This was my warmup today:
Draw a hexagon.
Draw a six-sided shape.
I followed up in our discussion with “Is a hexagon a 6-sided shape?” and “Are all 6-sided shapes hexagons?” Tomorrow they’re going to be in groups to categorize the shapes from Christopher Danielson’s Hierarchy of Hexagons project. These are my probably incoherent notes:
1st Period: Tenth graders were taking the ACT Plan, so they were not writing down warmup. Still had time to have a lively debate about hexagon- I had asked them to draw a hexagon and a six sided shape. Then I asked if they were different? Lots of people said yes, so we had to look up the definition of a hexagon
3rd Period: 4 9th graders only due to testing. Had them do the warmup- they focused on the definition of hexagon as having 720˚ internal angles. Were able to prove a polygon a hexagon by reasoning using the right angles. Then inferred that this example meant their previous notion of what a hexagon was needed to expand. WHOA. Then we worked on groupings- group the hexagons from Chris Danielson however you want. All 4 of them put each hexagon into one category only- I asked them if they thought a hexagon could be in more than one category. They were not convinced, but I could also tell they were rapidly losing interest. Next time I would try to push them more to write down more categories. Pics (disclaimer: one board is mine).
5th period: Got hung up on the terminology “irregular hexagon”. Big argument (unsettled) over if “irregular hexagons” could be called “hexagons”. S: “Why do they have the name irregular hexagons then?” Good question. First time seeing some people draw a six-sided shape as a 3-D rectangular prism or cube- different interpretation of the word “side”. Reminds me of Chris Danielson’s video “One is one. Or is it?”
6th period: Much less debate than 5th period. More students came up to board. Used online definition of hexagons, was able to use that to prove other shapes were hexagons. The 3D shape came up again. I felt good that we forced the need to define hexagon, especially with the 2-D “flat” and the fact that the sides didn’t need to be any particular length.
Many students had an idea of how a hexagon was “supposed” to look, probably based on a vast majority of experience with a hexagon being regular and not as much, or any, experience with irregular hexagons. Makes me realize how important it is to show a bunch of different examples to use to test any definition. Also makes students start thinking about how to go by definitions instead of just looks.