Today in geometry we started incenter/circumcenter, here is a problem one of my colleagues shared with me; I really liked it. So did my students.
I passed out a paper with the same text/image on it. Here it is. Almost all my students were about to locate an point to place the tower, however most of them did this by guess and check. When I asked them to explain why that point made sense they took their compass and drew a circle, indicating they were equidistant.
I lost ’em after this. This seems to happen quite a bit, I need to think through followup and extension questions. Students pushed back when I asked them to explain how they could use math to help make sense why the point they chose made sense.
Tomorrow we are going to follow up by creating the circumcenter by finding the intersection of perpendicular bisectors and look a little deeper into the congruent distances from the three cities and what sort of triangles are created.