Measuring Pi

After yesterday’s Family Math project I was thinking about a project with spheres so that we could talk about the area of the spherical caps from our printed shapes.  This morning i changed my mind and thought that a slightly more laid back project was in order, so we spent the morning trying to measure $\pi.$

The first thing that we talked about was basic definitions.  Just trying to set the stage for thinking about geometry, especially since I’ve not really spent much time talking about geometry with my younger son:

After getting through the definitions we started measuring.   We started with a can of chickpeas and then talked for a bit about why doing the same measurements with a cube would be different.

Now we moved on to some larger circles.  This required a larger area, so we moved to the garage.   Our first attempt here didn’t go so well as our estimate for $\pi$ was about 3.5.  I wasn’t too disappointed, though, since learning that measurements don’t always produce what you expect is an important lesson.

Our last prop was a bicycle wheel.  This experiment required a little bit more room than our camera could handle, so we split it into three pieces.  We got an estimate for $\pi$ that was a little low, but it the best estimate of the bunch.    After we finished the calculations on this one we talked through a few of the aspects of our measurements – is it easier to get an estimate for $\pi$ with a large circle or a small circle, for example.

Definitely a fun little set of experiments.  Fun to see the boys rolling up their sleeves and taking a few measurements, too.