I will soon be implementing Christopher Danielson’s Hierarchy of Hexagons in my high school geometry class, and would love suggestions.

Some necessary background: I teach in an all-girls private school with a pretty high academic reputation. The girls at my school are generally very academically motivated. We do have tracking, and my class is the “standard” track, which in the context of geometry mostly means they are not usually ready to dive right into the formal rigors of traditional geometric proof without a good bit of build-up (thank goodness, since I hate teaching 2-columns). We have small class sizes – my larges is 17 – and a block schedule with 80-minute periods.

Here is my current plan:

Four groups per class, 3-5 students per group (only one group of five). 2 sets of hexagons, 16 different ones each sketch. Not giving out hexagon 1, which is the regular one: saving that one for me.

I will be doing this after defining all of the geometric building blocks – point, line, segment, ray, angle, parallel, perpendicular – but we will NOT have defined any polygon terms. I also really hit formal definition-writing hard at the beginning of the year, and they will have been assessed on definition-writing in a formal setting TWICE by then. I still think it will be difficult for them to define the hexagon categories, but hopefully easier than a cold-turkey class.

**Day 1 – 80 minutes**

- Give each group 7/8 hexagons. Have them look at them, trade them around, and choose one each that “speaks to them.” So now each group has 3-5 shapes.
**10 minutes**

- Students work individually to write a definition of their
*hexagon category*and give it a name. In the process: try to sketch / geogebra-sketch at least one other hexagon that fits their category, and at least one that*almost*fits, but doesn’t.**20 minutes.**

- In groups, students share their shape and their definitions. They can discuss the definitions and their potential downsides for
**10 minutes**after which the definitions become “locked” (at least without approval from me for unlocking).

- Then they start Venn diagramming. Taking their shapes two at a time, then three at a time, they start trying to figure out where there is overlap in their categories. I will go around during this period and add the regular hexagon (with the traditional definition) to the mix, so they can start seeing how it fits. I will also document their definitions and category names during this time.
**Remaining class time**. Key questions: Do any categories fit inside any of the other categories? Are some categories mutually exclusive? Can you find an example of a hexagon that is a _______ and a _______? A ______ but not a ________? Neither a ________ nor a _________?

**Day 2 – 80 minutes**

- In their groups, students will continue the venn diagramming and hierarchy process. If they want, they can create additional names for “overlap” categories (a Bob is both a Utah and a Stacy).
**30 minutes**?

- At this point, the venn diagrams should either all be complete or students will be stuck on something. Have them join up with another group (one that had different hexagons), so now have groups of sizes 6-9. Going around the circle, each person presents which hexagon they chose, what they named the category, and their final definition. Then they explain each of their venn diagrams and their conclusions. They start taking notes about where their shapes would fit inside of each other’s hierarchies. They

**Day 3 – 80 minutes**

- In their large groups, the students work to create a poster that includes all of their hexagon categories, definitions, and examples. They will glue on drawings and printed geogebra sketches as needed.
**50 minutes** - Each group presents their poster to the other large group (and me). They will likely have many of the same shapes, but completely different hierarchies, definitions, and names. We discuss this – we have just found some of the same truths, but attacked them from completely different angles. This is math.
**Remainder of class.**

Does this pacing seem remotely reasonable? Does doing it in half-classes like this make the most sense? Is there anything I’m misisng that is going to bite me in the bottom? I can’t really spend much more than three class periods on it, so if if this is going to fail miserably, I think I’d rather know it now before diving in.