Aren’t infinite geometric series cool? If you just shouted “yes”, then you are potentially as geeky as I am. A “proof without words” from MathFail kicked off today’s discussion:
I wasn’t quite sure what sort of observations I would receive from my class. But just enough ideas were generated to get us going:
There are an infinite number of triangles down the right side.
All those triangles on the right add up to the half-triangle on the left.
Both are great starts for what I hope my students will learn today. A video I made in my driveway continued the ideas of geometric series and their infinite terms.
A few students wanted to argue that the sequence in the video was arithmetic, but some meaningful debate yielded agreement that geometric made more sense. Groups then worked through a similar problem involving a Superball being dropped, leading to terms and total distance traveled.
Many groups employed a “brute force” method to find their answers. Using the Desmos calculator (many students chose to use the iPhone app), we found value in developing the equation and using tables and summation symbols to find solutions. This was my first time usign Desmos with this particular lesson, and it was an awesome addition, which added value to the need for writing a clear function to define your situation.