Note: this is the closest I get to 3-Act Math.  For the real thing, pop over to Dan Meyer’s page.

My friend Andy is getting ready to sell his house, and so he decided to undertake a few projects.  He asked me to come by and help him build a set of stairs that run from his front yard down to the back yard.  Ever think about how to build stairs?

To make what you see above, we used a pre-cut template from Home Depot.  We laid the template on a piece of wood, then traced it with a pencil.  Andy used a circular saw to cut the board.  Want to see something cool?  Look at the top of the board after he made the cut:

That looks about right.  Now get this: after he cuts the whole board, he flips it over…what do you think it should look like?  Think it over and then scroll down.  [Note: I made my students wait *24 hours* before I showed them this next image.]

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Wow!  That shocked me to the core.  I could not believe my own eyes!  What is going on here?  [Note: I made my students wait *another 24 hours* before discussing this any further.]

So at the end of the week, I asked my students to try to explain this phenomenon of the lines-that-don’t-meet.  Suddenly I’ve got half a dozen volunteers eager to go the the board.  Students are watching each other make drawings and try to explain what’s happening.  I let each person have their say, then the next student got to go up.  Want to know the hardest part of all this?  Making the drawing.  Here are their attempts to represent the board and the saw:

Wow!  It’s tough to get the picture right, isn’t it?  I think if I had a board and a saw to demonstrate with, it would be a whole lot easier.

Anyway, aside from this being a neat visual puzzler, I’m sharing this story as a testimony about *student engagement.*  Want to know the truth?  My students don’t appear to be nearly that engaged on any given day.  So here’s my question: how can we transform math class into a space where this level of engagement is the norm?  Where students are eager to go to the board and *represent their ideas with pictures?*  Where they are willing to *speak in front of their peers?*  Where they are trying their hardest to *construct a convincing argument?*  Where every person in the room *knows what the outcome looks like* but is *struggling to understand why?*