These two write-ups were for the following problem

Jamie Johnson rides frequently with her father to Chicago. On one particular trip it took 2 hours for them to travel the 110 miles from home to Chicago. They made the trip in two parts. Jamie kept an eye on the speedometer and estimated that in the first part they averaged 40 miles per hour. She estimated that in the second part they averaged 60 miles per hour. About how long did they drive in each part of the trip?

Compare the two write-ups according to these considerations:

1. The quality of the solutions.
2. How clearly a student would understand what is being represented and the reasoning behind it were it written on the board.
3. The implications for student learning were each typical of a practice promoted by the teacher.

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#6.       a) Let x = time traveling at a particular speed

f(x) = 40x                     represents the distance traveled at 40 mph.

g(x) = 60(2-x)               represents the distance traveled at 60 mph.

h(x) = 110                     represents the distance of the trip.

#6.       a) Let x = number of hours traveling at 40 mi/hr.

f(x) = 40x                     represents the distance traveled after driving at 40 mi/hr for x hours.

g(x) = 60(2-x)               represents the distance traveled at 60 mi/hr after having driven x hours at 40 mi/hr.

h(x) = 110                     represents the distance from home to Chicago after having driven x hours at 40 mi/hr and (2-x) hours at 60 mi/hr.