Math Number Lines

9 times (9x) Multiplication Table

Related Resources The Multiplication and division resource above is aligned (wholly or partially) with standard 3OA07 taken from the Common Core Standards For Mathematics (see the extract below). The various…

Number Line: 0 to 60 at Intervals of 5

Related Resources The Counting and cardinality Number Line above is aligned, either partially or wholly, with standard 2NBT02 taken from the CCSM (Common Core Standards For Mathematics) – see the…

Blank Number Line – Ticks at 5s and 10s

Related Resources The Counting and cardinality Number Line above is aligned, either partially or wholly, with standard 2MD06 taken from the CCSM (Common Core Standards For Mathematics) – see the…

Blank Number Line – No Tick Marks

Related Resources The Counting and cardinality Number Line above is aligned, either partially or wholly, with standard 2MD06 taken from the CCSM (Common Core Standards For Mathematics) – see the…

Big Decimal Number Line: -10 to 10 in hundredths

Related Resources The Decimals Number Line above is aligned, either partially or wholly, with standard 4NF06 taken from the CCSM (Common Core Standards For Mathematics) – see the extract below)….

Time Number Lines

Related Resources The Time Number Line above is aligned, either partially or wholly, with standard 3MD01 taken from the CCSM (Common Core Standards For Mathematics) – see the extract below)….

Clock face with hours and minutes number lines

Related Resources The Time Number Line above is aligned, either partially or wholly, with standard 2MD07 taken from the CCSM (Common Core Standards For Mathematics) – see the extract below)….

Large Scale Number Line: 0 to 100 on 13 Pages

Related Resources The Counting and cardinality Number Line above is aligned, either partially or wholly, with standard KCC01 taken from the CCSM (Common Core Standards For Mathematics) – see the…

What is a number line?

A number line is a straight horizontal line with numbers placed at even intervals that provides a visual representation of numbers. Primary operations such as addition, subtraction, multiplication, and division can all be performed on a number line. The numbers increase as we move towards the right side of a number line while they decrease as we move left.

Representation on a Number Line

Above is a visual representation of a standard number line. As is clearly visible, as we move from left to right, there is an increase in the value of numbers while it decreases when we move from right to left.

Examples

1.         On which number is the ball sitting on?

Answer: Count the points from 0 and you will notice that the ball is sitting on number 3.

2.         Suppose the ball in the example above moves 5 points towards its left side. Which number it would be sitting on now?

Answer: Make the ball jump 5 points towards its left and you would find that it lands on the number -2.

Finding out the greater number among two or more numbers

A number line helps you visualize which is a greater number among two or more numbers. The farther a number is on the right, the greater it is.

For example, let us consider the following numbers: -2, 8 and 3

Plot these numbers on a number line.

Out of the three given numbers, -2 is on the farthest left while 8 is on the farthest right placing 3 between these numbers.

Hence the increasing orders of the numbers -2, 8 and 3 is

-2 < 3 < 8

Operations on a Number Line

The four basic operations- addition, subtraction, multiplication, and division are the fundamentals of mathematics. The number line is one of the methods that allow visually understanding of these operations.

 Addition on a Number Line

We move to the right on our number line for adding two numbers. The following example shall help you understand how to add two numbers to a number line.

For example, you want to add 3 + 2

Steps involved:

1.         First draw a number line having both negative as well as positive numbers.

2.            Mark the first number 3 on this number line.

3.            Move 2 points right as we have to add the numbers.

4.         The number we have our point on is our answer, i.e. 5

Hence 3 + 2 = 5

Subtraction on a Number Line

Subtraction on a number line is similar to what we do in addition with the only difference being that instead of moving right on the number line, we move left. This can be better understood through the visual depiction of subtraction in the example below –

Suppose we want to obtain the value of  3 – 2

We proceed in the same manner we did for addition.

Steps Involved :

1.            First draw a number line having both negative as well as positive numbers.

2.            Mark the first number 3 on this number line.

3.            Move 2 points left as we have to add the numbers. (Notice the change- we move left and not right as we did in addition)

4.            The number we have our point on is our answer, i.e. 1

Hence 3 – 2 = 1

Multiplication on a Number Line

Multiplication is nothing but repeated addition. We move towards the right side of the number line for a given number of times in order to multiply two numbers.

For example, we want to obtain the value of 2 x 3

Steps Involved:

  1. In order to multiply 2 by 3, we first mark 2 on the number line.
  2. Then we jump 2 points each from 2 three times. The number we land on is our answer, i.e. 6

Hence 2 x 3 = 6

Division on a Number Line

Division on a number line is similar to what we do in multiplication with the only difference being that instead of moving right on the number line, we move left. This can be better understood through the visual depiction of subtraction in the example below.

For example, we want to obtain the value of 12 ÷ 3

Steps Involved:

  1. First we mark the number 12 on the number line.
  2. Then we divide the numbers from 0 to 12 into 3 equal groups which gives us the answer 4. Hence 12 ÷ 3 = 4

The above example can be visualized on a number as highlighted below:

 

Importance of Number Lines

Numbers lines are mostly overlooked and taught as introductory topics for mathematical operations only. However, they form the basics of understanding these very operations that are the backbone of mathematics. Number lines are an important concept as

  1. They help you visualize the mathematical operations, especially when dealing with negative numbers that make you understand the operations in a better manner.
  2. Also, they promote good mental arithmetic strategies.

Have you ever noticed the readings of a clinical thermometer? It is based on the concept of number lines. The temperature increases as you move right and decreases as you move left. There are many other examples where number lines are used in real-life situations such as a ruler that we use in everyday life. Find out more about such objects in your house/school and other areas and you will be surprised at the large-scale usage of these number lines.