"Look, Mama! A triangle! Except...I didn't know triangles could do that. I knew that two triangles make a square..."
And therein lies the rub, doesn't it? For a kid who has played with tangrams (right triangles) and pattern blocks (equilateral triangles) for years, those are what triangles 'are' aren't they? Already shaped and scaled to make a whole of some other shape (rhombi, squares, rectangles, hexagons). But there this triangle was, obviously not dividing the space evenly, just a modest, unbalanced slice out of this square-ish rectangle portion of the sidewalk.
As we walked further I wondered about how to respond to her observation. As luck would have it, I had a stray piece of sidewalk chalk in my bag!
"There are a lot of ways to divide a square or rectangle into triangles. Let's see how many we can find!"
A little later on, "Look! More triangles!"
And here, a triangle? She thought it was at first, but what does a triangle need to have to be a triangle?
As a bonus, at the hardware store we found a section that specializes in tools used in real-life geometry -- things that help builders measure lengths, widths, diameters and angles!
In closing, and in honor of triangles, take a look at this triangle interactive from the Triangulation Blog. All you need to do is move your cursor/mouse. I swear, it'll be worth your time. Who knew triangles could be so funny!?
You may also be interested in a previous post, Channeling Tana Hoban: Juxtaposition Edition, where we discovered many, many more shapes on a similar walk, especially an incredible number of circles in juxtaposition with other shapes.