## 2011/08/26

### What number is this?

We were working with Unix Cubes, exploring numbers and trying to think of how we can represent numbers using concrete objects.  I started with a basic questions, how can these blocks be turned into numbers?  From there, the students sat on the floor, alone or with a partner (social dynamics of the first week of school are still being worked out!), and just experimented.  I had no idea where the lesson was going to go, but I knew that something would come up and we could make a mess of ideas and turn into some conceptual understanding.  That is what is so great about free play.

Some students did the obvious, and turned the blocks into pictures of numbers, while others made flat blocks and showed multiplication facts.  Then, one boy came up to me and showed me this;

He asked, what number do you think this is?  I loved it.  We had an emergency Math Congress on the carper to discuss this stunning revelation.  I asked the boy who made the shape to stay quiet and just listen as the rest of the class discussed his work.  Originally a group of students thought it represented a simple number line, 19, since there are 19 blocks in the chain.  However, one girl decdided to take a risk and offer a different point and a mini-math debate erupted.

A: I think the colors represent something.

B: Colors aren't numbers!

A: Neither are blocks, but we are trying to think about numbers in different ways.

B: So what does it mean?

A: Maybe the green blocks represent something and you have to times it by the red block next to it.

B: And then times that number by the blue blocks.  So, we have 2 x 1 x 5 x 1 x 3 x 4 x 3.

A: Yeah, what does that equal (gets a calculator).... 360?

B: This seems like a silly way to represent 360.

Creator: It is not 360.

A: Does each color represent a number in a bigger number?

B: So it would be 2  151 343.

A: Because you are sitting on the other side you are reading it that way, on this side it reads 3 431 512

Creator:  That's right.

What a great conversation.  At this point I felt we had made a breakthrough and were ready to deconstruct this complex tangle of ideas we had developed.  It turned into a wonderful way to delve into place value.

## 2011/08/24

### Newness - The First Day Back

It has been a wonderful summer.  I started my M.Ed at the University of Calgary and I couldn't be happier about the direction that is going in.  The family successfully moved from Northern Japan to not so Northern Japan.  We are almost settled into our new house.  I have moved into a new school and prepared a new plan for a new class, working with a new curriculum.  My son is starting at a new daycare for the first time, and my wife is starting a new job.  And today, I met my new class.

I have a feeling this will be a year filled with new experiences and new directions.  I have a new lens on teaching and I am seeing the world in a new light.

More newness to come.