### Visualize Algebra as a Pattern

**Student:** Hi Kimi. What you are up to? What are you doing?

**Tutor:** Nothing much. I am just playing *and that will take* my mind off this Algebra exam I have next week.

How is randomly playing going to help you?

**Student:** At least it is going to take my mind off?

**Tutor: **Why don’t I actually try teaching you Algebra and this may probably will help you get a better grade in school?

Let’s take these pencils. And this is something I used to do in school when I actually liked stacking these pencils up till they actually tripped off and fell. Right now, let me just stack these pencils as we go along. When I am taking these 2 pencils and putting them there, I call them as levels.

So let me ask you a questions. How many levels do we have here?

**Student:** Hmm…3.

**Tutor:** And how many pencils have I used in total?

**Student:** 1,2,3,4,5,6.

**Tutor:** 6 right? So let me build 2 more levels. This… This is level 5. So, how many pencils do I have in total?

**Student:** So 6 + 12,3,4 …that is 10.

**Tutor:** Yes.

Now, so if I make this 30 levels…let me make it complicate it further…If I make it 60. How many pencils have I used?

You don’t need to be this perplexed. We can actually use Algebra to actually solve this particular problem. Now that’s exactly what we do in mathematics as well. We try finding out patterns and let’s try finding patterns out here.

Let me just remove all of these out and let’s reconstruct this. The initial level has got 2 pencils. The next level has got 2 more pencils, which effectively means if I have built 2 levels, I have used 4 pencils. Now, if I build 3^{rd} level, it’s got 6 pencils.

Now do you observe a pattern? Do you see that 2 pencils is always a constant for every level, which effectively means every level we are adding 2 pencils and 2 becoming a constant. Therefore, as and when I keep increasing level, all that I will have to do is to keep adding 2. And in Algebra that we basically do is to have this written as **2 into n**, where n is the number of levels that you will basically be having. There for you will have 2n, and if it 30 levels, you will have 2 into 30, that is going to be 60 pencils. If you have 100 levels, you will have 2 into 100, which is going to be 200 pencils. And Algebra actually made it very very easy for you to solve all of this. This is what mathematics and Algebra does. They take complex concepts and puts them into simple patterns. And in this case the pattern was **2n.**

Now. Let me try showing you another pattern. Now let’s take a single triangle.

And let me flip this and make it into another bigger triangle.

Now there are 3 triangles in the second row. Let me do the same action again.

Let’s flip this once more and I see 5 triangles in the third row.

The first row has got 3 triangles, the second row has got 3 triangles and 3^{rd} row has got 5 triangles.

Let me continue and show u a pattern here.

Now if I start tallying the number of triangles that are there: first row has got triangle; the first and the second row put together has got 4 triangles; the first second and the third row put together has got 9 triangles.

Do u see a pattern?

1, 4, 9.

And that happens to be square numbers.

And such a complex diagram in terms of algebra and in terms of pattern has been simplified into a pattern which is n^{2} where n is the number of rows that are there in the triangle.

So when I say n = 1, I get 1 triangle.

When n=2, I get 4 triangles. When n= 3, I get 9 triangles…and I can continue.

N=4 gives me 16, N= 5 gives me 25, n= 6 gives me 36 and I can go on and on and on and even if I have to actually find if n =100, that will just give me 10,000 triangles.

Have u seen triangles in pattern this way?

Do u want to learn Algebra in this format?

Do u want to learn Algebra in this format?