When first teaching about the interior angles of a polygon I had an elaborate lesson that involved students drawing quadrilaterals, pentagons, hexagons, etc and measuring and collecting data and finally making a theory. They’d then verify that theory by drawing triangles inside the polygons and realizing Interior Angles of a Triangle had returned.
I didn’t feel like students were convinced or satisfied, partly because the measurements were off enough due to error there was a “whoosh it is true” at the end but mostly because the activity took so long the idea was lost. That is, even though they had scientifically investigated and rigorously proved something, they took it on faith because the path that led to the formula was a jumble.
I didn’t have as much time this year, so I threw this up as bellwork instead:
Nearly 80% of the students figured out the blanks with no instructions from me. They were even improvising the formulas. Their intuitions were set, they were off the races, and it took 5 minutes.