This week I have had students look up speeds for certain animals in preparation for other activities. I wrote a warm-up problem based on information from that web search.. Today I asked if a cheetah can go 60 mph, would it be reasonable to say that the cheetah can go 180 miles in three hours. I was stunned that most of my students stated "yes" because "180/3 = 60" So I asked if a cross country runner could maintain his/her top speed for a whole hour and the students said no but when I asked if a cheetah could go at top speed for an hour, they said "yes."
I suddenly realized that my student's conception of reasonableness does not extend to something like this. I wonder if we focus too much on the reasonableness of our calculated answers and not enough time on the general picture. Using the straight math, yes it works but if you factor in that most humans and animals can only run at top speed for so long, then it does not work and my students have not looked at the whole picture.
In the fall, I had students calculate some rate/time/distance problems that gave them 120 mph and they would say yes its possible for a vehicle to go that fast if it has jet packs. This lead to a discussion of possible vs probable and would it really happen in every day situations. I am not sure that we spend enough time exploring the reasonableness under real world circumstances, rather than a strictly mathematical perspective.