Build a staircase pattern

I needed some pictures of staircase patterns for a presentation I was doing at the recent Canberra Mathematical Association conference. So I put out the Cuisenaire rods out and the kids went for it.

I gave them 5 minutes and looking down, I saw a couple of standard staircases in front of me.

I was just about to say, "Can you do it another way?" when I looked around.

Here is what I saw. 

My creative bunch of crazy kids had already pre-empted my request and they had come up with 17 different staircases.

Here they are:

And then there was....

So in a class of 23 kids, we had 19 different staircases. 

There is so much maths to explore in these patterns. 
- What changes between each step of each staircase?
- How much does it increase (or decrease) by?
- What patterns can you see?
- Can you make predictions about what the 20th step would look like? or the 100th? or the nth?

Interestingly, the adults in my conference workshop didn't come up with quite as many different staircase patterns.

Never undersell the creativity of the students in front of you.