Mail time: a daily quiz question about average speed

What is the purpose of this question from one of the daily quizzes in your AP class? My guess is that you're highlighting a misconception.

True or false: One method of finding an object’s average speed is to find its speed during one part of its motion, add to the speed during the rest of its motion, and divide by 2.

Yup, you got it!  I'm highlighting this amazingly common misconception.  Usually the misconception appears in response to questions like "a car travels the first 50 km of its trip at a constant speed of 20 km/hr, and the second 50 km of its trip at a constant speed of 40 km/hr.  What is the average speed for the whole trip?"  The answer is NOT 30 km/hr, because more time is spent in the first 50 km than the second 50 km.  But no matter how we try, still a significant portion of the class will say "average speed?  Oh, I know how to take an average!  (20+40)/2, of course!  :-)

When I *do* pose this kind of problem to my (AP) classes, I ask it more conceptually: "a car travels the first 50 km of its trip at a constant speed of 20 km/hr, and the second 50 km of its trip at a constant speed of 40 km/hr.  Is the average speed greater than, less than, or equal to 30 km/hr?" I mean, they could do the full-on calculation of the time spent in each half of the trip, then use the definition of average speed = total distance / total time to get 27 km/hr.  But the simple conceptual approach is to notice more time was spent at 20 km/hr than 40 km/hr, so the average speed will be closer to 20 km/hr than 40 km/hr.  

(In my lowest-level conceptual physics course, the whole concept of "average speed" is out of bounds.  Let's get students understanding basic one-dimensional motion with constant speed, or with speeding up from rest / slowing down to rest.  The whole idea of "average speed" is extremely confusing, even to strong second- or third-year physics students!  So save the complexities for advanced courses.)