## Tuesday, January 10, 2017

### Homeschool Math: Marking Giant Circles in the Snow (and Measuring the Radius of a Signal)

It was snowing up a storm on the day that I'd planned for us to explore acoustic signals in animal communication, specifically how to measure the range of a signal.

Snow was absolutely perfect. It meant that I didn't have to get out the upside-down spray paint!

But first, it was really important that we play with the dog. You understand.

 The relationship between this kid and her dog is my favorite thing.
Our measurement of the radius of a signal was a little wild and woolly, but basically, it goes like this:

1) We set Will up in a clear spot, with Mozart playing on her tablet at a level of about 60 decibels (as measured using an app on my phone--what would we do without technology?). Will had one end of a rope, and Syd had the rest of the rope, feeding it out as she backed away, to the point at which she could no longer hear the music. She might be able to hear a little bit of the sound, but she shouldn't be able to understand what she was hearing. The information of the signal should be lost.

2) When she reaches that point, she and Will keep the rope taught between them as Syd shuffles her feet around the circumference of the circle that the radius makes:

3) When she's back to her starting point, the kids use a tape measure to measure the radius of the circle that they've created:

With this information, you can calculate the diameter that measure the full linear distance of the signal, or the circumference that is the outer edge of the signal, or the area of the circle in which the signal can be understood.

And look at what a lovely circle they've created!

To play with our understanding, I had the kids go into our woods and perform the same experiment to find the radius of the signal:

My hypothesis (which I didn't share with the kids) was that the radius would be shorter, as trees and brush would be in the way of the signal. Actually, however, the kids found that the radius was longer than it was in the open field!

New hypothesis: the woods is further away from the road and the houses than the field, so is less subject to ambient noise that interferes with the signal.

We marked our giant circle in the snow as a tool for a science project, but of course this is the perfect activity for geometry units. Get yourself a nice, big, snowy field, and you can make those circles in the book come to life, as well as practice the real-life measurements and calculations that are always so much more interesting when they're done on anything other than paper.