This only takes about 5 minutes of class time, maybe 10. But it went well for me.
Here’s the question as it was written in the book (Discovering Geometry by M. Serra):
“Make a set of sketches to show how two quadrilaterals can intersect in exactly one point, two points, three points, four points, five points, six points, seven points, and eight points.”
The answers are all practically there already–it’s just a formality for the students to draw them.
But, ENOboard space being limited, I decided to shorten it up and wrote this on the board:
“Make a set of sketches to explore if 2 quadrilaterals can intersect in exactly 1 point, 2 points, 3 points, and so on. How many different points can they intersect in?”
Then, when I listened in, I heard some groups arguing about whether you could have ODD numbers of intersections. One student said “put a kite inside a square, that’s 3 points.” Surprisingly, one group found a way to make 16 intersections. It turns out that by shortening the question, I opened the question up, and the kids surprised themselves and me!