So I did the cup exploration the first day of school with my Geometries and Precalcs. I didn't do the theatric hangman intro that I had dreamed up. It didn't seem like me.
Kids wrote down great "I wonder" statements.
-I wonder why the cup rolls in a circle.
-I wonder how the shape of the cup affects the way it rolls.
-I wonder if bigger cups roll in bigger circles.
Some kids thought of cones and cylinders (extreme cases) right away.
One kid came up with the idea of his cup being a truncated cone.
Kids worked together.
Kids had good intuition about how oddly shaped cups would roll.
Kids thought about what was important to measure at the end when I was about to collect the cups.
Kids came up with ideas of slant affecting the roll and the difference/ratio of the size of the top circle to the bottom circle.
Kids wanted to "do this all year". (Maybe because it's low-pressure?)
Even after I explained why we were doing a "pointless" exploration (foster curiosity, researching theories, growing the creative part of our brain) some kids complained.
Some kids were off task unless I was with them asking probing questions.
Toward the end of the day, I responded to apathy with entirely too much help and prodding. Not sure how to avoid this - most of my questions got bored looks in response.
I wish I had a greater variety of cups. I found some bowls which really promoted some ideas. More variety might make kids more curious too.
-A girl brought in some plastic martini/wine glass style cups the second day. The kids predicted which would roll a bigger circle. And they were right! And it made the biggest circle of any cup I had - they even knew why. :)
-I got pretty excited when I started to wonder what the square bottom/circle top cups I left at Walmart would do. I wonder if they'd roll a polygon. If so, I wonder if I could figure out what type.
I'm glad I was given permission from the online community to end class without having a nice tidy answer to all of our wonderings. I'll bring it back with similar triangles when the time comes in geometry. With precalc, who knows. I tried to drive home the point with the kids that it's the thinking process, not necessarily the solution, that is valuable.
Letting them work freely and cooperatively gave me a quick look at which classes would benefit from a seating chart. Day 2 went pretty darn smoothly because of this!