I gave the 4th Graders meter sticks today, and (of course) they did all sorts of weirdo things with them. Drumming, whacking things, marching while cradling the meter stick like a rifle.

They were *supposed *to be measuring the perimeter of the classroom.

One kiddo seemed to be trying to poke the ceiling, but he seemed to be doing it with enough care that I thought he might be measuring something.

—

**Me: **Wha?

**Him**: I’m measuring that jut in the ceiling.

**Me**: Why?

**Him**: Because it’s in the way, you’d have to follow it if you were walking on the ceiling.

(Note: I’d previously described perimeter in terms of path. The perimeter is the path you take around some region.)

**Me**: But you wouldn’t have to go around that thing if you were walking around the room this way, while standing on the floor.

**Him**: But you would if you were on the ceiling.

**Me**: But we’re not measuring the path on the ceiling, we’re going on the floor.

**Him**: Oh, I thought that we were measuring the perimeter of the *whole *room.

—

Now, maybe he was just being a punk because he wanted an excuse to poke the ceiling with a long stick. Maybe, though, he had a really interesting interpretation of perimeter, as *all *the paths that you take around a room. After all, there’s some ambiguity in the way I talked about the perimeter of the room, since the room is a 3D object, and perimeter is usually applied to objects in the plane.

That ambiguity, though, is a feature, not a flaw of the task assigned. Too many perimeter problems that I see young kids do only take place around rectangles or other polygonal shapes. This conversation with the kid was a really interesting one because it pushed on the messy process of finding 2D ways of seeing our 3D world.

## 2 replies on “Weird Conversation About Perimeter”

Not sure if you ever saw the Thought Provokers books. There is a great problem about the shortest route for an ant to get across a room. They can walk on walls and ceilings.

If they had only seen the concept of perimeter in the context of two-dimensional shapes, I can see where he got confused because now he’s looking at a three-dimensional shape.