start with the pencil along one side, move it along the side until it is half sticking out. Rotate it to point along the next side. Repeat until back to start position.

If you rotated it through the external angle at each vertex then the pencil has turned through 360 degrees. each vertex contains an external angle and an internal angle, total 180, so for n vertices the total vertex angle is 180n.

We used up 360 on the external angles, so the sum of the internal angles is 180n – 360

Test for triangle: n = 3, so 180×3 – 360 = 180 ]]>

It’s something of a “what is the learning we want to get across?” sort of question.

If the emphasis is the measurements, pattern analysis, generalizing, sure, I prefer my normal way.

If the emphasis is what is the formula for the internal angles of a convex polygon, the shorter version did come across better.

In this case I really didn’t have the time for the long version anyway.

]]>The “look for and make use of structure” becomes the focus with your new 5-minute version but there’s so many practice standards going on in what you’ve done in the past.

Both worthy of students time, and no argument with the design of this abbreviated approach… I like that it still allows them to form the conclusions. But … Time permitting… The struggle of the old design is hopefully productive and I think warrants students time.

]]>