Used non-examples in a good way today, improving on a lesson I did last year.
I was teaching a lesson to my 7th graders on finding volume by multiplying cross-sectional area (using the beautiful formula ). I had a lot of fun bringing in Eggos, bread, lifesavers, cd’s, odd post-it notes and other containers so they could gain facility at picking how to slice their objects. Then I did a small thing I neglected last year – I brought in objects which do not have identical cross sections.
Instead of going through each object and asking ‘How would you slice this?’, the question was ‘Can you slice this identically?’ It was such a minor change, but I am that much more confident about their ability to pick the appropriate cross sections.
On a side note, the great part about teaching both Calculus and Algebra is that I get to grease my own wheels in stuff like this.