Hexagons, part II: Return of The Pakman

When we left our intrepid adventurers they were faced with the perplexing question:


The class was divided. Consensus seemed impossible. The original group was adamantly opposed to the idea; the rest of the class seemed open. Some students–*gasp*–seemed not to care one way or the other!

Ambiguity in a math classroom. It must have been a cold day in a very hot place…

However, that place was not San Francisco:

weather 1.6

Clearly *we* did not have school off because it was “too cold.”


Before re-addressing this delightful question, I began class by using Bongard Problems. This turned out to be a genius plan. The big idea of Bongard Problems is that there is a common defining characteristic that differentiates the left hand side from the right hand side images:


Thinking about what makes something a defining characteristic, rather than being a property of the object, helped to create a much more streamlined definition of each of our hexagons. We returned to the question from yesterday’s class.

We looked at our exemplar Pakman card again. We went back and forth, forth and back. Until finally we agreed that a Pakman was (drumroll please)…

A hexagon formed by reflecting a parallelogram across one of its sides.

Much rejoicing was had by all–though come to think of it, maybe that rejoicing was due to the fact that I said we didn’t have to go through this process for all of the other hexagons…

I passed out the remaining hexagons, printed on regular paper this time as I have just about used up my school’s entire supply of cardstock by now. Students determined whether any of the new hexagons belonged to an existing group and created new names and definitions for those that needed one.

Our final collection of definitions looked something like this:

The Hexagons

At this point we had officially run out of time. However by this point we had created a very rich and interesting sandbox to play in. Stay tuned for tomorrow’s final (at least for now) installment in the saga. In which the Hexagon Talking Points will make an appearance.

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