odds & evens

How could you add the first four odd numbers?

1 + 3 + 5 + 7 = ?

Just add them, right? How difficult is that? You could even use your fingers or a calculator. It’s simple!

But how could you add the first 1000 odd numbers? Or the first 1,000,000 odd numbers?

Let’s take a look! In Grades 2-3 and in Grade 11.

Below are the odd numbers 1, 3, and 5 represented using blocks:


  • Notice how the pattern grows.
  • Build similar models of odd numbers 7 and 9.
  • Without changing the shape of each number, move them around and see if you can make them fit together to form a single shape.
  • What did you notice?

How can you find the sum of the first n odd numbers?

1 + 3 + 5 + 7 + … + (2n-1) = ?



Can you find the answer using blocks?

See the animation below:




What about even numbers?

Below are the even numbers 2 and 4 represented using blocks:


  • Notice how the pattern grows.
  • Build similar models of odd numbers 6, 8, and 10.
  • Without changing the shape of each number, move them around and see if you can make them fit together to form a single shape.
  • What did you notice?

Can you find the sum of the first n even numbers in the same way you did with odd numbers?

2 + 4 + 6 + 8 + … + 2n = ?



Can you find the answer using blocks?

The hint is in the animation below:

The Natural Numbers

Aren’t odds and evens natural too?
Or are they unnatural?
The Natural numbers are the counting numbers.

1 , 2 , 3 , 4 , 5

So, the odd and even numbers are Natural numbers also. But each of them, on their own, make up only half of the Natural numbers.


Drawing Natural Numbers


Let’s build a growing pattern of the natural numbers. You can use building blocks or colour crayons and a grid (grid pdf file) as in the image below:


  • Notice how the pattern grows. Continue the pattern for numbers 4 and 5.
  • How is this pattern different from the one you did for odds and evens?
  • What happens if you make two copies of the natural numbers?

Can you find the sum of the first n natural numbers?

1 + 2 + 3 + 4 + … + n = ?



The answer is in the animation below: