Divide a Square in Half

Some time last year, I got my Year 4 class to divide a square in half and see how many ways they could do it. We had a lot of fun.

So there I was sitting in my first session at the National Council for Teachers of Mathematics (NCTM) conference in Denver this morning. 

The session was titled "And The Area Is...Because!" and the presenters were Kathleen Fick and Nicola Edwards-Omolewa.

The session was fantastic. I loved it.

And the first activity set the pace. 

We were given pieces of paper - origami squares - and asked to fold it in half.

How hard could that be? And how many ways could there be?

Here are some of the ways 

- I'm sure there are more!

See how many you can work out!

Here is the original origami square - you can see some of the folds I used for one of the shapes.

Here is a hexagon - the fold lines might help you see how it is half of the original square

The house - simple yet effective

Square - explain this to the kids in terms of fractions of the whole!

An octagon - not regular which I find annoying - I'm still working on a regular one

The kite - very nice combination of triangles

Isosceles triangle - very nice

Parallelogram - hint: the two short sides were edges of the original square

Trapezoid - this one my 4th graders showed me last year. 

As one of the boys said, "Any straight line that goes through the middle of the square will cut it in half!"