# Number Line

Milton is making his way up the stairs. He stops at a specific location to rest. He now considers that location as a reference point and chooses either to go up or down the stairs. When he goes up, he adds one to each stair. When he goes down, he subtracts one from each stair. The concept of Number Line can be used to illustrate this mathematically.

A number line is a straight horizontal line where the numbers are placed at equal distances in the increasing order.

Illustration 1:
In a class, consider two students, Steve and Peter. Teacher instructed students to jump over the horizontally arranged blocks pictured below. According to the teacher, Steve had to jump 5 blocks; Peter had to jump 6 blocks. How did they jump? Where did they start from? Refer to the images below.

A student will be able to observe that as Steve and Peter jump, they move forward. They both started from the block numbered ‘0’; 0 is their initial point.

When you move forward on the number line, you will add one to the previous number. Similarly, when you move backward on the number line, you will subtract one from the next number. Refer to the image below.

Number line has both positive numbers and negative numbers along with zero in it. Observe the image given below. The arrows at the two ends of the number line indicate that the numbers go on and on. There is no end for the numbers. Zero is a number that represents no quantity by itself. Positive numbers are nothing but counting numbers.

Numbers that are greater than ‘zero’ are described as positive numbers. Plus (+) sign in front of the number indicates the number to be positive. However, we do not put ‘+’ sign to positive numbers in most of the cases; without a + sign, a number is considered to be positive. For example, 2 can be written as +2.

Numbers that are lesser than ‘zero’ are described as negative numbers. Minus (-) sign in front of the number indicates the number to be negative. For example, 8 with the negative sign can be written as -8 (minus 8). Negative numbers are used in giving penalty (Quizzes), freezing point (Temperature), credit points (Banking).

## What are the uses of Number Lines?

A number line is useful to

• Perform mathematical operations such as addition, subtraction and multiplication.
• Solve many real life example problems can be used using a number line.
• Compare and order numbers.
• Illustration 2:

Ms. Bunny, a rabbit, likes to jump on the number line in the positive direction as shown in the image below. While she jumps, she notices a few numbers are missing on the number line. Could you help her find them?

Remember that when the rabbit is jumping in the positive direction, it adds one to its previous number. Thus, when she needs to jump after 2, the number should be ‘2 + 1’, that is 3; the number after 4 will be ‘4+1’, that is 5. Refer to the image below.

## How do you write a number line?

One can follow the steps shown below to draw the number line.

Step 1: Draw a horizontal line with arrows in both the ends. Mark points or small lines equally spaced as shown below.

Step 2: Mark ‘0’ at any point on the line. Mark positive numbers to the right of ‘0’ and negative numbers to the left of ‘0’.

Illustration 3:
In a school, a group of students were given cards with numbers on them as shown below.

Each student should arrange the number on the number line in the correct order. Let us see how the students make an arrangement. The number line with blank is provided below.

When you observe the number line, you notice that numbers are arranged in the ascending order from the left corner to the right. Here, -3 is the least number, followed by -2, -1 and so on. Therefore, we can arrange numbers on the number line as pictured.

## Math Facts

• When creating the first accurate thermometer, Fahrenheit chose 32 as the figure for the freezing point of water. He seemed to understand how to use a number line to represent temperature, but he couldn’t explain how to convey a measurement of less than 0.
• ### Can you do it for yourself?

Fill the missing numbers in the given number lines.

## Mathemagician

A number line is an abstract concept that was discovered in the 20th century.

Wallis has made outstanding contributions in the fields of calculus, geometry, and trigonometry. He is generally credited for introducing the idea of the number line, in which the positive and the negative numbers are represented geometrically on a straight line, on either side of ‘0’.

Know more about other concepts of Number Sense on Cardinality, Ordering Numbers, Odd and Even Numbers, Counting Numbers and Rounding Numbers

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