‘Imagine that there is a Line of Numbers, and each Number is a Person that is standing up straight. Take any number in the middle. It has a ‘Friend’ before it, and another Friend after it.’ Now, that’s probably the best way to begin describing Consecutive Numbers to Preschoolers.
While the above might seem a good option, it’s only the beginning of a far more elaborate process that is designed towards teaching children about Consecutive Numbers. Needless to say, learning about Consecutive Numbers is of great significance. After all, they do tend to crop up every now and then in Math problems, and even in Real Life!
In this article, we will attempt to uncover a detailed explanation of What are Consecutive Numbers. We will explore Consecutive Number Examples, as well as sneak a glimpse into things like the Sum of Consecutive Numbers, and even a Consecutive Numbers Formula!
Are you ready for some Consecutive Learning Fun? It would be a good idea to begin, with a closer look at what Consecutive Numbers really are.
Consecutive Numbers: A Closer Look
What are consecutive numbers?
Like we briefly touched upon in the introduction to this article, Consecutive Numbers are akin to a ‘Team of Numbers’, with the individual teammates standing beside one another. That is, without any gaps in between!
The ‘friend’ that we talked about earlier, the one ‘before’ a number in the line, is called the Predecessor. On the other hand, the friend that finds itself ‘after’ the number in question, is called the Successor.
Example: Consider the Team of Numbers 1, 2, 3, 4, 5, 6.
In the above example, the Predecessor of the number 2 would be ‘1.’ Its Successor would be ‘3’.
A good way to understand Consecutive Numbers is by likening them to ‘A sequence of Integers in which each number follows the earlier one with a consistent difference.’
Note: In general, this ‘consistent difference’ is the number 1.
Consecutive Numbers Examples: Taking the first number to be ‘x’, the series of Consecutive Numbers will be: ‘x, x+1, x+2, x+3, x+4’, etc.
Also Read: Learn How to Memorise Multiplication Tables
Consecutive Numbers: How to Find Them
Want to find consecutive numbers? It’s really not that hard!
- To do: Start with an initial value. In mathematical parlance, this is called the ‘First Term.’
- For Positive Consecutive Numbers: Add a constant difference to the numbers in sequence. So, you need to add ‘1 ‘1’to the first term, to get the next number in sequence. Then, you repeat the process until you get all the consecutive numbers you need.
- For Negative Consecutive Numbers: Use the same pattern as outlined above, but subtract 1 from the first term, to get the numbers in succession.
Consecutive Numbers: Even Integers
What are Even Integers? They are the Integers that are divisible by the number 2.
Example: 2, 4, 22, 104, -36, -44, etc.
To understand consecutive even integers better, take the case of the following number range: 10, 12, 14, 16, 18, 20
In the above example, you will find that the pair of Predecessor and Successor is the number 2.
Consecutive Numbers: Odd Integers
Odd Integers are Integers that are not divisible by 2. Examples: -3, -15, 47, 93, 1, 343, etc.
Once again, we can employ the use of the following Range of Numbers, to help preschoolers better understand Consecutive Odd Integers: 1, 3, 5, 7, 9, 11
In the above example, we can see that we start with an Odd Number. Further, the difference between the Successor and Predecessor, is yet again the number 2.
Also Read: Different types of quadrilaterals: Parallelograms And Rectangles
Sum of Consecutive Numbers: The Formula
Up until now, learning Consecutive Numbers has been a breeze. It’s whenever the word ‘Formula’ steps into the field of Maths, that things get a wee bit difficult. Like, with Consecutive Numbers! Luckily, it’s not all that tricky!
Let us consider the following example, to explain the ‘Sum of Consecutive Numbers Formula.’ When we take the number ‘n’, the couple of consecutive numbers that are next in sequence are (n+1) and (n+2).
- Here is the formula for adding ‘n’ consecutive numbers: [a + (a + 1) + (a + 2) + …. {a + (n-1)}] So, in this instance, the sum of n consecutive numbers will be (n/2) × (first number + last number)
- In the case of Even Consecutive Numbers, the formula will be 2n, 2n+2, 2n+4, 2n+6,…
- In the case of Odd Consecutive Numbers, the formula will be 2n+1, 2n+3, 2n+5, 2n+7,…
Also Read: Surface Areas and Volumes: Calculating surface areas and volumes of various geometric solids.
The Properties of Consecutive Numbers: A Summary
To summarise all Consecutive Numbers, we must tell children that they must keep in mind the following:
- When it comes to the Predecessor-Successor Pair in Consecutive Numbers, the difference needs to be ‘fixed.’ Namely, 1 or more.
- The difference between any two Even or Odd Consecutive Numbers is always 2.
Solved Examples of Consecutive Numbers
Children will only get the concept of Consecutive Numbers firmly entrenched in their minds when they get to see Solved Examples of Consecutive Numbers. The following are some examples of solved Consecutive Numbers Problems:
- Question: For numbers that begin with 30 and end in 50, what are the Consecutive Numbers?
- Answer: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.
- Question: What is the sum of the consecutive numbers 11 and 12?
- Answer: The sum of these consecutive numbers is 11 + 12 = 23.
- Question: What are all the consecutive odd integers from 1 to 20?
- Answer: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
- Question: What are the consecutive even integers in the number range 1 to 20?
- Answer: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
Also Read: Memorisation Techniques for Students
At EuroSchool, we believe that learning Consecutive Numbers is an essential practice that must be encouraged by parents of all preschoolers. It helps children make use of their Analytical Skills, and find patterns in things. Besides, there are plenty of real-life situations where they will need a good knowledge of those Consecutive Numbers.
