|Work Sample & Commentary: Gas Tank|
If Jed fills the tank with gas, how long will the generator run? Explain how you arrived at your answer.
This student had a conversion table which contained many conversions including the two needed to solve this problem.
Mathematics required by the task
Students can derive (1) using basic proportional reasoning from the statement that says the generator will run for 2 hours on 1 liter of gas.
Relationship (2) is the conversion between cubic centimeters and liters.
Relationship (3) is the basic volume formula for rectangular solids.
Putting the three together provides a solution to the task:
(Note the units of the constants: 0.5 has the units hours per liter and 1,000 has the units liters per cubic centimeter. A dimensional analysis of the formula (4) shows that combining all the units on the right hand side of the formula yields just hours, as it should.)
What the work shows