## Monday, September 28, 2015

### Does "center" always mean "half"?

I'm spending the next couple months trying out some new non-dance, moving- and body-scale math lessons for my new book.  There's an activity in Mathematics Their Way (from the '70s) that I want to try out.

The lesson is ostensibly about using your whole, moving body to find the "middle" or the "center" of a space that you can't fold. I was thinking I'd start my version of the lesson by asking first and second graders "What is half?" I planned to give them a piece of 8 1/2" x 11" paper and see what they come up with.

Except, as I was getting the materials ready today I noticed some paper cut into big triangles. I took one up to my 10yo who was doing her homework. I asked her to fold it in half. This is what she did.

Then I asked her to fold it into half again. The image below illustrates what she was doing for a split second before she said..."ah...no..."

At which point she said, "I can't fold it into half that way. But I can fold it into fourths."

I tried to get her to tell me how she knew when she had folded it in half, but she wasn't interested in talking. But it did make me wonder how I might fold this triangle into eighths.

Then I thought: Wait a minute! We've folded this triangle into eight one-eighths and still haven't found its center/middle. Or, well, maybe we did on the first fold ... but maybe there's another center we haven't yet found?

I love it when what I think I know is challenged. We need to do this for our students on a regular basis.

And, I'm rethinking my lesson for tomorrow. I'll focus on the language of "middle" or "center" and use rectangular and triangular paper. But "half"?  Half I'll save for another time.

1. Nice! I like the centre of a triangle - because there isn't just one:
http://seekecho.blogspot.fr/2012/12/journey-to-centre-of-triangle.html
Which fits with how I like my learning - there's more than one way.
I got my class hunting for the centre of triangles last year, and I think it's a great activity.

I've thought about asking, where is the centre of this room? How could you find out? So I'm interested how you will take this into big spaces, Malke.

2. Math has always been my favorite subject but I never tried to find out the center of a triangle. One gets more triangle while searching for the center. I will say that your 10 year old is one intelligent girl.

3. Wow i never wondered this! This is a very valid questions and our students must have this in their minds as well! i will clarify as well

Thanks for reading. I would love to hear your thoughts and comments!