If I needed to choose the most productive portion of most students’ week, Monday morning, first hour would be pretty low on the hierarchy of engagement. I was undeterred because making sure we had the correct solution was important.
We discussed that the radius of the spool would decrease every time a layer of wire was used. They began calculating the resulting wire as layers were removed. This served as an excellent opportunity to introduce summation notation and a great practical use for the mathematics behind it. It seemed like a much better option than to add up dozens of calculations anyway.
When we arrived at our correct answer (with the desired units) of 1.98 miles, the questions and estimating didn’t end. They wanted to know how far they could stretch such a wire. Would it go to the edge of our campus and back? Would it go from here to the middle school? Could you go all the way to the grocery store?
They settled on taking the wire, running it out to the edge of the soccer practice fields and then running it all the way to the middle school sign. It ended up being, to the hundredth, the exact amount of wire we had, provided that someone would stand and hold the wire at the edge of the soccer field. I loved the attention to precision. I also loved that they were so savvy with Google Earth.