This Pledged Homework counts for 10% of the final grade on the course, so it will be graded as carefully as possible. At the same time, since the students know this is an important assignment and have a week to work on it, sloppy or careless work is not acceptable.
What are we looking for?
Evidence that the student has understood the problem and worked on it in a reasonably logical manner, and has found a sensible answer: we expect to see a clearly presented argument (but it doesn’t have to be long!)
The answer must make sense: for example, in the question about mud settling in a lake in a couple of days, students should know that particles a millimeter or more in diameter (large sand grains) will fall almost instantly to the bottom, and a tenth of a millimeter will drop pretty quickly. They should also know that 10-10 m. or less is a silly answer, mud particles are bigger than atoms!
They should also have realized that for a satellite in low earth orbit to increase its height by six thousand kilometers is going to take more than a 1% or so increase in speed, as some of them wrote. If they had used the Newton’s cannon applet or the spreadsheet at all this should be very clear. So an answer like that means little thought has gone into the problem.
For the satellite problem, I gave the earth’s radius to two significant figures. I saw answers presented with eight figures, at least six of which were of course garbage. Students must show they have grasped the appropriate level of accuracy a problem should be worked at. It can never be a higher level than that of the input data.