reach 0.

Number of jumps = 5.

Therefore, 10 ÷ 2 = 5.

Solved Examples

Ques 1: Fill in the blank: 
On a number line, the greater whole number lies to the ___ of the smaller whole number.
Sol: The greater whole number lies to the right of the smaller number.

Ques 2: Solve 12 ÷ 6 using a number line.
Sol: We start from 12 and make jumps of an interval of 6 points to the left.
After the first jump we reach 6.
After the second jump we reach 0.
There are two jumps. So, 12 ÷ 6 = 2.

Natural numbers

Natural numbers are the counting numbers: 1, 2, 3, 4, ....

If we subtract 1 from any natural number we get its predecessor. If we add 1 to any natural number we get its successor.

The predecessor of 5 is 5 − 1 = 4.

The successor of 5 is 5 + 1 = 6.

Is there any natural number that has no predecessor? The predecessor of 2 is 1. The predecessor of 1 would be 1 − 1 = 0, but 0 is not a natural number (it is a whole number). So, among natural numbers, 1 has no predecessor that is also a natural number.

Whole numbers

Whole numbers are obtained by adding 0 to the set of natural numbers. Thus, whole numbers are: 0, 1, 2, 3, ....

Example: If you have 5 chocolates and give all 5 away, the number you have left is 0.

Properties of zero

• Any number multiplied by 0 gives 0.
• Adding 0 to any number does not change the number.
• Subtracting 0 from any number does not change the number.
• 0 is the smallest whole number.

Even and odd numbers

The whole numbers are classified into even and odd numbers.

Even numbers

Numbers divisible by 2 are even. Even numbers leave 0 as remainder when divided by 2. Their unit digit is one of 0, 2, 4, 6, 8. Examples: 2, 4, 6, 8, 10,....

The set of even numbers can be written as Even = {2n : n ∈ integer}.

Is 0 an even number? Yes, because 0 = 2 × 0.

Odd numbers

Numbers not divisible by 2 are odd. Odd numbers leave 1 as remainder when divided by 2. Their unit digit is one of 1, 3, 5, 7, 9. Examples: 1, 3, 5, 7, 9, 11, ....

The set of odd numbers can be written as Odd = {2n + 1 : n ∈ integer}.

Steps to check for odd and even numbers

• Divide the number by 2.
• Check the remainder.
• If the remainder is 0, the number is even. If the remainder is 1, the number is odd.

If you subtract any two odd numbers, the result is an even number. If you multiply any two odd numbers, the product is an odd number. These properties can be verified by writing odd numbers as 2n + 1 and using simple algebra.

Solved Examples

Ques 1: Is 134256791 an even number?
Sol: The unit digit of the given number is 1 which is odd. The above number will leave 1 as a remainder when divided by 2. The number 134256791 is odd.

Ques 2: What is the sum of two even numbers? What is the sum of two odd numbers?
Sol: The sum of two even numbers is always an even number. Two odd numbers add up to give an even number.

Teaching tips for classroom use

• Use a long floor number line or a taped/hung number line in the classroom for group activities.
• Ask pupils to use coloured counters or hop along a floor number line to perform additions and subtractions physically.
• Use real-life contexts (steps climbed, money gained/lost) to make number-line jumps meaningful.
• Introduce multiplication and division as repeated addition and repeated subtraction on the number line with small whole-number examples first.
• Highlight common misconceptions: (a) greater numbers always on the right, (b) consistent unit spacing is essential, (c) negative numbers lie to the left of zero.
• Design quick formative checks: ask students to show 3 + 5 on the number line, or to show where −2 would be after introducing negatives.

Summary

The number line is a visual tool to represent whole numbers, perform addition, subtraction, multiplication and division, and classify numbers as even or odd. Consistent unit spacing and correct direction of jumps (right for addition, left for subtraction) are the key ideas. Using physical and visual activities helps pupils internalise these concepts effectively.