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

Can you find the answer using blocks?

See the animation below:

**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

Can you find the answer using blocks?

The hint is in the animation below:

**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.

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:

Or are they unnatural?

The Natural numbers are the counting numbers.

**1**,**2**,**3**,**4**,**5**…#### 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

The answer is in the animation below:

**n**natural numbers?**1 + 2 + 3 + 4 + … + n = ?**The answer is in the animation below: