Polygons and Non-polygons

We are moving in to looking at 2D shapes. Our conversation started with a bit of a provocation.

My colleague and I drew up a chart on the white board and we had a stack of pictures of different shapes. Without saying anything, we started placing our shapes into either category - polygons or non-polygons.

We ended up with this:

The idea was to get the kids to think about what we had used as criteria for making decisions about placing items into categories. 

...and the ideas started coming. 


Here is our conversation and the ideas from the kids:

Question: So what is a "polygon"?

Piper – It’s probably a shape.

Sam – They’re shapes that don’t have any round bits on them. All of the lines are straight.

Sarah – They have straight sides.

Josiah – The oval is not a polygon because it has no straight sides.

Andrew – Polygons have straight and non polygons have curved sides.

Rupert – Some of them have four or five sides.

Liam – They have 3 or more sides.

Carys – They can’t have 2 sides; it would have to be curved.There are only two points on the straight line to get joined up so you need a curve.

Alexander – If a side is not joined up then it is not a polygon.

Andrew – The sides of a polygon don’t have to be the same size.
Molly – The sides can’t cross over.

So we distilled it down to one statement:

A polygon is a 2D closed shape with 3 or more straight sides that do not cross over each other.

Happy with that?

Well, then we started throwing out a few more examples and asked the kids to place them in the appropriate group.

One of our very perceptive students was given this picture and sat for a significant time pondering where to place it:

I was confused. Why was she hesitating?

I soon found out.

"Well," she said, "It has most of the things. It is a 2D shape, the lines all join up so it is a closed shape. They don't cross over. It has more than 2 sides. The only thing it doesn't have is straight sides. So it has 4 out 5 things for a polygon."

Nice thinking Abbey!

This raised the important point: being a polygon means you have to have all 5 criteria:
1. 2D shape
2. Closed - no gaps
3. Straight sides
4. 3 or more sides
5. No crossing over

If you fail one of these things, you are not a polygon.

So I went looking for examples that were "almost" polygons: 4 out of 5 of these things but only missing one of them.

Like this one:

straight sides - check

3 or more sides - check

closed shape - check

no crossing over - check

2D shape - uh-oh!

straight sides - check

no crossing over - check

closed shape - check

2D shape - nope

3 or more sides - nope

I wonder what other shapes we could find that are "almost" polygons? I think this question helps use to examine shapes using our definition and make appropriate decisions when classifying shapes. 

And the kids went off to search for new shapes to look at...